An Analytic Simulator for Rapid Forecasting Rate Behavior of Oil Wells
Authors: Kabir C.S. , Ainley C.M. , Brown D.R. 
Published: December 2007

Abstract
A generalized analytic approach is used for forecasting an oil well's rate behavior. Well orientation from vertical to horizontal can be adapted in this formulation. In this approach, the well is produced at a constant bottomhole pressure, in which flow periods of infinite-acting, transitional, and pseudosteady-state (pss) are modeled. The method of images is used to compute pressure solution during the transitional and pss flows for bounded reservoirs. Thereafter, rates are discerned. Both no-flow and a combination of no-flow and constant-pressure boundaries may be used.
We developed a sensitivity analysis procedure to account for uncertainty in reservoir parameters. Here, a number of parameters, such as drainage area, permeability, decline coefficient can be varied within specified bounds to generate a cumulative probability distribution function (cdf). The individual simulations that fall closest to 10, 50, and 90 percent of this cdf are selected to represent low, medium, and high forecasts for oil rates. This analysis readily allows one to perform an economic evaluation of existing or new well prospects. Direct comparison of a vertical well with that of an inclined or a horizontal well's performance is also feasible in this approach.
Illustrative examples constitute the paper's backbone. Several plausible scenarios are presented to show the simulator's applications. The first three cases, taken from actual files, show how project economics can be analyzed from the results of a large number of rapid simulations. We also considered a hypothetical case involving an offshore project where a large capital investment is required. Following a stepwise procedure, we show how to evaluate the reservoir parameters that are required to make the project an economic success even before drilling a well.

Introduction
Once a well is drilled and tested, questions arise about its performance so that an economic appraisal can be made of a prospect. The same questions surface even before drilling an infill step-out or an exploratory well. Often the cost and availability of a numeric simulator, limited reservoir data and/or their uncertainties, all contribute adversely to the potential use of a numeric simulator. Thus, we cannot overemphasize the need for a rapid rate forecasting tool.
The obvious advantage of an analytic method is its simplicity and the speed of computation. The intent of this approach is to be the precursor of detailed simulation studies that can include reservoir heterogeneities, drive and displacement mechanisms, and other complexities. The proposed method is rooted in decline curve analysis.
Arps pioneered but Fetkovich and his coworker advanced the technology for decline curve analysis. In this approach, a well's historical rate behavior is matched with a type curve or analytic solution so that its future performance can be predicted. Fetkovich also showed that reservoir parameters can be obtained by solving the inverse problem using rate data, in analogy to pressure. One major implicit assumption is that the well is produced at a constant bottomhole pressure (BHP) throughout its life. Because this inner-boundary condition may be too restrictive, methods have been suggested to handle variable-BHP cases.
In this work, we used some elements of the decline curve analysis. However, our approach is very different in that we attempt to solve the forward problem only. In other words, we compute a well's rate behavior given its orientation, reservoir size and shape, rock, and fluid properties. This approach is no different than generating the analogous pressure-transient solution in a bounded system.
Two-phase gas/oil flow is modeled by specifying decline coefficient, which implicitly accounts for the reservoir drive mechanism, relative permeability effects, etc. Results of numerical simulation studies verity this approach.
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