Numerical investigation on the effect of boundary conditions on the scaling of spontaneous imbibition

Abdul Salam Abd,Nayef Alyafei

doi:10.2516/ogst/2018060

Abstract

We present a numerical validation of the scaling group presented by Schmid and Geiger ((2012) Water Resour. Res. 48, 3) for Spontaneous Imbibition (SI) through simulating a core sample bounded by the wetting fluid. We combine the results of the simulations with the semi-analytical model for counter-current spontaneous imbibition presented by Schmid et al. ((2011) Water Resour. Res. 47, 2) to validate the upscaling of laboratory experiments to field dimensions using dimensionless time. We then present a detailed parametric study on the effect of Boundary Conditions (BC) and characteristic length to compare imbibition assisted oil recovery with several types of boundary conditions. We demonstrate that oil recovery was the fastest and most efficient when all faces are open to flow. We also demonstrate that all cases scale with the non-dimensionless time suggested by Schmid and Geiger ((2012) Water Resour. Res. 48, 3) and show a close match to the numerical simulation and the semi-analytical solution. Moreover, we discuss how the effect of constructing a model with varying grid sizes and dimensions affects the accuracy of the results through comparing the results of the 2-D and 3-D models. We observe that the 3-D model proved superior in the accuracy of the results to simulate simple counter-current SI. However, we deduce that 2-D models yield satisfying enough results in a timely manner in the One End Open (OEO) and Two Ends Open (TEO) cases, compared to 3-D models which are time-consuming. We finally conclude that the non-dimensionless time of Schmid and Geiger ((2012) Water Resour. Res. 48, 3) works well with counter-current SI cases regardless of the boundary condition imposed on the core.

Highlights

The physical phenomenon of imbibition is important in the understanding of fluid flow in water drive reservoirs as it directly affects water movement and areal sweep efficiency (Meng et al, 2016)
The following boundary conditions were studied in the counter-current simulation case (Yildiz et al, 2006): (i) One End Open (OEO) is when most sides of the core sample are isolated, permitting the wetting phase to flow into the core through one open end located at the left side of our horizontal core (Fig. 3a)
During the imbibition assisted oil recovery phenomenon, the rate of oil recovered is significantly affected by the geometric elements of the matrix including the size, shape and boundary conditions applied to the core sample

Summary

Introduction

The physical phenomenon of imbibition is important in the understanding of fluid flow in water drive reservoirs as it directly affects water movement and areal sweep efficiency (Meng et al, 2016). Imbibition is scientifically defined as the absorption of a-wetting phase into a porous rock and can be divided into two main categories: forced and spontaneous (Ge et al, 2015). The physical transfer of the water into the paper towels or the ink onto the sheet of paper is described as spontaneous imbibition (Morrow and Mason, 2001). The fluid imbibes into the porous structure of the paper towel or the sheet of paper due to capillary forces. The forms of spontaneous imbibition are divided into two categories: co-current and countercurrent, in which the fluid phases flow in identical and opposite directions respectively (Al-Lawati and Saleh, 1996; Bourbiaux and Kalaydjian, 1990; Iffly et al, 1972; Parsons and Chaney, 1966)

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Conclusion