While a number of methods, including semi-log/linear plot of water cut versus cumulative oil and water-oil ratio versus cumulative oil, have been published for extrapolating water cut during oil decline, the challenges of internal consistency, accuracy and limited areas of application have remained unresolved. These make the application of the methods threatening to the associated estimates of oil reserves and investments on water-handling facilities.
In this paper, based on an investigation of internal/practical consistency and the physics of fluid flow, a didactic analysis of water cut models derivable from popular oil rate models of Arps, Li and Horne, as well as the Flowing Material Balance is carried out. This culminated in the development of an internally consistent water cut model, applicable during exponential decline of oil production. The development supports an exponential function of oil-cut vs production time.
Using both hypothetic and field examples, applicability and performance of the derived model are demonstrated, and compared with six of the popular water cut models, including those of Ershagi and Omoregie, Liu, Warren and Purvis. Besides its simplicity, the proposed model consistently performs better and shows robustness.
Although the form of the proposed model is here limited to exponential oil rate decline, the principles can easily be extended to other oil production decline trends.
Introduction
Besides the traditional focus of applying water cut data for reserves estimation, reservoir surveillance and management, the need to comply with increasingly stringent regulatory requirements for disposal of produced water, is fast becoming another key driver for reliable forecasts of water production. Clearly, for making robust investment decisions on water-handling facilities, it is critical to have reliable methods of predicting associated water production.
There are several correlations in the literature and commercial packages dedicated to fitting water cut trends during oil decline. In general, these correlations can be divided into three main classes:using fractional flow theory, in which relative permeability functions are approximated, to establish water cut (or water-oil ratio) variation with oil recovery (1–4),using Arps' model and its modifications, for example semi-log water cut versus oil recovery, andobserved trends, for example linear water cut versus oil recovery.
While these methods have been applied extensively, none has been found to be sufficiently robust (5), and for those not based on the fractional flow theory, besides the problem of internal consistency, curve-fitting by simple polynomial approximation do not result in satisfactory answers in most cases (6). Assumption of constant gross liquid production is also an inherent limitation of the three classes.