Page 36 - Principles of Catalyst Development

Part I: Reservoir Engineering Primer 1 7

independent variable*, $n q corresponds to the dependent variable y, $n q i is the
intercept b, and -a is the slope m of the straight line. Cumulative production for
decline curve analysis is the integral of the rate from the initial rate q t at t - 0
to the rate q at time t. For example, the cumulative production for the exponential
decline case is
f (2J5)
N
<*
The decline factor a is for the exponential decline case and is found by re-
arranging Eq. (2. 11), thus

fl=--ln — (2.16)
t

Exercises

Exercise 2.1 Copy file EXAM1 .DAT to file WTEMP.DAT and run WINB4D.
What are the volumes of initial fluids in place in the model? Hint: Open the run
output file WTEMP.ROF to find initial fluids in place.

Exercise 2.2 Derive the material balance equation for a system with no gas cap
beginning with Eqs. (2.3) and (2.4).

Exercise 2.3 Use Eq. (2.9) to show that the material balance equation for a
depletion drive gas reservoir is

" (P/Z).

where G is original free gas in place, G^ is cumulative free gas produced, P is
reservoir pressure, and Z is the real gas compressibility factor. Subscript t
indicates that the ratio P/Z should be calculated at the time / that corresponds
to G pc, and subscript / indicates that the ratio P/Z should be calculated at the
initial time. The units of G P and G must agree for the equation to be consistent.