RU2634677C2  System and method for performing well operations with hydraulic fracture  Google Patents
System and method for performing well operations with hydraulic fracture Download PDFInfo
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 RU2634677C2 RU2634677C2 RU2014107732A RU2014107732A RU2634677C2 RU 2634677 C2 RU2634677 C2 RU 2634677C2 RU 2014107732 A RU2014107732 A RU 2014107732A RU 2014107732 A RU2014107732 A RU 2014107732A RU 2634677 C2 RU2634677 C2 RU 2634677C2
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 E—FIXED CONSTRUCTIONS
 E21—EARTH DRILLING; MINING
 E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
 E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells

 E—FIXED CONSTRUCTIONS
 E21—EARTH DRILLING; MINING
 E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
 E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
 E21B43/12—Methods or apparatus for controlling the flow of the obtained fluid to or in wells

 E—FIXED CONSTRUCTIONS
 E21—EARTH DRILLING; MINING
 E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
 E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
 E21B43/25—Methods for stimulating production
 E21B43/26—Methods for stimulating production by forming crevices or fractures

 G—PHYSICS
 G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
 G16Z—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS, NOT OTHERWISE PROVIDED FOR
 G16Z99/00—Subject matter not provided for in other main groups of this subclass
Abstract
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority to provisional application for the grant of US patent No. 61/574521, filed August 4, 2011, and provisional application for the grant of US patent No. 61/574131, filed July 28, 2011, which are incorporated herein by reference in full.
BACKGROUND
[0002] The present invention relates generally to systems and methods for performing operations at a well site. More specifically, the present invention relates to methods and systems for performing fracturing operations, such as examining subsurface formations and describing hydraulic fracture systems in a subsurface formation.
[0003] In order to facilitate hydrocarbon recovery from oil and gas wells, subterranean formations surrounding such wells may be subject to hydraulic fracturing. Hydraulic fracturing can be used to create fractures in subterranean formations to allow oil or gas to move in the direction of the well. The formation is destroyed by introducing a specially designed fluid (hereinafter referred to as “hydraulic fracturing fluid” or “fracturing fluid”) under high pressure and at a high injection rate through one or more wells. Hydraulic fractures can extend hundreds of feet from the wellbore in two opposite directions, in accordance with the natural pressure inside the formation. Under certain circumstances, they can form a complex system of cracks.
[0004] Hydraulic fracturing fluids can be loaded with proppants that are particles of such a size that they can be mixed with the fracturing fluid to provide an efficient channel for hydrocarbon production from the reservoir / reservoir into the wellbore. The proppant may include natural granules of sand or gravel, manmade or specially designed proppants, for example, fibers, resin coated sand, or high strength ceramic materials, such as sintered bauxite. The proppant accumulates inside the fracture heterogeneously or homogeneously in order to wedge out and create new fractures or pores in the formation. The proppant forms cracks in the permeable channels through which drilling fluids can flow into the wellbore. Preferably, the fracturing fluids have a high viscosity and, therefore, can transfer effective volumes of proppant.
[0005] The fracturing fluid may be a viscous fluid, sometimes a socalled “cushion”, that is pumped into the working well at a speed and pressure sufficient to initiate and propagate the fracture in the hydrocarbon reservoir. The “pillow” injection continues until a crack of sufficient geometry is obtained to ensure the distribution of proppant particles. After pumping the “cushion”, the fracturing fluid may consist of fracturing fluid and a proppant. The fracturing fluid may be gelled, oil based, water based, saline, acid, emulsion, foam, or any other similar liquid. Hydraulic fracturing fluid may contain several additives, thickeners, chemicals to reduce hydraulic losses, to reduce water loss, corrosion inhibitors, etc. the proppant may have a density close to that of the fracturing fluid used.
[0006] Proppants can be composed of any commercially available sintered materials, such as silicon or oxides. These sintered materials may contain various commercially available glass or high strength ceramic products. After the proppant is injected, the well may be closed for some time, necessary to ensure a decrease in pressure in the formation. This causes the crack to close and affects the pressure causing the crack to close in the proppant particles. The stop period can vary from a few minutes to several days.
[0007] Modern methods of monitoring hydraulic fracturing allow you to map the places where the gaps, as well as the length of the cracks. Some microseismic control methods and systems can analyze the location of seismic events by mapping the arrival time of the seismic wave and polarization information in threedimensional space by modeling the travel time and / or ray paths. These methods and systems can be used to make a conclusion about the spread of hydraulic fracture over time.
[0008] Models of conventional hydraulic fracturing can also come from a doublewing artificially generated crack. Using these diptera fractures, one can briefly imagine the complex nature of artificially formed cracks in some unconventional reservoirs with a previous natural fracture. Released models can map the complex geometry of discrete hydraulic fractures based on an analysis of the microseismic distribution of events.
[0009] In some cases, the models may not be limited by considering the amount of pumped fluid or mechanical interaction between the cracks, as well as the injected fluid between the cracks. Some of the limited models may provide an overview of complex mechanisms, but may be complex in the mathematical description and / or require computer processing of resources and time to ensure accurate modeling of hydraulic fracture propagation.
[0010] Nonconventional formations, such as shales, are developed as sources of hydrocarbon production. Once they were considered only maternal and impermeable rocks, now shale strata are considered weakly porous and low fluid permeable unconventional reservoirs. Models of hydraulic fracturing created by stimulation of fractures can be complex and form a system of fractures, as indicated by the propagation of accompanying microseismic waves. Sophisticated hydraulic fracture systems have been developed to represent the hydraulic fractures created. Examples of fracture models are given in US Pat. 6101447, 7363162, 7788074, 20080133186, 20100138196 and 20100250215.
[0011] Hydraulic fracturing of shales can be used to stimulate and produce from the reservoir. Production modeling was developed to evaluate production from wells. Various production modeling techniques have been used for typical wells. Examples of production modeling are presented in publications by Warren et al., “The Behavior of Naturally Fractured Reservoirs, Soc.Pet.Eng.J., Vol. 3 (3): pp. 245255 (1963) (hereinafter “Warren &Root”); Basquet et al., “Gas Flow Simulation in Discrete Fracture Network Models”. Material SPE 79708 presented at the Symposium on Hydrodynamic Modeling in Houston, Texas, February 35, 2003 (hereinafter "Basquet"); Gong et al., Detailed Modeling of the Complex Fracture Network of Shale Gas Reservoirs, material SPE 142705, presented at the Middle East Conference and Exhibition on Unconventional Gas Resources in Muscat, Oman, January 31, 2011 (“Gong”); CincoLey et al., Pressure Transient Analysis for Naturally Fractured Reservoirs, SPE 11026, presented at the Fall Annual Technical Conference in New Orleans, Louisiana, September 26, 1982 (hereinafter referred to as “CincoLey”); Xu et al., “Quick Estimate of Initial Production from Stimulated Reservoirs with Complex Hydraulic Fracture Network,” SPE 146753, presented at the Annual Technical Conference in Denver, Colorado, USA, October 30, 2011 (“Xu 2011”) ; and publication C.E. Cohen et al. “Production Forecast After Hydraulic Fracturing in Naturally Fractured Reservoir: Coupling a Complex Fracturing Simulator and a SemiAnalytical Production Model,” SPE 152541, presented at the Woodlands, Texas, USA February 8, 2012 the entire contents of which are incorporated herein by reference. However, reservoirs may be unconventional and / or have a natural fracture, such as shale.
SUMMARY OF THE INVENTION
[0012] In at least one aspect, the present invention relates to a method for performing a production operation around a wellbore penetrating an underground formation. An underground formation with many cracks. The method includes determining the flow rate through a discrete system of cracks, characterized by many underground gaps. A discrete crack system includes a plurality of support fractures with intersections and a plurality of matrix blocks. The method further includes forming a pressure profile of a discrete crack system for an initial time based on the flow rate and determining a production rate based on the pressure profile.
[0013] In another aspect, the invention relates to a method for performing an oilfield operation around a wellbore penetrating an underground formation. The method includes performing a fracturing operation, including the formation of cracks around the wellbore. Cracks define the hydraulic system of cracks around the wellbore. The method also includes forming a discrete fracture system around the wellbore by extrapolating fracture characteristics from the hydraulic fracture system. A discrete crack system includes a plurality of support fractures with intersections and a plurality of matrix blocks. The method further includes determining the drainage depth by means of a discrete fracture system, determining at least one production parameter and performing a production operation to obtain fluids from the subterranean formations based on the depth of the drainage and at least one production parameter.
[0014] Finally, in yet another aspect, the invention relates to a method for performing an oilfield operation around a wellbore penetrating an underground formation. The method includes stimulating the wellbore by pumping fluid into the subterranean formation such that cracks form around the wellbore, measuring the fractures, and determining the hydraulic fracture system based on the measured fractures.
[0015] The method also includes forming a discrete fracture system around the wellbore by extrapolating fracture characteristics from the hydraulic fracture system. A discrete crack system includes a plurality of support fractures with intersections and a plurality of matrix blocks. The method also includes determining the depth of the drainage through a discrete system of fractures, determining at least one production parameter, estimating the rate of production over a period of time based on the depth of the drainage and the production parameter (s), and also obtaining fluids from the subterranean formation Based on estimated production rate.
[0016] This description of the invention is provided to introduce a sample of principles, which are described in detail below. This description of the invention does not provide a definition of key or essential features of the claimed subject matter, and is also not intended to limit the scope of the claimed subject matter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] Embodiments of a system and method for characterizing wellbore pressures are described with reference to the following drawings. The same numbers are used throughout the drawings to refer to features and components.
[0018] FIG. 1.11.4 schematically illustrate various oilfield operations in a borehole;
[0019] FIG. 2.12.4 schematically illustrate data obtained in the operations illustrated in FIG. 1.11.4;
[0020] FIG. 3 schematically illustrates a hydraulic fracturing site in which a fracturing operation is presented;
[0021] FIG. 4.1 and 4.2 are flowcharts illustrating methods for performing an oilfield operation and a production operation, respectively;
[0022] FIG. 5 schematically illustrates a discrete fracture system (DST) production simulation obtained by simulating hydraulic fracturing;
[0023] FIG. 6 schematically illustrates the DST of FIG. 5 with many matrix blocks;
[0024] FIG. 7 schematically illustrates the approximation of a flow through a matrix block;
[0025] FIG. 8.18.3 graphically illustrate production, cumulative production and well pressure, respectively;
[0026] FIG. 9 schematically illustrates the coordinates of cracks in a matrix block;
[0027] FIG. 10 schematically illustrates the flow rate from the matrix block to the DST branch;
[0028] FIG. 11.1 and 11.2 graphically illustrate pressure versus time for a highly conductive DST;
[0029] FIG. 12 graphically illustrates normalized pressure and delay over a period of time for highly conductive DST;
[0030] FIG. 13 graphically illustrates cumulative production over a period of time for highly conductive DST;
[0031] FIG. 14.1 and 14.2 graphically illustrate pressure versus time for a low conductive DST;
[0032] FIG. 15 graphically illustrates normalized pressure and delay over a period of time for a low conductive DST;
[0033] FIG. 16 graphically illustrates cumulative production over a period of time for low conductivity DST;
[0034] FIG. 17 graphically illustrates the normalized pressure and delay over time for a low conductive DST using the Atypical Production Model (NMD);
[0035] FIG. 18 graphically illustrates cumulative production over a period of time for low conductivity DST using NMD;
[0036] FIG. 19 illustrates a table of graphs of pressure and time delays;
[0037] FIG. 20 graphically illustrates a comparison of simulated production over a period of time using a reservoir simulator and BFM;
[0038] FIG. 21.1 and 21.2 schematically illustrate the DST made by the reservoir simulator and NPM, respectively;
[0039] FIG. 22 graphically illustrates a comparison of simulated production over a period of time for fractures with different conductivities, using a reservoir simulator and reservoir; and
[0040] FIG. 23.1 and 23.2 graphically illustrate the flow rate and cumulative production, respectively, over a period of time in the reservoir simulator, NMD and NMD without delay.
DETAILED DESCRIPTION OF THE INVENTION
[0041] The following description includes exemplary systems, devices, methods, and a sequence of instructions that embody the technical means of the subject invention in this document. However, it should be understood that the described embodiments may be practiced without these characteristic details.
[0042] The present invention relates to methods for performing fracturing operations for estimating and / or predicting production. Fracture operations include fracture modeling using elliptical and mesh modeling to estimate production.
[0043] FIG. 1.11.4 illustrate various oilfield operations that may be performed at a drilling site, and FIG. 2.12.4 illustrate the various information that can be collected at the drilling site. FIG. 1.11.4 simplify and schematically illustrate an oil field or a drilling site 100 with an underground formation 102 containing, for example, a reservoir 104 therein and illustrate various oilfield operations carried out at a drilling site 100. FIG. 1.1 illustrates well geophysical surveys carried out by well curvature measuring instruments, such as a mobile seismic station 106.1 for measuring the properties of subterranean formations. Geophysical exploration can be a seismic exploration operation to create acoustic vibrations. In FIG. 1.1 such acoustic vibration 112 created by source 110 is reflected from many horizons 114 in the rock mass 116. Acoustic vibration (s) 112 can be obtained by sensors, such as geophonesreceivers 118 located on the surface of the earth, and geophones 118 also produce electrical output signals, the socalled received data 120 in FIG. 1.1.
[0044] In response to the received acoustic vibration (s) 112, characteristic of different parameters (eg, amplitude and / or frequency) of the acoustic vibration (s) 112, geophones 118 can produce electrical output signals containing data about the subterranean formation. The obtained data 120 can be used as input for the computer 122.1 of the mobile seismic station 106.1 and can be changed rapidly depending on the input data, the computer 122.1 can generate seismic and microseismic output data 124. The output seismic data can be stored, transmitted or further processed, if desired, for example , shrink.
[0045] FIG. 1.2 illustrates a drilling operation carried out by a drilling tool 106.2, which is suspended on a drilling rig 128 and distributed into subterranean formations 102 to form a borehole 136 or other channel. The mud reservoir 130 can be used to supply the drilling fluid to the drilling tools through the production line 132 to transfer the drilling fluid through the drilling tools through the borehole 136 and back to the surface. The drilling fluid can be filtered and returned back to the drilling fluid reservoir. The circulation system can be used to store, control or filter fluid drilling fluids. This figure illustrates that drilling tools are recessed into subterranean formations to reach reservoir 104. Each well may reach one or more reservoirs. Drilling tools can be adapted to measure properties in borehole conditions using geophysical surveys of wells during drilling. In addition to adapting the drilling tools for use in geophysical exploration, they can be used to take 133 core samples, as illustrated in the figure, or they can be removed so that core samples can be taken using another tool.
[0046] The surface unit 134 may be used for communication with drilling tools and / or offsite operations. A surface unit can communicate with boring tools to send commands to boring tools, as well as to obtain data from them. The surface unit may be equipped with computer technology for receiving, storing, processing and / or analyzing production data. A surface unit may collect data obtained during a drilling operation and provide output data 135 that may be stored or transmitted. Computer technology, such as a surface unit, can be located in various places around the well site and / or in remote areas.
[0047] Sensors (S), for example, measuring devices, may be located around the field to collect data on various operations, as described above. As shown, the sensor (S) can be located in one or more places of the drilling tools and / or on the drilling rig for measuring drilling parameters, for example, the load on the bit, the torque on the bit, pressure, temperature, flow rate, composition, speed and / or other production parameters. Sensors (S) can also be located in one or more places in the circulation system.
[0048] Data obtained by sensors may be collected by a surface unit and / or other sources of information collection for analysis or other processing. The data collected by the sensors can be used separately or in combination with other data. Data can be collected in one or more databases and / or transferred to or from the site. All or part of the data can be selectively used to analyze and / or predict the operations of a given and / or other wellbore. The data may be historical data, realtime data, or combinations thereof. Realtime data can be used online or stored for future use. This data can also be combined with historical data or other input data for further analysis. Data can be stored in separate databases or be combined into a single database.
[0049] The collected data can be used to perform analysis, for example, modeling operations. For example, seismic output can be used to perform geological, geophysical and / or field development analysis. Data on the reservoir, borehole, ground data and / or processed data can be used to simulate the reservoir, borehole, geological, geophysical and other simulations. The output of the production operation can be obtained directly from the sensors or after preprocessing or simulation. This output can serve as input for further analyzes.
[0050] Data may be collected and stored at surface unit 134. One or more surface units may be located on the rig site or remotely connected to it. A surface unit can be an independent installation or a complex network of plants used to perform the necessary data management functions throughout the field. The surface unit can be manual or automatic. Surface unit 134 may be controlled and / or adjusted by the user.
[0051] A surface unit may be provided with a transceiver 137 to allow data exchange between a surface unit and other areas of a given field or other sites. Surface unit 134 may also be equipped with or functionally connected to one or more automatic controllers for actuating mechanisms at the drilling site 100. Thus, surface unit 134 may send signals to the field in response to the received data. A surface unit can receive commands through a transceiver, or it can itself issue commands to automatic controllers. The processor can be used to analyze data (onsite or remotely), make decisions and / or actuate automatic controllers. Thus, operations can be selectively adjusted based on the data collected. Parts of operations such as guided drilling, bit loading, pumping unit productivity and other parameters can be optimized based on this information. These adjustments can be made automatically based on a computer protocol and / or manually by the operator. In some cases, well designs may be adjusted to select optimal operating conditions or avoid problems.
[0052] FIG. 1.3 illustrates wireline work in a well performed by wireline tool 106.3, which is suspended on a rig 128 and in a well bore 136 of FIG. 1.2. Rope tool 106.3 may be adapted to be deployed in well 136 to form a geophysical survey of the well, to perform well tests and / or to collect samples. Rope tool 106.3 may be used to provide another method and apparatus for performing a seismometric survey operation. Rope tool 106.3 in FIG. 1.3 may, for example, have a source of explosive, radioactive, electrical or acoustic waves 144, which sends and / or receives electrical signals into the surrounding rock 102, as well as fluids.
[0053] The cable tool 106.3 can be operatively connected to, for example, geophones 118 and computer 122.1 of the mobile seismic station 106.1 in FIG. 1.1. Rope tool 106.3 can also provide data to surface unit 134. Surface unit 134 can collect data obtained during wireline work in the well and provide output data 124 that can be stored or transmitted. Rope tool 106.3 may be located at different depths of the wellbore to provide research or other information regarding the subterranean formation.
[0054] Sensors (S), such as measuring devices, may be located around the field 100 to collect data on various operations, as described above. As shown, the sensor (S) is located in the cable equipment 106.3 for measuring drilling parameters, which include, for example, porosity, permeability, fluid composition and / or other production parameters.
[0055] FIG. 1.4 illustrates the operation carried out by process equipment 106.4 going from production equipment or gushing 129 and in the completed wellbore 136 of FIG. 1.3 to take fluid from the well to the surface equipment 142. The fluid flows from the reservoir 104 through the perforations in the casing (not shown) and enters the process equipment 106.4 in the well bore 136 and to the ground equipment 142 through the collection network 146.
[0056] Sensors (S), such as measuring instruments, may be located around the field to collect data on various operations, as described above. As shown, the sensor (S) may be located on processing equipment 106.4 or auxiliary equipment, for example, gushing 129, ground equipment and / or production equipment for measuring fluid parameters, for example, fluid composition, flow rate, pressure, temperature and / or other parameters of the mining operation.
[0057] Although only simplified configurations of the drilling site are shown, it should be borne in mind that the field or drilling site 100 may cover a land area, sea and / or water bodies in which one or more drilling sites are located. Production may also include injection wells (not shown) to increase the recovery or storage of hydrocarbons, carbon dioxide or water, for example. One or more field gathering systems may be operatively connected to one or more drilling sites for selectively collecting downhole fluid from the drilling site (s).
[0058] Note that FIG. 1.21.4 illustrate tools that can be used to measure not only the properties of an oil field, but also not in an oil field, such as mines, aquifers, storage facilities and other underground structures. Also, despite the fact that certain data collection tools are illustrated, it should be borne in mind that various measuring tools can also be used (for example, wireline tool, telemetric drilling support (MWD), logging tool (LWD), core samples, etc.) capable of measuring parameters such as double seismic wave propagation time, density, resistivity, production rate, etc. underground layer and / or its geological formations. Various sensors (S) may be located in different places around the wellbore and / or monitoring tools to collect and / or monitor the desired data. Other data sources may also be provided from offsite locations.
[0059] The field configuration in FIG. 1.11.4 illustrates examples of the well 100 and various operations that can be used with the methods presented in this document. A part or the whole field may be land, water and / or sea. Also, while one measurement is illustrated at one field, field development technology can be used with any combination of one or more fields, one or more process equipment, and one or more drilling sites.
[0060] FIG. 2.12.4 graphically illustrate examples of data obtained by the tools illustrated in FIG. 1.11.4, respectively. FIG. 2.1 illustrates the seismic track 202 of the subterranean formation illustrated in FIG. 1.1, which was received by the mobile seismic station 106.1. A seismic trace can be used to provide data, such as twoway response over a period of time. FIG. 2.2 illustrates core samples 133 taken with boring tools 106.2. Core samples can be used to provide data such as a graph of density, porosity, permeability, and other physical properties of the core sample along the length of the core. Density and viscosity tests with different pressures and temperatures can be performed on core fluids. FIG. 2.3 illustrates a log 204 of the subterranean formation illustrated in FIG. 1.3, which was obtained using a rope tool 106.3. A log may provide resistivity or other formation parameters at different depths. FIG. 2.4 illustrates a curve or graph 206 of declining production of fluid flowing through a subterranean formation, as illustrated in FIG. 1.4, measured on ground equipment 142. A production decline curve can provide a production rate Q as a function of time t.
[0061] The corresponding graphs in FIG. 2.1, 2.3, and 2.4 illustrate examples of static measurements that can describe or provide information about the physical characteristics of a formation and a reservoir therein. These measurements can be analyzed to determine the characteristics of the formation (s), determine the accuracy of the measurements and / or check errors. The graphs of each of the corresponding measurements can be aligned and scaled for comparison and verification of characteristics.
[0062] FIG. 2.4 illustrates an example of a dynamic study of fluid characteristics throughout a wellbore. When a fluid flows through a wellbore, its characteristics are measured, for example, flow rate, pressure, composition, etc. As described below, static and dynamic measurements can be analyzed and used to create models of an underground formation to determine its characteristics. Similar measurements can also be used to measure changes in aspects of the formation over time.
OIL OPERATIONS
[0063] Production operations can be simulated before, during, or after production from the wellbore has been completed. Modeling production from a complex fractured formation can be carried out using various methods. Double porosity models can be used to account for differences in the properties of the formation and other reservoir formations (matrices). Double porosity can consider two mesh discharges to be connected, one for a system of cracks and the second for a matrix. This method may also include averaged characteristics (for example, for a system of cracks) and simplifications for modeling exchange terms between two means. This method can be used, for example, for reservoirs with natural fracturing. Additional analysis may be provided for the nearwellbore effects of a fracture system, for example, when fractures were created by hydraulic fracturing. Double porosity methods are described in the publication Warren & Root, which is incorporated herein by reference.
[0064] Another approach involves using a single medium containing both the reservoir and the reservoir, as well as an improved numerical grid. Additional processing time may be required for processing. The flexibility of the coordinate reference (for example, the generation of an unstructured grid) can be carried out using, for example, a special simulator of the reservoir.
[0065] Another approach involves the use of double porosity equations in a discrete crack system (DST). An example of DST is given in the Basquet publication, which is incorporated herein by reference. Additional methods can be used to simulate flow from the matrix to the gap. In some cases, for example, as in the case of compressed formation fluid (for example, gas), the history of production from each matrix block in the DST can be taken into account. A grid can be applied to the matrix block using additional unknowns in the system of equations. Examples of applying the grid are given in the publication Gong, which is incorporated herein by reference. Analytical solutions can also be presented for flow modeling. Solutions can be derived from the continuity equation of the Laplace transform. Examples of analytical solutions are provided in the publications of CincoLey and Xu 2011, which are incorporated herein by reference.
[0066] The transient hydraulic fracturing pressure can be considered to obtain a complex expression that can use numerical integration over time. The constant hydraulic fracturing pressure can also be considered and an expression can also be obtained for the flow rate between the matrix and the fracture, which is linear with respect to pressure. This solution can be used, for example, in conducting fractures, where the pressure fluctuations inside the DST are insignificant (for example, constant pressure in the wellbore). The present invention may use one or more approaches to formulate an analytical solution. This solution can take place over a wide range of fractures with specific conductivity under the condition of hydraulic fracturing and / or natural fracturing of the reservoir.
[0067] The present invention provides an analytical solution in a wide range of conductivity fractures under the condition of hydraulic fracturing and / or natural fracturing of the reservoir. Such modeling can be applied to unconventional reservoirs, such as shale gas, although it can also be applied to other underground formations. These unconventional reservoirs have two main features: low rock permeability and a dense network of natural fractures. The modeling approach can be used to take into account potential differences in the operating mode of unconventional and other reservoirs, which may contain horizontal wells and large hydraulic fractures for production. In some cases, these treatment methods cause hydraulic fractures that interact with natural fractures and can lead to a complex fracture system that connects the well to the reservoir.
[0068] The present invention discloses a methodology for simulating production from a reservoir, for example, an unconventional (with natural fracturing) well after a complex hydraulic fracture system has been created. The disclosed method first extrapolates the results obtained from an unconventional fracture model (NMR), and then processes them using a methodology that would provide the user with a forecast of production in the well for several years, within the time and degree of accuracy. The current model method extends the rationale for the semianalytical model for a number of crack conductivities to consider them in real cases. This model can be compared with simulators of reservoir formations, for example, ECLIPSE ™, which is manufactured by Schlumberger Technology Corporation (see: www.slb.com), to demonstrate the capabilities of the algorithm in order to obtain accurate results for a given range of fracture conductivity.
[0069] The present invention also discloses a method for simulating production from naturally fractured reservoirs, where the fractures were caused by hydraulic fracturing. Parts of the method can be implemented in a program that simulates a hydraulic fracturing operation. The method may first extrapolate the simulation results to recreate an adapted hydraulic fracture system with averaged characteristics between the intersections of the system, and then estimate the equivalent block depth against the background of each crack surface. Finally, parameters can be entered to start a well operating mode and simulate production. Extraction from each matrix block in contact with the discontinuity uses an analytical expression that can extend to a whole range of real values for applied parameters (conductivity, permeability, etc.). This is achieved by adjusting the initial period of operation at each time step and for each surface of the fracture in order to take into account the production delays of each matrix block and partially maintain the mass balance of the reservoir fluid in the reservoir / reservoir. Correction is performed by a search algorithm that determines this initial period in such a way that the mass actually produced on each side of the matrix block is equal to the same mass, provided that the current pressure conditions in the immediately adjacent gap were constant in time and were would start at the adjusted starting point in time. The method can be compared to simulations using a reservoir simulator, for example, ECLIPSE ™. The results for a wide range of conductivity cracks can be performed and rechecked on the reservoir simulator.
[0070] FIG. 3 illustrates a typical production site for hydraulic fracturing of a subterranean formation (hereinafter “fracture site”) in accordance with the present invention. The fracture site 300 may be located on land or in the aquatic environment and includes a working well 301 located in the subterranean formation, as well as an observation well 303 located in the subterranean formation and offset from the working well 301. Observation well 303 includes a group of geophonesreceivers 305 ( for example, threecomponent geophones) located at a certain distance, as can be seen from the illustration.
[0071] During the fracturing operation, hydraulic fracturing fluid is pumped from surface 311 into the working well 301, causing the host rock in the hydrocarbon reservoir 307 to fracture and form a hydraulic fracture system 308. Such a discontinuity triggers microseismic events 310 that emit longitudinal waves (also called primary waves or Pwaves) and shear waves (also called secondary waves or Swaves), which propagate through the earth and are recorded using a group of geophonic receivers 305 observational wells 303.
[0072] The distance to microseismic events 310 can be calculated by measuring the difference in the arrival times of the P waves and S waves. Also, particle displacement analysis can be used to determine the azimuth angle to an event, which studies the motion of Pwave particles. The depth of event 310 is limited by the use of Pwave and Swave arrival delays between a group of receivers 305. The distance, azimuth angle, and depth of such microseismic events 310 can be used to obtain the geometrical boundary or fracture profile caused by the fracturing fluid over time, for example, an elliptical boundary characterized by a height h, an elliptical compression ratio e and a major axis, as illustrated in FIG. 3.
[0073] Site 301 also includes the delivery of fracturing fluid and pumping devices (not shown) for supplying highpressure fracturing fluid to a working well 301. The fracturing fluid may be stored with a proppant (and possibly other special ingredients) premixed therein. Alternatively, a fracturing fluid may be stored without proppants and other special ingredients mixed therein, and a proppant (and / or other special ingredients) organized into the fracturing fluid in accordance with the process control system described in US Pat. 7516793, which is incorporated herein by reference in its entirety. Work well 301 also includes a flow sensor (S), which is schematically illustrated, for measuring the pump flow rate of fracturing fluid supplied to the work well and the fracture fluid pressure in the wellbore 301.
[0074] The data processing system 309 is coupled to a group of receivers 305 of the observation well 303 and a sensor S (for example, a flow sensor and a pressure sensor in the wellbore) of the working well 301. The data processing system 309 may be included in and / or operate with surface unit 134 . The data processing system 309 performs the data processing illustrated in FIG. 4 and described herein. As will be understood by those skilled in the art, the data processing system 309 includes data processing functionality (for example, one or more microprocessors, associative memory, and other hardware and / or software) for carrying out the invention as described herein.
[0075] The data processing system 309 may be implemented using a workstation or other suitable data processing system located on site 301. Alternatively, the data processing system 309 may be performed using a distributed data processing system in which data is transmitted (preferably in real time) via a communication channel (usually via satellite link) to a remote site for data analysis, as described in this document. Data analysis can be performed on a workstation or other suitable data processing system (for example, a cluster of computers or grid computing). In addition, the data processing functionality of the present invention can be stored on a storage software device (for example, one or more optical disks or a portable device for longterm storage of data, or a server accessible via a network) and, if necessary, downloaded to a suitable data processing system for processing as described in this document.
[0076] The block diagram of FIG. 4.1 illustrates a method 400.1 for performing an oilfield operation. Method 420 includes performing a fracturing operation (real or simulated), 422 forming a DST around the wellbore, 424 determining a drainage depth by DST, 426 determining at least one production parameter, and 428 performing a production operation.
[0077] FIG. 4.2 illustrates a method 400.2 for performing a mining operation. This mining operation may be the same as the mining operation 428 of FIG. 4.1. In the case of method 400.2, a mining operation is simulated. As shown in FIG. 4.2, method 400.4 includes 421 determining a flow rate through a discrete crack system, 423 generating a pressure profile of a discrete crack system based on a flow rate, and 425 determining a production rate based on a pressure profile. The method may also include 427 checking the rate of production. The method may include other characteristics or performed in a different order.
[0078] Performing a fracture operation 421 includes generating cracks around the wellbore and determining a hydraulic fracture system around the wellbore. This fracturing operation can be performed by directly injecting fluid, as illustrated, for example, in FIG. 3. Hydraulic fracturing of the wellbore can also be modeled using hydraulic fracturing models. Modeling may include the formation of a system of cracks around the wellbore. Discrete crack system methods are described in U.S. Patent Application No. 20100307755. Data obtained by real or simulated hydraulic fracturing can be used to generate data describing the received DST.
[0079] The fracturing simulation 530 may be visually represented by computer animation, as illustrated in FIG. 5. The hydraulic fracturing simulation 530 includes a plurality of fractures 534, which form a hydraulic fracture system 536. Components 536 of the fracture system, for example, mortar 538, fluid 540, and reservoir reservoir 542, are depicted in fracture system 536.
[0080] The formation of DST 422 involves extrapolating fracture characteristics from a hydraulic fracture system. DST can be formed by extrapolating fracture characteristics. Fracture characteristics can be extrapolated from Model 530 hydraulic fracturing. Data can be automatically exported to create a visualization 532 of the production system, as schematically illustrated by arrow 533. FIG. 5 illustrates an example of exporting data from a hydraulic fracturing model 530 to a visualization of a production system 532. The visualization of production system 532 is an example of creating a simulated hydraulic fracture system from measured fracture characteristics into an equivalent DST system. Export can be done to create DST 535 in a format that can be used by the production model.
[0081] In the example illustrated in FIG. 5, DST 535 contains branches 544 and intersections (or ends of cracks) 546. These support fractures 544 and intersections 546 highlight portions of hydraulic fracturing model 530 that display fluid flow 536 through a fracture system. The remaining cracks 534 were excluded.
[0082] The DST 535 format considers an individual average value for each characteristic in each support crack 544. The support crack 544 is defined as the crack connecting two intersections 536. These intersections 536 may be the intersection of cracks or the intersection of a crack and the end of a crack. The characteristics in each support fracture 544 may include, for example, spatial coordinates at the end of the fracture, averaged conductivity, averaged height, averaged reservoir pressure at the branch location and / or averaged permeability at the branch location.
[0083] The description of DST 535 at intersections 546 and at branches 544 can be used in this model to calculate the pressure at intersections 546. This description can also use branches 544 to connect intersection 546 and calculate production from adjacent matrix blocks.
[0084] Returning to FIG. 4, determination of drainage depth 424 by DST 535 may be carried out using matrix blocks. As illustrated in FIG. 6, a visualization of the production system 532 of FIG. 5 was changed to render a production system 532 depicting a modified DST 535 ′ with a matrix unit 648 in front of each fissure crack 544, as illustrated in FIG. 6. Each matrix block has its own depth of 650.
[0085] A visualization of the extraction system 532 ′ provides an example of determining the depth of the matrix 650 to be depleted on each side of all branches 544. The modified DST 535 ′ can be used to automatically or manually determine the depth of the drainage 650 for each matrix block 648. This can be done so that the total and actual volume of a given matrix block (not in contact with any of the boundaries of the reservoir) can be drained.
[0086] FIG. 7 schematically illustrates fluid flow through a matrix block. This figure illustrates the determination of the equivalent block length and the calculation of the equivalent block length. In the example shown for a square matrix block 648.1 surrounded by four supporting cracks 544 of equal length, it can be assumed that each quarter of the matrix 752 of the matrix block 648 may be depleted through the operating crack 544 with which it is in contact. Also shown is the volume 754.1 of the matrix block 648, which is depleted, and the equivalent depth of the block, which is subject to depletion.
[0087] Based on the fact that the linear flow from the matrix block 648.1 goes into the support crack 544 (as will be described in more detail herein), it can also be assumed that this quarter 752 of the matrix block 648 has the length L of the support crack 544. Thus , the depth of this “quarter” 752 of the matrix block 648.2 should be equal to one fourth of a block of length L (or L / 4) for the total volume to be depleted, which should also be the same. As indicated by arrow 733, using a linear approximation of the flow, the equivalent depth of the L / 4 block can be determined for the volume 754.2 of the matrix block 648.2 to be depleted. More complex block forms may be used, but this may lead to the use of more complex methods.
[0088] Again, referring to FIG. 4, determining 426 of one or more production parameters can be performed by obtaining user input. The user can define one or more parameters that are to be considered in the simulation. The user can select these production parameters based on some criteria or at will. Examples of production parameters that can be selected include bottomhole pressure (BHP), reservoir fluid viscosity under reservoir conditions, reservoir fluid compression ratio under reservoir conditions, and the period over which production will be simulated.
[0089] Performing a production operation 428 includes producing fluid from a subterranean formation based on the depth of the drainage and at least one production parameter. The mining operation may be real or simulated. Actual production operations include withdrawing fluids to the surface, as shown in FIG. 1.4. Simulated mining can be performed using mining simulators. Visualization of production results can also be presented. Such visualization can allow the user to visualize a decrease in production and cumulative production, as well as the dynamics of the pressure field in the system of cracks and matrix blocks. FIG. 8.18.3 provide examples of the visualization of production data over time (for example, 140 days).
[0090] Graph 800.1 in FIG. 8.1 illustrates the production rate of 856.1. Graph 800.1 illustrates daily production (Mscf / d  thousand cubic feet per day) (y axis) in relation to time t in days (x axis). Graph 800.2 in FIG. 8.2 illustrates cumulative production of 856.2. Graph 800.2 illustrates cumulative production of P (MMscf  million cubic feet per day) (y axis) in relation to time t (x axis). FIG. 8.3 is a threedimensional graph 800.3 illustrating reservoir pressure (z axis) with respect to distance x (m) (x axis) and distance y (m) (y axis), as well as pressure in fracture system 858 and matrix blocks 848. These and Other illustrations may be presented. Production operations can be adjusted based on production estimates.
MINING OPERATIONS
[0091] The mining operation (428 and / or 400.2) will be described in three parts. First, the analysis uses equations and provides their analytical solutions. Secondly, the conductivity effect of the model is provided along with an example that includes a single fissure crack, both for high and low conductivities. Third, a rationale is provided for the model and ways to address issues such as conductivity.
1. ANALYTICAL DECISION
[0092] The rate of production can be determined using basic equations and analytical solutions. The continuity equation for a compressible fluid in a porous medium is applied both to matrices and to discontinuities. Inside the crack system, the continuity equation can be transformed as follows:
[0093] Q _{mf} is the flow rate from the matrix to the reservoir, Q _{f} is the flow rate inside the fracture, ρ is the fluid density, and X _{f} is the axis along the fracture. It is believed that the permeability of the fracture (permeability divided by the width) is so great that we can neglect the transition value of the continuity equation on the time scale considered for modeling production (from days to years). It can also be assumed that a laminar flow takes place inside the crack system.
[0094] P _{f} is the pressure inside the fracture, C is the conductivity, T is the temperature. Function m  pseudopressure (AlHussainy et al. “The Flow of Real Gases Through Porous Media”, Journal of Petroleum Technology, 1966, pp. 62436).
[0095] In the matrix, the continuity equation for a compressible fluid takes the following form.
[0096] P _{m} is the pressure inside the matrix, k _{m} is the primary permeability, c _{t} is the fluid compressibility, μ is the viscosity, Z is the volume coefficient, and φ _{m} is the matrix porosity. For simplicity, Equation 4 can be converted as follows:
a is defined in Equation 6.
[0097] To calculate Q _{mf,} it is necessary to solve Equation 5, where X _{m} is the coordinate along the axis, orthogonal to the crack 964 and its coordinate X _{f} . FIG. 9 illustrates the coordinates on crack 964 and matrix block 648.
[0098] The solution to Equation 5 can be found using the Laplace transform, as explained in the publication Jeannot, Yves. Thansfert Thermique, Textbook, Ecole des Mines de Nancy, 2009. http://www.thermique55.com/principal/thermique.pdf; and Bello, R.O., “Rate Transient Analysis in Shale Gas Reservoirs with Transient Linear Behavior,” PhD Thesis, 2009. A detailed list of equations, embodiments, algorithms, and variables for this method is provided herein.
[0099] The pressure profile in the matrix can be determined for a constant fracturing pressure. The first assumption of the model is that the behavior of the gas can be described by the following equation of real gas:
inside matrix (7)
inside crack system (8)
[0100] The basic equation for calculating the linear gas flow inside the matrix block
Where
[0101] The following pseudopressure definition will simplify the solution of the previous equation
[0102] Then Equation 11 takes the form
Where
and boundary conditions:
[0103] Application of the Laplace transform to the solution of equation (15) gives
Where
[0104] For the decision as a form
applying the Laplace transform to equation (16)
which gives B = 0, therefore
[0105] While it is assumed that the pressure in the system of cracks is almost constant.
[0106] Thus, applying the Laplace transform to equation (15) gives
what gives
and
[0107] Conversion
using the Taylor series you can get the following:
[0108] The inverse Laplace transform gives
[0109] Thus, it is possible to determine the flow rate from the matrix into the fracture with a constant hydraulic fracturing pressure. The flow rate from the matrix to the gap according to Darcy's law:
[0110] L _{k} corresponds to the maximum drainage length on the rupture side k.
what gives
[0111] The flow inside the support crack between the intersection i and j can also be determined. The flow inside the crack system is described in the following equation:
where Q _{mf} is the flow rate (m ^{3} / s) from the matrix to the gap and Q _{f of the} flux (m ^{2} / s) from the gap. Assuming that the gas behavior can be described by the following real gas equation, this equation takes the form:
where the following boundary conditions:
where L _{f} is the length of the crack between two intersections. Using the following:
and introducing equation (30) into equation (32), we obtain the following:
Where
[0112] The solution to equation (35) has the form
and equation (34) gives
[0113] The flow rate can also be obtained at the intersection, for example, i from branch i, j.
[0114] When entering equation (48) into equation (39)
if it is an element from the casing, the equation takes the form
[0115] You can also determine the mass balance at the intersection between gaps
where N_ij is the number of branches reaching this intersection.
[0116] This can be converted as follows
[0117] The function of the time t _{0, k} (t) of the fluid flow through the matrix block can also be adjusted. The objective function F can be defined as the difference between the real masses obtained to date from each face of each matrix block, as well as the mass that would be obtained provided that the current pressure field inside the DST was constant, and the initial time period considered in the analytical solution was constant and equal to t _{0, k} (t).
or
[0118] The initial time period t _{0, k} (t) can be calculated by determining t _{0, k} (t), which would give F _{0, k} (t) = 0. Thus, the total mass extracted from the face k of the branch is equal to the mass that would have been produced by the same branch to date under certain conditions, for example, provided that the current pressure regime in the fracture would be the same and constant from the initial moment of production t _{0, k} (t), and / or provided that mining from this face would not have been carried out until the initial time t _{0, k} (t).
[0119] The value of t _{0, k} (t) was found using Newton's iterative algorithm:
[0120] Derivative
calculated using a quantitative gradientWhere
a = variable
c _{t} = compressibility (Pa ^{1} )
C = conductivity (m ^{2} .m)
F _{o, k} = objective function (m ^{3} )
H = crack height (m)
k _{m} = matrix permeability (m ^{2} )
L = maximum drainage length (m)
m = real gas pseudopressure (Pa / s)
m * = normalized pseudopressure of real gas (Pa / s)
m _{f} = pseudopressure of real gas in cracks (Pa / s)
m _{f} ^{*} = normalized pseudopressure of real gas in cracks (Pa / s)
m _{m} = pseudopressure of the real gas in the matrix (Pa / s)
m _{m} ^{*} = normalized pseudopressure of real gas in the matrix (Pa / s)
m _{m_0} = primary pseudo _{pressure of the} real gas in the matrix (Pa / s)
M = molar mass (kg / mol)
P _{m} = pressure in the matrix (Pa)
P _{m0} = primary pressure in the matrix (Pa)
P _{f} = primary crack pressure (Pa)
P _{LB} = low base pressure (Pa)
Q _{tot} = total flow rate from the matrix block to the crack (m ^{3} / s)
Q _{mf} = local flow rate from the matrix block to the fracture (m ^{2} / s)
Q _{f} = flow rate inside the matrix (m ^{3} / s)
R = universal gas constant (J / mol / K)
t = time (s)
t _{0, k} = initial production time (s)
T = temperature (K)
x _{f} = coordinates on the crack (m)
x _{m} = coordinates on the matrix (m)
Z = volume ratio
µ = viscosity (Pa⋅s)
φ _{m} = porosity
ρ = density of the reservoir fluid (kg / m ^{3} )
γ = variable
[0121] Where t _{0, k} (t) is known, the pressure profile can be calculated as follows:
[0122] This solution is linear with respect to pressure, Equation 2 can be transformed and solved.
[0123] Knowing the pressure profile within the system, it is possible to calculate the production rate according to Darcy's law.
[0124] The calculation can be performed in different systems of cracks, not limited to a time step. In some cases, for example, where production is performed at a constant bottomhole pressure (BHP) and high conductivity, the flow from the matrix may be based on the assumption that the pressure inside the fracture remains constant. But in fact, only cracks in the support crack of a system can have high conductivity. Calculation examples are provided by Cipolla, C. L., Lolon, E. P., Mayerhofer, M. J., “Reservoir Modeling and Production Evaluation in shaleGas Reservoirs,” SPE 13185, presented at the International Conference on Petroleum and Gas Technologies in Doha, Qatar, December 7, 2009.
SUBSTANTIATION OF AN ANALYTICAL DECISION
[0125] An analytical solution can be justified 427 by analyzing the solution to determine its applicability in a given gap. To study the justification of the analytical model for different values of the permeability of the crack, we can analyze the evolution of pressure and production in a single branch of a complex system of cracks. This study may consist of two sets of equidistant parallel cracks, as illustrated in FIG. 10. This figure describes a single branch 1070 in DST 1072 near the wellbore 1074 to be analyzed. It is shown that the matrix unit 1048 DST 1072 has a flow rate of 1076 from the matrix unit 1048 to the fissure crack 1070.
[0126] For high conductivity (finite) in a fracture system (for example, 2500 mD.ft (milliDars ft) (762 mD.m) (milliDars meter)) in the reservoir, approximately 0.0001 mD, BHP dissipates almost instantly in the system Based on this, the pressure fluctuation inside the DST can be neglected as compared to the pressure drop between the primary pressure in the reservoir and the BHP.
[0127] FIG. 11.1 and 11.2 are threedimensional graphs 1100.1 and 1100.2 illustrating reservoir pressure P (z axis) with respect to distance y (m) (y axis) for 1 and 365 days, respectively. This figure illustrates the pressure of the DST and the primary pressure in the reservoir 1178 for two different periods of production time for highly conductive DST. These and other illustrations may be presented. Production operations can be adjusted based on production estimates.
[0128] As illustrated in FIG. 12, the pressure inside the selected support fracture (for example, branch 1070 in FIG. 10) can be considered constant for ten years of production. This figure illustrates a plot of 1200 pressures (P _{mo} P _{f} ) (left y axis) and the initial time period T in days (right y axis) over a period of time t in days (for example, during three years of production) (x axis) at high conductivity condition. Formed lines for a pressure of 1280 and a time delay of 1281 are almost straight.
[0129] A consequence of this almost constant pressure in the DST is illustrated in FIG. 13, where the total production volume (from the matrix block into the operating fracture (for example, 1048 to 1070 in FIG. 10)) is reduced to the maximum recoverable volume, which is determined by the mass balance (or the primary gas volume in the reservoir reserve). In FIG. 13 illustrates a graph 1300 that depicts cumulative production P (y axis) versus time t (x axis) as a production curve 1384 that reaches maximum recovery volume 1382. This figure illustrates cumulative production from an operating fracture with respect to time under high conductivity. Due to the fact that we are considering compressible fluids, in this example, volume measurement can be done under surface conditions. This convergence indicates that the analytical solution controls the mass balance in the case of high DST conductivity. The same analysis for the low conductivity (terminal conductivity) DST (50 mD.ft (15.24 mD.ft)) may lead to a different conclusion.
[0130] As illustrated in FIG. 14.1 and 14.2, the pressure in the DST can fluctuate in comparison with the pressure range of the model (for example, VNR, primary pressure in the reservoir, etc.). This figure illustrates the pressure inside the DST over two different periods of production time for a low conductive DST. FIG. 14.1 and 14.2 are threedimensional graphs 1400.1 and 1400.1 illustrating reservoir pressure P (zaxis) with respect to distance x (xaxis) and distance y (yaxis) for 1 and 365 days, respectively. This figure illustrates the pressure inside the DST for two different periods of production time for highly conductive DST. The primary pressure in the reservoir 1478 and the pressure of the DST 1435 are also shown.
[0131] This pressure fluctuation can be seen on the pressure recorded in the support crack in relation to time, as shown in FIG. 15. As shown in FIG. 15, where the pressure inside the selected support fracture (for example, branch 1070 in FIG. 10) can be considered constant over ten years of production. This figure illustrates a plot of 1500 pressure (P _{mo}  P _{f} ) (left y axis) and delay time T in days (right y axis) over a period of time t in days (for example, over three years of production) (x axis) provided low conductivity (infinite). Formed lines for normalized pressure 1580 and time delay 1581 are almost straight. The oscillation of boundary conditions 1584 is also shown.
[0132] This pressure fluctuation in the DST means that the assumption of a constant pressure of the boundary condition in the analytical solution may require additional analysis to confirm the justification. As a result, the calculated flow rate from the matrix may be underestimated and the mass balance may be incorrect, as illustrated in FIG. 16. FIG. 16 is a graph 1600 illustrating cumulative production of P (y axis) with respect to time t (x axis), in the form of a production curve 1684, which reaches a maximum recovery volume of 1682. This figure illustrates cumulative production from an operating fracture with respect to time under low conductivity. Also shown is a deviation of 1686 between the production curve of 1684 and the maximum recovery volume of 1682.
[0133] A low diffusion coefficient in the fracture system can lead to a “delay” in production from the block, depending on how far (or reportedly) it is located from the wellbore. This observation is the starting point for a method to expand the rationale for the analytical solution for low conductivity discontinuities.
ADVANCED SUBSTANTIATION OF AN ANALYTICAL DECISION
[0134] The justification of the analytical solution can be extended to modify the “initial” time t _{0} (or t _{0, k} (t)) so that the volume extracted at the moment from the matrix block is equal to the volume that would be produced according to the analytical solution if condition of the current pressure inside the DST. During the execution of this study at each time step and on each side of each supporting crack, the analytical solution is forced to satisfy the mass balance. Search t _{0} begins with the determination of the objective function F in order to minimize.
M _{tot} is the volume mined during time t from the matrix block on the side k of the supporting crack. It is comparable with the integration of the flow rate from the matrix over the length of the supporting crack and from the initial time t _{0, k} to t. To search for t _{0, k} , such that F is equal to zero, the iterative NewtonRaphson algorithm can be used, as described in Equation 51.
[0135] The derivative of the function F _{0, k is} calculated using a quantitative gradient. If t _{0, k} crosses the time line, the optimization uses the half division method. Such an optimization algorithm is very effective due to the fact that the solution from the time step is used as an initial approximation for the next cycle. From a quantitative point of view, the calculation of the approximated volume requires integration over time, which is the most processorintensive part of the simulation. An optimization algorithm is used for each side of each branch with a minimal dependence between the variables, making this part of the algorithm a contender for parallel data processing.
[0136] To illustrate the mechanism underlying this approach, one can use the above analysis of a single operating fracture DST with low conductivity (finite conductivity) (50 mD.ft (15,24 mD.ft)). This pressure fluctuation can be seen on the pressure recorded in the support crack in relation to time, as illustrated in FIG. 17. As illustrated in FIG. 17, where the pressure inside the selected support fracture (for example, branch 1070 in FIG. 10) can be considered constant over ten years of production. This figure illustrates a graph 1700 of normalized pressure (P _{m, o}  P _{f} ) (left y axis) and time delay T in days (right y axis) over time t in days (for example, over three years of production) (x axis ) subject to low conductivity. The resulting lines for the normalized pressure 1780 and the delay time 1781 have a slope.
[0137] FIG. 17 also illustrates the design pressure within the fracture and the initial time t _{0, k} corrected according to the proposed method. An increase in t _{0, k} over time may be necessary to maintain flow rate from the matrix and cumulative production, as illustrated in FIG. 18. In FIG. Figure 18 illustrates a plot of 1800 that depicts cumulative production (y axis) versus time (x axis) as a production curve 1884 that reaches a maximum recovery volume of 1882. This figure illustrates cumulative production from an operating fracture with respect to time under low conductivity.
[0138] This figure shows that the method reduces the mass balance error because aggregate production is close to the maximum recoverable volume in FIG. 18, in comparison with FIG. 16, thus meaning that the rationale for the method can be extended with an analytical solution.
[0139] FIG. 19 is a table illustrating the pressure profile P and the initial time delay T, as calculated by the algorithm, over the entire system of cracks at different time steps t _{1} (1 day), t _{2} (200 days) and t _{3} (3 years). The table includes DST 1935.1, 1935.2 and 1935.3 for pressure and DST 1935.4, 1935.5 and 1935.6 for time delay at time steps t _{1} , t _{2} and t _{3} , respectively. This figure illustrates the pressure and the initial period of time (or “delay”) in the reservoir during different production times. The “pressure” column shows the pressure inside the formation blocks and the pressure inside the fracture system. Column T "start time" shows the start time for each block, calculated using the algorithm.
[0140] The analysis above can be performed using an atypical production model (NMD). To illustrate the capabilities of NMD, models were compared with those obtained using commercial reservoir simulators. Two different fracture geometries are compared: a simple twowinged and "mesh" fracture system.
[0141] In the example of a simple twowinged fracture, the hydraulic fracturing is a simple symmetrical fracture with a half length of 1263 feet (384.96 m) and a fracture height of 98.4 feet (19.99 m). Permeability of the formation is equal to 0,0001 mD porosity at 8%, the initial reservoir pressure is 4000 psi (lb / ^{in2)} (281.29 kg / cm) and the pressure at the bottom is 1000 psi (70,32 kg / cm). In this example, the volume coefficient Z and the viscosity of the gas were constant and equal to 1 and 0.02 cP, respectively. FIG. 20 is a comparison of simulated cumulative production on a reservoir simulator and onsite simulator, assuming different conductivities of the cracks ranging between 0.005 and 5000 mD.ft (1524 mD.m), and for a dipteral crack. FIG. 20 illustrates that the greater the pressure from the perforation channels (center of the mesh of the model), the smaller the initial time.
[0142] FIG. 20 is a graph 2000 of total surface production (y axis) versus time t (x axis). This figure illustrates the rationale by comparison with a reservoir simulator. The resulting solid lines 2088.12088.7 and the dashed lines 2089.12089.7 show production based on the reservoir simulator and production model, respectively, at different locations. This 2000 plot shows that the greater the distance from the perforation channels, the longer it will take for BHP to spread to this location.
[0143] For a mesh fracture system, this case is a complex fracture system consisting of 13 identical fractures in each orthogonal direction with a vertical well in the middle. In this example, the permeability of the reservoir is about 0.001 mD with porosity of about 8%, the primary reservoir pressure is about 4000 psi (281.29 kg / cm) and the bottom pressure is 1000 psi (70.32 kg / cm). The example also shows that the volume coefficient Z and the viscosity of the gas were constant and equal to 1 and 0.02 cP, respectively.
[0144] FIG. 21.1 and 21.2 represent different visualizations of DST performed by different simulators. This figure illustrates the reservoir and NMD used to compare models made using a commercial reservoir simulator and NMD. FIG. 21.1 illustrates an example of DST 2135.1 and 2135.2, as shown by a reservoir simulator, for example, ECLIPSE ™. FIG. 21.2 illustrates DST 2135.3 created using NMD. As shown, each of the depicted DSTs may be the same DST with which various images were obtained.
[0145] FIG. 2224 compare the results obtained by the reservoir simulator and NMD using examples where the conductivity of DST may fluctuate. FIG. 22 is a comparison of simulated cumulative production on a production simulator and NMD for various fracture conductivities that range from 0.082 mD.ft (24.99 mD.mm) to 8200 mD.ft (2499.36 mD.m), as well as for a doublewing crack .
[0146] FIG. 22 illustrates that the greater the distance from the perforation channels (the center of the mesh of the model), the smaller the initial time. FIG. 22 is a graph 2000 of total surface production (y axis) versus time t (x axis). This figure illustrates the rationale by comparison using a reservoir simulator. The resulting solid lines 2288.12288.6 and the dashed lines 2289.12289.6 show the production based on the reservoir simulator and reservoir, respectively, at different locations. This graph 2200 shows that the greater the distance from the perforation channels, the longer it will take for BHP to spread to this location.
[0147] For the purposes of this document, UDM without a “delay” means that the UDM simulator uses the analytical part of the model, where the constant initial time is 0. When the fracture conductivity increases, the difference between the reservoir simulator and the UDM simulation without a “delay” can be reduced .
[0148] These comparisons show a fairly good match between the two simulators, in particular at low conductivity, where the initial time adjustment algorithm plays an important role. To illustrate the importance of the start time adjustment algorithm of FIG. 23.1 and 23.2 compare the simulation results with a fracture conductivity of 82 mD.ft (24.99 mD.m).
[0149] FIG. 23.1 is a graph 2300.1 illustrating flow rate in surface conditions. The resulting lines 2390.12390.3 illustrate the simulation created by the reservoir simulator, NMD and NMD without delay, respectively. FIG. 23.2 is a graph 2300.2 illustrating current production in surface conditions. The cumulative production of P (y axis) is plotted against time t (x axis). The resulting lines 2390.42390.6 illustrate the simulation created by the reservoir simulator, NMD and NMD without delay, respectively. These figures illustrate the comparison of the rate (Fig. 23.1) and cumulative production (Fig. 23.2) of a commercial production simulator, NMD and NMD without a “delay”.
[0150] It should be noted that for the development of any such actual embodiment, it is necessary to make numerous implementations and make appropriate decisions in order to achieve the specific goal of the developer, for example, compliance with systemically related requirements and requirements related to business activity, which vary from one embodiment to another . In addition, it should be noted that such development efforts can be complex and time consuming, but nonetheless be commonplace for those skilled in the art who benefit from the present invention. In addition, the composition used / disclosed in this document may also contain other components than those that were given. In the conclusion and detailed description, each numerical value should be read once, taking into account the peculiarities of the term “about” (unless the corrections are clearly visible) and then read again, as they are not adjusted at all, unless otherwise indicated in the context. Also in the conclusion and detailed description, it should be understood that the concentration range mentioned or described as useful, suitable, etc., is intended so that any and every concentration within the range, including end and start points, is considered as given. For example, “a range of 1 to 10” should be read as indicating all possible numbers in the range between about 1 and about 10. Thus, even if specific data points in a range, or even the absence of data points in a range, are explicitly defined or referenced only a few specific, it should be understood that the inventors appreciate and understand that all up to one data point within the range should be considered as defined, and that the inventors have studied the entire range and all points in the range.
[0151] The statements made herein merely provide information related to the present invention and may not be considered prior art, and may also describe some embodiments illustrating the disclosed subject. All references made in this document are hereby incorporated by reference in their entirety.
[0152] The foregoing description has been presented with reference to some embodiments. Those skilled in the art to which this invention pertains will appreciate that corrections and changes to the described structures and methods of operation can be practiced without significant deviation from the principle and scope. Accordingly, the foregoing description should not be read only in relation to the exact structures described and illustrated in the accompanying drawings, but rather should be read as appropriate and as support for subsequent formulas that provide their most comprehensive and detailed scope.
[0153] Although only a few examples of embodiments have been described in detail above, those skilled in the art will appreciate that many modifications to these embodiments are possible without substantially departing from the system and method for performing wellbore modeling operations. Accordingly, all such modifications should be included in the composition of the present invention, as defined in the following claims. In the claims, the meansplusfunction clauses are intended to encompass the structures described herein as performing the specified function, as well as not only structural equivalents, but also equivalent structures. Thus, although the nail and the screw may not be structural equivalents, since the nail uses a cylindrical surface to fix the wooden parts together, while the screw uses a screw surface, and in the fastener environment of wooden parts, the nail and screw can be equivalent structures. This is an explicit expression of the applicant's intention not to invoke 35 U.S.C. § 112, paragraph 6, for any limitation of any of the claims, except those where the claims explicitly use the words “intended for” together with an associated function.
Claims (46)
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US61/574,521  20110804  
PCT/US2012/048871 WO2013016733A1 (en)  20110728  20120730  System and method for performing wellbore fracture operations 
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