$(30$ points$)$ Consider a $10,000ft$ deep well that is to produce $500$ stb$/$d with gradient curves given in Figure $1.$ The natural GLR is $200$ scf$/$stb$,$ the average reservoir pressure is $3750$ psi, and the IPR for the well is

$q=0\mathrm{.}25((\frac{?}{\text{b}\text{a}\text{r}}(p))-p_{wf})$

Pressure drop across the gas lift valve is $100$ psi. If the gas is to be injected at $8,000ft$ :

a$.$ What is the GLR in the tubing above the injection point?

b$.$ What is $p_{\text{s}\text{u}\text{r}\text{f}\text{?}}?$

c$.$ What is $q_g?$

Suppose the maximum possible surface pressure was limited to $100$ psi less than the value calculated in part b$.$ In order to produce the same liquid rate with this lower gas pressure, assuming the pressure gradient in the tubing below the gas injection point is $0\mathrm{.}33\frac{}{f}t($use this number and not what you have calculated or determined above$)$:

d$.$ What is $H_{\text{i}\text{n}\text{j}}?$

e$.$ What is GLR in the tubing above the injection point?

f$.$ What is $p_{\text{i}\text{n}\text{j}}?$

g$.$ What is $q_g?$

Pressure $$

Figure $1$: Pressure gradient for Question $1$