Coupled Geomechanical Simulation of Stress Dependent Reservoirs

Abstract

A geomechanics option that features the three dimensional elastoplastic stress equations which are fully or partly coupled to a commercial reservoir simulator is applied to a field and a synthetic case. Sanding, fracturing and stress dependent flow are analysed. First the basic formulation is discussed. Elastic stress equations and boundary conditions are described including their implementation in the finite difference simulator. Comparison is made with an industry standard finite element code with an option for coupled single phase flow. It is demonstrated that the finite difference implementation of the stress equations, which is second order, can produce acceptable accuracy when compared against finite element simulators. Non-orthogonal corner-point gridding is also reviewed in this context when the gridding is skewed. Some features of other gridding types including unstructured grids are also presented. Plasticity, stress dependent permeability and faults are available as options. Two cases are presented which were designed to demonstrate the applications of sand management, simulation of tight gas reservoirs with stress dependent permeability and propped/etched fractures. The sand management case is based on an offshore gas field. Reservoir geometry, properties and geological (tectonic) details were provided by the operator. A case which simulates fracturing was designed as a tutorial. Although synthetic, it offers a workflow for the use of predicted stress and pore pressure as input to calculations of fracture conductivities/geometries whose output is returned to the simulator. This geomechanics option is currently under development. Some areas of further work are mentioned. Introduction The topic of coupled stress and fluid flow has received much attention recently in the literature. Koutsabeloulis and Hope1 discuss two couplings of fluid flow and rock stress. The first involves coupling a finite element stress analysis simulator with a streamline fluid flow simulator. A second method is to calculate a fully coupled solution of these equations within the finite element simulator. Coupling to other reservoir simulators is also possible. It is stated that there may be substantial differences when running uncoupled versus coupled flow simulations, although the fully coupled finite element flow simulation took no account of stress directionality, magnitude and neglected discontinuities in the rock. A second case shows differences in bottom hole pressure (BHP) at a well with and without including a stress analysis. With a stress calculation, the observed change in time of the BHP was qualitatively predicted, without it the trends predicted by the stand-alone flow simulator were almost opposite. Settari and Mourits2 and Settari and Walters3 analyse different degrees of modular coupling. Decoupled systems can be solved, firstly, with the reservoir model only, where the compressibility must be modified to account for the expected type of containment (free deformation or laterally constrained).Secondly, a reservoir simulation prediction of the entire time history of pressure can then be used to compute a transient stress solution. Coupled predictions were classified as explicit, in which the coupling is lagged by a timestep, iterative in which a repeated solution of the flow and stress equations takes place during the timestep or fully in which the full system of equations is solved simultaneously. Comparisons were made of predictions with linear and nonlinear elastic models. Aspects of plasticity and thermoporoelasticity were discussed. Chin, Raghavan and Thomas4 also discuss a fully coupled finite element implementation. Yale5 gives an overview of many aspects of coupling, referring to some of the pioneering work of Biot6 and Terzaghi7 as well as the more recent work of Gutierrez8.The same coupled geomechanics-fluid flow finite element method in Reference 1 was used to investigate critical state constitutive modeling, elastic-plastic effects, stress path effects and permeability alteration. Tran, Settari and Nghiem9 explore a new iterative coupling by examining in detail the porosity formulation.

Sensitivity of time‐lapse seismic to reservoir stress path

“…1991), can be calculated for arbitrary reservoir geometry using a coupled geomechanical stress and reservoir fluid‐flow simulator (e.g. Stone et al . 2003).…”

“…In general, the change in the effective stress tensor as a function of position in the reservoir can be calculated for arbitrary reservoir geometry using a coupled geomechanical stress and reservoir fluid‐flow simulator (e.g. Stone et al . 2003), and traveltimes may then be calculated from an integral of slowness over the appropriate raypath using the theory for the change in elastic stiffnesses given in this paper.…”

Asymmetry in the time‐lapse seismic response to injection and depletion

“…In general, K h and K H are functions of the reservoir geometry, and can be determined using a coupled geomechanical stress and reservoir fluid flow simulator (e.g. Stone et al . 2003).…”

“…In general, K h and K H are functions of the reservoir geometry, and can be determined using a coupled geomechanical stress and reservoir fluid flow simulator (e.g. Stone et al 2003). The simplest case corresponds to an infinite, linearly elastic, horizontal layer undergoing a decrease in pressure for which γ h and γ H in equation (11) take the values,…”

Visualizing Flow Patterns in Coupled Geomechanical Simulation Using Streamlines

“…Steady state rock momentum balance equations 14,15 in the x, y and z directions used in coupled geomechanical simulator by ECLIPSE 300® can be written as: The elastic normal stresses σ and shear stresses τ can be expressed n terms of strains, ε and γ , as: …”