Abstract
The estimation of relative permeabilities from displacement experiments by the parameter estimation method was examined. In using this method the relative permeabilities, which are continuous functions of saturation (a state variable), are written in terms of a set of adjustable parameters in a functional representation of the relative permeability curves. A linearized covariance analysis was developed to study the accuracy with which these quantities can be estimated from these data. The accuracy with which the parameters can be estimated was related to the accuracy with which the relative permeabilities can be estimated. It was shown that, for a typical core-flood experiment, it is not necessary to assume a simple functional form to represent the curves (and hence bias the estimates), since accurate estimates can be obtained if cubic splines are used. An algorithm was developed to estimate relative permeabilities from displacement experimental data using a variety of functional forms to represent the curves. Inequality constraints are placed on the parameters to ensure that the estimated relative permeabilities will be physically realistic. The algorithm was tested on a number of cases using simulated data in order to demonstrate that the method converges to the correct solution in a reasonable number of iterations. A core-flood apparatus was developed to provide experimental data on a number of core samples in order to further test the method of estimation. This apparatus and the subsequent raw-data treatment method incorporated several new features which are presented and discussed. Results from analysis of the data showed that the algorithm performs well and that cubic splines can give significantly better estimates of relative permeability than the simple functional forms previously available.
Kerig, Philip Dwan (1985). Estimation of relative permeabilities from displacement experiments. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -426129.