$($Points: $12+18+10=40)-$ A gas reservoir containing $106$ MMMSCF gas initially in place has an initial

pressure of $3,500$ at reservoir temperature of $248F.$ The reservoir formation contains irreducible

water saturation. When the reservoir pressure declined down to $500$ the gas field produced $85\mathrm{.}52$

MMMSCF of gas, $0\mathrm{.}1$ MMSTB of condensate oil and $0\mathrm{.}1$ MMSTB of condensate water. The surface

produced condensed oil has $0\mathrm{.}75$ specific gravity and $177l\frac{b}{l}\frac{?}{lb}-$mole molecular weight. Following gas

production, $C{O}_2$ is scheduled to be sequestered in the depleted gas field.

a$.$ Estimate the volume of $($i$)$ cumulative equivalent gas produced, $G_{pe},$ at field's abandonment

pressure of $500,$ and $($ii$)$ cumulative gas produced at average reservoir pressure of $2,500$

psi assuming negligible condensate oil and water production for the latter case.

b$.$ Show the first step $($iteration$)$ of your calculations to estimate the volume of injected $C{O}_2$

$($MMMSCF$)$ into formation when the average reservoir pressure reaches $2,500.$ Describe

how you will proceed in the remaining steps to determine the injected $C{O}_2$ volume at $2,500$

psi. $($Note: Although calculations must be shown, no final answer is expected for this question.$)$

c$.$ Using only the equations provided below, estimate the theoretical maximum $C{O}_2$ volume

$($MMMSCF$)$ that can be stored in pore space when the reservoir pressure reaches $3,500.$

The gas and $C{O}_{2}z-$factors as a function of pressure and at reservoir temperature are given below:

Material balance equations:

$\frac{(\frac{?}{\text{b}\text{a}\text{r}}(p))}{z}=-\frac{1}{G}\frac{p_i}{z_i}{G}_{pe}+\frac{p_i}{z_i}$

Gas production cycle

$\frac{(\frac{?}{\text{b}\text{a}\text{r}}(p))}{z_m}=-\frac{1}{G}\frac{p_i}{z_i}(G_{pe}-G_{C{O}_2\text{i}\text{n}\text{j}})+\frac{p_i}{z_i},C{O}_2$ injection cycle

Cumulative gas equivalent: $,G_{pe}=G_p+133,000\frac{{}_o}{M_{wo}}{N}_p+7,390W_{pv}$

$G_{pe}(SCF)=$ cumulative equivalent gas production; $G_p(SCF)=$ cumulative gas production

$N_p(STB)=$ cumulative oil production; $W_{pv}(STB)=$ cumulative water $($vapor$)$ production

$M_{wo}(l\frac{b_m}{l}b\}$ mole