Estimation of Relative Permeability from Displacement Pressure Data

The solution of the inverse problem to estimate oil-water relative permeabilities, or history matching, has been widely used in the oil industry for many years. Usually, in this procedure, the production behavior, i.e., observed oil and water flow rates and pressure data versus time, is modeled and matched using a numerical regression process where the model relative permeabilities are modified until an acceptable solution is obtained. In some cases, only the production data versus time (without corresponding pressure data) are used to obtain the model relative permeability curves. To our knowledge, there have been very few instances where researchers attempted to use only pressure versus time data from core flood experiments (without the corresponding fractional flow) to estimate relative permeability curves. In the laboratory environment, the pressure drop across a core during a displacement test can be determined with extraordinary precision - much more accurately than fractional flow data measurements. Since pressure measurements can be obtained easily, accurately and inexpensively, the number of data points collected during the experiment could be significantly increased, and also, data measured before breakthrough could be included. Based on this, a method has been developed to determine relative permeabilities through the solution of the inverse problem (numerical regression), by modeling, through the Buckley-Leverett procedure, the observed pressure versus time data only, and dismissing the recovery measurements. This approach significantly reduces the cost and time required to perform displacement experiments. The results of the new technique, using power law representations for water relative permeability and oil relative permeability, are compared with relative permeability curves obtained using the standard history matching technique (finite difference simulator) and with relative permeability curves obtained using the standard unsteady state laboratory procedure (JBN). It is shown that there are only minor differences in the results, both from the point of view of the generated relative permeability curves and the estimated fractional recoveries, when the new approach is compared with the standard history matching procedure. Thus, the new method represents a viable and economically attractive procedure for determining relative permeability curves from laboratory displacement experiments.