Patent Publication Number: US-9416642-B2

Title: Modeling subterranean rock blocks in an injection treatment simulation

Description:
BACKGROUND 
     This specification relates to simulating subterranean rock blocks in an injection treatment simulation. During a fracture treatment, fluids are pumped under high pressure into a rock formation through a well bore to fracture the formation and increase permeability and production from the formation. Applied mathematical models can be used to numerically simulate certain aspects of a fracture treatment. For example, discontinuous deformation analysis (DDA) can be used to simulate rock deformation, rock stress, and fracture propagation. 
     SUMMARY 
     In a general aspect, rock blocks are modeled in the simulation of an injection treatment of a subterranean zone. 
     In some aspects, physically separate rock blocks of a subterranean zone are modeled by separate block models. The block model for each physically separate rock block represents intra-block mechanics of the rock block as discrete block elements. Interactions between adjacent pairs of the rock blocks are modeled by separate joint models. The joint model for each adjacent pair of rock blocks represents inter-block mechanics between the adjacent rock blocks. An injection treatment of the subterranean zone is simulated by data processing apparatus with the block models and the joint models. 
     Implementations may include one or more of the following features. The block models represent intra-block mechanics using a discontinuous deformation analysis. The block model for each rock block represents intra-block mechanics of the rock block in response to inter-block forces calculated by the joint models. The joint model for each adjacent pair of rock blocks represents inter-block mechanics between adjacent rock blocks in response to rock block movement calculated by the block models. 
     Additionally or alternatively, these and other implementations may include one or more of the following features. The joint model for each adjacent pair of rock blocks represents the inter-block mechanics as pre-defined joints. One or more of the adjacent pairs of rock blocks contact each other at physical contact locations, and the joint model for each adjacent pair of rock blocks represents inter-block forces between the rock blocks at predefined joint model locations that are different from the physical contact locations. The joint model for each adjacent pair of rock blocks represents all inter-block forces between the rock blocks as equivalent forces acting at two predefined joint model locations. 
     Additionally or alternatively, these and other implementations may include one or more of the following features. Simulating an injection treatment includes simulating time-evolution of the rock blocks and their interactions during an injection treatment applied to the subterranean zone. Fracture initiation and propagation are modeled by time-evolution of the joint models. Normal and shear failure of the rock blocks are modeled by time-evolution of the block models. Simulating an injection treatment includes simulating fluid flow in and about the rock blocks during an injection treatment applied to the subterranean zone. Simulating an injection treatment includes simulating fracture initiation and propagation in a complex fracture network. 
     The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features, objects, and advantages will be apparent from the description and drawings, and from the claims. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG. 1A  is a diagram of an example well system;  FIG. 1B  is a diagram of the example computing subsystem  110  of  FIG. 1A . 
         FIG. 2  is a schematic diagram of an example rock mass. 
         FIG. 3  is a schematic diagram of an example fracture simulation architecture. 
         FIG. 4  is a schematic diagram of an example joint model. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     In some aspects, multiple different types of applied mathematical models are used to numerically simulate an injection treatment system. The applied mathematical models can represent various physical subsystems of an injection treatment system, such as rock blocks, fractures, fracture flows, fluid junction, leakoff, wellbores, etc. Appropriate subsystem models can be chosen and combined to model the overall injection treatment system. In some examples, physically separate rock blocks of the subterranean zone are modeled by separate block models, and the interactions between adjacent rock blocks are modeled by separate joint models. The block model for a given rock block represent the rock block&#39;s intra-block mechanics, and the joint model for a given pair of rock blocks represents the pair&#39;s inter-block mechanics. In some cases, the block models and the joint models are different types of applied mathematical models. For example, the block models can have different governing equations than the joint models, they have different parameters and variables than the joint models, they can model different types of physical phenomena than the joint models, etc. 
     In some instances, one or more of the adjacent pairs of rock blocks contact each other at multiple physical contact locations. Rather than using the physical contact locations, the joint models can use predefined joint model locations to model the mechanical interactions between the rock blocks. The physical contact locations can be different from the predefined joint locations. In this manner, the joint model for each adjacent pair of rock blocks can represent all inter-block forces between the rock blocks as equivalent forces acting at the predefined joint model locations. In some examples, the Cohesive Zone Models (CZM) can be chosen as the joint model to simulate fracture behavior as well as interaction between the discrete rock blocks. 
     In some implementations, the block models represents the intra-block mechanics by modeling a solid, physical rock block as a group of discrete block elements. This discrete characterization of the rock blocks, at least in some instances, provides an appropriate representation of the hydraulic fractures and their interaction with natural fractures. For example, a discrete block model can simulate fractured formation, for example, as an opening formed by the movement of discrete rock block elements. In some examples, a discontinuous deformation analysis (DDA) model can be chosen as the block model. In some implementations, the DDA model is an implicit version of the distinct element method (DEM), and it can be used to perform deformation analysis for discrete rock blocks. 
     The block models and joint models can be combined, and in some instances they may be combined with other subsystem models, and used to simulate a hydraulic fracturing process, which can include fracture initiation and propagation in a complex fracture network. The DDA model and CZM can be linked, for example, at the nodal contacts defined by the CZM model for each adjacent pair of rock blocks. As a specific example, the predefined joint model locations used for connecting the DDA model and the CZM can be simplified to two nodal contacts between two corner nodes of adjacent discrete blocks. CZM can then be used on these nodal contacts for fracture behavior simulation. The simulation system can be developed using additional or different types of models and components, or the models can be configured in another manner. 
     In some instances, the resulting simulation system can more accurately simulate fracture initiation and propagation in complex fracture networks, such as, for example, induced complex fracture networks and the naturally-occurring complex fracture networks commonly observed in shale and other types of rock formation. The simulation system can, in some instances, better capture the discrete characterization of a rock mass in a complex fracture network, for example, due to the selected block model (e.g., the DDA model or another type of model), and can accurately describe the gradual process of fracture initiation and propagation process and describe both failure in normal and shear direction as well as their effluence between them, for example, due to the selected joint model (e.g., CZM or another type of model). 
     Moreover, in some implementations, numerical simulations can be simplified or made more computationally efficient. Using the joint models to model the block interactions may avoid or trivialize certain tasks that would otherwise require computationally-intensive computations, such as, for example, searching for physical contact locations between the rock blocks at each time step. In some instances, the simulation system can better represent the dynamics of the physical rock system, for example, because the simplified predefined joint model locations may reduce the motion and enhance robustness of the block models compared with the motion and sensitivity of some other models. For example, some block models simulate forces at every physical contact location and interactions between each pair of discrete block elements. The reduced motion of the block models can, in some instances, enable the simulation system to reflect limited deformation of an underground complex fracture network, for example, confined by a high pressure environment. 
     In some implementations, additional or different subsystems models can be used in a simulation system to build a comprehensive software package that simulates and analyzes injection treatments. For example, fracturing fluid simulation models, wellbore models, and other types of models can be combined with the block models and joint models, for instance, to simulate hydraulic fracturing of a subterranean zone. 
       FIG. 1A  shows a schematic diagram of an example well system  100  with a computing subsystem  110 . The example well system  100  includes a treatment well  102  and an observation well  104 . The observation well  104  can be located remotely from the treatment well  102 , near the treatment well  102 , or at any suitable location. The well system  100  can include one or more additional treatment wells, observation wells, or other types of wells. The computing subsystem  110  can include one or more computing devices or systems located at the treatment well  102 , at the observation well  104 , or in other locations. The computing subsystem  110  or any of its components can be located apart from the other components shown in  FIG. 1A . For example, the computing subsystem  110  can be located at a data processing center, a computing facility, or another suitable location. The well system  100  can include additional or different features, and the features of the well system can be arranged as shown in  FIG. 1A  or in any other suitable configuration. 
     The example treatment well  102  includes a well bore  101  in a subterranean zone  121  beneath the surface  106 . The subterranean zone  121  can include one or less than one rock formation, or the subterranean zone  121  can include more than one rock formation. In the example shown in  FIG. 1A , the subterranean zone  121  includes various subsurface layers  122 . The subsurface layers  122  can be defined by geological or other properties of the subterranean zone  121 . For example, each of the subsurface layers  122  can correspond to a particular lithology, a particular fluid content, a particular stress or pressure profile, or any other suitable characteristic. In some instances, one or more of the subsurface layers  122  can be a fluid reservoir that contains hydrocarbons or other types of fluids. 
     The subterranean zone  121  may include any suitable rock formation. For example, one or more of the subsurface layers  122  can include sandstone, carbonate materials, shale, coal, mudstone, granite, or other materials. In some instances, the subterranean zone  121  includes a fracture network in a fractured rock formation. Fracture networks can include natural fractures, induced fractures, or both. A fracture network can define multiple rock blocks in the rock formation, and the rock blocks can range in size from centimeters, or smaller, in size to hundreds of meters, or larger. 
     The example treatment well  102  includes an injection treatment subsystem  120 , which includes instrument trucks  116 , pump trucks  114 , and other equipment. The injection treatment subsystem  120  can apply an injection treatment to the subterranean zone  121  through the well bore  101 . The injection treatment can be a fracture treatment that fractures the subterranean zone  121 . For example, the injection treatment may initiate, propagate, or open fractures in one or more of the subsurface layers  122 . A fracture treatment may include a mini fracture test treatment, a regular or full fracture treatment, a follow-on fracture treatment, a re-fracture treatment, a final fracture treatment or another type of fracture treatment. 
     The fracture treatment can inject a treatment fluid into the subterranean zone  121  at any suitable fluid pressures and fluid flow rates. Fluids can be injected above, at or below a fracture initiation pressure, above at or below a fracture closure pressure, or at any suitable combination of these and other fluid pressures. The fracture initiation pressure for a formation is the minimum fluid injection pressure that can initiate or propagate artificial fractures in the formation. Application of a fracture treatment may or may not initiate or propagate artificial fractures in the formation. The fracture closure pressure for a formation is the minimum fluid injection pressure that can dilate existing fractures in the subterranean formation. Application of a fracture treatment may or may not dilate natural or artificial fractures in the formation. 
     A fracture treatment can be applied by any appropriate system, using any suitable technique. The pump trucks  114  may include mobile vehicles, immobile installations, skids, hoses, tubes, fluid tanks or reservoirs, pumps, valves, or other suitable structures and equipment. In some cases, the pump trucks  114  are coupled to a working string disposed in the well bore  101 . During operation, the pump trucks  114  can pump fluid through the working string and into the subterranean zone  121 . The pumped fluid can include a pad, proppants, a flush fluid, additives, or other materials. 
     A fracture treatment can be applied at a single fluid injection location or at multiple fluid injection locations in a subterranean zone, and the fluid may be injected over a single time period or over multiple different time periods. In some instances, a fracture treatment can use multiple different fluid injection locations in a single well bore, multiple fluid injection locations in multiple different well bores, or any suitable combination. Moreover, the fracture treatment can inject fluid through any suitable type of well bore, such as, for example, vertical well bores, slant well bores, horizontal well bores, curved well bores, or any suitable combination of these and others. 
     A fracture treatment can be controlled by any appropriate system, using any suitable technique. The instrument trucks  116  can include mobile vehicles, immobile installations, or other suitable structures. The instrument trucks  116  can include an injection control system that monitors and controls the fracture treatment applied by the injection treatment subsystem  120 . In some implementations, the injection control system can communicate with other equipment to monitor and control the injection treatment. For example, the instrument trucks  116  may communicate with the pump truck  114 , subsurface instruments, and monitoring equipment. 
     The observation well  104  shown in  FIG. 1A  includes a well bore  111  in a subterranean region beneath the surface  106 . The observation well  104  includes sensors  112  and other equipment that can be used to detect microseismic information. The sensors  112  may include geophones or other types of listening equipment. The sensors  112  can be located at a variety of positions in the well system  100 . In  FIG. 1A , sensors  112  are installed at the surface  106  and beneath the surface  106  in the well bore  111 . Additionally or alternatively, sensors may be positioned in other locations above or below the surface  106 , in other locations within the well bore  111 , or within another well bore. The observation well  104  may include additional equipment (e.g., working string, packers, casing, or other equipment) not shown in  FIG. 1A . In some implementations, microseismic data are detected by sensors installed in the treatment well  102  or at the surface  106 , without use of an observation well. 
     In some cases, all or part of the computing subsystem  110  can be contained in a technical command center at the well site, in a real-time operations center at a remote location, in another appropriate location, or any suitable combination of these. The well system  100  and the computing subsystem  110  can include or access any suitable communication infrastructure. For example, well system  100  can include multiple separate communication links or a network of interconnected communication links. The communication links can include wired or wireless communications systems. For example, sensors  112  may communicate with the instrument trucks  116  or the computing subsystem  110  through wired or wireless links or networks, or the instrument trucks  116  may communicate with the computing subsystem  110  through wired or wireless links or networks. The communication links can include a public data network, a private data network, satellite links, dedicated communication channels, telecommunication links, or any suitable combination of these and other communication links. 
     The computing subsystem  110  can simulate application of the fracture treatments to the subterranean formation through one or more well bores. For example, the computing subsystem  110  can simulate and predict fracture initialization and propagation during fracture treatments applied through the well bores  101 . The simulation may rely on a fracture simulation system that can reflect the physical process of fracture treatments. The computing subsystem  110  can design or modify fracture treatments based on the simulations. For example, the computing subsystem  110  may calculate, select, or optimize fracture treatment parameters for initialization, propagation, or opening fractures in one or more of the subsurface layers  122 . 
     Some of the techniques and operations described herein may be implemented by a computing subsystem configured to provide the functionality described. In various embodiments, a computing device may include any of various types of devices, including, but not limited to, personal computer systems, desktop computers, laptops, notebooks, mainframe computer systems, handheld computers, workstations, tablets, application servers, storage devices, or any type of computing or electronic device. 
       FIG. 1B  is a diagram of the example computing subsystem  110  of  FIG. 1A . The example computing subsystem  110  can be located at or near one or more wells of the well system  100  or at a remote location. All or part of the computing subsystem  110  may operate independent of the well system  100  or independent of any of the other components shown in  FIG. 1A . The example computing subsystem  110  includes a processor  160 , a memory  150 , and input/output controllers  170  communicably coupled by a bus  165 . The memory can include, for example, a random access memory (RAM), a storage device (e.g., a writable read-only memory (ROM) or others), a hard disk, or another type of storage medium. The computing subsystem  110  can be preprogrammed or it can be programmed (and reprogrammed) by loading a program from another source (e.g., from a CD-ROM, from another computer device through a data network, or in another manner). The input/output controller  170  is coupled to input/output devices (e.g., a monitor  175 , a mouse, a keyboard, or other input/output devices) and to a communication link  180 . The input/output devices receive and transmit data in analog or digital form over communication links such as a serial link, a wireless link (e.g., infrared, radio frequency, or others), a parallel link, or another type of link. 
     The communication link  180  can include any type of communication channel, connector, data communication network, or other link. For example, the communication link  180  can include a wireless or a wired network, a Local Area Network (LAN), a Wide Area Network (WAN), a private network, a public network (such as the Internet), a WiFi network, a network that includes a satellite link, or another type of data communication network. 
     The memory  150  can store instructions (e.g., computer code) associated with an operating system, computer applications, and other resources. The memory  150  can also store application data and data objects that can be interpreted by one or more applications or virtual machines running on the computing subsystem  110 . As shown in  FIG. 1B , the example memory  150  includes treatment data  151 , geological data  152 , fracture data  153 , other data  155 , and applications  156 . In some implementations, a memory of a computing device includes additional or different information. 
     The treatment data  151  can include information on fracture treatment plans. For example the treatment data  151  can indicate a pumping schedule, parameters of a previous injection treatment, parameters of a future injection treatment, and/or parameters of a proposed injection treatment. Such parameters may include information on flow rates, flow volumes, slurry concentrations, fluid compositions, injection locations, injection times, or other parameters. The treatment data  151  can include treatment parameters that have been optimized or selected based on numerical simulations of complex fracture propagation. 
     The geological data  152  can include information on the geological properties of the subterranean zone  121 . For example, the geological data  152  may include information on the subsurface layers  122 , information on the well bores  101 ,  111 , or information on other attributes of the subterranean zone  121 . In some cases, the geological data  152  includes information on the lithology, fluid content, stress profile, pressure profile, spatial extent, or other attributes of one or more rock formations in the subterranean zone. The geological data  152  can include information collected from well logs, rock samples, outcroppings, microseismic imaging, or other data sources. 
     The fracture data  153  can include information on fracture planes in a subterranean zone. The fracture data  153  may identify the locations, sizes, shapes, and other properties of fractures in a model of a subterranean zone. The fracture data  153  can include information on natural fractures, hydraulically-induced fractures, or any other type of discontinuity in the subterranean zone  121 . The fracture data  153  can include fracture planes calculated from microseismic data or other information. For each fracture plane, the fracture data  153  can include information (e.g., strike angle, dip angle, etc.) identifying an orientation of the fracture, information identifying a shape (e.g., curvature, aperture, etc.) of the fracture, information identifying boundaries of the fracture, or any other suitable information. The fracture data  153  can include information on rock blocks and rock block intersections. For each rock block, the fracture data  153  can include information identifying a location and orientation of the rock block, a shape and boundaries of the rock block, the stress, strain, and other mechanical properties of the rock block, permeability, transmissibility, or other material properties of the rock block, thermodynamic properties of the rock block, contact locations or joint locations with other rock blocks, or a combination of these and any other suitable information. 
     The applications  156  can include software applications, scripts, programs, functions, executables, or other modules that are interpreted or executed by the processor  160 . Such applications may include machine-readable instructions for performing one or more of the operations associated with an injection treatment simulation system as described below. The applications  156  may include machine-readable instructions for generating a user interface. The applications  156  can obtain input data, such as treatment data, geological data, or other types of input data, from the memory  150 , from another local source, or from one or more remote sources (e.g., via the communication link  180 ). The applications  156  can generate output data and store the output data in the memory  150 , in another local medium, or in one or more remote devices (e.g., by sending the output data via the communication link  180 ). 
     The processor  160  can execute instructions, for example, to generate output data based on data inputs. For example, the processor  160  can run the applications  156  by executing or interpreting the software, scripts, programs, functions, executables, or other modules contained in the applications  156 . The processor  160  may perform one or more of the operations associated with the simulation system as illustrated in  FIG. 3 . The input data received by the processor  160  or the output data generated by the processor  160  can include any of the treatment data  151 , the geological data  152 , the fracture data  153 , or the other data  155 . 
       FIG. 2  is a schematic diagram of an example rock mass  200 . Fracture treatments and other activities can cause complex fracture patterns to develop within the natural fracture pattern in the formation. For example, hydraulic fracturing may include pumping fracturing fluid into a subterranean formation through a wellbore under a pressure exceeding the formation stress so that the formation can be artificially fractured. The hydraulic fractures and their interaction with natural fractures can, in some instances, form discrete rock blocks in the formation. As illustrated in  FIG. 2 , the example rock mass  200  includes a number of discrete rock blocks such as, for example,  205   a ,  205   b  and  205   c , etc. The discrete rock blocks  205   a ,  205   b  and  205   c  can have different sizes and shapes. The example rock mass  200  includes a number of fractures such as  210   a ,  210   b , and  210   c , etc. In the example shown, the fractures define at least a portion of the rock block geometries. The fractures  210   a ,  210   b , and  210   c  between the rock blocks can have different orientations and can be initially open, or closed. The fractures can form complex fracture networks. The fractures can provide flow channels for fracturing fluid for fracturing treatment. 
     A simulation system can define data structures to model the behavior of the rock blocks and the fractures during an injection treatment. For example, the simulation system may include block models for deformation analysis of discrete rock block, joint models for simulating fracture behavior as well as interactions between discrete rock blocks, or any other suitable models. In some instances, simulating an injection treatment can include simulating fracture initiation and propagation in a fracture network such as, for example, the example fracture network shown in  FIG. 2 . In some instances, numerical models are operated to simulate fluid flow in and about the example rock blocks  205   a ,  205   b ,  205   c , etc., time-evolution of the example rock blocks  205   a ,  205   b ,  205   c , etc., interactions between the example rock blocks  205   a ,  205   b ,  205   c , etc., time evolution of the example fractures  210   a ,  210   b ,  210   c , etc., fluid flow in the example fractures  210   a ,  210   b ,  210   c , etc., and other behavior during an injection treatment. 
       FIG. 3  is a schematic diagram of an example fracture simulation architecture  300 . The example fracture simulation architecture  300  includes two block models  302   a  and  302   b , and a joint model  303 . The example block models  302   a  and  302   b  each represent a discrete rock block. For example, the block model  302   a  can represent one of the example rock blocks  205   a ,  205   b , or  205   c  shown in  FIG. 2 , and the other block model  302   b  can represent a different, adjacent one of the example rock blocks  205   a ,  205   b , or  205   c . The block models  302   a  and  302   b  can be the same type of block model, or they can be different types of block models. 
     Each of the example block models  302   a  and  302   b  can represent mechanical properties of an individual rock block, which may include static mechanical properties (e.g., position, stress, strain, Young&#39;s Modulus, Poisson&#39;s Ratio), dynamic mechanical properties (e.g., deformation, movement, rotation, etc.), or a combination of these and other types of mechanics. In some instances, the block models are operable to perform a deformation analysis or other types of analysis of the discrete rock block. 
     The joint model  303  can represent an interaction of two adjacent rock blocks. In the example shown in  FIG. 2 , the joint model  303  can represent the fracture between the adjacent rock blocks  205   a  and  205   b , between the adjacent rock blocks  205   b  and  205   c , etc. In some cases, the rock blocks  205   a  and  205   c  may also be considered adjacent, and a joint model can represent their interaction. In some cases, the joint model  303  is a different type of numerical model from the block models  302   a ,  302   b . The joint model  303  can represent mechanical properties of a fracture between two adjacent rock blocks, which may include static mechanical properties (e.g., aperture, length, etc.), dynamic mechanical properties (e.g., dilation, contraction, etc.), or a combination of these and other types of mechanics. 
     The joint model  303  can be coupled with the block models  302   a  and  302   b , for example, via links  304   a  and  304   b , respectively. A joint model can be used, in some instances, to simulate fracture behavior as well as interactions between rock blocks. As an example, the joint model  303  can simulate the behavior of the fracture  210   b  and interactions between the two adjacent rock blocks  205   a  and  205   b . In some instances, a block model may take force as an input parameter and return the location, orientation, stresses and strains of the block as output variables. In some instances, a joint model can take the input parameters, for example, positions of the adjacent rock blocks, distances between the two blocks, and return, for example, forces towards each of the two blocks as output. There may be a joint model for each pair of adjacent rock blocks (e.g., pairs of blocks that contact each other, pairs of blocks without substantial structure separating them, etc.). 
     In some instances, the example simulation architecture  300  can include additional or different models, such as a fluid junction model, a fracture flow model, a leakoff model, a wellbore model, etc. In some implementations, the example fracture simulation architecture  300  can include additional block models and joint models to represent all rock blocks and joints, or a portion of the rock blocks and joints, in a complex fracture network. The example fracture simulation architecture  300  can be configured to simulate an injection treatment on a computing system. For example, one or more of the applications  156  on the computing subsystem  110  shown in  FIG. 1B  can be implemented based on the example simulation architecture  300  shown in  FIG. 3 . In some cases, the example simulation architecture  300  can be used to implement numerical simulations based on the example predefined joint model locations between rock blocks shown in  FIG. 4 , or the simulation architecture  300  can be used in another manner. Generally, a simulation system can include additional or different modules or components with suitable functionality, and the features of a simulation system can function as represented with respect to the example shown in  FIG. 3  or in another manner. In some cases, fracture initiation and propagation are modeled by time-evolution of the joint models; and normal and shear failure of the rock blocks can be modeled by time-evolution of the block models. Additional or different aspects of a subterranean zone may be modeled. 
     Some example techniques that can be used by the block models (e.g.,  302   a  and  302   b ) to perform deformation and stresses analysis include the finite element method (FEM), distinct element method (DEM, also called discrete element method), or other variations or combinations thereof. These techniques can include continuum-based models and discontinuum-based models. For example, FEM may treat the rock media as continuum, while DEM may treat the rock media as discrete particles. Fracture analysis may include explicit spatial discretization along fracture surfaces to simulate discontinuities and may use fine meshes around the fracture tips to obtain accurate results. When the fracture propagates, re-meshing can be applied. In some instances, discontinuum models are more suitable for some types of fracture network simulations, for example, by allowing finite displacements and rotations of discrete particles and reproducing normal and shear failure mechanisms in discontinuous media. DEM has been implemented in some conventional software packages to simulate hydraulic fracturing in fractured rocks. 
     Various techniques can be used by the joint models (e.g.,  303 ) to simulate fracture behavior as well as interactions between discrete rock blocks. In some implementations, the Mohr-Coulomb shear failure criterion and tensile strength criteria can be used to describe the failure between rock blocks. In some implementations, Cohesive Zone Models (CZM) can be used to describe fracture behavior. For example, CZM can be used in numerical simulations of dynamic crack growth in brittle (or quasi-brittle) solids. In some computational simulations, the cohesive law is used to model the behavior of a weak interface in the solids. CZM can treat fracture as a gradual process in which separation of fractures is resisted by cohesive traction forces. Compared with the traditional empirical methods, CZM can predict entire fracture process from crack initiation to propagation accurately for any joint geometry and any applied load. In some implementations, CZM also can correlate the effects between shear and normal failure. 
     In some implementations, physically separate rock blocks of a subterranean zone can be modeled by separate block models. For example, the discrete rock blocks  205   a  and  205   b  of the example rock mass  200  may be modeled by the example block models  302   a  and  302   b , respectively. The block model for each physically separate rock block can represent intra-block mechanics of the rock block. Each block model can represent an intra-block mechanics of a rock block as a group of discrete block elements. For example, the block models  302   a  and  302   b  can be the discontinuum models such as DDA models. In some implementations, the block model for each rock block can represent intra-block mechanics of the rock block in response to inter-block forces determined by the joint models. For example, the block models  302   a  and  302   b  may represent intra-block mechanics of the discrete rock blocks  205   a  and  205   b  in response to inter-block forces derived by the joint model  303 . 
     In some implementations, interactions between adjacent pairs of the rock blocks are modeled by separate joint models. The joint model for each adjacent pair of rock blocks can represent inter-block mechanics between the adjacent rock blocks. In some instances, the joint model for each adjacent pair of rock blocks can represent inter-block mechanics between the adjacent rock blocks as predefined inter-block joints. The inter-block mechanics can include, for example, fracture behavior such as fracture initiation and propagation. In the example shown in  FIG. 3 , the example joint model  303  may be used to model the behavior of the fracture  210   b  and the inter-block mechanics between the two adjacent rock blocks  205   a  and  205   b , or the example joint model  303  may be used to model the behavior of the fracture  210   c  and the inter-block mechanics between the two respective adjacent rock blocks  205   b  and  205   c . As an example, the joint model  303  can be CZM or another type of joint model. In some implementations, the joint model for each adjacent pair of rock blocks can represent inter-block mechanics between adjacent rock blocks in response to rock block movement derived by the block models. For example, the joint model  303  may represent the inter-block mechanics between the two adjacent rock blocks  205   a  and  205   b  in response to the movements of the rock blocks  205   a  and  205   b , or the inter-block mechanics between the two adjacent rock blocks  205   b  and  205   c  in response to the movements of the rock blocks  205   b  and  205   c.    
     In some implementations, one or more of the adjacent pairs of rock blocks contact each other at physical contact locations. For example, the adjacent rock blocks (e.g.,  205   a  and  205   b , etc.) may physically contact each other at multiple locations. The joint model for each adjacent pair of rock blocks can represent inter-block forces between the rock blocks at predefined joint model locations that are different from the physical contact locations. In other words, instead of using the actual physical contact locations, a few predefined joint model locations can be set and regarded as reference contact locations that can be used for calculating the inter-block forces, for instances. Based on the predefined joint model locations, the joint model for each adjacent pair of rock blocks can represent all inter-block forces between the rock blocks as equivalent forces acting at the predefined joint model locations. 
       FIG. 4  is a schematic diagram of an example joint model  400 . In the example shown in  FIG. 4 , the two blocks  402  and  404  are adjacent to each other. The surfaces  406  and  408  of the two adjacent rock blocks  402  and  404  define at least part of a fracture. As such, the surfaces  406  and  408  may be considered fracture surfaces. The two rock blocks  402  and  404  may physically contact each other at one or more points along the surfaces  406  and  408 , or there may be no physical contact between the two rock blocks  402  and  404 . A joint model can be used to represent the interactions between the two adjacent rock blocks  402  and  404 . In some implementations, instead of modeling each and every physical contact location of the two rock blocks  402  and  404 , the example joint model  400  may use a small number (e.g., one, two, three, four, etc.) of predefined joint model locations to simplify the contacts between the two rock blocks  402  and  404 . For instance, the example joint model  400  shown in  FIG. 4  includes predefined joint model locations at two nodal contacts  410  and  412 . The example nodal contacts  410  and  412  are the contacts between two corner nodes of adjacent discrete blocks. The predefined joint model locations can include additional or different locations, or they can be configured in another manner. 
     In some instances, using predefined joint model locations can provide advantages, for example, in a numerical simulation of an injection treatment. For example, rather than searching and calculating the forces applied at each physical contact location between each adjacent pair of rock blocks, the equivalent forces can be calculated only at the predefined joint model locations. In some implementations, the joint model can calculate the equivalent forces acting at the predefined joint model locations, which can represent all inter-block forces between the rock blocks. Computational complexity can be reduced, for example, because the contact locations of the joint models are known, which can avoid the computationally expensive contact tracking process. In some instances, with the predefined joint model locations, a simulation system can better represent an actual physical system. For example, in some instances, an underground complex fracture network can be confined by a high pressure environment, and the deformation of the complex fracture network during the hydraulic fracturing process may be relatively small. The block models with equivalent forces acting at the simplified contact locations (e.g.,  406  and  408 ) may demonstrate less rock movement and enhanced robustness, for example, due to reduced sensitivity to forces at every physical contact location as well as the potentially complicated interactions between each pair of discrete block elements. In some instances, the block models with reduced motion may better reflect the actual underground complex fracture network, for example, where only limited deformations occur due to high pressure imposed by the environment, and in other environments. 
     In some examples, a DDA-type model can be used to define the block models (e.g.,  302   a  and  302   b ) for deformation and stresses analysis of discrete rock block, and CZM can be chosen as the joint model (e.g.,  303 ) to describe fracture behavior as well as interactions between discrete rock blocks. The DDA model and CZM can be coupled together, for example, via nodal contacts of discrete rock blocks. The predefined joint model locations can be simplified, for example, to two nodal contacts (e.g.,  410  and  412  as illustrated in  FIG. 4 ) or another number of locations. CZM can then be used on these nodal contacts for fracture behavior simulation. 
     In a DDA model, displacements and strains can be defined as unknowns on each discrete block. In some implementations, the DDA model can include governing equations to represent the rock dynamics. An example governing equation of the DDA model can be formulated as a system of time-dependent equations such as illustrated in Equation (1),
 
 M{umlaut over (x)}+C{dot over (x)}+Kx=F   (1),
 
where M, C and K are the mass matrix, the damping matrix and the stiffness matrix respectively, and F represents the forces vector applied to the rock block. In the example approach where the DDA and CZM are coupled via nodal contacts, the forces vector F can be the forces applied at the block nodal points. In Equation (1), the variable x is an unknown vector which contains, for example, displacements at the centroid of the block and strain components of the rock block. The variable
 
               x   .     =       ⅆ   x       ⅆ   t             
is the time derivative of the vector x, and
 
               x   .     =       ⅆ     x   .         ⅆ   t             
is the time derivative of the vector {dot over (x)}, or equivalently the second time derivative of the vector x. As a specific example, the vector x can include three displacements components and three strain components. The displacements can include, for example, an x-coordinate and a y-coordinate in an xy-coordinate system (which can indicate a location or movement of the centroid of the rock block), and a rotation value that can indicate the orientation of the rock block. The strain components can include the strains along the x direction, the y direction, and a shear xy direction.
 
     In the above example, the Equation (1) can be rewritten as six equations with six variables. Together with the equations 
               x   .     =       ⅆ   x       ⅆ   t                 and                 x   ¨     =       ⅆ     x   .         ⅆ   t         ,         
a system of eighteen equations with eighteen variables can be formulated. The eighteen unknown variables included in x, {dot over (x)}, and {umlaut over (x)} can be solved, for example, by some solvers such as an ordinary differential equations (ODEs) solver, a differential algebraic equations (DAEs) solver, or any other appropriate system or algorithm. In some implementations, the above system of equations can be solved at each time step for each rock block, which can provide time-dependent solution of displacement and strains for all discrete rock blocks. In some instances, normal and shear failure of the rock blocks can be modeled by time-evolution of the block models, for example, by monitoring the time-dependent displacements and strains of the rock blocks and identifying the variations of the displacements and strains with respect to time. Different modifications can be made to Equation (1) to represent the DDA model, and additional or different components can be included in the variable or the parameters. Alternatively or additionally, other formulations can be used for modeling the discrete rock block.
 
     CZM fracture model can provide a correlation between traction forces and fracture openings, and it can incorporate meaningful physical parameters. There are different variations of CZM. An example general governing equation for CZM can be represented as shown in Equation (2),
 
 F=F (δ n ,δ t ,σ max ,τ max  . . . )  (2),
 
where F includes the variables and can represent the traction forces. This general equation can be modified or adapted for a particular variation of CZM. In the above example, the traction forces F are functions of normal separations of fracture δ n , shear separation of the fracture δ t , maximum tensile strength σ max , maximum cohesive strength τ max , and any other appropriate parameters. In some implementations, the normal separation δ n , can influence shear failure, and vice versa. In some implementations, the traction forces F can represent the equivalent nodal forces acting at the predefined joint model locations. The CZM model may calculate the equivalent forces at predefined joint model locations. Using the example shown in  FIG. 4  where contacts between the two adjacent rock blocks  402  and  404  are simplified to two nodal contacts  410  and  412 , the forces F in this case can include four elements, for instance, one normal and one shear components for each nodal contact. As a result, Equation (2) can be rewritten as four equations and each equation can represent the equivalent normal or shear force component acting at one of the nodal contacts. In some instances, the equivalent forces acting at the predefined nodal contact locations can represent all inter-block forces between the two rock blocks.
 
     In some implementations, a procedure for solving the system of equations of the CZM model can be performed at each time step for each joint in a considered fracture network. The time-dependent calculation can help the simulation system track fracture initiation and propagation in the fracture network. In some instances, the predefined joint model locations can be the same at each time step, or the joint model locations can change over simulated time. As such, searching for and tracking the physical contact locations between the two rock blocks at every time step can be avoided in some instances, and the computational load associated with the search and tracking can be reduced or eliminated. Different modifications can be made to Equation (2) for the CZM model, and additional or different components can be included in the variable or the parameters. In some instances, properties (e.g., numbers, locations, etc.) of the predefined joint model locations for the joint models can be set as default values, adjusted according to system requirements or simulations progress, or configured based on any other settings as appropriate. Alternatively or additionally, other formulations can be used for modeling the joint between adjacent discrete rock blocks. 
     The interactions between DDA model and CZM can be represented, for example, by the links  304   a  and  304   b  in  FIG. 3 . In some implementations, the links  304   a  and  304   b  can map the variables or parameters of one of the models into the parameters of the other model based on some predefined relationships. As a specific example, the block models  302   a  and  302   b  can be the DDA models and the joint model  303  can be the CZM fracture model. With parameters such as the mass matrix M, damping matrix C, and stiffness matrix K and an initial boundary condition (e.g., initial forces vector F applied to the rock blocks), solving the governing equations (e.g., Equation (1)) of the DDA models can obtain the displacements and strain of the rock blocks. Based on the displacements and strain information, fracture separations (both in normal and shear direction, e.g., δ n , and δ t ) can be derived and then served as input parameters to the fracture CZM model. The governing equations (e.g., Equation (2)) of the fracture CZM model can then be solved for the traction forces F. The traction forces F can in return serve as force boundary conditions of the discrete rock block DDA type models. 
     In some cases, the block model (e.g., DDA model) for each rock block can represent intra-block mechanics of the rock block in response to inter-block forces (e.g., F) determined by the joint models. The joint model (e.g., CZM) for each adjacent pair of rock blocks can represent inter-block mechanics between adjacent rock blocks in response to rock block movement (e.g., displacements and strain of the rock blocks) determined by the block models. In this way, these two types of models can be tightly coupled together in the simulation system. Governing equations of each discrete rock block can be solved and equilibrium of the whole fracture network can be obtained at every time step. 
     The simulation techniques described here can be implemented in an injection treatment simulation system that uses tightly coupled subsystem models. Examples of injection treatment simulation systems that use tightly couple system models are described in a concurrently-filed U.S. Patent Application entitled “Simulating an Injection Treatment of a Subterranean Zone,” by inventors Samuel Johnson and Harold Grayson. Some example technique for simulating an injection treatment using tightly coupled models include defining subsystem models for each physical subsystem of the injection treatment system, and creating separate structures (e.g., couples) that represent relationships between the variables of each model and the parameters of other models. The simulation can proceed, for example, by defining a common solution vector from the subsystem models; updating the parameters of all subsystem models based on the common solution vector according to the predefined relationships (e.g., the couples); calculating residual values of the subsystem models based on the common solution vector and the updated parameters; and refining the common solution vector based on the residual values. 
     In some implementations, for the rock model and the discrete rock block deformation and stresses analysis, different constitutive laws can be applied for different rock materials, such as linear elasticity, elastic-plasticity, creep, etc. For the joint model, alternatively or additionally, some other models, methods, or techniques can be used to describe fracture behavior, such as linear spring, discontinuous models, etc. In using the predefined joint model locations (e.g., nodal contacts) to couple the joint models and block models, other types of fracture models can be implemented to replace or complement CZM and work with the block models to simulate fracture initiation and propagation in a subterranean zone for various circumstances. 
     In some implementations, additional or different subsystem models (for example, a fluid junction model, a fracture flow model, a leakoff model, a wellbore model, etc.) can be incorporated to perform injection treatment simulations. As a specific example, fracturing fluid models can be coupled with the block models and the joint models to simulate hydraulic fracturing process in the fracture network. The initial or existing fractures can provide fluid channels for fracturing fluid, and when fracturing fluid is injected into these fractures in the subterranean zone, fluid pressure can be applied on rock blocks. Because of fluid pressure, new fractures may be opened and then fractures can propagate. The interactions between the fracturing fluid models and block models, as well as the fracturing fluid models and the fracture models can be established based on, for example, one or more of the fluid pressure, displacements of the rock blocks, separations and orientations of the fractures, etc. The combined block models, joint models, and the fracturing fluid models can help simulate fluid flow about the rock blocks during an injection treatment applied to the subterranean zone. 
     Some embodiments of subject matter and operations described in this specification can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Some embodiments of subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions, encoded on computer storage medium for execution by, or to control the operation of, data processing apparatus. A computer storage medium can be, or can be included in, a computer-readable storage device, a computer-readable storage substrate, a random or serial access memory array or device, or a combination of one or more of them. Moreover, while a computer storage medium is not a propagated signal, a computer storage medium can be a source or destination of computer program instructions encoded in an artificially generated propagated signal. The computer storage medium can also be, or be included in, one or more separate physical components or media (e.g., multiple CDs, disks, or other storage devices). 
     The term “data processing apparatus” encompasses all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, a system on a chip, or multiple ones, or combinations, of the foregoing. The apparatus can include special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). The apparatus can also include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, a cross-platform runtime environment, a virtual machine, or a combination of one or more of them. The apparatus and execution environment can realize various different computing model infrastructures, such as web services, distributed computing and grid computing infrastructures. 
     A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, declarative or procedural languages. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network. 
     Some of the processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform actions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). 
     Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read only memory or a random access memory or both. A computer includes a processor for performing actions in accordance with instructions and one or more memory devices for storing instructions and data. A computer may also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Devices suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices (e.g., EPROM, EEPROM, flash memory devices, and others), magnetic disks (e.g., internal hard disks, removable disks, and others), magneto optical disks, and CD ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry. 
     To provide for interaction with a user, operations can be implemented on a computer having a display device (e.g., a monitor, or another type of display device) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse, a trackball, a tablet, a touch sensitive screen, or another type of pointing device) by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user&#39;s client device in response to requests received from the web browser. 
     A client and server are generally remote from each other and typically interact through a communication network. Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”), an inter-network (e.g., the Internet), a network comprising a satellite link, and peer-to-peer networks (e.g., ad hoc peer-to-peer networks). The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. 
     While this specification contains many details, these should not be construed as limitations on the scope of what may be claimed, but rather as descriptions of features specific to particular examples. Certain features that are described in this specification in the context of separate implementations can also be combined. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple embodiments separately or in any suitable subcombination. 
     A number of embodiments have been described. Nevertheless, it will be understood that various modifications can be made. Accordingly, other embodiments are within the scope of the following claims.