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Abstract
Field experience and laboratory investigations have shown that dispersion is an important factor in miscible displacement oil recovery processes. Dispersion in these processes can be due to a number of mechanisms, including: molecular diffusion, microscopic convective dispersion and macroscopic dispersion. Recent experimental work performed at the Shell Canada Calgary Research Center has shown that high levels of dispersion can result from turbulent mixing effects occurring when the miscible solvent and reservoir oil exhibit a large volume change on mixing. Mixing via any one or combination of these mechanisms can be characterized by an effective dispersion coefficient.
This dissertation describes methods for modeling displacements with dispersion using a compositional simulator. A standard simulator, which does not treat dispersion explicitly, is used as the base to which dispersion models are added. The dispersion models are derived from Fick's first law and second law (i.e., the diffusion equation) employing effective dispersion coefficients in place of the usual diffusion coefficient. The solutions of the diffusion equation required for these models are derived here using the Green's function method.
The first law and second law models both prove capable of predicting dispersion in three example systems tested. The total level of dispersion predicted by the simulator is dependent on the level of numerical dispersion and the physical dispersion model chosen. Techniques for numerical dispersion control also limit the prediction of physical dispersion. A front tracking model based on the standard error function solution of the diffusion equation is developed, and is found to significantly alleviate the numerical dispersion problems for one dimensional simulations.
