Modeling miscible injection in fractured porous media using random walk simulation

Abstract

The objective of this paper is to introduce an adaptation of a non-classical simulation method (random walk, RW) for simulation of fully miscible displacement in fractured porous media, and to validate this method using production and visual data obtained from an experimental work.First, the limitations of a classical (continuum models) modeling approach in the simulation of miscible displacement in fractured media were identified by matching the numerical and experimental results obtained earlier. Classical simulation yielded reasonable matches for low viscosity oil but failed to capture the flow patterns of heavy oil displacement, especially in the cases of vertical displacement. This was attributed to two reasons: (1) numerical dispersion and grid size limitations and (2) the random nature of the phenomenon (mainly the viscous fingering process). Beyond that, the classical modeling scheme required the intensive use of “pseudo parameters” to account for the diffusive and dispersive transfer between matrix and fracture during experimental matching.To overcome these problems, a non-classical modeling approach, the Random Walk (RW) model was adapted. This technique deals with particles (walkers), each of which moves randomly, but the probability of the movement is defined considering the physics of the process. By tracing a large number of particles, one can model the process and have an idea about the transport of injected and displaced fluid in complex systems. The RW technique allows capturing micro heterogeneities, the random nature of the diffusion process and viscous fingering. It also requires less computational time compared to classical simulation methods.The RW model introduced was validated using experimental-visual-data for different oil types, displacement directions (horizontal and vertical), and injection rates. This exercise showed that the model presented here captures the physics of the process and hence, can be extended and used for larger (field) scale processes of miscible displacement in complex fracture networks, which would not be possible with classical finite-difference models. Eventually, diffusion coefficient correlations (both oil and solvent), which are the only unknowns required in the proposed RW model, as a function of oil viscosity were defined for the horizontal displacement cases.