Numerical Aspects of Convection-Dispersion Equation

Virtually all reservoir simulators obtain solutions to fluid flow equations, usually nonlinear partialdifferential equations, by making discrete approximations to derivatives. Whether finite‐difference or finite‐element methods are used, these approximations always introduce truncation errors that often can distort the accuracy and stability of the solution. The truncation error is often referred to as numerical dispersion because, to lowest order, it can be represented as a second spatial derivative term, added to any true dispersion term in the problem. Distortion of numerical solution is most significant in the simulation of EOR processes where sharp displacement, concentration, and/or temperature fronts are an important part of the efficiency of the processes, and artificial smearing as a result of numerical dispersion can render the simulation meaningless. In this work two different methods; namely Finite Difference and Method of Line are considered to investigate numerical dispersion. In continue the effect of grid sizes on smearing and oscillation is investigated by selecting various values for grid size. The results indicate that by using the method of line as solution method for general difference equation, numerical dispersion can be minimized.