Development of a refinement criterion for adaptive mesh refinement in steam-assisted gravity drainage simulation

Abstract

Steam-assisted gravity drainage (SAGD) is an enhanced oil recovery process for heavy oils and bitumens. Numerical simulations of this thermal process allow us to estimate the retrievable volume of oil and to evaluate the benefits of the project. As there exists a thin flow interface (compared to the reservoir dimensions), SAGD simulations are sensitive to the grid size. Thus, to obtain precise forecasts of oil production, very small-sized cells have to be used, which leads to prohibitive CPU times. To reduce these computation times, one can use an adaptive mesh refinement technique, which will only refine the grid in the interface area and use coarser cells outside. To this end, in this work, we introduce new refinement criteria, which are based on the work achieved in Kröner and Ohlberger (Math Comput 69(229):25-39, 2000) on a posteriori error estimators for finite volume schemes for hyperbolic equations. Through numerical experiments, we show that they enable us to decrease in a significant way the number of cells (and then CPU times) while maintaining a good accuracy in the results.Keywords SAGD · Adaptive mesh refinement · A posteriori error estimator · Error bounds (65M15) · Finite volume methods (76M12) · Conservation laws (35L65)

Large scale cavity dissolution: From the physical problem to its numerical solution

“…The applications of AMR have covered lots of physical problems, such as shock hydrodynamics analysis [34,35], compressible flow [36], turbulent flow [37], flow in porous media [38][39][40], and oil displacement [41,42]. The AMR methods can be distinguished into two categories: patch-based and cell-based.…”

Numerical Modeling of Thermal EOR: Comprehensive Coupling of an AMR-Based Model of Thermal Fluid Flow and Geomechanics

“…The flow interfaces are located using the criteria proposed in Mamaghani et al (2011). These criteria have been derived from an a posteriori error estimate which has been obtained by assuming that the oil saturation is solution to a simplified transport problem.…”

“…In Mamaghani et al (2011), the local estimators, proposed to control the global error of the simplified problem, are proved to be independent on the time step and the mesh resolution. Numerical tests, performed also on SAGD cases, showed that these criteria were indeed less dependent on the grid size.…”

“…As shown in Mamaghani et al (2011) on SAGD cases, the reduction of the grid size varies during the simulation and also depends on the criteria used to follow the flow interface. At the beginning of the simulation, when the extent of the steam chamber is small, AMR methods enable to reduce considerably the grid size.…”

“…In this work, the approaches proposed by Guy et al (2011), on one hand and by Lacroix et al (2003) and Mamaghani et al (2011), on the other hand, are combined to propose a new coupling scheme of geomechanical and reservoir simulators to obtain precise production forecasts with reduced computational times. The methodology is described in Section 1 and numerical results are presented in Section 2.…”