Clarifying and Improving the Application of Waterflood Analytical Methods in X-Plot Conditions – From Empirical Approach to Analytical Approach

Abstract

Abstract X-plot method is the waterflood analysis method derived from 1-D Buckley-Leverett equation (Ershaghi and Omoregie, 1978) based on a semi-log relationship between oil/water relative permeability ratio and water saturation. X-plot method (Qo=mX+n) is a linear relationship between cumulative oil (Qo) and a water-cut feature variable X=ln(1/fw-1)-1/fw. Using an empirical approach, the slope m and intercept n are determined by linear-regression of historical production data and then extrapolated to a higher water-cut to predict recoverable oil. The limitations to field application include: 1) post-breakthrough waterflood period; 2) unfavorable mobility ratio in 3-D field condition; and 3) major pattern reconfiguration events such as infill-drilling and perforation interval addition may impact parameters m and n. Clarifying those limitations and their impact will minimize uncertainty and bias in the practical application. X-plot condition is defined as the water saturation range or recovery period when the X-plot method applies which is from water breakthrough to an economically feasible higher water-cut. The objective of this paper is to clarify and improve the application of waterflood analytical methods in X-plot conditions. Various analytical methods have been developed and their internal relation with the X-plot method in field condition are clarified. An analytical approach is proposed, where the X-plot method slope m and intercept n are determined by diagnosing production performance rather than by empirical regression. With parameters m and n determined analytically, the X-plot method is applied to forecast recoverable oil. The 1-D model case and field case studies compare the X-plot method in analytical and empirical approaches. The case studies indicate that with only minimal post-breakthrough waterflood production data the analytical approach for X-plot method will reduce uncertainty and bias in the long-term recoverable oil prediction.