SUMMARYThis paper presents an overview of two-stage decoupling preconditioning techniques employed in the implicit parallel accurate reservoir simulator (IPARS) computational framework for modelling multicomponent multi-phase ow in porous media. The underlying discretization method is implicit Euler in time and mixed ÿnite elements or cell-centred ÿnite di erences in space. IPARS permits rigorous, physically representative coupling of di erent physical and numerical ow models in di erent parts of the domain and accounts for structural discontinuities; the framework currently includes eight physical models. For simplicity of exposition, we have restricted our discussion to a two-phase oil-water model and a three-phase black oil model. Our decoupling approach involves extracting a pressure equation from the fully coupled linearized system thus allowing for a more accurate preconditioning of a discrete elliptic problem of lower dimension.
In addition to standard oil recovery methods by depletion, various fluids (water, nitrogen or many types of gas) can be injected from the surface in order to produce the trapped oil. Among all gas, air is the most convenient one since it presents the advantage of being available everywhere. Therefore air injection can be an economical alternative for pressure maintenance of fractured reservoirs as it avoids re-injecting a valuable associated gas and/or generating or importing a make-up gas. A major contribution of this technique is that the oil recovery can be enhanced significantly thanks to the thermal effects associated with oil oxidation. In addition, from an operating point of view, economical and feasibility studies concluded on favourable future perspectives. However, its use is limited by safety reasons due to the explosive mixture resulting from oxygen and hydrocarbons. In the reservoir rock, the microscopic size of the pores prevents any explosion. On the other hand, a commingled arrival of oxygen and hydrocarbons in production wells may result in dramatic damages. Therefore, air-injection methods require a careful assessment of the involved reservoir displacement mechanisms, in particular the magnitude and kinetics of matrix-fracture transfers. Actually, the latter will largely control the displacement efficiency as well as the composition of well effluents from which residual oxygen has to be absent. The aim of this paper is to identify and model the physical mechanisms controlling matrix-fracture transfers during air injection in light-oil fractured reservoirs, first at the matrix block scale then at the field scale. The study actually relies on a careful analysis and compositional thermal simulations on a fine-grid single-porosity model of a matrix block surrounded by air-invaded fractures that allows us to study the influence of block size on the kinetics of oil recovery as well. These fine-grid simulations mainly show that gas diffusion and thermodynamic transfers are the major physical mechanisms controlling the global kinetics of matrix-fracture transfers and the resulting oxidation of oil. The chronology of extraction of oil components from the matrix blocks can then clearly be interpreted in relation with phase transfers. Once all the mechanisms have been identified, we focus on the equivalent (up-scaled) dual-porosity modelling. This model, rooted in a specific numerical formulation which ensures a proper up-scaling of diffusion and inter-phase transfers at the overall scale of matrix blocks, eventually appears to be a reliable simulation tool usable for field-scale predictions, in agreement with the previously defined reference model. Thus, results could be simulated and interpreted at different scales closer to the field scale than the matrix block scale. In addition, some conclusions were drawn regarding the sensitivity of the process to the kinetics of oxidation and the water saturation conditions. Petrophysical Data The petrophysical and thermodynamic properties used in our simulations are largely inspired from the Ekofisk field (Thomas et al., 1983, 1991, Agarwal et al., 1999, Jensen et al. 2000). The matrix medium has a permeability K of 1mD, a porosity F equal to 30%. The calorific capacity of the unsaturated rock is equal to 2.35 Jg−11°C−1 and the overall thermal conductivity of the fluid-saturated rock equals 1.8 Wm−1°C−1. The working pressure is 5600 Psi, very close to the bubble point pressure and temperature is 266°F. The irreducible water saturation, Swi, is 0.15 and the residual oil saturations, Sorw and Sorg, are both equal to 0.25. Capillary pressures and relative permeability curves are shown figure 1. Petrophysical Data The petrophysical and thermodynamic properties used in our simulations are largely inspired from the Ekofisk field (Thomas et al., 1983, 1991, Agarwal et al., 1999, Jensen et al. 2000). The matrix medium has a permeability K of 1mD, a porosity F equal to 30%. The calorific capacity of the unsaturated rock is equal to 2.35 Jg−11°C−1 and the overall thermal conductivity of the fluid-saturated rock equals 1.8 Wm−1°C−1. The working pressure is 5600 Psi, very close to the bubble point pressure and temperature is 266°F. The irreducible water saturation, Swi, is 0.15 and the residual oil saturations, Sorw and Sorg, are both equal to 0.25. Capillary pressures and relative permeability curves are shown figure 1.
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