Abstract
This study provides a pore-scale investigation of two-phase flow dynamics during primary drainage in a realistic heterogeneous rock sample. Using the lattice Boltzmann (LB) method, a series of three-dimensional (3D) immiscible displacement simulations are conducted and three typical flow patterns are identified and mapped on the capillary number (Ca)-viscosity ratio(M) phase diagram. We then investigate the effect of the viscosity ratio and capillary number on fluid saturation patterns and displacement stability in Tuscaloosa sandstone, which is taken from the Cranfield site. The dependence of the evolution of saturation, location of the displacement front, 3D displacement patterns and length of the center of mass of the invading fluid on the viscosity ratio and capillary number have been delineated. To gain a quantitative insight into the characteristics of the invasion morphology in 3D porous media, the fractal dimension Df of the non-wetting phase displacement patterns during drainage has been computed for various viscosity ratios and capillary numbers. The logarithmic dependence of Df on invading phase saturation appears to be the same for various capillary numbers and viscosity ratios and follows a universal relation.
Highlights
The detail of moment m and transformation matrix M can be found in previous studies[45,68]
Th equilibrium moment vector meq is calculated by taking the effect of interfacial tension into consideration, as shown below[25,45]
The optimal values of these parameters can be found in previous studies[69,70]
Summary
Σ incorporates into the collision operator, which has been described by a multiple-relation-time (MRT) scheme as follows: www.nature.com/scientificreports Where M is the transformation matrix, which transforms the distribution function f to the moment space m as shown below: m = Mf , meq = Mf eq , (6) Where f eq and meq are equilibrium functions at distribution and moment space, respectively. The detail of moment m and transformation matrix M can be found in previous studies[45,68].
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