The API or "Arps" equation for oil recovery of solution gas drive reservoirs, is the result of an empirical multiple regression of 80 solution gas reservoirs. It is as follows:
Per Reference 1. Looks impressive, but is it any good? Many argue that it is no better than analogies to other producing formations. Certainly even a highly simplistic reservoir simulation model would be better. However, it is in the PE Handbook, at least the 1987 version. More recently, the Arps equations were presented in Basic Applied Reservoir Simulation, by Ertekin et al. (2001).
A basic assumption in multiple regression is that the variables are independent, which means that the value of porosity should not affect initial water saturation or permeability. Of course these are related variables. Viscosity, Bop and bubble point pressure are also related variables. This introduces a systemic error in the analysis.
If necessary to use, it would best to program in a spreadsheet, remembering that a/b^c is not the same as (a/b)^c. If using a calculator, calculate the four products first and then multiply to keep your work organized.
Water drive Reservoirs
The API equation for waterdrive reservoirs is similar in form, based on multiple regression:
where A= 0.0422, B= 0.77, C= -0.1903 and D= -0.2159.
Similar comments as before apply to the validity of the regression analysis.
Additional Regression based equations
- Jacoby Correlation for gas condensate recovery (1959)
Reference:
1. Arps, J.J. et al.," Statistical Analysis of Crude Oil Recovery and Recovery Efficiency," Bulletin D14, American Petroleum Institute, Washington D.C. (October 1967)
2. Statistical Analysis of Crude Oil Recovery and Recovery Efficiency, American Petroleum Institute, Dallas, (April 1984).
3. Jacoby, R. H. et al., "Effect of Compositional and Temperature on Phase Behavoir and Depletion Performance of Rich Gas-Condensate Systems," JPT (July 1959)58.: Trans AIME, 216.
4. Bradley, Handbook of Petroleum Engineering, (1987), Page 44-48 for waterdrive equation.
5. Ertekin, T. et al, Basic Reservoir Simulation (2001), page 5 for summary of regression based recovery equations.