Couplled Geomechanical-thermal Simulation For Deforming Heavy-oil Reservoirs
Authors: Fung L.S.K. , Buchanan L. , Wan R.G. 
Published: March 2010

Abstract
The paper describes a novel numerical model for the solution of poro-elasto-plasticity and multiphase, thermal flow in unconsolidated heavy-oil and oil-sand reservoirs. The elasto-plastic deformation is calculated using a finite-element incremental plasticity model with Mohr-Coulomb and Drucker-Prager as the yield criteria. This model is coupled with CMG's thermal simulator STARS which is capable of handling many advanced thermal recovery processes.
The geomechanical calculation is in fact an effective stress analysis which solves a set of force balance (equilibrium) equations based on total stresses. These are augmented by the elastic material behaviors, plastic yield criteria, plastic flow rule, work-hardening law, and the strain-displacement relationships. Besides volumetric deformation, the solution gives the displacements in each direction, stresses, and strain distribution in the reservoir. The behaviors of reservoir multiphase flow and heat transfer processes are most significantly affected by the volume change and the associated permeability increase. The volume change is calculated by the plasticity model, whereas the permeability increase is related to the volume change via tabular data. The prediction of shear failure region, the rotation of principal stress axis, and the reduction of effective stresses as a result of pore pressure increase, are all important phenomena affecting the placement of fluid and hear in the formation.

Introduction
Considerable experiences on the in-situ recovery of heavy oil and bitumen from unconsolidated media have been accumulated both in field operations and in laboratory research over the last two decades. The significance of geomechanical responses on the recovery of these reservoirs is now generally recognized. In order to understand the recovery processes, we must consider the complex interaction of multiphase fluid flow, heat transfer, changes in stress state, and formation deformation as a result of injection and production operations.
Previous work on the coupling of stress modeling with reservoir simulation(1,2) uses linear elasticity. However, extensive experimental data on oil sands indicate extremely complex constitutive behaviors at elevated pore pressure and temperature(3–6). Oil sands are dense frictional materials which tend to dilate under shear. This dilatancy is the result of an increase in deviatory stresses which leads to the slippage and loss of grain-to-grain contacts. Since the original sand fabric is disturbed, strains thus accumulated are irrecoverable. More recent contributions to this class of coupled simulations(7–11) treat the nonlinearity and plasticity behaviors of oil sands with varying degrees or sophistication.
The stresses and strains are related by the material constructive model which must be satisfied for the geomechanical calculation. In this work, an elastoplastic formulation is chosen such that plastic deformation as a result of shear dilatancy can he modeled. During cyclic steam stimulation, the sand matrix goes through several loading and unloading cycles. This leads to complex deformation history which must be properly accounted for. As a reservoir grid block is loaded in the elastic regime, elastic strains accumulate which are recoverable upon unloading. The stress space is delimited by the yield surface. As the stress state reaches the yield surface, additional loading will cause the material to yield plastically.