oa Magnifying the Numerical Aspects of Convection-Dispersion Equation by Selecting Different Methods and Grid Sizes

Virtually all reservoir simulators obtain solutions to fluid flow equations, usually nonlinear partialdifferential<br>equations, by, making discrete approximations to derivatives.1 Whether finite-difference or<br>finite-element methods are used, these approximations always introduce truncation errors that often<br>can distort the accuracy and stability of the solution. The truncation error is often referred to as<br>numerical dispersion because, to lowest order, it can be represented as a second spatial derivative<br>term,2 added to any true dispersion term in the problem.<br>Distortion of numerical solution is most significant in the simulation of EOR processes3 where sharp<br>displacement, concentration, and/or temperature fronts are an important part of the efficiency of the<br>processes, and artificial smearing as a result of numerical dispersion can render the simulation meaningless.<br>At this paper to investigate the effect of solution method on Numerical Dispersion two computer<br>programs that the first one is based on method of Finite Difference and the second is based on method<br>of Line-Explicit are written in MATLAB Software. Also at this paper stability of 9 cases that are included<br>various time and distance weighting for each method are discussed. In continue the effect of grid sizes<br>(Δx) on smearing and oscillation is investigated by selecting various values for Δx. The results indicate<br>that by using the method of Line-Explicit as solution method for general difference equation (equation<br>(32)), numerical dispersion will be minimized. Also, it is showed that cases of 7, 8, and 9 have<br>minimum numerical dispersion. At the last part of the paper, as it can be seen from Figures.37-54<br>decreasing the grid sizes, reduces the numerical dispersion.