Two-porous phase co-current and counter-current imbibition in a medium

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Scaling laws of laboratory imbibition experiments are very important to be used to predict oil recovery from matrix blocks. The importance of this concept being the oil recovery from reservoir matrix blocks in the field can be predicted experimentally from tests on small samples in laboratory. Laboratory results of oil recovery are commonly represented as a function of dimensionless time which in turn is a universal parameter including several physical parameters of fluids and rocks. It is considered as a good scaling group if the measured oil recovery is represented in a single universal curve with sharing less primary physical parameters. In the present work, we introduce a new dimensionless time formula in terms of characteristic velocity (e.g. injection velocity) which in turn is very important of some enhanced oil recovery (EOR) mechanisms such as water injection stage. We derive a power-law formula for dimensionless time that reduces the number of complexities in characterizing two-phase imbibition through a porous medium. The theory and characteristic velocity function is tested against some oil recovery experimental data for oil-water system from the literature. Through a comprehensive evaluation of available time scaling formulas, a simplified tool is provided for characterizing two-phase flow, through the use of a reference capillary number. In this context, we introduce a theoretical analysis and numerical computations of the counter-current imbibition. The one-dimensional macroscopic governing equation is transformed into a non-dimensional form which includes the dimensionless physical parameters (capillary number Ca and Darcy number Da). Additionally, numerical experiments are performed for wide ranges of values of capillary and Darcy numbers to illustrate their influences on water saturation as well as relative water/oil permeabilities. In the second part of this talk we introduce numerical and theoretical investigations of the problem of gravity and the inlet/outlet location effects of a two-phase countercurrent and cocurrent imbibition in a porous medium. We consider 2D computations of the problem with considering different locations of the open-boundary. The results indicate that gravity has a significant effect depending on open-boundary location. Then 1D computation for dimensional and non-dimensional cases and a theoretical analysis of the problem under consideration are carried out. A time-scale based on characteristic velocity is used to transform the macroscopic governing equations into a non-dimensional form. The resulting dimensionless governing equations involved some important dimensionless physical parameters such as Bond number Bo, capillary number Ca and Darcy number Da. Numerical experiment on Bond number effect is performed for two cases, gravity opposing and assisting. The theoretical analysis illustrates that common formulations of the time-scale enforce the coefficient Da <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> /Ca to be equal to one, while, formulation of dimensionless time based on a characteristic velocity allows to the capillary and Darcy numbers to appear in the dimensionless governing equation which leads to a wide range of scales and physical properties of fluids and rocks. The results indicate that the buoyancy effects due to gravity force take place depending on the location of the open-boundary.