Material Balance Equation

Expansion, Production, and Influx Terms The material balance equation is an expression of the conservation of the mass of oil, gas, and water in the reservoir. The application of the conservation principle to the gas phase, for example, requires that the mass of gas in the reservoir at any time be equal to the mass of gas initially in place minus the mass of gas that has been produced.

Note: only the expansion of rock and its associated water in oil zone is considered.

where:
Np = cumulative oil production, STB
Bt = two-phase formation-volume factor, RB/STB
Rp = cumulative produced GOR, SCF/STB
Rsi = initial gas in solution, SCF/STB
Bg = gas formation-volume factor, RB/SCF
Bw = water formation-volume factor, RB/STB
Wp = total water produced in STB
N = initial oil in place, STB
Bti = initial two-phase formation-volume factor
m = ratio of gas cap pore volume to oil leg pore volume
Bgi = initial gas formation-volume factor
Swi = initial water saturation, fraction of pore volume
Sw = water saturation, fraction of pore volume
cr = rock compressibility, vol/vol/psi
cw = water compressibility, vol/vol/psi
Dp = pi - Pr(t)
pi= initial reservoir pressure, Psi
PR(t)= average reservoir pressure at the time of interest t, psi
We = cumulative water influx, RB

The two terms on the left-hand side indicate the total fluids production in reservoir volumes. The first three terms on the right-hand side are, respectively, the total expansion of the hydrocarbon in oil zone, the total expansion of the gas in gas cap, and the total expansion of the rock and its associated water. The last term is the water influx. Thus, a statement of the MBE which is simple and easy to remember is: total fluids produced in reservoir volumes equals total expansion of the hydrocarbon in the oil zone, the gas in the gas cap, and the rock and its associated water, plus the water influx in oil zone.

Compressibility of Rock and Water Terms
Normally one thinks of the water and rock as being incompressible. In fact, they are compressible. The rock compressibility is a function of its porosity and consolidation.

It can be as low as 3 l0-6 vol/vol/psi and higher than 20 l0-6 (Coats 1980). The water compressibility does not vary widely like the rock compressibility. It normally ranges between 3 and 6 l0-6 vol/vol/psi.
To illustrate the meaning of compressibility and the unit vol/ vol/Psi consider two cubic feet of water that are under pressure. Assume the Pressure is decreased by 10 Psi and the water compressibility is 3 10-6 per psi. Since the pressure decreases by 10 psi, the two cubic feet of water expand by 2 x 10 3 10-6 = 6 l0-5. The volume of water is now (2 + 6 10-5) cubic feet.

Advantages and Limitations of the MBE
The primary advantage of the material balance equation is that it provides a valuable insight into the behavior of the reservoir, and the contribution of the various drive mechanisms to recovery. In the case of reservoirs with reasonable reservoir-wide fluid communication, the MBE provides a method of calculating the initial oil or gas in place, as well as the expected aquifer effects, by using actual production and pressure data. The MBE is the only method that employs the dynamic response of the reservoir to production as a means of estimating the volume of original fluid. What the MBE calculates is the fluid volume in the reservoir that is affected by production.

The dynamic response of the reservoir fluid to production is manifested in the pressure change. Thus, the initial fluid in place calculated by the MBE is indicative of the fluid volume in communication with the wells. In contrast, the volumetric method of estimating the fluid in Place is a static method. It does not differentiate between connected and isolated areas. For this reason, the fluid in place calculated by the MBE cannot be larger than that calculated volumetrically, assuming an accurate volumetric estimate.

The main disadvantage of the MBE is that it is based on a tank model (i.e., a zero-dimensional model). Therefore, it deals with average values of rock and fluid properties for the whole reservoir. As a result, it cannot be used to calculate fluid or pressure distributions, nor can it be used to identify new well locations or the effect of well locations and production rates on recovery. The MBE cannot be used to predict water or gas channeling, and cannot account for the effect of heterogeneities on the behavior of the reservoir. When any of these factors is significant, reservoir simulation is required to predict precisely the behavior of the reservoir.