Pool-Production And Weil-Count Forecasts
Authors: Purvis Ra 
Published: March 2010

Abstract
A new method for forecasting the decline-curve performance of multi-well pools is presented. The inputs to the method are the pool-decline rate, a statistical distribution of well rates, and the economic limit. The forecast outputs are the number of producing wells, pool rate, pool cumulative, and the mean and variance of the oil-rate distribution.
The method is statistically sound and is consistent with historical trends in the example pools. The forecast is determined numerically and a short section of FORTRAN code is presented to facilitate the calculations.
The four example pools had harmonic decline and the distribution of their oil rates was approximately lognormal. However, the method is general in concept and could be applied to other distributions and other types of decline.
The method can be used to evaluate the sensitivity of ultimate recovery to economic limit. It can also be used in econometric forecasts which need producing well counts for cost analysis.

Introduction
Decline curves were empirically developed to quantify the trends observed in the unconstrained production from a single well. Despite their empirical origin, decline curves for individual wells have been shown(l,2) to have a theoretical basis. They have gained wide acceptance as a method of forecasting well performance and reserves. A factor contributing to their utility is that the economic limit is commonly expressed as a rate per day per well. The economic limit can, therefore, be directly applied to terminate a graph.
It is also common practice to apply decline-curve methodology to aggregated production from a lease or pool. The extension to aggregated-well production is currently done without knowing the distribution of well rates in the aggregate. The aggregate is sometimes characterized by its arithmetic average with the usual assumption that the average is the median. It will be shown that this is not a good assumption. The extension to aggregated production does not have a theoretical relationship with pool performance similar to that for individual wells. In fact, Nind(3) cautions against the pratice. He noted that the sum of rates from two wells with exponential decline results in the aggregate having an exponential decline only when both wells have the same decline rate. It will be shown that this concern is lessened when there are sufficient wells to give a statistical distribution. It was previously shown(4) that there are slope interdependencies among rate and ratio graphs because the product or quotient of two exponentials is also an exponential. It appears that most of the difficulty in extending from single to aggregated wells results from the inevitable variation in the number of producing wells over time. This variation blurs the concept of an economic limit and destroys the one-to-one correspondence that exists between an individual well's rate and its cumulative production.
The well economic limit for aggregated production is poorly defined and cannot be directly related to the graphed variables. The most common way to mask this difficulty is to use a pool economic limit (i.e. a per well limit times some arbitrary number of wells used to terminate the pool's production).