Vol.20, Special Issue, 2020, pp. S38–S44 
MATHEMATICAL PERSPECTIVE OF MODELLING FLUID FLOW INSIDE FRACTURED CARBONATE RESERVOIR PRODUCING UNDER STEAM FLOODING ENHANCED OIL RECOVERY V. Thokala, S.S. Pandey, S.K. Govindarajan Reservoir Simulation Laboratory, Indian Institute of Technology Madras, Chennai, INDIA email: tvjanny2003@gmail.com ; pshantanu784@gmail.com ; gskumar@iitm.ac.in

Abstract A total of around ~2 trillion barrels of viscous crude oil is held in a carbonate reservoir. The heavy oil held in a Fractured Carbonate Reservoir (FCR) encompasses an enormous potential to contribute to the world's oil needs. Continuous steam flooding Enhanced Oil Recovery (EOR) is used as a tertiary method to increase recovery from these complex classes of reservoirs. The mathematical perspective of modelling these reservoirs involves the inclusion of three flow equations (oil, water, and steam) and one heat balance equation. In recent studies, for modelling FCR, flow equations are defined for two different subdomains, namely fracture and matrix. Both the grid blocks possess high porosity and permeability contrast, in which fracture has high transmissibility and the matrix has a high storage capacity of hydrocarbons. In this study, an attempt is made to derive flow equations (partial differential equation) for all phases in two dimensions, including gravity effect with the help of Darcy's law. The presence of pressure and saturation terms in flow equation for steam, oil, and water makes the modelling of steam flooding EOR in FCR more challenging. The derivation of fluid flow equations (oil, water, and steam) involves deriving of the continuity equation first, followed by combining it with Darcy's law. An undersaturated reservoir considered in this case, where the reservoir pressure is always higher than the bubblepoint pressure, and hence, the fluid of interest is of aqueous phase only in the absence of any phase changes between steam and liquid. The present study is aimed at deducing an improved mathematical model by considering the reservoir fundamental parameters, namely, porosity, permeability, and compressibility, as a function of petrophysical parameters associated with a dualcontinuum system. The correlations used in the derivation of the fluid flow equation incorporate separate equations defined mathematically for fracture and matrix porosity and permeability, respectively. Also, porosity is considered as a variable coefficient which changes with change in pressure. This work will help in modelling fractured reservoirs more efficiently by solving fluid flow equations with more ease. Keywords: fractured carbonate reservoir, partial differential equation, correlations, improved mathematical model, implicit pressure and explicit saturation (IMPES) 
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