As fluid is produced from the reservoir it doesn’t leave a void, something has to fill the space. Gas, oil, water and rock can all expand, to varying degrees, to fill up the space but it results in a decrease in the reservoir pressure. In addition, water can migrate into the reservoir area. The material balance equation was derived in order track the production of oil, gas and water; the expansion of existing fluid and rock; and the migration of water into the reservoir. The material balance provides reservoir engineers a great deal of insight in knowing the initial hydrocarbon in place, how much hydrocarbon can be produced at different pressures, the primary mechanism for reservoir production and the potential usefulness of varying enhanced recovery techniques. For a detailed derivation, please refer to Chapter 3 of Applied Petroleum Reservoir Engineering.
The material balance equation can be written as:
Oil Expansion + Gas Expansion + Formation and Water Expansion + Water Influx
=Oil and Gas Production + Water Production
where
N Initial reservoir oil, STB
Boi Initial oil formation volume factor, bbl/STB
Np Cumulative produced oil, STB
Bo oil formation volume factor, bbl/STB
G Initial reservoir gas, SCF
Bgi Initial gas formation volume factor, bbl/SCF
Gf Amount of free gas in the reservoir, SCF
Rsoi Initial solution gas-oil ratio, SCF/STB
Rp Cumulative produced gas-oil ratio, SCF/STB
Rso Solution gas-oil ratio, SCF/STB
Bg Gas formation volume factor, bbl/SCF
W Initial reservoir water, bbl
Wp Cumulative produced water, STB
Bw Water formation volume factor, bbl/STB
We Water influx into reservoir, bbl
cw Water isothermal compressibility, psi–1
Swi Initial water saturation
Vf Initial pore volume, bbl
cf Formation isothermal compressibility, psi–1
Terry, Ronald E., J. Brandon. Rogers, and B. C. Craft. Applied Petroleum Reservoir Engineering. Third ed. Massachusetts: Prentice Hall, 2014. Print.