Material Balance Equations (short version):
Below, find the essential MBE, stripped clean of any theoretical discussion. For those who wish to wade deeper, see references at the end.
Above bubble point)
Note that water influx is in cumulative reservoir barrels. Excluding compressibilities will result in overestimation of OOIP, particularly in friable sands with high formation rock compressibilities.
We will address means of calculating the water influx in Part II of this discussion.
Below bubble point
As reservoir pressure declines below bubble point pressure, free gas starts to evolve and a free gas phase develops. A secondary gas cap may or may not form. The movement of free gas will depend on several factors, one is the gas-oil relative permeability curve. A critical saturation may need to develop before the onset of gas movement. The free gas may remain distributed throughout the reservoir as insoluble bubbles. The following material balance equations apply in both cases:
Notes: a) Some sources present 3 MBE, one for above bubble point, one for saturated conditions without gas cap and one with gas cap. I did not think this was necessary since m = 0 without a gas cap. b) To minimize constants, I have used a Bg calculated as Rbbl/SCF instead of Rcf/STB, so divide the unitless Bg by 5.615, or multiply by 0.1781 c) I note in the 1982 Petroleum Handbook, water influx was in STB (Chapter 37), while Craft, Hawkins and Terry use Rbbls. Updated handbook, Vol V, V-1549, has it in Rbbls.
1. Craft. B.C., Hawkins, M. and Terry, R.E. Applied Petroleum Reservoir Engineering, 1991, Pages 172-177. Includes many good examples and exercises.
2. Lake, Petroleum Engineering Handbook, Reservoir Engineering and Petrophysics, 2007, page V-1519 also V-906.
3. Bradley, Petroleum Engineering Handbook, Chapter 37. Pages 37-5 to 37-8.