The impact of spatial and temporal variability of anomalous diffusion flow mechanisms on reservoir performance in structurally complex porous media

The research article “The impact of spatial and temporal variability of anomalous diffusion flow mechanisms on reservoir performance in structurally complex porous media”, authored by METU member Asst. Prof. Salam Al-Rbeawi, has been published in Journal of Natural Gas Science and Engineering.

The main objective of this paper is understanding the phenomenal anomalous diffusion flow mechanisms in unconventional fractured porous media. The targets are hydraulically fractured unconventional reservoirs characterized by porous media with scomplex structures. These media are consisted of a matrix and naturally induces fractures embedded in the matrix as well as hydraulic fractures. Several analytical models for pressure drop and decline rate as wells productivity index in ultralow permeability reservoirs are presented in this study for the two inner wellbore conditions. Numerical solution is also presented in this study for pressure behavior using a linearized implicit finite difference method. The analytical models are developed from trilinear flow models presented in the literature with a consideration given to the temporal and spatial fractional pressure derivative for the anomalous diffusion flow that could be the dominant flow mechanism in the stimulated reservoir volume between hydraulic fractures. Mittag-Leffler functions are used for solving fractional derivatives of pressure and flow rate considering that temporal and spatial fractional exponents are less than one. Analytically, two solutions are developed in this study for the two inner wellbore conditions. The first represents the transient state condition that controls fluid flow in unconventional reservoirs for a very long production time. The second is the solution of pseudo-steady state condition that might be observed after transient state flow. While numerically, the temporal and spatial domains are discretized into several time steps and block-centered grids respectively. The study has pointed out: 1) Temporal and spatial diffusion flows have a significant impact on pressure drop, flow rate, and productivity index. 2) Wellbore pressure drop for constant Sandface flow rate declines rapidly as the temporal diffusion flow mechanism is the dominant flow pattern in the porous media. 3) Wellbore pressure drop for constant Sandface flow rate slightly increases during transient state flow as the spatial diffusion flow mechanisms increase and rapidly increases during pseudo-steady state flow. 4) Productivity index of diffusion flow is higher than the index of normal diffusion flow during transient and pseudo-steady state conditions. 5) The linear flow regime is most affected by anomalous diffusing flow and can be used to characterize the type of diffusion flow.

Al-Rbeawi, S. (2020). The impact of spatial and temporal variability of anomalous diffusion flow mechanisms on reservoir performance in structurally complex porous media. Journal of Natural Gas Science and Engineering, 78 doi:10.1016/j.jngse.2020.103331

Article access: https://www.sciencedirect.com/science/article/pii/S1875510020301852

Tags/Keywords:

Diffusion flow mechanisms, Fractured reservoirs, Reservoir performance, Temporal and spatial heterogeneity, Unconventional resources