Patent application title: SYSTEM AND METHOD FOR PERFORMING OPTIMIZED DOWNHOLE STIMULATION OPERATIONS
Schlumberger Technology Corporation (Sugar Land, TX, US)
SCHLUMBERGER TECHNOLOGY CORPORATION
IPC8 Class: AE21B4326FI
Class name: Processes placing fluid into the formation fracturing (epo)
Publication date: 2013-06-06
Patent application number: 20130140031
A method of performing a stimulation operation for an unconventional
wellsite having natural fractures and hydraulic fractures. The method
involves providing at least one treatment parameter with a corresponding
objective function value and performing a fracture operation based on the
treatment parameter. The fracture operation involves defining a treatment
schedule, conducting a hydraulic fracture operation, and estimating
production. The objective function value is based on an objective
function. The method also involves modifying the treatment parameter and
performing the fracture operation based on the modified treatment
parameter. The modified treatment parameter has a corresponding modified
objective function value based on the objective function. The method
continues with optimizing the treatment operation by comparing the
objective function value with the modified objective function value, and
repeating the modifying and optimizing for new modified treatment
parameters until convergence about a desired outcome whereby an optimized
parameter is defined at convergence.
1. A method of performing an optimized stimulation operation for a
wellsite having a wellbore extending into a subterranean formation, the
wellsite being an unconventional wellsite having complex fractures
extending through the subterranean formation, the method comprising:
providing at least one treatment parameter with a corresponding at least
one objective function value, the at least one objective function value
based on an objective function; performing a fracture operation based on
the at least one treatment parameter, the fracture operation comprising
defining a treatment schedule, conducting a hydraulic fracture operation,
and estimating production; modifying the at least one treatment parameter
and performing the fracture operation based on the modified at least one
treatment parameter, the modified at least one treatment parameter having
a corresponding modified at least one objective function value based on
the objective function; optimizing the treatment operation by comparing
the at least one objective function value with the modified at least one
objective function value; and repeating the modifying and optimizing for
at least one new modified at least one treatment parameter until
convergence about a desired outcome whereby an optimized parameter is
defined at convergence.
2. The method of claim 1, further comprising collecting data about the wellsite.
3. The method of claim 1, further comprising treating the wellsite according to the treatment schedule and the fracture operation corresponding to the optimized parameter.
4. The method of claim 1, further comprising adjusting the treatment schedule and the fracture operation based on one of new data, a new desired outcome, at least one new treatment parameter, at least one new objective function, and combinations thereof.
5. The method of claim 1, wherein the fracture operation comprises one of hydraulically fracturing the subterranean formation about the wellbore and simulating hydraulic fracturing.
6. The method of claim 1, wherein the objective function is a scalar variable.
7. The method of claim 6, wherein the objective function comprises: f ( x ( t ) , y ) = a . y b + c . x ( t ) . ##EQU00002##
8. The method of claim 1, wherein the convergence occurs where the desired outcome is one of minimized or maximized.
9. The method of claim 1, wherein the at least one treatment parameter and the modified at least one treatment parameter comprises a range of values and wherein the performing, modifying and optimizing are repeated for the range of values.
10. The method of claim 9, further comprising selecting at least one value from the range of values based on a relation between the at least one objective function value and the estimated production.
11. The method of claim 1, wherein the at least one treatment parameter and the at least one modified treatment parameter comprises at least one of proppant parameters, fluid parameters, financial parameters, treatment parameters, wellsite parameters and combinations thereof.
12. The method of claim 1, further comprising holding at least one objective function value constant during the performing, optimizing and repeating.
13. A method of performing an optimized stimulation operation for a wellsite having a wellbore extending into a subterranean formation, the wellsite being an unconventional wellsite having complex fractures extending through the subterranean formation, the method comprising: collecting data about the wellsite; providing at least one treatment parameter with a corresponding at least one objective function value, the at least one objective function value based on an objective function; performing a fracture operation based on the at least one treatment parameter, the fracture operation comprising defining a treatment schedule, conducting a hydraulic fracture operation, and estimating production; modifying the at least one treatment parameter and performing the fracture operation based on the modified at least one treatment parameter, the modified at least one treatment parameter having a corresponding modified at least one objective function value based on the objective function; optimizing the treatment operation by comparing the at least one objective function value with the modified at least one objective function value; and repeating the modifying and optimizing for at least one new modified at least one treatment parameter until convergence about a desired outcome whereby an optimized parameter is defined at convergence. treating the wellsite according to the treatment schedule and hydraulic fracture operation corresponding to the optimized parameter.
14. The method of claim 13, wherein the collecting comprises one of measuring wellsite data, receiving historical data, collecting data from other wellsites, and combinations thereof.
15. The method of claim 13, further comprising adjusting the treating based on one of new data, a new desired outcome, at least one new treatment parameter, at least one new objective function, and combinations thereof.
16. A method of performing an optimized stimulation operation for a wellsite having a wellbore extending into a subterranean formation, the wellsite being an unconventional wellsite having complex fractures extending through the subterranean formation, the method comprising: performing reservoir characterization using a reservoir characterization model to generate a mechanical earth model based on integrated wellsite data; generating a stimulation plan by performing well planning, staging design, stimulation design and production prediction based on the mechanical earth model, the stimulation design and production prediction, comprising: providing at least one treatment parameter with a corresponding at least one objective function value, the at least one objective function value based on an objective function; performing a fracture operation based on the at least one treatment parameter, the fracture operation comprising defining a treatment schedule, conducting a hydraulic fracture operation, and estimating production; modifying the at least one treatment parameter and performing the fracture operation based on the modified at least one treatment parameter, the modified at least one treatment parameter having a corresponding modified at least one objective function value based on the objective function; optimizing the treatment operation by comparing the at least one objective function value with the modified at least one objective function value; and repeating the modifying and optimizing for at least one new modified at least one treatment parameter until convergence about a desired outcome whereby an optimized parameter is defined at convergence.
17. The method of claim 16, further comprising measuring at least a portion of the combination of petrophysical, geomechanical, geological and geophysical data at the wellsite.
18. The method of claim 16, further comprising optimizing the stimulation plan based on the optimized parameter.
19. The method of claim 18, further comprising executing the optimized stimulation plan at the wellsite.
20. The method of claim 19, further comprising measuring real time data from the wellsite during the executing the optimized stimulation plan.
21. The method of claim 20, further comprising performing real time interpretation based on the measured real time data.
22. The method of claim 21, further comprising performing real time stimulation design and production prediction based on the real time interpretation.
 The present disclosure relates to techniques for performing oilfield operations. More particularly, the present disclosure relates to techniques for performing stimulation operations, such as perforating, injecting, and/or fracturing, a subterranean formation having at least one reservoir therein. The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
 Oilfield operations may be performed to locate and gather valuable downhole fluids, such as hydrocarbons. Oilfield operations may include, for example, surveying, drilling, downhole evaluation, completion, production, stimulation, and oilfield analysis. Surveying may involve seismic surveying using, for example, a seismic truck to send and receive downhole signals. Drilling may involve advancing a downhole tool into the earth to form a wellbore. Downhole evaluation may involve deploying a downhole tool into the wellbore to take downhole measurements and/or to retrieve downhole samples. Completion may involve cementing and casing a wellbore in preparation for production. Production may involve deploying production tubing into the wellbore for transporting fluids from a reservoir to the surface. Stimulation may involve, for example, perforating, fracturing, injecting, and/or other stimulation operations, to facilitate production of fluids from the reservoir.
 Oilfield analysis may involve, for example, evaluating information about the wellsite and the various operations, and/or performing well planning operations. Such information may be, for example, petrophysical information gathered and/or analyzed by a petrophysicist; geological information gathered and/or analyzed by a geologist; or geophysical information gathered and/or analyzed by a geophysicist. The petrophysical, geological and geophysical information may be analyzed separately with dataflow therebetween being disconnected. A human operator may manually move and analyze the data using multiple software and tools. Well planning may be used to design oilfield operations based on information gathered about the wellsite.
 This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.
 The techniques disclosed herein relate to stimulation operations involving reservoir characterization using a mechanical earth model and integrated wellsite data (e.g., petrophysical, geological, geomechanical, and geophysical data). The stimulation operations may also involve well planning staging design, stimulation design and production prediction optimized in a feedback loop. The stimulation plan may be optimized by performing the stimulation design and production prediction in a feedback loop. The optimization may also be performed using the staging and well planning in the feedback loop. The stimulation plan may be executed and the stimulation plan optimized in real time. The stimulation design may be based on staging for unconventional reservoirs, such as tight gas sand and shale reservoirs.
 In another aspect, one or more embodiments of the present disclosure relates to optimizing the design of the treatment in order to maximize the production. Optimizing may include a simulation workflow going from the simulation of hydraulic fracturing to production forecast for evaluating the cumulated production obtained from a particular treatment design. The method may further comprise modifying the parameters of the treatment to try to increase the production. Embodiments of the present disclosure may also relate to proppant selection and fluid selection in a treatment design and optimization of completion parameters (such as number of perforation clusters and perforation cluster spacing and location of the perforation clusters based on the petrophysical and geomechanical evaluation of the reservoir) for hydraulic fracturing in shale.
 In yet another aspect, the disclosure relates to a method of performing a stimulation operation for a wellsite having a wellbore extending into a subterranean formation. The wellsite is an unconventional wellsite having natural fractures and hydraulic fractures extending through the subterranean formation. The method involves providing at least one treatment parameter with a corresponding objective function value and performing a fracture operation based on the treatment parameter. The fracture operation involves defining a treatment schedule, conducting a hydraulic fracture operation, and estimating production. The objective function value is based on an objective function. The method also involves modifying the treatment parameter and performing the fracture operation based on the modified treatment parameter. The modified treatment parameter has a corresponding modified objective function value based on the objective function. The method continues with optimizing the treatment operation by comparing the objective function value with the modified objective function value, and repeating the modifying and optimizing for new modified treatment parameters until convergence about a desired outcome whereby an optimized parameter is defined at convergence. The method may also involve collecting data about the wellsite, treating the wellsite and adjusting the treating.
BRIEF DESCRIPTION OF THE DRAWINGS
 Embodiments of the method and system for performing a downhole stimulation operation are described with reference to the following figures. Like reference numerals are intended to refer to similar elements for consistency. For purposes of clarity, not every component may be labeled in every drawing.
 FIGS. 1.1-1.4 are schematic views illustrating various oilfield operations at a wellsite.
 FIGS. 2.1-2.4 are schematic views of data collected by the operations of FIGS. 1.1-1.4.
 FIG. 3.1 is a schematic view of a wellsite illustrating various downhole stimulation operations.
 FIGS. 3.2-3.4 are schematic views of various fractures of the wellsite of FIG. 3.1.
 FIG. 4.1 is a schematic flow diagram depicting a downhole stimulation operation.
 FIGS. 4.2 and 4.3 are schematic diagrams depicting portions of the downhole stimulation operation.
 FIG. 5.1 is a schematic diagram and FIG. 5.2 is a flow chart illustrating a method of staging a stimulation operation in a tight gas sandstone formation.
 FIG. 6 is a schematic diagram depicting a set of logs combined to form a weighted composite log.
 FIG. 7 is a schematic diagram depicting a reservoir quality indicator formed from a first and a second log.
 FIG. 8 is a schematic diagram depicting a composite quality indicator formed from a completion and a reservoir quality indicator.
 FIG. 9 is a schematic diagram depicting a stage design based on a stress profile and a composite quality indicator.
 FIG. 10 is a schematic diagram depicting stage boundary adjustment to enhance the homogeneity of composite quality indicators.
 FIG. 11 is a schematic diagram depicting stage splitting based on a composite quality indicator.
 FIG. 12 is a diagram depicting perforation placement based on a quality indicator.
 FIG. 13 is a flow diagram illustrating a method of staging a stimulation operation for a shale reservoir.
 FIG. 14 is a flow diagram illustrating a method of performing a downhole stimulation operation.
 FIG. 15 is a schematic diagram depicting a stimulation operation at a wellsite.
 FIG. 16 is a flow chart depicting a method of performing an optimized stimulation operation.
 FIG. 17 is a flow chart depicting iteration of a portion of the method of FIG. 16.
 FIG. 18 is a schematic diagram depicting an example parametric study.
 FIG. 19 is a schematic diagram depicting optimization of proppant mesh.
 FIG. 20 is a schematic diagram depicting optimization of viscosity.
 FIG. 21 is a schematic diagram depicting optimization of proppant type.
 FIG. 22 is a schematic diagram depicting optimization of fluid viscosity and proppant type.
 The description that follows includes exemplary systems, apparatuses, methods, and instruction sequences that embody techniques of the subject matter herein. However, it is understood that the described embodiments may be practiced without these specific details.
 The present disclosure relates to design, implementation and feedback of stimulation operations performed at a wellsite. The stimulation operations may be performed using a reservoir centric, integrated approach. These stimulation operations may involve integrated stimulation design based on multi-disciplinary information (e.g., used by a petrophysicist, geologist, geomechanicist, geophysicist and reservoir engineer), multi-well applications, and/or multi-stage oilfield operations (e.g., completion, stimulation, and production). Some applications may be tailored to unconventional wellsite applications (e.g., tight gas, shale, carbonate, coal, etc.), complex wellsite applications (e.g., multi-well), and various fracture models (e.g., conventional planar bi-wing fracture models for sandstone reservoirs or complex network fracture models for naturally fractured low permeability reservoirs), and the like. As used herein unconventional reservoirs relate to reservoirs, such as tight gas, sand, shale, carbonate, coal, and the like, where the formation is not uniform or is intersected by natural fractures (all other reservoirs are considered conventional).
 The stimulation operations may also be performed using optimization, tailoring for specific types of reservoirs (e.g., tight gas, shale, carbonate, coal, etc.), integrating evaluations criteria (e.g., reservoir and completion criteria), and integrating data from multiple sources. The stimulation operations may be performed manually using conventional techniques to separately analyze dataflow, with separate analysis being disconnected and/or involving a human operator to manually move data and integrate data using multiple software and tools. These stimulation operations may also be integrated, for example, streamlined by maximizing multi-disciplinary data in an automated or semi-automated manner.
 FIGS. 1.1-1.4 depict various oilfield operations that may be performed at a wellsite, and FIGS. 2.1-2.4 depict various information that may be collected at the wellsite. FIGS. 1.1-1.4 depict simplified, schematic views of a representative oilfield or wellsite 100 having subsurface formation 102 containing, for example, reservoir 104 therein and depicting various oilfield operations being performed on the wellsite 100. FIG. 1.1 depicts a survey operation being performed by a survey tool, such as seismic truck 106.1, to measure properties of the subsurface formation. The survey operation may be a seismic survey operation for producing sound vibrations. In FIG. 1.1, one such sound vibration 112 generated by a source 110 reflects off a plurality of horizons 114 in an earth formation 116. The sound vibration(s) 112 may be received in by sensors, such as geophone-receivers 118, situated on the earth's surface, and the geophones 118 produce electrical output signals, referred to as data received 120 in FIG. 1.1.
 In response to the received sound vibration(s) 112 representative of different parameters (such as amplitude and/or frequency) of the sound vibration(s) 112, the geophones 118 may produce electrical output signals containing data concerning the subsurface formation. The data received 120 may be provided as input data to a computer 122.1 of the seismic truck 106.1, and responsive to the input data, the computer 122.1 may generate a seismic and microseismic data output 124. The seismic data output 124 may be stored, transmitted or further processed as desired, for example by data reduction.
 FIG. 1.2 depicts a drilling operation being performed by a drilling tool 106.2 suspended by a rig 128 and advanced into the subsurface formations 102 to form a wellbore 136 or other channel. A mud pit 130 may be used to draw drilling mud into the drilling tools via flow line 132 for circulating drilling mud through the drilling tools, up the wellbore 136 and back to the surface. The drilling mud may be filtered and returned to the mud pit. A circulating system may be used for storing, controlling or filtering the flowing drilling muds. In this illustration, the drilling tools are advanced into the subsurface formations to reach reservoir 104. Each well may target one or more reservoirs. The drilling tools may be adapted for measuring downhole properties using logging while drilling tools. The logging while drilling tool may also be adapted for taking a core sample 133 as shown, or removed so that a core sample may be taken using another tool.
 A surface unit 134 may be used to communicate with the drilling tools and/or offsite operations. The surface unit may communicate with the drilling tools to send commands to the drilling tools, and to receive data therefrom. The surface unit may be provided with computer facilities for receiving, storing, processing, and/or analyzing data from the operation. The surface unit may collect data generated during the drilling operation and produce data output 135 which may be stored or transmitted. Computer facilities, such as those of the surface unit, may be positioned at various locations about the wellsite and/or at remote locations.
 Sensors (S), such as gauges, may be positioned about the oilfield to collect data relating to various operations as described previously. As shown, the sensor (S) may be positioned in one or more locations in the drilling tools and/or at the rig to measure drilling parameters, such as weight on bit, torque on bit, pressures, temperatures, flow rates, compositions, rotary speed and/or other parameters of the operation. Sensors (S) may also be positioned in one or more locations in the circulating system.
 The data gathered by the sensors may be collected by the surface unit and/or other data collection sources for analysis or other processing. The data collected by the sensors may be used alone or in combination with other data. The data may be collected in one or more databases and/or transmitted on or offsite. All or select portions of the data may be selectively used for analyzing and/or predicting operations of the current and/or other wellbores. The data may be historical data, real time data or combinations thereof. The real time data may be used in real time, or stored for later use. The data may also be combined with historical data or other inputs for further analysis. The data may be stored in separate databases, or combined into a single database.
 The collected data may be used to perform analysis, such as modeling operations. For example, the seismic data output may be used to perform geological, geophysical, and/or reservoir engineering analysis. The reservoir, wellbore, surface and/or processed data may be used to perform reservoir, wellbore, geological, and geophysical or other simulations. The data outputs from the operation may be generated directly from the sensors, or after some preprocessing or modeling. These data outputs may act as inputs for further analysis.
 The data may be collected and stored at the surface unit 134. One or more surface units may be located at the wellsite, or connected remotely thereto. The surface unit may be a single unit, or a complex network of units used to perform the necessary data management functions throughout the oilfield. The surface unit may be a manual or automatic system. The surface unit 134 may be operated and/or adjusted by a user.
 The surface unit may be provided with a transceiver 137 to allow communications between the surface unit and various portions of the current oilfield or other locations. The surface unit 134 may also be provided with or functionally connected to one or more controllers for actuating mechanisms at the wellsite 100. The surface unit 134 may then send command signals to the oilfield in response to data received. The surface unit 134 may receive commands via the transceiver or may itself execute commands to the controller. A processor may be provided to analyze the data (locally or remotely), make the decisions and/or actuate the controller. In this manner, operations may be selectively adjusted based on the data collected. Portions of the operation, such as controlling drilling, weight on bit, pump rates or other parameters, may be optimized based on the information. These adjustments may be made automatically based on computer protocol, and/or manually by an operator. In some cases, well plans may be adjusted to select optimum operating conditions, or to avoid problems.
 FIG. 1.3 depicts a wireline operation being performed by a wireline tool 106.3 suspended by the rig 128 and into the wellbore 136 of FIG. 1.2. The wireline tool 106.3 may be adapted for deployment into a wellbore 136 for generating well logs, performing downhole tests and/or collecting samples. The wireline tool 106.3 may be used to provide another method and apparatus for performing a seismic survey operation. The wireline tool 106.3 of FIG. 1.3 may, for example, have an explosive, radioactive, electrical, or acoustic energy source 144 that sends and/or receives electrical signals to the surrounding subsurface formations 102 and fluids therein.
 The wireline tool 106.3 may be operatively connected to, for example, the geophones 118 and the computer 122.1 of the seismic truck 106.1 of FIG. 1.1. The wireline tool 106.3 may also provide data to the surface unit 134. The surface unit 134 may collect data generated during the wireline operation and produce data output 135 which may be stored or transmitted. The wireline tool 106.3 may be positioned at various depths in the wellbore to provide a survey or other information relating to the subsurface formation.
 Sensors (S), such as gauges, may be positioned about the wellsite 100 to collect data relating to various operations as described previously. As shown, the sensor (S) is positioned in the wireline tool 106.3 to measure downhole parameters which relate to, for example porosity, permeability, fluid composition and/or other parameters of the operation.
 FIG. 1.4 depicts a production operation being performed by a production tool 106.4 deployed from a production unit or Christmas tree 129 and into the completed wellbore 136 of FIG. 1.3 for drawing fluid from the downhole reservoirs into surface facilities 142. Fluid flows from reservoir 104 through perforations in the casing (not shown) and into the production tool 106.4 in the wellbore 136 and to the surface facilities 142 via a gathering network 146.
 Sensors (S), such as gauges, may be positioned about the oilfield to collect data relating to various operations as described previously. As shown, the sensor (S) may be positioned in the production tool 106.4 or associated equipment, such as the Christmas tree 129, gathering network, surface facilities and/or the production facility, to measure fluid parameters, such as fluid composition, flow rates, pressures, temperatures, and/or other parameters of the production operation.
 While only simplified wellsite configurations are shown, it will be appreciated that the oilfield or wellsite 100 may cover a portion of land, sea and/or water locations that hosts one or more wellsites. Production may also include injection wells (not shown) for added recovery or for storage of hydrocarbons, carbon dioxide, or water, for example. One or more gathering facilities may be operatively connected to one or more of the wellsites for selectively collecting downhole fluids from the wellsite(s).
 It should be appreciated that FIGS. 1.2-1.4 depict tools that can be used to measure not only properties of an oilfield, but also properties of non-oilfield operations, such as mines, aquifers, storage, and other subsurface facilities. Also, while certain data acquisition tools are depicted, it will be appreciated that various measurement tools (e.g., wireline, measurement while drilling (MWD), logging while drilling (LWD), core sample, etc.) capable of sensing parameters, such as seismic two-way travel time, density, resistivity, production rate, etc., of the subsurface formation and/or its geological formations may be used. Various sensors (S) may be located at various positions along the wellbore and/or the monitoring tools to collect and/or monitor the desired data. Other sources of data may also be provided from offsite locations.
 The oilfield configurations of FIGS. 1.1-1.4 depict examples of a wellsite 100 and various operations usable with the techniques provided herein. Part, or all, of the oilfield may be on land, water and/or sea. Also, while a single oilfield measured at a single location is depicted, reservoir engineering may be utilized with any combination of one or more oilfields, one or more processing facilities, and one or more wellsites.
 FIGS. 2.1-2.4 are graphical depictions of examples of data collected by the tools of FIGS. 1.1-1.4, respectively. FIG. 2.1 depicts a seismic trace 202 of the subsurface formation of FIG. 1.1 taken by seismic truck 106.1. The seismic trace may be used to provide data, such as a two-way response over a period of time. FIG. 2.2 depicts a core sample 133 taken by the drilling tools 106.2. The core sample may be used to provide data, such as a graph of the density, porosity, permeability or other physical property of the core sample over the length of the core. Tests for density and viscosity may be performed on the fluids in the core at varying pressures and temperatures. FIG. 2.3 depicts a well log 204 of the subsurface formation of FIG. 1.3 taken by the wireline tool 106.3. The wireline log may provide a resistivity or other measurement of the formation at various depts. FIG. 2.4 depicts a production decline curve or graph 206 of fluid flowing through the subsurface formation of FIG. 1.4 measured at the surface facilities 142. The production decline curve may provide the production rate Q as a function of time t.
 The respective graphs of FIGS. 2.1, 2.3, and 2.4 depict examples of static measurements that may describe or provide information about the physical characteristics of the formation and reservoirs contained therein. These measurements may be analyzed to define properties of the formation(s), to determine the accuracy of the measurements and/or to check for errors. The plots of each of the respective measurements may be aligned and scaled for comparison and verification of the properties.
 FIG. 2.4 depicts an example of a dynamic measurement of the fluid properties through the wellbore. As the fluid flows through the wellbore, measurements are taken of fluid properties, such as flow rates, pressures, composition, etc. As described below, the static and dynamic measurements may be analyzed and used to generate models of the subsurface formation to determine characteristics thereof. Similar measurements may also be used to measure changes in formation aspects over time.
 FIG. 3.1 depicts stimulation operations performed at wellsites 300.1 and 300.2. The wellsite 300.1 includes a rig 308.1 having a vertical wellbore 336.1 extending into a formation 302.1. Wellsite 300.2 includes rig 308.2 having wellbore 336.2 and rig 308.3 having wellbore 336.3 extending therebelow into a subterranean formation 302.2. While the wellsites 300.1 and 300.2 are shown having specific configurations of rigs with wellbores, it will be appreciated that one or more rigs with one or more wellbores may be positioned at one or more wellsites.
 Wellbore 336.1 extends from rig 308.1, through unconventional reservoirs 304.1-304.3. Wellbores 336.2 and 336.3 extend from rigs 308.2 and 308.3, respectfully to unconventional reservoir 304.4. As shown, unconventional reservoirs 304.1-304.3 are tight gas sand reservoirs and unconventional reservoir 304.4 is a shale reservoir. One or more unconventional reservoirs (e.g., such as tight gas, shale, carbonate, coal, heavy oil, etc.) and/or conventional reservoirs may be present in a given formation.
 The stimulation operations of FIG. 3.1 may be performed alone or in conjunction with other oilfield operations, such as the oilfield operations of FIGS. 1.1 and 1.4. For example, wellbores 336.1-336.3 may be measured, drilled, tested and produced as shown in FIGS. 1.1-1.4. Stimulation operations performed at the wellsites 300.1 and 300.2 may involve, for example, perforation, fracturing, injection, and the like. The stimulation operations may be performed in conjunction with other oilfield operations, such as completions and production operations (see, e.g., FIG. 1.4). As shown in FIG. 3.1, the wellbores 336.1 and 336.2 have been completed and provided with perforations 338.1-338.5 to facilitate production.
 Downhole tool 306.1 is positioned in vertical wellbore 336.1 adjacent tight gas sand reservoirs 304.1 for taking downhole measurements. Packers 307 are positioned in the wellbore 336.1 for isolating a portion thereof adjacent perforations 338.2. Once the perforations are formed about the wellbore fluid may be injected through the perforations and into the formation to create and/or expand fractures therein to stimulate production from the reservoirs.
 Reservoir 304.4 of formation 302.2 has been perforated and packers 307 have been positioned to isolate the wellbore 336.2 about the perforations 338.3-338.5. As shown in the horizontal wellbore 336.2, packers 307 have been positioned at stages St2 and St2 of the wellbore. As also depicted, wellbore 304.3 may be an offset (or pilot) well extended through the formation 302.2 to reach reservoir 304.4. One or more wellbores may be placed at one or more wellsites. Multiple wellbores may be placed as desired.
 Fractures may be extended into the various reservoirs 304.1-304.4 for facilitating production of fluids therefrom. Examples of fractures that may be formed are schematically shown in FIGS. 3.2 and 3.4 about a wellbore 304. As shown in FIG. 3.2, natural fractures 340 extend in layers about the wellbore 304. Perforations (or perforation clusters) 342 may be formed about the wellbore 304, and fluids 344 and/or fluids mixed with proppant 346 may be injected through the perforations 342. As shown in FIG. 3.3, hydraulic fracturing may be performed by injecting through the perforations 342, creating fractures along a maximum stress plane σhmax and opening and extending the natural fractures.
 FIG. 3.4 shows another view of the fracturing operation about the wellbore 304. In this view, the injected fractures 348 extend radially about the wellbore 304. The injected fractures may be used to reach the pockets of microseismic events 351 (shown schematically as dots) about the wellbore 304. The fracture operation may be used as part of the stimulation operation to provide pathways for facilitating movement of hydrocarbons to the wellbore 304 for production.
 Referring back to FIG. 3.1, sensors (S), such as gauges, may be positioned about the oilfield to collect data relating to various operations as described previously. Some sensors, such as geophones, may be positioned about the formations during fracturing for measuring microseismic waves and performing microseismic mapping. The data gathered by the sensors may be collected by the surface unit 334 and/or other data collection sources for analysis or other processing as previously described (see, e.g., surface unit 134). As shown, surface unit 334 is linked to a network 352 and other computers 354.
 A stimulation tool 350 may be provided as part of the surface unit 334 or other portions of the wellsite for performing stimulation operations. For example, information generated during one or more of the stimulation operations may be used in well planning for one or more wells, one or more wellsites and/or one or more reservoirs. The stimulation tool 350 may be operatively linked to one or more rigs and/or wellsites, and used to receive data, process data, send control signals, etc., as will be described further herein. The stimulation tool 350 may include a reservoir characterization unit 363 for generating a mechanical earth model (MEM), a stimulation planning unit 365 for generating stimulation plans, an optimizer 367 for optimizing the stimulation plans, a real time unit 369 for optimizing in real time the optimized stimulation plan, a control unit 368 for selectively adjusting the stimulation operation based on the real time optimized stimulation plan, an updater 370 for updating the reservoir characterization model based on the real time optimized stimulation plan and post evaluation data, and a calibrator 372 for calibrating the optimized stimulation plan as will be described further herein. The stimulation planning unit 365 may include a staging design tool 381 for performing staging design, a stimulation design tool 383 for performing stimulation design, a production prediction tool 385 for prediction production and a well planning tool 387 for generating well plans.
 Wellsite data used in the stimulation operation may range from, for example, core samples to petrophysical interpretation based on well logs to three dimensional seismic data (see, e.g., FIGS. 2.1-2.4). Stimulation design may employ, for example, oilfield petrotechnical experts to conduct manual processes to collate different pieces of information. Integration of the information may involve manual manipulation of disconnected workflows and outputs, such as delineation of a reservoir zones, identification of desired completion zones, estimation of anticipated hydraulic fracture growth for a given completion equipment configurations, decision on whether and where to place another well or a plurality of wells for better stimulation of the formation, and the like. This stimulation design may also involve semi-automatic or automatic integration, feedback and control to facilitate the stimulation operation.
 Stimulation operations for conventional and unconventional reservoirs may be performed based on knowledge of the reservoir. Reservoir characterization may be used, for example, in well planning, identifying optimal target zones for perforation and staging, design of multiple wells (e.g., spacing and orientation), and geomechanical models. Stimulation designs may be optimized based on a resulting production prediction. These stimulation designs may involve an integrated reservoir centric workflow which include design, real time (RT), and post treatment evaluation components. Well completion and stimulation design may be performed while making use of multi-disciplinary wellbore and reservoir data.
 FIG. 4.1 is a schematic flow diagram 400 depicting a stimulation operation, such as those shown in FIG. 3.1. The flow diagram 400 is an iterative process that uses integrated information and analysis to design, implement and update a stimulation operation. The method involves pre-treatment evaluation 445, a stimulation planning 447, real time treatment optimization 451, and design/model update 453. Part or all of the flow diagram 400 may be iterated to adjust stimulation operations and/or design additional stimulation operations in existing or additional wells.
 The pre-stimulation evaluation 445 involves reservoir characterization 460 and generating a three-dimensional mechanical earth model (MEM) 462. The reservoir characterization 460 may be generated by integrating information, such as the information gathered in FIGS. 1.1-1.4, to perform modeling using united combinations of information from historically independent technical regimes or disciplines (e.g., petrophysicist, geologist, geomechanic and geophysicist, and previous fracture treatment results). Such reservoir characterization 460 may be generated using integrated static modeling techniques to generate the MEM 462 as described, for example, in US Patent Application Nos. 2009/0187391 and 2011/0660572. By way of example, software, such as PETREL®, VISAGE®, TECHLOG®, and GEOFRAME® commercially available from SCHLUMBERGER®, may be used to perform the pre-treatment evaluation 445.
 Reservoir characterization 460 may involve capturing a variety of information, such as data associated with the underground formation and developing one or more models of the reservoir. The information captured may include, for example, stimulation information, such as reservoir (pay) zone, geomechanical (stress) zone, and natural fracture distribution. The reservoir characterization 460 may be performed such that information concerning the stimulation operation is included in pre-stimulation evaluations. Generating the MEM 462 may simulate the subterranean formation under development (e.g., generating a numerical representation of a state of stress and rock mechanical properties for a given stratigraphic section in an oilfield or basin).
 Conventional geomechanical modeling may be used to generate the MEM 462. Examples of MEM techniques are provided in US Patent Application No. 2009/0187391. The MEM 462 may be generated by information gathered using, for example, the oilfield operations of FIGS. 1.1-1.4, 2.1-2.4 and 3. For example, the 3D MEM may take into account various reservoir data collected beforehand, including the seismic data collected during early exploration of the formation and logging data collected from the drilling of one or more exploration wells before production (see, e.g., FIGS. 1.1-1.4). The MEM 462 may be used to provide, for example, geomechanical information for various oilfield operations, such as casing point selection, optimizing the number of casing strings, drilling stable wellbores, designing completions, performing fracture stimulation, etc.
 The generated MEM 462 may be used as an input in performing stimulation planning 447. The 3D MEM may be constructed to identify potential drilling wellsites. In one embodiment, when the formation is substantially uniform and is substantially free of major natural fractures and/or high-stress barriers, it can be assumed that a given volume of fracturing fluid pumped at a given rate over a given period of time will generate a substantially identical fracture network in the formation. Core samples, such as those shown in FIGS. 1.2 and 2.2 may provide information useful in analyzing fracture properties of the formation. For regions of the reservoir manifesting similar properties, multiple wells (or branches) can be placed at a substantially equal distance from one another and the entire formation may be sufficiently stimulated.
 The stimulation planning 447 may involve well planning 465, staging design 466, stimulation design, 468 and production prediction 470. In particular, the MEM 462 may be an input to the well planning 465 and/or the staging design 466 and stimulation design 468. Some embodiments may include semi-automated methods to identify, for example, well spacing and orientation, multistage perforation design and hydraulic fracture design. To address a wide variation of characteristics in hydrocarbon reservoirs, some embodiments may involve dedicated methods per target reservoir environments, such as, but not limited to, tight gas formations, sandstone reservoirs, naturally fractured shale reservoirs, or other unconventional reservoirs.
 The stimulation planning 447 may involve a semi-automated method used to identify potential drilling wellsites by partitioning underground formations into multiple set of discrete intervals, characterizing each interval based on information such as the formation's geophysical properties and its proximity to natural fractures, then regrouping multiple intervals into one or multiple drilling wellsites, with each wellsite receiving a well or a branch of a well. The spacing and orientation of the multiple wells may be determined and used in optimizing production of the reservoir. Characteristics of each well may be analyzed for stage planning and stimulation planning. In some cases, a completion advisor may be provided, for example, for analyzing vertical or near vertical wells in tight-gas sandstone reservoir following a recursive refinement workflow.
 Well planning 465 may be performed to design oilfield operations in advance of performing such oilfield operations at the wellsite. The well planning 465 may be used to define, for example, equipment and operating parameters for performing the oilfield operations. Some such operating parameters may include, for example, perforating locations, operating pressures, stimulation fluids, and other parameters used in stimulation. Information gathered from various sources, such as historical data, known data, and oilfield measurements (e.g., those taken in FIGS. 1.1-1.4), may be used in designing a well plan. In some cases, modeling may be used to analyze data used in forming a well plan. The well plan generated in the stimulation planning may receive inputs from the staging design 466, stimulation design 468, and production prediction 470 so that information relating to and/or affecting stimulation is evaluated in the well plan.
 The well planning 465 and/or MEM 462 may also be used as inputs into the staging design 466. Reservoir and other data may be used in the staging design 466 to define certain operational parameters for stimulation. For example, staging design 466 may involve defining boundaries in a wellbore for performing stimulation operations as described further herein.
 Examples of staging design are described in US Patent Application No. 2011/0247824. Staging design may be an input for performing stimulation design 468.
 Stimulation design defines various stimulation parameters (e.g., perforation placement) for performing stimulation operations. The stimulation design 468 may be used, for example, for fracture modeling. Examples of fracture modeling are described in US Patent Application No. 2008/0183451, 2006/0015310 and PCT Publication No. WO2011/077227. Stimulation design may involve using various models to define a stimulation plan and/or a stimulation portion of a well plan.
 Stimulation design may integrate 3D reservoir models (formation models), which can be a result of seismic interpretation, drilling geo-steering interpretation, geological or geomechanical earth model, as a starting point (zone model) for completion design. For some stimulation designs, a fracture modeling algorithm may be used to read a 3D MEM and run forward modeling to predict fracture growth. This process may be used so that spatial heterogeneity of a complex reservoir may be taken into account in stimulation operations. Additionally, some methods may incorporate spatial X-Y-Z sets of data to derive an indicator, and then use the indicator to place and/or perform a wellbore operation, and in some instance, multiple stages of wellbore operations as will be described further herein.
 Stimulation design may use 3D reservoir models for providing information about natural fractures in the model. The natural fracture information may be used, for example, to address certain situations, such as cases where a hydraulically induced fracture grows and encounters a natural fracture (see, e.g., FIGS. 3.2-3.4). In such cases, the fracture can continue growing into the same direction and divert along the natural fracture plane or stop, depending on the incident angle and other reservoir geomechanical properties. This data may provide insights into, for example, the reservoir dimensions and structures, pay zone location and boundaries, maximum and minimum stress levels at various locations of the formation, and the existence and distribution of natural fractures in the formation. As a result of this simulation, nonplanar (i.e. networked) fractures or discrete network fractures may be formed. Some workflows may integrate these predicted fracture models in a single 3D canvas where microseismic events are overlaid (see, e.g., FIG. 3.4). This information may be used in fracture design and/or calibrations.
 Microseismic mapping may also be used in stimulation design to understand complex fracture growth. The occurrence of complex fracture growth may be present in unconventional reservoirs, such as shale reservoirs. The nature and degree of fracture complexity may be analyzed to select an optimal stimulation design and completion strategy. Fracture modeling may be used to predict the fracture geometry that can be calibrated and the design optimized based on real time Microseismic mapping and evaluation. Fracture growth may be interpreted based on existing hydraulic fracture models. Some complex hydraulic fracture propagation modeling and/or interpretation may also be performed for unconventional reservoirs (e.g., tight gas sand and shale) as will be described further herein. Reservoir properties, and initial modeling assumptions may be corrected and fracture design optimized based on microseismic evaluation.
 Examples of complex fracture modeling are provided in SPE paper 140185, the entire content of which is hereby incorporated by reference. This complex fracture modeling illustrates the application of two complex fracture modeling techniques in conjunction with microseismic mapping to characterize fracture complexity and evaluate completion performance. The first complex fracture modeling technique is an analytical model for estimating fracture complexity and distances between orthogonal fractures. The second technique uses a gridded numerical model that allows complex geologic descriptions and evaluation of complex fracture propagation. These examples illustrate how embodiments may be utilized to evaluate how fracture complexity is impacted by changes in fracture treatment design in each geologic environment. To quantify the impact of changes in fracture design using complex fracture models despite inherent uncertainties in the MEM and "real" fracture growth, microseismic mapping and complex fracture modeling may be integrated for interpretation of the microseismic measurements while also calibrating the complex stimulation model. Such examples show that the degree of fracture complexity can vary depending on geologic conditions.
 Production prediction 470 may involve estimating production based on the well planning 465, staging design 466 and stimulation design 468. The result of stimulation design 468 (i.e. simulated fracture models and input reservoir model) can be carried over to a production prediction workflow, where a conventional analytical or numerical reservoir simulator may operate on the models and predicts hydrocarbon production based on dynamic data. The preproduction prediction 470 can be useful, for example, for quantitatively validating the stimulation planning 447 process.
 Part or all of the stimulation planning 447 may be iteratively performed as indicated by the flow arrows. As shown, optimizations may be provided after the staging design 466, stimulation design 468, and production prediction 470, and may be used as a feedback to optimize 472 the well planning 465, the staging design 466 and/or the stimulation design 468. The optimizations may be selectively performed to feedback results from part or all of the stimulation planning 447 and iterate as desired into the various portions of the stimulation planning process and achieve an optimized result. The stimulation planning 447 may be manually carried out, or integrated using automated optimization processing as schematically shown by the optimization 472 in feedback loop 473.
 FIG. 4.2 schematically depicts a portion of the stimulation planning operation 447. As shown in this figure, the staging design 446, stimulation design 468 and production prediction 470 may be iterated in the feedback loop 473 and optimized 472 to generate an optimized result 480, such as an optimized stimulation plan. This iterative method allows the inputs and results generated by the staging design 466 and stimulation design 468 to `learn from each other` and iterate with the production prediction for optimization therebetween.
 Various portions of the stimulation operation may be designed and/or optimized. Examples of optimizing fracturing are described, for example, in U.S. Pat. No. 6,508,307. In another example, financial inputs, such as fracture costs which may affect operations, may also be provided in the stimulation planning 447. Optimization may be performed by optimizing stage design with respect to production while taking into consideration financial inputs. Such financial inputs may involve costs for various stimulation operations at various stages in the wellbore as depicted in FIG. 4.3.
 FIG. 4.3 depicts a staging operation at various intervals and related net present values associated therewith. As shown in FIG. 4.3, various staging designs 455.1 and 455.2 may be considered in view of a net present value plot 457. The net present value plot 457 is a graph plotting mean post-tax net present value (y-axis) versus standard deviation of net present value (x-axis). The various staging designs may be selected based on the financial analysis of the net present value plot 457. Techniques for optimizing fracture design involving financial information, such as net present value are described, for example, in U.S. Pat. No. 7,908,230, the entire contents of which are hereby incorporated by reference. Various techniques, such as, Monte Carlo simulations may be performed in the analysis.
 Referring back to FIG. 4.1, various optional features may be included in the stimulation planning 447. For example, a multi-well planning advisor may be used to determine if it is necessary to construct multiple wells in a formation. If multiple wells are to be formed, the multi-well planning advisor may provide the spacing and orientation of the multiple wells, as well as the best locations within each for perforating and treating the formation. As used herein, the term "multiple wells" may refer to multiple wells each being independently drilled from the surface of the earth to the subterranean formation; the term "multiple wells" may also refer to multiple branches kicked off from a single well that is drilled from the surface of the earth (see, e.g., FIG. 3.1). The orientation of the wells and branches can be vertical, horizontal, or anywhere in between.
 When multiple wells are planned or drilled, simulations can be repeated for each well so that each well has a staging plan, perforation plan, and/or stimulation plan. Thereafter, multi-well planning can be adjusted if necessary. For example, if a fracture stimulation in one well indicates that a stimulation result will overlap a nearby well with a planned perforation zone, the nearby well and/or the planned perforation zone in the nearby well can be eliminated or redesigned. On the contrary, if a simulated fracture treatment cannot penetrate a particular area of the formation, either because the pay zone is simply too far away for a first fracture well to effectively stimulate the pay zone or because the existence of a natural fracture or high-stress barrier prevents the first fracture well from effectively stimulating the pay zone, a second well/branch or a new perforation zone may be included to provide access to the untreated area. The 3D reservoir model may take into account simulation models and indicate a candidate location to drill a second well/branch or to add an additional perforation zone. A spatial X'-Y'-Z' location may be provided for the oilfield operator's ease of handling.
Post Planning Stimulation Operations
 Embodiments may also include real time treatment optimization (or post job workflows) 451 for analyzing the stimulation operation and updating the stimulation plan during actual stimulation operations. The real time treatment optimization 451 may be performed during implementation of the stimulation plan at the wellsite (e.g., performing fracturing, injecting or otherwise stimulating the reservoir at the wellsite). The real time treatment optimization may involve calibration tests 449, executing 448 the stimulation plan generated in stimulation planning 447, and real time oilfield stimulation 455.
 Calibration tests 449 may optionally be performed by comparing the result of stimulation planning 447 (i.e. simulated fracture models) with the observed data. Some embodiments may integrate calibration into the stimulation planning process, perform calibrations after stimulation planning, and/or apply calibrations in real-time execution of stimulation or any other treatment processes. Examples of calibrations for fracture or other stimulation operations are described in US Patent Application No. 2011/0257944, the entire contents of which are hereby incorporated by reference.
 Based on the stimulation plan generated in the stimulation planning 447 (and calibration 449 if performed), the oilfield stimulation 445 may be executed 448. Oilfield stimulation 455 may involve real time measurement 461, real time interpretation 463, real time stimulation design 465, real time production 467 and real time control 469. Real time measurement 461 may be performed at the wellsite using, for example, the sensors S as shown in FIG. 3.1. Observed data may be generated using real time measurements 461. Observation from a stimulation treatment well, such as bottomhole and surface pressures, may be used for calibrating models (traditional pressure match workflow). In addition, microseismic monitoring technology may be included as well. Such spatial/time observation data may be compared with the predicted fracture model.
 Real time interpretation 463 may be performed on or off site based on the data collected. Real time stimulation design 465 and production prediction 467 may be performed similar to the stimulation design 468 and production prediction 470, but based on additional information generated during the actual oilfield stimulation 455 performed at the wellsite. Optimization 471 may be provided to iterate over the real time stimulation design 465 and production prediction 467 as the oilfield stimulation progresses. Real time stimulation 455 may involve, for example, real time fracturing. Examples of real time fracturing are described in US Patent Application No. 2010/0307755, the entire contents of which are hereby incorporated by reference.
 Real time control 469 may be provided to adjust the stimulation operation at the wellsite as information is gathered and an understanding of the operating conditions is gained. The real time control 469 provides a feedback loop for executing 448 the oilfield stimulation 455. Real time control 469 may be executed, for example, using the surface unit 334 and/or downhole tools 306.1-306.4 to alter operating conditions, such as perforation locations, injection pressures, etc. While the features of the oilfield stimulation 455 are described as operating in real time, one or more of the features of the real time treatment optimization 451 may be performed in real time or as desired.
 The information generated during the real time treatment optimization 451 may be used to update the process and feedback to the reservoir characterization 445. The design/model update 453 includes post treatment evaluation 475 and update model 477. The post treatment evaluation involves analyzing the results of the real time treatment optimization 451 and adjusting, as necessary, inputs and plans for use in other wellsites or wellbore applications.
 The post treatment evaluation 475 may be used as an input to update the model 477. Optionally, data collected from subsequent drilling and/or production can be fed back to the reservoir characterization 445 (e.g., the 3D earth model) and/or stimulation planning 447 (e.g., well planning module 465). Information may be updated to remove errors in the initial modeling and simulation, to correct deficiencies in the initial modeling, and/or to substantiate the simulation. For example, spacing or orientation of the wells may be adjusted to account the newly developed data. Once the model is updated 477, the process may be repeated as desired. One or more wellsites, wellbores, stimulation operations or variations may be performed using the method 400.
 In a given example, a stimulation operation may be performed by constructing a 3D model of a subterranean formation and performing a semi-automated method involving dividing the subterranean formation into a plurality of discrete intervals, characterizing each interval based on the subterranean formation's properties at the interval, grouping the intervals into one or more drilling sites, and drilling a well in each drilling site.
Tight Gas Sand Applications
 An example stimulation design and downstream workflow useful for unconventional reservoirs involving tight gas sandstone (see, e.g., reservoirs 304.1-304.3 of FIG. 3.1) are provided. For tight gas sandstone reservoir workflow, a conventional stimulation (i.e. hydraulic fracturing) design method may be used, such as a single or multi-layer planar fracture model.
 FIGS. 5A and 5B depict examples of staging involving a tight gas sand reservoir. A multi-stage completion advisor may be provided for reservoir planning for tight gas sandstone reservoirs where a plurality of thin layers of hydrocarbon rich zones (e.g., reservoirs 304.1-304.3 of FIG. 3.1) may be scattered or dispersed over a large portion of the formation adjacent the wellbore (e.g., 336.1). A model may be used to develop a near wellbore zone model, where key characteristics, such as reservoir (pay) zone and geomechanical (stress) zone, may be captured.
 FIG. 5A shows a log 500 of a portion of a wellbore (e.g., the wellbore 336.1 of FIG. 3.1). The log may be a graph of measurements, such as resistivity, permeability, porosity, or other reservoir parameters logged along the wellbore. In some cases, as shown in FIG. 6, multiple logs 600.1, 600.2 and 600.3 may be combined into a combined log 601 for use in the method 501. The combined log 601 may be based on a weighted linear combination of multiple logs, and corresponding input cutoffs may be weighted accordingly.
 The log 500 (or 601) may correlate to a method 501 involving analyzing the log 500 to define (569) boundaries 568 at intervals along the log 500 based on the data provided. The boundaries 568 may be used to identify (571) pay zones 570 along the wellbore. A fracture unit 572 may be specified (573) along the wellbore. Staging design may be performed (575) to define stages 574 along the wellbore. Finally, perforations 576 may be designed (577) along locations in the stages 574.
 A semi-automated method may be used to identify partitioning of a treatment interval into multiple sets of discrete intervals (multi-stages) and to compute a configuration of perforation placements, based on these inputs. Reservoir (petrophysical) information and completion (geomechanical) information may be factored into the model, simultaneously. Zone boundaries may be determined based on input logs. Stress logs may be used to define the zones. One can choose any other input log or a combination of logs which represents the reservoir formation.
 Reservoir pay zones can be imported from an external (e.g., petrophysical interpretation) workflow. The workflow may provide a pay zone identification method based on multiple log cutoffs. In the latter case, each input log value (i.e. default logs) may include water saturation (Sw), porosity (Phi), intrinsic permeability (Kint) and volume of clay (Vcl), but other suitable logs can be used. Log values may be discriminated by their cutoff values. If all cutoff conditions are met, corresponding depth may be marked as a pay zone. Minimum thickness of a pay zone, KH (permeability multiplied by zone height) and PPGR (pore pressure gradient) cutoff conditions may be applied to eliminate poor pay zones at the end. These pay zones may be inserted into the stress based zone model. The minimum thickness condition may be examined to avoid creation of tiny zones. The pay zones may also be selected and the stress based boundary merged therein. In another embodiment, 3D zone models provided by the reservoir modeling process may be used as the base boundaries and the output zones, finer zones, may be inserted.
 For each identified pay zones, a simple fracture height growth estimation computation based on a net pressure or a bottom hole treating pressure may be performed, and the overlapping pays combined to form a fracture unit (FracUnit). Stimulation stages may be defined based on one or more of the following conditions: minimum net height, maximum gross height and minimum distance between stages.
 The set of FracUnits may be scanned, and possible combinations of consecutive FracUnits examined. Certain combinations that violate certain conditions may be selectively excluded. Valid combinations identified may act as staging scenarios. A maximum gross height (=stage length) may be varied, and combinatory checks run repeatedly for each of the variations. Frequently occurring staging scenarios may be counted from a collection of all outputs to determine final answers. In some cases, no `output` may be found because no single staging design may be ascertained that meets all conditions. In such case, the user can specify the priorities among input conditions. For example, maximum gross height may be met, and minimum distance between stages may be ignored to find the optimum solution.
 Perforation locations, shot density and number of shots, may be defined based on a quality of pay zone if the stress variations within a stage are insignificant. If the stress variations are high, a limited entry method may be conducted to determine distribution of shots among fracture units. A user can optionally choose to use a limited entry method (e.g., stage by stage) if desired. Within each FracUnit, a location of perforation may be determined by a selected KH (permeability multiplied by perforation length).
 A multi-stage completion advisor may be used for reservoir planning for a gas shale reservoir. Where a majority of producing wells are essentially horizontally drilled (or drilled deviated from a vertical borehole) an entire lateral section of a borehole may reside within a target reservoir formation (see, e.g., reservoir 304.4 of FIG. 1). In such cases, variability of reservoir properties and completion properties may be evaluated separately. The treatment interval may be partitioned into a set of contiguous intervals (multi-stages). The partitioning may be done such that both reservoir and completion properties are similar within each stage to ensure the result (completion design) offers maximum coverage of reservoir contacts.
 In a given example, stimulation operations may be performed utilizing a partially automated method to identify best multistage perforation design in a wellbore. A near wellbore zone model may be developed based upon key characteristics, such as reservoir pay zone and geomechanical stress zone. A treatment interval may be partitioned into multiple set of discrete intervals, and a configuration of perforation placement in the wellbore may be computed. A stimulation design workflow including single or multi-layer planar fracture models may be utilized.
 FIGS. 7-12 depict staging for an unconventional application involving a gas shale reservoir (e.g., reservoir 304.4 in FIG. 3.1). FIG. 13 depicts a corresponding method 1300 for staging stimulation of a shale reservoir. For gas shale reservoirs, a description of naturally fractured reservoirs may be utilized. Natural fractures may be modeled as a set of planar geometric objects, known as discrete fracture networks (see, e.g., FIGS. 3.2-3.4). Input natural fracture data may be combined with the 3D reservoir model to account for heterogeneity of shale reservoirs and network fracture models (as opposed to planar fracture model). This information may be applied to predict hydraulic fracture progressions.
 A completion advisor for a horizontal well penetrating formations of shale reservoirs is illustrated in FIGS. 7 through 12. The completions advisor may generate a multi-stage stimulation design, comprising a contiguous set of staging intervals and a consecutive set of stages. Additional inputs, such as fault zones or any other interval information may also be included in the stimulation design to avoid placing stages.
 FIGS. 7-9 depict the creation of a composite quality indicator for a shale reservoir. The reservoir quality and completion quality along the lateral segment of borehole may be evaluated. A reservoir quality indicator may include, for example, various requirements or specifications, such as total organic carbon (TOC) greater than or equal to about 3%, gas in place (GIP) greater than about 100 scf/ft3, Kerogen greater than high, shale porosity greater than about 4%, and relative permeability to gas (Kgas) greater than about 100 nD. A completions quality indicator may include, for example, various requirements or specifications, such as stress that is `-low`, resistivity that is greater than about 15 Ohm-m, clay that is less than 40%, Young's modulus (YM) is greater than about 2×106 psi, Poisson's ratio (PR) is less than about 0.2, neutron porosity is less than about 35% and density porosity is greater than about 8%.
 FIG. 7 schematically depicts a combination of logs 700.1 and 700.2. The logs 700.1 and 700.2 may be combined to generate a reservoir quality indicator 701. The logs may be reservoir logs, such as permeability, resistivity, and porosity logs from the wellbore. The logs have been adjusted to a square format for evaluation. The quality indicator may be separated (1344) into regions based on a comparison of logs 700.1 and 700.2, and classified under a binary log as Good (G) and Bad (B) intervals. For a borehole in consideration, any interval where all reservoir quality conditions are met may be marked as Good, and everywhere else set as Bad.
 Other quality indicators, such as a completions quality indicator, may be formed in a similar manner using applicable logs (e.g., Young's modulus, Poisson's ration, etc. for a completions log). Quality indicators, such as reservoir quality 802 and completion quality 801 may be combined (1346) to form a composite quality indicator 803 as shown in FIG. 8.
 FIGS. 9-11 depict stage definition for the shale reservoir. A composite quality indicator 901 (which may be the composite quality indicator 803 of FIG. 8) is combined (1348) with a stress log 903 segmented into stress blocks by a stress gradient differences. The result is a combined stress & composite quality indicator 904 separated into GB, GG, BB and BG classifications at intervals. Stages may be defined along the quality indicator 904 by using the stress gradient log 903 to determine boundaries. A preliminary set of stage boundaries 907 are determined at the locations where the stress gradient difference is greater than a certain value (e.g., a default may be 0.15 psi/ft). This process may generate a set of homogeneous stress blocks along the combined stress and quality indicator.
 Stress blocks may be adjusted to a desired size of blocks. For example, small stress blocks may be eliminated where an interval is less than a minimum stage length by merging it with an adjacent block to form a refined composite quality indicator 902. One of two neighboring blocks which has a smaller stress gradient difference may be used as a merging target. In another example, large stress blocks may be split where an interval is more than a maximum stage length to form another refined composite quality indicator 905.
 As shown in FIG. 10, a large block 1010 may be split (1354) into multiple blocks 1012 to form stages A and B where an interval is greater than a maximum stage length. After the split, a refined composite quality indicator 1017 may be formed, and then split into a non-BB composite quality indicator 1019 with stages A and B. In some cases as shown in FIG. 10, grouping large `BB` blocks with non-`BB` blocks, such as `GG` blocks, within a same stage, may be avoided.
 If a `BB` block is large enough as in the quality indicator 1021, then the quality indicator may be shifted (1356) into its own stage as shown in the shifted quality indicator 1023. Additional constraints, such as hole deviation, natural and/or induced fracture presence, may be checked to make stage characteristics homogeneous.
 As shown in FIG. 11, the process in FIG. 10 may be applied for generating a quality indicator 1017 and splitting into blocks 1012 shown as stages A and B. BB blocks may be identified in a quality indicator 1117, and split into a shifted quality indicator 1119 having three stages A, B and C. As shown by FIGS. 10 and 11, various numbers of stages may be generated as desired.
 As shown in FIG. 12, perforation clusters (or perforations) 1231 may be positioned (1358) based on stage classification results and the composite quality indicator 1233. In shale completion design, the perforations may be placed evenly (in equal distance, e.g., every 75 ft (22.86 m)). Perforations close to the stage boundary (for example 50 ft (15.24 m)) may be avoided. The composite quality indicator may be examined at each perforation location. Perforation in `BB` blocks may be moved adjacent to the closest `GG`, `GB` or `BG` block as indicated by a horizontal arrow. If a perforation falls in a `BG` block, further fine grain GG, GB, BG, BB reclassification may be done and the perforation placed in an interval that does not contain a BB.
 Stress balancing may be performed to locate where the stress gradient values are similar (e.g. within 0.05 psi/ft) within a stage. For example, if the user input is 3 perforations per stage, a best (i.e. lowest stress gradient) location which meets conditions (e.g., where spacing between perforations and are within the range of stress gradient) may be searched. If not located, the search may continue for the next best location and repeated until it finds, for example, three locations to put three perforations.
 If a formation is not uniform or is intersected by major natural fractures and/or high-stress barriers, additional well planning may be needed. In one embodiment, the underground formation may be divided into multiple sets of discrete volumes and each volume may be characterized based on information such as the formation's geophysical properties and its proximity to natural fractures. For each factor, an indicator such as "G" (Good), "B" (Bad), or "N" (Neutral) can be assigned to the volume. Multiple factors can then be synthesized together to form a composite indicator, such as "GG", "GB", "GN", and so on. A volume with multiple "B"s indicates a location may be less likely to be penetrated by fracture stimulations. A volume with one or more "G"s may indicate a location that is more likely to be treatable by fracture stimulations. Multiple volumes can be grouped into one or more drilling wellsites, with each wellsite representing a potential location for receiving a well or a branch. The spacing and orientation of multiple wells can be optimized to provide an entire formation with sufficient stimulation. The process may be repeated as desired.
 While FIGS. 5A-6 and FIGS. 7-12 each depict specific techniques for staging, various portions of the staging may optionally be combined. Depending on the wellsite, variations in staging design may be applied.
 FIG. 14 is a flow diagram illustrating a method (1400) of performing a stimulation operation. The method involves obtaining (1460) petrophysical, geological and geophysical data about the wellsite, performing (1462) reservoir characterization using a reservoir characterization model to generate a mechanical earth model based on integrated petrophysical, geological and geophysical data (see, e.g., pre-stimulation planning 445). The method further involves generating (1466) a stimulation plan based on the generated mechanical earth model. The generating (1466) may involve, for example, well planning, 465, staging design, 466, stimulation design 468, production prediction 470 and optimization 472 in the stimulation planning 447 of FIG. 4. The stimulation plan is then optimized (1464) by repeating (1462) in a continuous feedback loop until an optimized stimulation plan is generated.
 The method may also involve performing (1468) a calibration of the optimized stimulation plan (e.g., 449 of FIG. 4). The method may also involve executing (1470) the stimulation plan, measuring (1472) real time data during execution of the stimulation plan, performing real time stimulation design and production prediction (1474) based on the real time data, optimizing in real time (1475) the optimized stimulation plan by repeating the real time stimulation design and production prediction until a real time optimized stimulation plan is generated, and controlling (1476) the stimulation operation based on the real time optimized stimulation plan. The method may also involve evaluating (1478) the stimulation plan after completing the stimulation plan and updating (1480) the reservoir characterization model (see, e.g., design/model updating 453 of FIG. 4). The steps may be performed in various orders and repeated as desired.
Optimizing Production Using Parametric Analysis
 The present disclosure also relates to a method of performing an optimized stimulation operation. The method may be used, for example, as part or all (or in combination with) the stimulation design 468, production prediction 470 and optimizing 472 of the stimulation operation 400 of FIG. 4.1. The method involves optimizing stimulation by iteratively defining a treatment schedule and a hydraulic fracture operation, and estimating production by varying a select treatment parameter over time. Results are compared between objective function values corresponding to the treatment parameters for multiple treatment parameters and repeated until convergence. At least one optimized parameter is defined at convergence. A well plan may be generated and the wellsite may be treated according to the treatment schedule and the hydraulic fracture operation corresponding to the converged treatment parameter.
 A `conventional` wellsite as used herein refers to a wellsite having a reservoir with natural fractures that do not interact with man-made (or hydraulic) fractures. As used herein, an `unconventional` wellsite is a wellsite having a reservoir with interacting fractures natural and/or man-made fractures. An unconventional reservoir may be, for example, tight gas, shale, carbonate, coal, heavy oil, etc. (see, e.g., FIGS. 304.1-304.4). One or more unconventional reservoirs and/or conventional reservoirs may be present in a given formation. Complex fractures refer to fractures that are man-made or a combination of natural and man-made. The complex fractures may include, for example, bi-wing, separate, interlocking, propagated and/or other fracture configurations. The man-made fractures may be created, for example, by hydraulic fracturing.
 FIG. 15 depicts an example environment in which embodiments of the present disclosure may be performed. The environment includes wellsite 1500 having a wellbore 1504 extending from a wellhead 1508 at a surface location and through a subterranean formation 1502 therebelow. A fracture network 1506 extends about the wellbore 1504. A pump system 1529 is positioned about the wellhead 1508 for passing fluid through tubing 1542.
 The pump system 1529 is depicted as being operated by a controller, such as a field operator 1527 or a surface system, for recording maintenance and operational data and/or performing maintenance in accordance with a prescribed maintenance plan. The controller may provide manual and/or automatic control of part or all of the wellsite operations. The controller may also collect data from the wellsite from various sensors located thereabout for measuring wellsite and/or treatment parameters. The pumping system 1529 pumps fluid from the surface to the wellbore 1504.
 The pump system 1529 includes a plurality of water tanks 1531, which feed water to a gel hydration unit 1533. The gel hydration unit 1533 combines water from the tanks 1531 with a gelling agent to form a gel. The gel is then sent to a blender 1535 where it is mixed with a proppant from a proppant transport 1537 to form a fracturing fluid. The gelling agent may be used to increase the viscosity of the fracturing fluid, and to allow the proppant to be suspended in the fracturing fluid. It may also act as a friction reducing agent to allow higher pump rates with less frictional pressure.
 The fracturing fluid is then pumped from the blender 1535 to the treatment trucks 1520 with plunger pumps as shown by solid lines 1543. Each treatment truck 1520 receives the fracturing fluid at a low pressure and discharges it to a common manifold 1539 (sometimes called a missile trailer or missile) at a high pressure as shown by dashed lines 1541. The missile 1539 then directs the fracturing fluid from the treatment trucks 1520 to the wellbore 1504 as shown by solid line 1515. One or more treatment trucks 1520 may be used to supply fracturing fluid at a desired rate.
 Each treatment truck 1520 may be normally operated at any rate, such as well under its maximum operating capacity. Operating the treatment trucks 1520 under their operating capacity may allow for one to fail and the remaining to be run at a higher speed in order to make up for the absence of the failed pump. A computerized control system may be employed to direct the entire pump system 1529 during the fracturing operation.
 Various fluids, such as conventional stimulation fluids with proppants, may be used to create fractures. Other fluids, such as viscous gels, "slick water" (which may have a friction reducer (polymer) and water) may also be used to hydraulically fracture various conventional or unconventional wells. Such "slick water" may be in the form of a thin fluid (e.g., nearly the same viscosity as water) and may be used to create more complex fractures, such as multiple micro-seismic fractures detectable by monitoring.
 As also shown in FIG. 15, the fracture network includes fractures located at various positions around the wellbore 1504. The various fractures may be natural fractures 1544 present before injection of the fluids, or hydraulic fractures 1546 generated about the formation 1502 during injection.
 Optimization of stimulation operations may involve an understanding of parameters relating to the stimulation operations in view of desired outcomes, such as increased production. Production from unconventional wellsites, such as those with shale gas reservoirs, may depend on the efficiency of treatments, such as hydraulic fracturing treatments. The economics of shale gas reservoirs can be challenging, for example, in cases of high completion cost and an uncertainty on a production rate that tends to decline rapidly. Nevertheless, cumulated experience in the industry has in recent years constantly improved the production from shale gas reservoirs, and practices in treatment design have been identified for multistage fracturing of horizontal wells.
 Further developments in treatment design may require a deeper understanding of the complex physics involved in both hydraulic fracturing and production, such as stress shadow, proppant transport and interaction with pre-existing natural fractures. Currently, dedicated new simulation workflows, from fracturing to production, may provide an understanding of the complex relation between parameters of a treatment design and their impact on production.
 A sensitivity analysis on several parameters of a treatment design may be used to determine the properties of the reservoir and their impact on the final cumulated production. Treatment parameters that may affect production may include, for example, proppant parameters, fluid parameters, financial parameters, fracture parameters, and wellsite parameters. Proppant parameters may include, for example, proppant type, volume of proppant, mix of proppant type (e.g., injection of several proppants at the same time, Injection of several proppants separately at different times), volume of fluid system (e.g., predefined association of fluid type, proppant type, additives, and specific pumping technique (i.e., cyclical variations in pressure pumping at surface)), proppant concentration, variation of proppant concentration, etc. Fluid parameters may include, for example, fluid type (e.g., fluid composition, fluid concentration, types of additives), mix of fluid type, volume of fluid, pumping rate, flow back strategy, etc.
 Financial parameters may include, for example, material costs, budget limitations, net present value, revenue, etc. See, for example, the financial parameters discussed with respect to FIG. 4.3. Fracture parameters may include, for example, number and location of fracturing treatment stages in a wellbore, number and location of perforation clusters in each stage, number of perforations in each cluster, perforation parameters such as phasing, perforation diameter, Simultaneous or alternate fracturing operations in neighboring wellbores, etc. Wellsite parameters may include, for example, conventional vs. unconventional formations, etc. Other parameters as discussed herein may also be used.
 The relations between various treatment parameters and production may be shown with a simulation workflow that combines a hydraulic fracturing simulator for shale reservoir with a semi-analytical production model dedicated to fractured gas reservoir. The relation between the production and various treatment parameters, such as proppant selection, proppant volume, proppant concentration, fluid selection, and pumping schedule, may be determined.
 Simulations may be used to confirm some of the best practices, but also explain the underlying reasons. The detailed analysis of the simulation results may be used to reveal the relation between parameters, such as proppant transport in a complex fracture network, and other parameters, such as propped length, propped conductivity and cumulated production. Simulations may also be used to highlight the influence of the reservoir parameters, such as permeability, stress anisotropy and density of natural fractures. The conclusions from the sensitivity analysis may be used to provide guidelines for optimized fracturing treatment.
 Parameters may be selected based on, for example, a relation between the treatment design and production. The cumulated production may be given by a simulation workflow from fracturing to production. Embodiments may also include selection of certain treatment parameters. For example, proppant selection and fluid selection may be used in a treatment design and optimization of completion parameters for hydraulic fracturing operations. In an example involving a simulation workflow, an optimized set of treatment parameters may be used to define a treatment design for hydraulic fracturing in fractured reservoir, such as shale, so that production is maximized and costs are minimized.
 In some cases, financial parameters, such as the economic return on investment (NPV), may dictate the optimum treatment design. For example, at some point in the iteration of treatment design (COST) and production results (REVENUE) there will be point where the increase in COST is not offset by the increase in production (REVENUE) and therefore would be the best (or optimized) economic result for the given well under the given circumstances. Methods to achieve this goal may involve, for example, a parametric (or sensitivity analysis) study of these parameters, or an iterative inversion method that searches for the best parameter that minimizes an objective function considering cost and cumulated production. Ad-hoc, means of effectively performing the parametric analysis can be used, such as orthogonal and non-orthogonal experimental design methods. Proposed treatment designs may involve time dependent changes to the parameters of choice resulting in optimized treatment pumping schedules.
 FIG. 16 depicts an example method 1600 for performing an optimized stimulation operation 1600. In the example provided, the method is performed on an unconventional wellsite with complex fractures, such as the wellsite 1500 of FIG. 15. While the method is described with respect to unconventional wellsites, the method may also be used with conventional or unconventional wellsites with natural fractures, bi-wing, separate, integral and/or other fracture arrangements.
 The method involves collecting 1602 data at the wellsite. The wellsite data may relate to one or more of the treatment parameters. The wellsite data may be data measured at the wellsite, for example, as described in FIGS. 1.1-2.4, or collected from databases, other wellsites, historical data, client data, etc. In another example, data may be collected from sensors disposed about the simulation environment of FIG. 15. Data may be collected for real time and/or subsequent use.
 The method also involves providing 1604 at least one treatment parameter with a corresponding objective function value. One or more of the treatment parameters may be used separately or in combination. Initially, one or more of the treatment parameters may be selected. The treatment parameters may be selected for a range of values. Each treatment parameter has a corresponding objective function value.
 The objective function value may be a value generated for each parameter based on an objective function. The objective function value is based on an objective function. The objective function may define a relationship between the parameters and a desired outcome. The objective function may be a scalar variable based on a selected outcome. The definition of the objective function can vary and be more complex. For example, where the objective function represents market price, such price may include the impact of inflation, or prices of hydrocarbons (oil and gas) varying in time. An algorithm may be defined for the objective function as will be described further herein.
 The method 1600 continues by performing 1606 a fracture operation based on the treatment parameter(s). The fracture operation involves defining a treatment schedule, conducting a hydraulic fracture operation, and estimating production as will be described further herein.
 The method 1600 continues by modifying 1608 the treatment parameter and the corresponding objective function value and performing a fracture operation based on the modified at least one treatment parameter. The modifying may use the same process as the performing 1606 and provide a modified treatment parameter having a modified objective function value based on the objective function. Optimizing 1610 may then be performed for the treatment operation by comparing the objective function value with the modified objective function value.
 The modifying and optimizing may be iteratively repeated 1612 for new modified treatment parameter until convergence about a desired outcome. The optimizing may be performed for a range of values, parameters and/or objective functions to generate multiple outcomes. An optimized parameter may be selected at convergence. Thus, the optimized parameter may be defined based on a consideration of a variety of parameters over a number of ranges based on given desired outcomes. The optimized parameter may yield the optimized overall result, such as optimized production at a minimum cost given a variety of parameters, such as proppant type, fluid viscosities, etc.
 The method 1600 may also involve treating 1614 the wellsite according to the treatment schedule and hydraulic fracture operation corresponding to the converged objective function. A well plan may be defined based on the optimized parameter(s). Optionally, new data, a new desired outcome, at least one new treatment parameter, at least one new objective function and other new information may be considered and the treating adjusted accordingly. Adjustments may be made in real time, or as appropriate. The method may be repeated using part or all of the new information. Additional action may be taken, such as part or all of the methods herein. For example, post planning as described herein may also be performed.
 The method 1600 may be performed partially or wholly automatically or manually. The method 1600 may be implemented at the wellsite, for example, at the controller (e.g., operator 1527), or from an offsite location. The method 1600 may also be used in combination with conventional methods, such as those involving fracture length.
 FIG. 17 depicts a portion of the method 1600 depicting the performing 1606 and optimizing 1608 of FIG. 16 in greater detail. As shown in this figure, the method 1600 employs an iterative inversion method. At least a portion of the performing 1606 may be performed using a simulator, such as FRACADE®, UFM® and UPM® commercially available from SCHLUMBERGER TECHNOLOGY CORPORATION® (see: www.slb.com).
 The performing 1606 involves defining 1716 a treatment schedule, conducting 1718 a hydraulic fracture operation at the wellsite, and estimating 1720 production based on the treatment schedule and the hydraulic fracture operation. The treatment schedule defines a portion of the well plan relating to the stimulation. Treatment schedules define the equipment, materials and overall plan for performing a treatment operation, such as the operation of FIG. 15. FIG. 15 is an example of a hydraulic fracture operation that may be used to form the man-made and/or complex fractures as depicted. The hydraulic operation may also involve simulating the hydraulic fracturing using a simulator, such as UFM®. The production may be estimated based on the hydraulic fracturing using, for example, a production simulator, such as UPM®.
 The hydraulic operation may involve, for example, hydraulically fracturing the wellsite as shown in FIG. 15 and/or simulating hydraulic fracturing.
 The performing 1606 may be conducted iteratively using multiple parameters as shown by loop 1721. The performing 1606 is done in combination with the optimizing 1608 as depicted. The optimizing involves collecting 1722 the objective function values for each of the parameters based on an objective function. The objective functions for each of the parameters are tested 1724 for convergence. The testing 1724 for convergence may involve comparing the objective functions to determine if the objective function achieves the desired outcome (e.g., minimum cost, maximum production, etc.)
 If convergence is achieved, then an optimized parameter is generated 1726 at convergence. If not, then a new parameter is selected and the process repeated for the new parameter and its corresponding new objective function value. The repeating may be performed by iteratively selecting a new parameter for comparison with one or more of the previous parameters and/or one or more new objective function values for comparison with one or more of the previous objective function values.
 The methods of FIGS. 16 and 17 may involve iteratively modifying the initial treatment parameter (or input parameter) in order to optimize (e.g., minimize) the objective function. The optimization can be done by using different optimization algorithms, such as gradient based methods. Example methods may include simplex, complex, Gauss-Newton, Levenberg-Marquardt, and the like.
 The objective function may be used to account for selected conditions, such as the production and the economics of the completion and treatment. For example, the objective function may consider the conditions in such a way that the smaller the value of the objective function, the better the design of the treatment. For example, if the objective functions may be minimized when the cumulated production at a given time increases and the cost of the fracturing decreases, the objective function (f) could have the following form:
f ( x ( t ) , y ) = a . y b + c . x ( t ) ( Equation 1 ) ##EQU00001##
with x being the cumulated production after a given time t; y representing the cost of the operation (completion and stimulation); a, b and c being positive constants to be defined by the user; and c being defined based on the market price of the hydrocarbon produced. Equation provides an example objective function that may be used. A corresponding objective function value may be generated for each parameter using the objective function. These objective function values may be compared in the optimizing (see, e.g., 1612 of FIGS. 16 and 1724 of FIG. 17).
 The loop 1721 may begin with an initial guess Pi of the parameter to be considered. As the method iterates 1721, a modified parameter Pi+1 is generated. The objective function value Vi of the initial guess P, is compared with the objective function value Vi+1 of the modified parameter Pi+1 and tested for convergence 1724. If the comparison determines that the objective function meets certain criteria (e.g., minimized, maximized, or near within a desired threshold), then an optimized parameter Popt is generated 1726 from the converged objective function. If not, a new parameter Pi+n of the objective function may be selected 1728, and the method repeated for the new value. The method may continue until convergence is achieved.
 In a given example, if the parameter P is the concentration of proppant to be injected during the treatment, the initial guess Pi may be a value that is considered as a standard practice, like 1 ppa. The optimization algorithm then modifies this parameter Pi+i, and performs the operation 1606. The optimization 1608 is performed using the objective function to analyze if the modification of the parameter Pi+1 minimizes or maximizes the objective function, when compared to the value obtained with the initial guess Pi. Depending on this analysis, the algorithm considers a new guess Pi+n for the concentration before re-starting the loop. By successive iterations the algorithm will converge toward a value that produces the lowest (or optimized) value from the objective function. This example considers a single parameter, but it can be extended to more parameters.
 FIG. 18 shows an example of a parametric study 1800 of iterating the method 1600 for multiple parameters. The idea of a parametric study is to first run a certain number of simulations with a specific parameter varying in a way that describes the relation between the production and the parameter investigated. Then an optimum choice or value for this parameter may be chosen based on this analysis. For example, the optimum for a particular parameter at this stage may be a method to address more of the "weighting factor" for such a parameter when holding the other input data parameters constant.
 In some cases, the impact of a plurality of parameters may be evaluated simultaneously. For example, where a multi-parameter simulation is performed in order to determine the most optimum overall result. Such multi-parameter simulation will likely involve simultaneously solving multiple parameters with multiple sets of equations. A technique, such as optimized design of experiments, can be used to evaluate the parameter space most effectively.
 As shown in FIG. 18, the parametric study 1800 involves defining 1 through n number of treatment designs 1850. The different simulation cases are defined in such a way that the parametric space of the investigated parameter is properly covered. For example, if the parameter to be investigated is a proppant concentration that can vary between 0 and 3 ppa, at least seven simulation cases with different proppant concentration being equal to, for example, 0, 0.5, 1, 1.5, 2, 2.5 and 3 ppa, or the like, may be considered.
 The parametric study 1800 also involves performing 1 through n number of production simulations 1852. Production simulations 1852 are performed for each treatment design. The simulation workflow to these simulation cases are applied, and the resulting production output collected.
 An analysis 1854 of the results of the treatment design 1850 and production simulations 1852 may be performed. The analysis 1854 of the results may be used to provide the operator with the relation between the parameter and the production, and based on this analysis the operator can select the simulation case that provides the best (e.g., most profitable) production. As for the automated algorithm, the choice of the optimum cases can be made not only on the production data, but some other parameters, such as cost can also be included.
 For example, a parametric study may be used to identify a proppant type ratio in a particular treatment. In the following example, the simulation is used to find the best volume ratio in a pumping schedule between two pre-selected proppant type (80/100 mesh and 40/70 mesh). The invention may not be limited to the particular ratio described in this example, and that a number of ratios may be available. In this example, this parametric study is made of a series of nine simulations, in which the treatments and the reservoirs are identical except for the mix of proppant type. These simulations vary in their volume ratio of proppant type between 80/100 mesh sand and 40/70 mesh. Therefore, nine simulations were run in this case, starting with a case with only 900 Mgal of slurry made of 80/100 mesh sand at 1 ppa. The second case adds 100 Mgal of slurry made of 40/70 mesh sand at 1 ppa at the end of the treatment, and decreases the previous stage of 80/100 mesh sand from 900 to 800 Mgal. Therefore the total volume of proppant is similar in the two cases.
 The other cases are defined similarly, for example, by increasing the volume of 40/70 mesh sand and decreasing the volume of 80/100 mesh sand. The final stage is made of only 900 Mgal of 40/70 mesh sand. The method to define the simulation cases is aimed at covering evenly the parametric space of the ratio between the two types of proppants. Once all the simulation cases are defined, the simulation workflow is applied to each of them. The analysis of the simulations indicates the proppant ratio that gives the best cumulated production.
 FIGS. 19-22 depict various examples implementing the optimization methods. These figures illustrate examples of various parameters that are considered in order to optimize production. As illustrated in these figures one or more parameters over a range of values may be considered during optimization. The methods may also be used to consider one or more desired outcomes, such as production as depicted and/or other outcomes (e.g., NPV).
 FIG. 19 shows an example parametric study 1900. This figure illustrates a parametric study on the impact on production of proppant ratio between three meshes 1955.1-1955.3 (between 80/100 mesh and 40/70 mesh). The three meshes 1955.1-1955.3 generate production curves 1957.1-1957.3, respectively. The production curves 1957.1-1957.3 are used to generate a plot 1959 of production (y-axis) (MMcsf) versus days (x-axis). In this figure, normalized cumulated production curves 1956.1-1956.3 are generated for three different times (1 year, 3 years and 10 years) and compared for all nine simulations. Maximum production for each curve 1956.1-1956.3 is generated in the region 1957.
 In another example shown in FIG. 20, fluid viscosity may be optimized in accordance with the present disclosure. FIG. 20 provides a production plot 2000 depicting production (y-axis) versus time (x-axis) for various viscosities. Curves 2062.1-2062.4 are depicted for viscosities 1 cp, 5 cp, 10 cp and 50 cp, respectively. This example compares similar treatment designs except for the viscosity of the fluid.
 The viscosity (defined by the Newtonian rheological model) from 1 cp, 5 cp, 10 cp and 50 cp is modified. After applying the simulation workflow with these treatments, the different cumulated production after 1000 days of production is compared. The results shown in the plot 2000 illustrate that the best production is obtained with the fluid of 1 cp.
 In yet another example shown in FIG. 21, proppant type may be optimized in accordance with the present disclosure hereof. FIG. 21 provides a production plot 2100 depicting production (y-axis) versus time (x-axis) for various types of proppants. Curves 2162.1-2162.4 are depicted for four different proppants, respectively.
 This example is a comparison of several treatments mixing 600,000 gallons of slurry made of 40/70 mesh sand followed by 300,000 gallons of slurry made of another type of proppant (235/270 mesh sand, 80/100 mesh sand, 30/50 mesh sand and 20/40 mesh sand). After applying the simulation workflow on the different treatments, this parametric study indicates that the best production is obtained with the mix of 80/100 mesh sand and 40/70 mesh sand.
 FIG. 22 provides another example of optimization involving a combination of parameters. This figure depicts a plot 2200 of viscosity (left y-axis) and cumulative production verses (right y-axis) and cumulative production (x-axis) and proppant diameter (x-axis). The darkened region 2268 indicates a region of maximum production.
 In this example, the optimization approach is similar to the previous examples. In this version, multiple simulation cases may be used to visualize multiple parameters. FIG. 22 shows proppant size used in a pumping schedule containing only one proppant type and one fluid type. The fluid is assumed to be a Newtonian fluid and the viscosity may be replaced by the concentration of a gelling agent and a crosslinker (e.g., slickwater) added to the base fluid.
 In this case, 28 simulation cases were run to correspond to a matrix made of four different proppant sizes (e.g., 890/100, 40/70, 30/50 and 20/40 mesh sand) and seven different fracturing fluid viscosities (e.g., 1, 2, 5, 10, 20, 50, 100 cp). The color scale depicts cumulated production after three years as may be predicted, for example, by the simulation 1606 of FIG. 16. Optimum production is achieved with a combination of proppant size 30/50 mesh sand with 5 cp viscosity fracturing fluid. Thus, both fluid and proppant type may be optimized in combination. The combination may be used to account for interdependence between parameters and their impact on production.
 The methods as performed herein may be performed in any order and repeated as desired to achieve any desired output. In some cases certain portions of the method may be performed simultaneously, sequentially, repeatedly and/or in combination. Various of the methods may use or be used in combination with other methods, such as methods described in US Patent Publication No. 2012/0185225, US Patent Publication No. 2012/0179444, or US Patent Publication No. 2008/0183451, the entire contents of which are hereby incorporated by reference.
 Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this invention. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims. In the claims, means-plus-function clauses are intended to cover the structures described herein as performing the recited function and not only structural equivalents, but also equivalent structures. Thus, although a nail and a screw may not be structural equivalents in that a nail employs a cylindrical surface to secure wooden parts together, whereas a screw employs a helical surface, in the environment of fastening wooden parts, a nail and a screw may be equivalent structures. It is the express intention of the applicant not to invoke 35 U.S.C. §112, paragraph 6 for any limitations of any of the claims herein, except for those in which the claim expressly uses the words `means for` together with an associated function.
 In a given example, a stimulation operation may be performed involving evaluating variability of reservoir properties and completion properties separately for a treatment interval in a wellbore penetrating a subterranean formation, partitioning the treatment interval into a set of contiguous intervals (both reservoir and completion properties may be similar within each partitioned treatment interval, designing a stimulation treatment scenario by using a set of planar geometric objects (discrete fracture network) to develop a 3D reservoir model, and combining natural fracture data with the 3D reservoir model to account heterogeneity of formation and predict hydraulic fracture progressions.
Patent applications by SCHLUMBERGER TECHNOLOGY CORPORATION
Patent applications in class Fracturing (EPO)
Patent applications in all subclasses Fracturing (EPO)