Parameterization of Match-Derived Pseudo-Relative Permeabilities

Abstract

Pseudo-relative peraeability functions were Pseudo-relative peraeability functions were generated by autoaatically aatching the pressures and oil production voluaes obtained froa two-diaensional production voluaes obtained froa two-diaensional cross-sectional siitulations. The 2-D siaulations used actual reservoir fluid and rock properties, but incorporated hypothesized stratifications and dip angles. The resulting pseudo-relative permeability curves were correlated as a function of the water breakthrough tiae and the aaxiaua pressure differences observed in the corresponding siaulations. The resulting suite of relative peraeability curves then offered a siaple aethod of aatching historically observed pressures and production volumes in three-diaensional siaulations of the reservoirs. Siailar possibilities exist for altering pseudofunctions to obtain history aatches in areal aodels. pseudofunctions to obtain history aatches in areal aodels Introduction Despite the advent of ever larger and faster coaputers the use of pseudo-relative peraeabilities reaain a coaaon practice in reservoir siaulation. Pseudo-relative peraeabilities are applied to finite Pseudo-relative peraeabilities are applied to finite difference reservoir siaulation aodels to coapensate for intra-cell variations in rock properties and fluid saturations or coapositions. To coapensate for these difficulties through grid refineaent can be difficult because 1) reservoirs comaonly exhibit large and frequent variations in reservoir properties, e.g. peraeability and porosity. as a result of properties, e.g. peraeability and porosity. as a result of geological stratification, and because 2) very sharp saturation gradients can occur in the reservoir as one phase displaces another. Very saall finite difference grid blocks aay be required to represent these changes accurately. Achieving adequate accuracies can tax even the new super coaputers. Moreover, to represent these intricacies in a aodel through saall finite difference grid blocks can be very expensive. The use of pseudo-relative permeability functions offers a compromise to permeability functions offers a compromise to account for these errors without the increased expense of a larger model. Several methods have been proposed for the develop aent of pseudo-relative peraeabilities which would account for these intra-cell variations. Coats et al. suggested the assuaption of capilliary equilibrium within each cell to account for saturation variations. This method has received general acceptance. The assuaption of vertical equilibrium is justified when vertical communication is good, displaceitent velocities are saall, and phase density differences are large. Hearn has suggested a method for deteraining pseudo-relative per. eabilities in the other extreae pseudo-relative per.eabilities in the other extreae when convection forces doainate and vertical communication is small. He develops pseudo-relative permeability functions by assuming that the invading permeability functions by assuming that the invading fluid aoves along isolated strata in a piston-like fashion. Hawthorne has shown that Hearn's model can be modified to include the influence of capillary pressure. More recently, Simon and Koederitz have aodified Hearn's aethod to account for continuing oil production from each layer after water breakthrough. Jacks et al have suggested the use of "dynamic" pseudo-functions which involve detailed simulations pseudo-functions which involve detailed simulations of sections of the reservoir. Their procedure is suggested when neither of the above analytical techniques are applicable, which is often the case. Their method derives the pseudo-relative permeabilities from detailed vertical permeabilities from detailed vertical cross-sectional simulation studies of segments of the reservoir under conditions to be expected during the full scale simulations. The pseudos are derived by combining each column of cells in the vertical cross-sectional model to act as a single cell in the larger model. Average saturations and pressure gradients are calculated for the entire column of cells. The total flux from the column for each phase is also calculated. Then Darcy's Law is applied using these fluxes and pressure gradients to obtain the effective pseudo-relative permeabilities. This procedure was improved by Kyte and Berry to procedure was improved by Kyte and Berry to include an analogous pseudo-capillary pressure deteraination and to allow for differences in cell sizes between the vertical cross sections and the larger model. P. 445

Upscaling for Thermal Recovery

“…The pseudo values can vary independently until a match of saturation distribution and production rate between the fine grid model and the coarse grid model is observed. Hales (1983) presented an approach to obtain pseudo relative permeability curves by the use of regression techniques. He used an automatic history matching model to match the oil production rates and pressure of the fine grid model by varying quadratic representations of the relative permeability curves in the coarse grid model.…”

“…This is the most demanding in terms of computational power and was first discussed by Hales (1983). The idea is similar to history matching but instead uses results from the fine scale calculations rather than physical measurements.…”

Upscaling: a review

“…It is possibly the most demanding, in computer resources, of the various methods and was, as far as we know, ÿrst discussed by Reference [24]. There are not many papers using this method.…”

Upscaling Polymer Flooding to Model Sub-gridblock Geological Heterogeneity and Compensate for Numerical Dispersion

“…This was first introduced by Hales (1983) but has limited application in the literature. This is because this solution needs the fine scale model to be simulated for each flow scenario.…”