# Browsing by Subject "Viscous crossflow"

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Item A Pseudofunction Approach to the Description of Viscous Crossflow in Multi-Layered Permeable Media(1988-12) Thiele, Marco Roberto; Lake, Larry W.Show more Under the conditions of vertical equilibrium, viscous forces only, and sharp front displacement, Ream's model for the description of a waterflood in a twodimensional layered reservoir is not correct for end-point mobility ratios greater than one. Under these conditions, the flow does not remain segregated as the Hearn model assumes but instead the direction of crossflow creates viscous mixing zones. Compared to the Hearn model, viscous mixing aids recovery. A central assumption in the analysis of viscous mixing is that the system be in vertical equilibrium. Formally, this requires the vertical absolute permeability to be infinitely large. It is shown that for all practical purposes this must not be the case and that vertical equilibrium is attained as long as a dimensionless parameter, called the effective length-thickness ratio, exceeds a value of two. The functionality of viscous mixing is investigated with respect to three parameters: the end-point mobility ratio (Mo), the Craig coefficient (Vc), a measure of reservoir heterogeneity, and the type of layer ordering. The dominant factor controlling the extent of viscous mixing is found to be the layer arrangement. Four types of ordering schemes are proposed. Of the four, the "random" ordering arrangement is found to have the strongest degree of viscous mixing and the largest increase in recovery. If the type of layering is fixed, viscous mixing and the improved recovery because of it, can be related to the end-point mobility ratio only. The simplicity of the Hearn model allows for a pseudofunction approach to correct for viscous mixing by introducing an effective end-point mobility ratio. For a descending (ascending) type layer ordering, the effective end-point mobility ratio is linearly related to the true end-point mobility ratio of the displacement. Within certain limits of the Craig coefficient and the true end-point mobility ratio this approach works well. An alternative approach to correct for viscous mixing effects, using effective permeability-height products, is presented. Contrary to the effective mobility ratio approach this is a N-1 parameter fit, where N is the number of layers. It also allows for calculating the pseudo relative permeability curves of the system. In conclusion, it is pointed out that under the assumptions of the study, viscous mixing effectively makes the system look less heterogeneous than it really is and always aids in the overall recovery compared to the case in which the phenomenon is neglected.Show more