This paper presents results that theoretically and numerically support the log(WOR) vs cumulative oil plot for waterflood analysis. This plotting technique has traditionally been used to estimate the ultimate oil recovery from waterflooding; the results derived in this paper give other practical uses for this plot such as evaluating the efficiency of current waterflooding operations, estimating the original oil in place (OOIP), or determining the in situ water-oil relative permeability characteristics of the reservoir. The study results, primarily utilizing the dependence of the slope of the log(WOR) vs cumulative oil plot on various reservoir parameters, are based on the one-dimensional Buckley-Leverett theory after water breakthrough and multi-dimensional numerical simulations. Also the effect on this slope caused by different reservoir layering, flood configurations, and operational changes are presented. This approach has been applied to estimate the presented. This approach has been applied to estimate the original oil in place for two actual waterfloods and a comparison of these OOIP values is made to those calculated by volumetric methods.
A common practice in petroleum engineering has been to analyze the performance of waterfloods by plotting log (WOR) vs cumulative produced oil for individual wells or from field data. When plotted in this way, the data generally form a straight line and this straight line can be extrapolated to predict future performance and estimate ultimate oil recovery from waterflooding. This paper presents a theoretical basis for this approach and defines the dependence of the slope of this plot on various reservoir parameters.
The one-dimensional (ID) results in this study are developed from the Buckley-Leverett theory assuming a post-breakthrough saturation profile. The other key assumption is the functional form of the water-oil relative permeability ratio. These assumptions are generally valid when applied to waterfloods following water breakthrough.
Ershaghi and Omeregie previously derived a relationship between a factor X (= -ln(WOR)-1/WOR-1) and cumulative oil production. The slope of the log (WOR) vs cumulative oil production. The slope of the log (WOR) vs cumulative oil relationship derived here, when expressed in a natural log form, is equivalent to Ershaghi's results at high watercuts. Based on the ID Buckley-Leverett theory, Ershaghi's X-plot is more general than a simple ln(WOR) vs cumulative oil analysis; however, the difference is only the inclusion in Ershaghi's X of the -1/WOR-1 terms which tend to a value of-1 at high WOR's and when using field data, this simplification makes essentially no difference.
From a practical standpoint, it is more convenient to plot the readily available WOR values instead of the -X factor. Also, the dependence of the slope of the log (WOR) vs cumulative oil production plot can be more easily interpreted and used to production plot can be more easily interpreted and used to estimate various reservoir parameters than can the X-plot. Prior to breakthrough and at low watercuts, neither approach is applicable. At several points in this paper the relationship of the two approaches will be described. Also, as will be discussed elsewhere in this paper, the numerical simulator results indicate that the ln(WOR) vs cumulative oil plot (Figure 2c) exhibits a straight line behavior earlier than seen in the X-plot or suggested by the theoretical analysis. Finally, the numerical results do not require the simplifying assumptions needed to carry out the theoretical analysis.
This study generalizes the ID results to three dimensions (3D) using a black-oil numerical reservoir simulator to quantify the effects of areal sweepout, pattern configuration, multi-zone permeability contrasts and gravity. Key factors that affect the permeability contrasts and gravity. Key factors that affect the linear trend of the plot and the limitations on the applicability of the results are identified.