We were introduced to the concept of material balance earlier in this lesson when we discussed the derivation of the diffusivity equation. As we discussed in Lesson 2, an undersaturated oil reservoir is defined as a reservoir in which the initial pressure is greater that the bubble-point pressure of the crude oil. This results in a single, liquid hydrocarbon phase in the reservoir. As we discussed, there will be some water saturation in the reservoir also.

In this section, we will discuss the material balance method for * Volumetric Reservoirs* (reservoirs where the pore volume occupied by hydrocarbons remains constant with time – and pressure depletion). The Material Balance Method is applicable for both the reservoir in its entirety and to individual wells. From the volumetric method for estimating in-place fluids, we know that:

I have simplified this version of the equation (from **Equation 4.04a**) by assuming that the bulk volume in bbls, ${V}_{b}$, is based on the net rock volume (that is, the net-to-gross ratio and the unit conversion constant, 5.615 ft^{3}/bbl, have already been applied); the initial gas saturation is zero (because the reservoir is above the bubble-point pressure); and the water saturation is at its minimum value of $\overline{{S}_{wir}}$.

In the Volumetric Method for STOOIP determination discussed earlier, all of the pressure dependent properties are evaluated at the initial reservoir pressure. **Equation 4.56** is valid for any pressure conditions. If we evaluate **Equation 4.56** twice, once at the initial conditions and once at some arbitrary, future condition ($N\text{'}$), then we would have:

and

Subtracting these two equations results:

Now, $\Delta N$ in this equation is the change in the oil-in-place (STB) in the reservoir from the initial condition to the future condition. Now, from material balance (mass is neither created nor destroyed), this change in mass is due to the expansion of the oil and must have been the mass of the oil produced from the wells during the time period, ${N}_{p}$:

To make **Equation 4.58b** more convenient, we can substitute **Equation 4.57a** back into the equation:

or after multiplying both sides by the oil formation volume factor, $\overline{{B}_{o}}$, and rearranging:

Where:

- $N$ is the stock tank oil originally oil-in-place, STB
- $N\text{'}$ is the oil-in-place at a future date, STB
- ${V}_{b}$ is the net rock volume, bbl
- $\overline{\varphi}$ is the porosity averaged over the reservoir, fraction
- $\overline{{S}_{wir}}$ is the irreducible water saturation averaged over the reservoir, fraction
- $\overline{{B}_{oi}}$ is the initial oil formation volume factor averaged over the reservoir, bbl/STB
- $\overline{{B}_{o}}$ is the oil formation volume at a future time averaged over the reservoir, bbl/STB
- $\Delta N$ is the change in oil-in-place, STB
- ${N}_{p}$ is the oil production, STB

**Equation 4.58d** is the * Material Balance Equation* for volumetric reservoirs containing an undersaturated crude oil which remain above the bubble-point pressure. In this equation, the left-hand side represents the reservoir barrels removed from the reservoir through the production wells, while the right-hand side represents the expansion of oil in the reservoir. This equality is the general principle of material balance. We can use this equation in two ways:

- as a method to determine the STOOIP of the reservoir
- make future reservoir forecasts