Analytical Prediction of Natural Gas Reservoir Recovery Factors

Abstract

Abstract An analytical method for large-scale evaluation of recovery factors for natural gas reservoirs is presented. The effects of simplifying assumptions are discussed, in particular the effect of neglecting changes in 'reservoir flow turbulence. The possible effects of improved economics on recovery factors are discussed. A simplified method for determining the coefficients of the Katz quadratic reservoir" flow equation is introduced. Introduction THE CALCULATION of reserves of natural gas in a reservoir includes an estimate of the portion of the in-situ gas which will ultimately be produced. This is normally expressed in terms of a " recovery factor"; Le. the ratio of the ultimate raw gas production to the initial raw gas-in-place. In addition to this " ultimate" recovery factor, the " cumulative" recovery factor can be calculated at any time. It is the ratio of the cumulative raw gas production to the initial raw gas-in-place. Any discussion of recovery factors without consideration of gas-in-place estimates is academic. Only when both these parameters are well defined can raw gas recovery be accurately determined. Unfortunately, both parameters are subject to varying degrees of uncertainty - greatest in the early stages of the productive life of a reservoir and least during the latter stages. Two basic approaches to predicting recovery factors have evolved. They are:statistical empirical correlations relating abandonment conditions to reservoir parameters;analysis of physical, regulatory and economic factors affecting production. Stoian and Telford presented, in 1966, a statistical analysis of abandonment conditions. A useful equation was derived by regression analysis for estimating abandonment pressure from formation depth. This relationship was based on a study of 158 Alberta gas pools with an average ultimate recovery factor of 85.2%. This compared favorably with the average ultimate recovery factor of 84.6% for 76 depleted pools in the U.S. The majority of the 76 depleted pools were abandoned in the 1940's. Stoian and Telford's correlation should provide good average estimated ultimate recovery factors consistent with conditions at that time. The analytical method incorporates mathematical relationships of pressure, cumulative production, production rate and facility requirements (e.g. infill drilling, compression) with the economic parameters and regulatory guidelines that govern the productive life of a reservoir. It is technically more sophisticated than the statistical method, allows assessment of the effect of changes in individual factors on the production cycle and permits better analysis of pool production performance for unusual pools with 'Para-meters which deviate considerably from the average. However, because it reflects only certain basic elements of the production system and requires simplifying assumptions, care must be exercised in the absolute use of predicted results. The trends in two economic indices are shown in Figures 1 and 2. Figure 1 shows the semi-logarithmic relationship between an index of the average Western Canada Wellhead Natural Gas Price and time. Figure 2 shows the semi-logarithmic relationship between the Nelson Refinery Operating Cost Index and time. The long-term average growth rate in both these indices are in the range of 3% to 4% per year, up to and including 1972.