Cavities and fractures significantly affect the flow paths in carbonate reservoirs and should be accurately accounted for in numerical models.Herein,we consider the problem of computing the effective permeability of r...Cavities and fractures significantly affect the flow paths in carbonate reservoirs and should be accurately accounted for in numerical models.Herein,we consider the problem of computing the effective permeability of rock samples based on high-resolution 3DCT scans containingmillions of voxels.We use the Stokes-Brinkman equations in the entire domain,covering regions of free flow governed by the Stokes equations,porous Darcy flow,and transitions between them.The presence of different length scales and large(ten orders of magnitude)contrasts in permeability leads to highly ill-conditioned linear systems of equations,which are difficult to solve.To obtain a problem that is computationally tractable,we first analyze the relative importance of the Stokes and Darcy terms for a set of idealized 2D models.We find that,in terms of effective permeability,the Stokes-Brinkman equations are only applicable for a special parameter set where the effective free-flow permeability is less than four orders of magnitude different from the matrix permeability.All other cases can be accurately modeled with either the Stokes or the Darcy end-member flows,depending on if there do or do not exist percolating free-flow regions.The insights obtained are used to perform a direct computation of the effective permeability of a rock sample model with more than 8 million cells.展开更多
基金funded in part by Shell Norge AS and the Research Council of Norway through grants No.175962 and 186935Lie also acknowledges partial funding from the Center of Mathematics for Applications,University of Oslo.The Pipe Creek CT-scan data was originally collected by the Bureau of Economic Geology at The University of Texas at Austin with funding from the Industrial Associates of the Reservoir Characterization Research Laboratory.The authors are grateful to Bob Loucks,Chris Zahm,and Jim Jennings for assistance in accessing the data.
文摘Cavities and fractures significantly affect the flow paths in carbonate reservoirs and should be accurately accounted for in numerical models.Herein,we consider the problem of computing the effective permeability of rock samples based on high-resolution 3DCT scans containingmillions of voxels.We use the Stokes-Brinkman equations in the entire domain,covering regions of free flow governed by the Stokes equations,porous Darcy flow,and transitions between them.The presence of different length scales and large(ten orders of magnitude)contrasts in permeability leads to highly ill-conditioned linear systems of equations,which are difficult to solve.To obtain a problem that is computationally tractable,we first analyze the relative importance of the Stokes and Darcy terms for a set of idealized 2D models.We find that,in terms of effective permeability,the Stokes-Brinkman equations are only applicable for a special parameter set where the effective free-flow permeability is less than four orders of magnitude different from the matrix permeability.All other cases can be accurately modeled with either the Stokes or the Darcy end-member flows,depending on if there do or do not exist percolating free-flow regions.The insights obtained are used to perform a direct computation of the effective permeability of a rock sample model with more than 8 million cells.
