Pseudo-Relative Permeability for Well Modeling

Publisher Website
Google Scholar
Abstract
Several authors have described the use of pseudo-relative-permeability curves for modeling pseudo-relative-permeability curves for modeling the vertical performance of formation flow in areal reservoir simulators. The pseudo curves are usually determined from small cross-section or three-dimension models and then incorporated into large-scale areal models. The concept of pseudo-relative permeability can also be extended to the vertical performance of individual wells by a technique analogous to that for formation flow. In a cross-section model, the production of phase p from a well with nc completions can be expressed as(1) Eq. 1 follows the form of the well potential equation of Ref. 4. For an areal model in which the well has only one completion, the production is(2) The cross-section model can be constructed with the vertical detail necessary to account for phase segregation, partial penetration, etc. To obtain the same well performance in the areal model, we desire(3) or combining Eqs. 1 through 3,(4) If the cross-section model has been divided into nl layers, then an areal model block represents a composite of the nl layers and a well a composite of nc completions. Therefore, the following approximations are made.(5) and(6) Combining Eq. 4 through 6, the pseudo-relative permeability for the areal model well is obtained: permeability for the areal model well is obtained:(7) The corresponding saturation is(8) The wellbore pressure in the areal model, PwA, can be assumed to be an appropriate average of the Pw calculated in the cross-section model. Eqs. 6 Pw calculated in the cross-section model. Eqs. 6 and 8 am appropriate for an areal block equivalent to one column of the vertical model. If the areal block is larger, then the pressure and saturation must be averaged over the volume encompassed by the areal block. P. 7

This publication has 0 references indexed in Scilit: