Browsing by Author "Potempa,Thom"
Now showing 1 - 10 of 10
Results Per Page
Sort Options
Item A Finite Element Material Balance for Two Dimensional Convection-Diffusion Equations(1983-11) Potempa,ThomA consistent finite element material balance is developed for the two dimensional convection-diffusion equation. The resulting numerical scheme is an average of the conventional Galerkin procedure for both the divergence and nondivergence form of the continuity equations. This derivation is valid for finite dimensional approximating spaces having the property that the basis functions sum to unity. Computational molecules are associated with each basis function of the finite dimensional approximating space. The physical significance of coefficients appearing in the resulting material balance governing every computational molecule is discussed. The scheme is compared with standard finite difference procedures. Regularization of the resulting numerical scheme is accomplished by lumping and upstream weighting.Item A Lumped Finite Element Method for Cap Rock Heat Loss Calculations(1983-10) Potempa,ThomNumerical models of thermal recovery processes arising in petroleum engineering require accurate estimates of the interaction between a reservoir and the surrounding cap and base rock. It is important to obtain an accurate approximation of the energy flux at the interface between the reservoir and the surrounding rock, and the distribution of the temperature in the surrounding rock is of only secondary importance. A flux calculation procedure implemented as a post processing algorithm based upon a finite element method is used to calculate an accurate approximation to the energy losses. Oscillatory behavior is observed in the computed temperature distribution using a standard computational scheme. If the time derivatives are lumped, the oscillatory behavior is avoided. Computational experiments performed on sample test cases possessing analytical solutions indicate an excellent agreement between the approximations obtained using the lumped procedure and the exact solution.Item A Numerical Model of Two Dimensional, Two Component, Single Phase Miscible Displacement in Porous Media(1983-03) Potempa,ThomA new numerical procedure for modeling single phase miscible dispacement in a porous medium is presented. This model is based upon a material balance that is similar to that which is used to derive the differential equations that govern single phase miscible displacement. Since the procedure is defined in terms of a material balance, the data structures arising in a computational implementation are compatible with those that are present in finite difference models of miscible displacement. This procedure obeys a maximum principle due to the upstream weighting of the convective transport terms. This new procedure does not exhibit the grid orientation effect present in the five point finite difference models of this process.Item A User's Guide to the Rice Steam Displacement Model(1983-10) Potempa,ThomTo provide an accurate model of heavy oil steam displacement processes. The primary advantage of this model over other state-of-the-art models is that it does not exhibit grid orientation effects. Serious grid effects have been reported in other steam displacement models.Item An Improved Implementation of the McCracken and Yanosik Nine Point Finite Difference Procedure(1983-05) Potempa,ThomThe grid orientation phenomenon present in numerical models of fluid flow in a porous medium can give rise to unrealistic predictions when simulating adverse mobility displacements. McCracken and Yanosik proposed a nine point finite difference scheme for approximating the solution of the continuity equations that has the potential of eliminating many of the unrealistic predictions that are observed when using five point finite difference operators. Coats and Ramesh have implemented this scheme in a steamflooding model, and have noted that serious grid effects are present in the simulation of an inverted seven spot pattern. Potempa has described a procedure which exhibits minimal grid effects for the problem described by Coats and Ramesh. This paper describes modifications to the McCracken and Yanosik procedure which allow for realistic simulation of this inverted seven spot pattern under a steam drive. These modifications are based upon an approximation scheme that has been previously reported, and affect the incorporation of upstream weighting in a simulator.Item Crossflooding in Steamflood Operation: A Simulation Study(1983) Potempa,ThomCrossflooding techniques have the potential for increasing the ultimate oil yield in secondary or tertiary recovery operations. At least one field scale pilot study of crossflooding in a reservoir undergoing a steamflood is being undertaken at this time. The purpose of this investigation is to evaluate using a numerical simulation various crossflooding options on five and nine spot patterns under a continuous steam drive. As the simulation of a crossflooding process is demonstrated to be very sensitive to the grid orientation phenomenon, these studies are undertaken using a steam displacement model that does not exhibit a serious grid orientation effect. The numerical studies indicate that crossflooding significantly improves the ultimate oil yield in steamflooding operations. The simulation studies indicate that an increased yield is achieved without infill drilling by using an expanded pattern crossflood. Crossflood patterns involving infill wells perform only marginally better than the expanded pattern floods. A new crossflooding pattern introduced in an earlier theoretical investigation is shown to improve the ultimate net oil yield in steamflooding operations.Item Mobility Weighting in Numerical Reservoir Simulation(1983) Potempa,ThomThe sensitivity of a numerical steamflooding model with respect to mobility weighting is examined in depth. Three numerical discretization procedures are used in this investigation: a new numerical scheme, a five point finite difference method, and a procedure which, under certain assumptions, is equivalent to that introduced by McCracken and Yanosik. Three mobility weighting schemes are investigated. The first approach studied is upstream mobility weighting. The second method investigated uses harmonic total mobility weighting and upstream weighting of fractional flow terms. The approach introduced in this investigation uses the kinematic viscosity in the total mobility and fractional flow terms. Computational results for a simulated steam drive indicate that this new mobility weighting approach is superior to the other two mobility weighting schemes. In particular, the steam displacement model formed from t he combination of this new mobility weighting approach and the McCracken and Yanosik discretization procedure is shown to produce realistic simulation of an inverted seven spot pattern under a continuous steam drive.Item Quasi-Newton Methods and Galerkin Procedures for Nonlinear Elliptic Boundary Value Problems(1983-12) Potempa,ThomLeast change secant update strategies are derived that are compatible with algebraic systems of nonlinear equations arising when Galerkin procedures are applied to nonlinear elliptic boundary value problems. The resulting quasi-Newton procedures for solving the algebraic system of equations are observed to result in significant computational savings in experiments involving boundary value problems of one or two spatial variables.Item The Effect of the Definition of Fractional Flow Upon Grid Effects in a Numerical Model of Thermal Processes(1983-03) Potempa,ThomIn previous research regarding the numerical simulation of a single phase miscible displacement, a numerical procedure which does not exhibit serious grid effects and is highly compatible with nine point finite difference models has been developed. To determine if this procedure could successfully deal with grid effects in general reservoir simulators, this numerical procedure has been implemented in a simplified thermal recovery model. In the initial implementation of this procedure in a complex setting, multiple phase mass transfer between the computational molecules associated with the discretization procedure utilized the well known concepts of fractional flow and total Darcy velocity. The resulting numerical model exhibits unrealistic phenomena, which is unexpected in light of the realistic simulations earlier obtained for the model problem. By changing the model of multiple phase mass transfer, these physically unrealistic effects are eliminated. The new model uses the total molar flux instead of the total Darcy velocity. The fractional flows are defined in a fashion compatible with the total molar flux.Item Three Dimensional Simulation of Steam Displacement with Minimal Grid Orientation(1983-03) Potempa,ThomSteamflooding is a tertiary oil recovery mechanism with proven economic potential. Reliable numerical simulations of candidate injection schemes can aid in the optimization of process parameters. State-of-the-art numerical models exhibit varying degrees of grid effects which affect their reliability with respect to the modeling of pattern floods. This paper presents a numerical steamflood model which does not exhibit a significant amount of grid orientation. This model utilizes a numerical discretization technique which is an admixture of finite difference and finite element methods. Fluid properties are determined as a function of primary variables in a manner that allows a straightforward implementation of Newton's method for solving the nonlinear system of discretized equations. Fractional flows are defined using mass rather than volumetric mobilities, and are used to upwind the convective flow terms.