Question

For a hydrocarbon reservoir, the following parameters are used in the general material balance equation (MBE):

\[ \begin{aligned} N & = \text{Initial (original) oil in place, stb} \\ G & = \text{Initial volume of gas cap, scf} \\ m & = \text{Ratio of initial volume of gas cap to volume of oil initial in place, rb/rb} \\ S_{wi} & = \text{Initial water saturation} \\ S_{oi} & = \text{Initial oil saturation} \\ B_{oi} & = \text{Initial oil formation volume factor, rb/stb} \\ B_{gi} & = \text{Initial gas formation volume factor, rb/scf} \end{aligned} \]

The total pore volume (in rb) of the reservoir is:

• A. \(\dfrac{G B_{gi}(1+m)}{1-S_{oi}}\)
• B. \(\dfrac{N B_{oi}(1-m)}{1-S_{oi}}\)
• C. \(\dfrac{N B_{oi}(1+m)}{1-S_{wi}}\)
• D. \(\dfrac{G B_{gi}(1-m)}{1-S_{wi}}\)

Hint:

Always compute pore volume by summing hydrocarbon volumes (oil + gas) and then dividing by the hydrocarbon fraction \((1 - S_{wi})\). This ensures water-filled pores are correctly accounted for.

Answer 1

The Correct Option is C

Step 1: Volume of oil in place.
Initially, the reservoir contains \(N\) stock-tank barrels (stb) of oil. Converting this to reservoir barrels (rb): \[ V_o = N B_{oi} \] This is the reservoir volume occupied by the oil phase. 

Step 2: Volume of gas cap.
The gas cap volume is proportional to the oil volume, given by the gas–oil volume ratio \(m\). Therefore, \[ V_g = m V_o = m (N B_{oi}) \] 

Step 3: Hydrocarbon pore volume.
The hydrocarbon pore volume is the combined volume of oil and gas in the reservoir at initial conditions: \[ V_h = V_o + V_g = N B_{oi} + m N B_{oi} = N B_{oi}(1+m) \] 

Step 4: Incorporating water saturation.
The total pore space of the reservoir is occupied by both hydrocarbons and water. If the initial water saturation is \(S_{wi}\), the fraction of pore volume available for hydrocarbons is: \[ \text{Hydrocarbon fraction} = 1 - S_{wi} \] Therefore, \[ \text{Total pore volume } V_p = \frac{V_h}{1 - S_{wi}} \] Step 5: Final expression.
Substituting \(V_h = N B_{oi}(1+m)\): \[ V_p = \frac{N B_{oi}(1+m)}{1-S_{wi}} \] 

Final Answer: \[ \boxed{\dfrac{N B_{oi}(1+m)}{1-S_{wi}}} \]