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

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.

NMR Investigation of Brine Imbibition Dynamics in Pores of Tight Sandstones under Different Boundary Conditions

“…Validation of NMR Imbibition Data. From the conventional scaling theory, the generalized scaling equation for spontaneous imbibition is expressed in terms of dimensionless time (t D ) as t D = C*t, 12,35,36 where C*(s −1 ) are the coefficient related imbibition factors such as boundary conditions, sample shape, and viscosity ratio while t (s) is the imbibition time. From this expression, correlation of the recovery curves through a linear fit indicates that the conventional scaling theory can be applied to the imbibition process.…”

“…Several studies have considered boundary conditions in analyses of spontaneous imbibition but only a few studies have explored how BC influence imbibition dynamics at the pore scale. Abd and Alyafei explored how boundary conditions influence scaling of spontaneous imbibition and presented major scaling groups employed for modeling spontaneous imbibition. Meng et al employed boundary conditions in their imbibition experiment, but their focus was mainly on developing a new method capable of monitoring the changes in the imbibed volume with particle disintegration and clay swelling.…”

Study on Imbibition Characteristics of Glutenite with Different Boundary Conditions Based on NMR Experiments

“…During the soaking process, fracturing fluid is imbibed into the reservoir and displaces the oil therein, thereby enhancing oil recovery. In fractured reservoirs, due to the randomness of the fracture morphology, the contact modes and contact areas between the fracturing fluid and rock are different, thus forming different boundary conditions. ,, Generally, the boundary conditions of cores are divided into all-faces-open (AFO), one-end-closed (OEC), two-ends-closed (TEC), two-ends-open (TEO), and one-end-open (OEO). − ,− Among them, the researches on OEC boundary condition has not received much attention. In addition to boundary conditions, the parameters that affect the imbibition characteristics also include core size, porosity, permeability, fluid surface tension, viscosity, and so on.…”

Modeling the effects of capillary pressure with the presence of full tensor permeability and discrete fracture models using the mimetic finite difference method

“…Early efforts to understand the physical significance of the imbibition process focused on experimental work (Mattax and Kyte 1962;Iffly et al 1972;Du Prey 1978;Hamon and Vidal 1986;Zhang et al 1996), while subsequent efforts highlighted the key differences between the two modes of imbibition assisted oil recovery (co-current and counter current SI) and their unique characteristics (Bourbiaux and Kalaydjian 1990;Pooladi-Darvish and Firoozabadi 2000;Morrow and Mason 2001). These experimental efforts were later tested and verified using numerical techniques and semi-analytical solutions (Fischer and Morrow 2006;Schmid et al 2011Schmid et al , 2016Nooruddin and Blunt 2016;Khan et al 2018;Abd and Alyafei 2018;Abd and Alyafie 2019) allowing for better interpretation of spontaneous imbibition processes (Fig. 1).…”