Petroleum Reservoir Simulation Coupling Fluid Flow and Geomechanics
- M. Gutierrez (Virginia Tech) | R.W. Lewis (U. of Wales, Swansea) | I. Masters (U. of Wales, Swansea)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- June 2001
- Document Type
- Journal Paper
- 164 - 172
- 2001. Society of Petroleum Engineers
- 1.2.3 Rock properties, 6.5.2 Water use, produced water discharge and disposal, 5.8.5 Oil Sand, Oil Shale, Bitumen, 5.3.2 Multiphase Flow, 4.6 Natural Gas, 1.2.2 Geomechanics, 5.3.4 Integration of geomechanics in models, 5.8.6 Naturally Fractured Reservoir, 2.4.3 Sand/Solids Control, 5.1.5 Geologic Modeling, 1.10 Drilling Equipment, 5.2 Reservoir Fluid Dynamics, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 5.1.2 Faults and Fracture Characterisation, 5.5 Reservoir Simulation, 1.6 Drilling Operations, 4.1.2 Separation and Treating, 4.1.5 Processing Equipment
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This paper presents a discussion of the issues related to the interaction between rock deformation and multiphase fluid flow behavior in hydrocarbon reservoirs. Pore-pressure and temperature changes resulting from production and fluid injection can induce rock deformations, which should be accounted for in reservoir modeling. Deformation can affect the permeability and pore compressibility of the reservoir rock. In turn, the pore pressures will vary owing to changes in the pore volume. This paper presents the formulation of Biot's equations for multiphase fluid flow in deformable porous media. Based on this formulation, it is argued that rock deformation and multiphase fluid flow are fully coupled processes that should be accounted for simultaneously, and can only be decoupled for predefined simple loading conditions. In general, it is shown that reservoir simulators neglect or simplify important geomechanical aspects that can impact reservoir productivity. This is attributed to the fact that the only rock mechanical parameter involved in reservoir simulations is pore compressibility. This parameter is shown to be insufficient in representing aspects of rock behavior such as stress-path dependency and dilatancy, which require a full tensorial constitutive relation. Furthermore, the pore-pressure changes caused by the applied loads from nonpay rock and the influence of nonpay rock on reservoir deformability cannot be accounted for simply by adjusting the pore compressibility.
In the last two decades, there has been a strong emphasis on the importance of geomechanics in several petroleum engineering activities such as drilling, borehole stability, hydraulic fracturing, and production-induced compaction and subsidence. In these areas, in-situ stresses and rock deformations, in addition to fluid-flow behavior, are key parameters. The interaction between geomechanics and multiphase fluid flow is widely recognized in hydraulic fracturing. For instance, Advani et al.1 and Settari et al.2 have shown the importance of fracture-induced in-situ stress changes and deformations on reservoir behavior and how hydraulic fracturing can be coupled with reservoir simulators. However, in other applications, geomechanics, if not entirely neglected, is still treated as a separate aspect from multiphase fluid flow. By treating the two fields as separate issues, the tendency for each field is to simplify and make approximate assumptions for the other field. This is expected because of the complexity of treating geomechanics and multiphase fluid flow as coupled processes.
Recently, there has been a growing interest in the importance of geomechanics in reservoir simulation, particularly in the case of heavy oil or bituminous sand reservoirs,3,4 water injection in fractured and heterogeneous reservoirs,5-7 and compacting and subsiding fields.8,9 Several approaches have been proposed to implement geomechanical effects into reservoir simulation. The approaches differ on the elements of geomechanics that should be implemented and the degree to which these elements are coupled to multiphase fluid flow.
The objective of this paper is to illustrate the importance of geomechanics on multiphase flow behavior in hydrocarbon reservoirs. An extension of Biot's theory10 for 3D consolidation in porous media to multiphase fluids, which was proposed by Lewis and Sukirman,11 will be reviewed and used to clarify the issues involved in coupling fluid flow and rock deformation in reservoir simulators. It will be shown that for reservoirs with relatively deformable rock, fluid flow and reservoir deformation are fully coupled processes, and that such coupled behaviors cannot be represented sufficiently by a pore-compressibility parameter alone, as is done in reservoir simulators. The finite-element implementation of the fully coupled equations and the application of the finite-element models to an example problem are presented to illustrate the importance of coupling rock deformation and fluid flow.
Multiphase Fluid Flow in Deformable Porous Media
Fig. 1 illustrates the main parameters involved in the flow of multiphase fluids in deformable porous media and how these parameters ideally interact. The main quantities required to predict fluid movement and productivity in a reservoir are the fluid pressures (and temperatures, in case of nonisothermal problems). Fluid pressures also partly carry the loads, which are transmitted by the surrounding rock (particularly the overburden) to the reservoir. A change in fluid pressure will change the effective stresses following Terzaghi's12 effective stress principle and cause the reservoir rock to deform (additional deformations are induced by temperature changes in nonisothermal problems). These interactions suggest two types of fluid flow and rock deformation coupling:
Stress-permeability coupling, where the changes in pore structure caused by rock deformation affect permeability and fluid flow.
Deformation-fluid pressure coupling, where the rock deformation affects fluid pressure and vice versa.
The nature of these couplings, specifically the second type, are discussed in detail in the next section.
This type of coupling is one where stress changes modify the pore structure and the permeability of the reservoir rock. A common approach is to assume that the permeability is dependent on porosity, as in the Carman-Kozeny relation commonly used in basin simulators. Because porosity is dependent on effective stresses, permeability is effectively stress-dependent. Another important effect, in addition to the change in the magnitude of permeability, is on the change in directionality of fluid flow. This is the case for rocks with anisotropic permeabilities, where the full permeability tensor can be modified by the deformation of the rock.
Examples of stress-dependent reservoir modeling are given by Koutsabeloulis et al.6 and Gutierrez and Makurat.7 In both examples, the main aim of the coupling is to account for the effects of in-situ stress changes on fractured reservoir rock permeability, which in turn affect the fluid pressures and the stress field. The motivation for the model comes from the field studies done by Heffer et al.5 showing that there is a strong correlation between the orientation of the principal in-situ stresses with the directionality of flow in fractured reservoirs during water injection. There is also growing evidence that the earth's crust is generally in a metastable state, where most faults and fractures are critically stressed and are on the verge of further slip.13 This situation will broaden the range of cases with strong potential for coupling of fluid flow and deformation.
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