Development of a Numerical Simulation Model for Two-Phase, Cross-Sectional Flow Experiments to Test Relative Permeability Relationships

The present understanding of the frontal instabilities associated with the multiphase displacement process in the porous media is limited. The most obvious example is the inability to predict the conditions required to initiate, to maintain and to eliminate the fingering when one phase displaces another. To overcome this inability, most laboratory experiments are constrained in rate and direction so that the results can be analyzed through known formulations. For example, the gas-liquid displacement experiments are carried out in controlled rates and in vertical direction (where gas is injected from the top) to ensure gravity stable displacement and thereby to avoid fingering of the highly mobile gas in the porous media.SUPRI has recently designed an x-z cross-sectional flow apparatus that has glass on one side to observe the displacement of fluids in porous media. With this apparatus, the displacement of oil by gas will be observed, including the gravity over-riding and the fingering of the highly mobile injected gas. The ultimate objective of the experiments is to quantify the benefits of injecting foaming agents with the gas. Yet, other than the normal measurements such as the total oil produced per injected gas, no other capability exists to enumerate the displacement processes and to quantify the benefits of foams.The intent of this work was to develop a simple numerical simulator that enables the experimenter to model the displacement process and hence verify the parameters that control the displacement, such as relative permeability relationships. Besides not being available in SUPRI, the commercial numerical simulators use the time-march method. In simplest terms, given a starting condition, certain rate or pressure constraints, they calculate the change in saturation and pressure in the model for a given time period. Using a commercial simulator, the experimenter will have to perform a history match to duplicate the frontal location by time. Should there be frontal instability in the displacement, local permeability modifications will be required to achieve the history match.Instead of using the time-march method, the simulator that was developed in this research uses the frontal location as the input data, and solves for the instantaneous injection and production rates of the fluids. Having the frontal locations available at multiple times, through one simulation run, it is possible to test the applicability of the relative permeability correlations quickly. The experimenter will have to history match only the scalar data points (injection and production rates) rather than the x-z frontal locations of the displacement at each time.The simulator is only applicable to the laboratory experiment discussed here. In its current formulation, it can only simulate the experiment until the gas breakthrough, even though modifications can be made to simulate the experiment after the breakthrough.

Keywords:  Department of Petroleum Engineering
School of Earth Energy &amp; Environmental Sciences
Thesis
Advisor: Brigham William E.