A General Purpose Thermal Model

This paper describes a fully implicit four-phase (oil, water, gas, solid fuel) numerical reservoir model for simulating hot water injection, steam injection, dry combustion, and wet combustion in one, two, or three dimensions and in either a Cartesian, radial, or curvilinear geometry. The simulator rigorously models fluid flow, heat transfer (convective and conductive), heat loss to formation, fluid vaporization/condensation, and chemical reactions. Any number of oil or gas phase components may be specified, along with any number of solid phase components (fuel and catalysts). The simulator employs either D4 Gaussian elimination or powerful incomplete factorization methods to solve the often poorly conditioned matrix problems. An implicit well model is coupled to the simulator, where reservoir unknowns and well block pressures are primary variables. This paper includescomparisons of the numerical model's results with previously reported laboratory physical models' results for steam and combustion and physical models' results for steam and combustion andanalytical solutions to a hot waterflood problem. In addition, an actual field-scale history match is presented for a single-well steam stimulation problem. Introduction Recent papers by Crookston et al., Youngren Rubin and Vinsome, and Coats have outlined the current trend in thermal process simulation. The trend has been the development of more implicit, more comprehensive finite-difference simulators. Youngren describes a model based on a highly implicit steam model. The components representing air and combustion gases are treated explicitly. Burning reactions are handled not through rates but through the assumption of 100% oxygen utilization at the combustion front. Crookston et al. describe a linearized implicit combustion model that can describe the reaction of a predetermined set of gases and oils. Both of these models are predetermined set of gases and oils. Both of these models are multidimensional and do not handle wellbore-reservoir coupling fully implicitly. Rubin and Vinsome describe a fully implicit one-dimensional (ID) combustion tube simulator. Coats 4 describes a fully implicit four-phase multicomponent multidimensional combustion simulator. This model is general in nature except for the wellbore-reservoir coupling. This work describes a general, fully implicit, four-phase, multicomponent, multidimensional steam and combustion simulator that includes a fully implicit well model and a suite of powerful iterative techniques that can be used for the solution of large-scale thermal problems. The following sections of this paper describe the model's fluid and energy flow equations, property package, powerful iterative techniques capable of reliable package, powerful iterative techniques capable of reliable use with steam and combustion problems, fully implicit well model, and equation substitution formulation. Further, a section considering the applications of the model is presented. Mathematical Model The simulator ISCOM rigorously models fluid flow, vaporization/condensation phenomena, and heat transfer and is efficient enough to allow the simulation of realistically large reservoir problems. The formulation allows for any number of chemical components and reactions. The components can exist in any of four phases: oil, water, gas, or solid. A reaction also can occur in any of the above phases. Furthermore, water and any of the oil components can vaporize. The simulator development is based on the following assumptions.The model can operate in one, two, or three dimensions (1D, 2D, or 3D) with variable grid spacing.Cartesian, radial, non-Cartesian (variable-thickness grids), and specific curvilinear grids corresponding to the commonly used well patterns can be used. patterns can be used.The number of components existing in each phase is variable, and the components can be distributed among four phases.The number and type of chemical reactions can be varied.Each layer, well, or block in the reservoir can exhibit different properties (e.g., viscosities, relative permeabilities, and properties (e.g., viscosities, relative permeabilities, and compressibilities) at different times.Wells can operate under specified fluid rates or flowing pressures and are subject to a hierarchy of user-specified constraints.The simulator must be reasonably efficient to handle field-scale simulation economically, without sacrificing accuracy. Grid Generation The model defines a block-centered grid system in 1-, 2-, or 3D, normally based on Cartesian xyz coordinates. Radial geometries are accommodated by internal modification of the gridblock volumes and interblock transmissibilities. For rectangular grids with variable thickness layers, the interblock transmissibilities and gravity head terms are derived from gridblock dimensions and depth from reference. Curvilinear grids are generated by the method of conformal transformation, which yields analytical formulae for potential and stream functions. Two simple patterns are considered: one-eighth of a five-spot and one-eighth of a nine-spot. SPEJ P. 202