Laboratory measurement of relative permeability using either steady-state or unsteady-state methods can be expensive and time consuming. Each method has certain advantages, resulting in preferences of one particular method over the other. The primary advantage of the unsteady-state method is that it is faster than the steady-state method. This paper presents a Linear Regression Model approach for developing prediction equations for water-oil and gas-oil relative permeability from steady-state and unsteady-state experimental data. These equations offer an alternative technique in determining relative permeability values and provide a better statistical representation of relative permeability values for a reservoir as a whole since ample amounts of data were used in developing them. The data for this study were obtained from published literature of the Society of Petroleum Engineers and various industry sources. Equations were developed for water-oil and gas-oil systems based on formation type and wettability in addition to the methods of measurement. Only equations for sandstone formations are presented in this paper due to the lack of data available for other formations. The adjusted coefficient of multiple determination, R2adj is used as a criterion of a good prediction model in this study in addition to a residual plot. The equations developed in this study are easy to use: nine out of twelve developed equations require only one independent variable in order to generate a relative permeability curve, and consist of no more than seven terms in each equation. The prediction equations are compared with previously published correlations where possible and the plot of the prediction equations indicates that the unsteady-state method results in lower oil relative permeability values and higher water relative permeability values at a given saturation than the steady-state one.

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