Advances in Coupled Geomechanical and Reservoir Modeling With Applications to Reservoir Compaction
- A. Settari (Duke Engineering and Services Inc.) | Dale A. Walters (Duke Engineering and Services Inc.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2001
- Document Type
- Journal Paper
- 334 - 342
- 2001. Society of Petroleum Engineers
- 1.2.2 Geomechanics, 4.3.4 Scale, 5.5.5 Evaluation of uncertainties, 5.4.6 Thermal Methods, 5.1.5 Geologic Modeling, 5.5 Reservoir Simulation, 5.8.6 Naturally Fractured Reservoir, 5.8.5 Oil Sand, Oil Shale, Bitumen, 2.2.2 Perforating, 5.3.2 Multiphase Flow, 4.1.2 Separation and Treating, 5.5.8 History Matching, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 4.1.5 Processing Equipment, 5.3.4 Integration of geomechanics in models, 4.6 Natural Gas
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Coupled geomechanical and reservoir modeling is becoming feasible on a full-field scale. This paper describes the advances of the coupled model described previously,1 its extensions for modeling compaction, and the application of the model in full-field studies.
The advances of the theory and numerical implementation since the original work1 make it practical to perform full-field coupled studies with complex, realistic descriptions of the geomechanical behavior of the reservoir and shales, which allows prediction of stress changes, reservoir compaction, and surface subsidence. These capabilities are demonstrated in field examples that analyze and predict classical pressure-induced compaction in a gas field and thermally induced compaction in a heavy-oil field. In both cases, the methodology of interpreting the geomechanical laboratory and field data and their integration in the coupled modeling process was the key to obtaining a realistic predictive tool. The examples demonstrate that the technology is maturing to the point that conventional studies can be converted to coupled modeling on a fairly routine basis.
The geomechanical behavior of porous media has become increasingly important to hydrocarbon operations. Numerical modeling of such processes is complex and has been carried out historically in three separate areas: geomechanical modeling (with the primary goal of computing stress/strain behavior), reservoir simulation (essentially modeling multiphase flow and heat transfer in porous media), and fracture mechanics (dealing in detail with crack propagation and geometry). A modular system has been developed coupling these three modeling components in such a manner that the already highly developed modeling techniques for each component can be used fully.1 This model has been applied to several geomechanical/reservoir problems assisting in reservoir development.
The paper will first discuss the theory of different degrees of coupling and its consequences for the formulation of the constitutive models and running efficiency of the software. Next, the modeling of compaction by rigorous means (plasticity) and its simplifications, which lead to a considerable increase of computational efficiency, will be presented. In addition to classical pressure-depletion-induced compaction, the paper will describe the theoretical and modeling aspects of thermal compaction phenomena, which have been observed in some applications.
Methods of Coupling
The key idea in the modular coupled system is the reformulation of the stress-flow coupling so that the conventional stress-analysis code can be used in conjuction with a standard reservoir simulator. This is termed a partially coupled approach because the stress and flow equations are solved separately for each time increment. However, the method solves the problem as rigorously as a fully coupled (simultaneous) solution if iterated to full convergence.
The coupling takes place through the use of interface code developed to allow communication between simulators. In a geomechanics/reservoir problem, for instance, the pressure and temperature changes occurring in the reservoir simulator are passed to the geomechanical simulator. The updated strains and stresses are passed back to the reservoir simulator and used to compute coupled parameters in the reservoir formulation (i.e., porosity and permeability). An iterative method then must be used to obtain convergence. The interface is flexible enough to allow the user to choose several degrees of coupling. The degree of coupling may affect the accuracy of the solution as well as the computational efficiency; therefore, tradeoffs may be made to optimize run times.
To see the different degrees of coupling, consider first the general formulation of the coupled problem in a finite-element setting. After discretization in space and time, such a system can be written in matrix form as2,3
where [K]=the stiffness matrix, =the vector of displacements, [L]=the coupling matrix to flow unknowns, [E]=the flow matrix, and =the vector of reservoir unknowns (i.e., pressures, saturations, and temperatures). On the right side, =the vector of force boundary conditions, and =the right side of the flow equations. The symbol ?t denotes the change over timestep; i.e.,
Note that in the conventional reservoir simulation notation,4 [E]=[T]-[D], where [T]=the symmetric transmissibility matrix, [D]=the accumulation (block diagonal) matrix, and = -[T] , where =the vector of boundary conditions (well terms).
Consider now the flow part of the coupled system only, by assuming that ?t =0. This is the assumption made in reservoir simulation (i.e., stresses do not change), which gives the familiar matrix equation
Conversely, if we assume that ?t =0, we obtain the classical elasticity equations. In many stress analysis packages, pressure and/or temperature can be imposed as external loads, which corresponds to assuming that ?t is known. Then the top half of Eq. 1 can be decoupled and written as
In practice, decoupled simulations can be carried out in several ways.
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