Problem $1$: Code a reservoir simulator $($using Matlab$)$ to calculate the pressure behaviors for the single$-$phase

flow in $1$D radial coordinate with an implicit formula, applying the boundary

conditions of $\frac{\text{d}\text{e}\text{l}\text{p}}{\text{d}\text{e}\text{l}\text{r}}=0$@$r=r_e$ and $q=\frac{2rkh}{}\frac{\text{d}\text{e}\text{l}\text{p}}{\text{d}\text{e}\text{l}\text{r}}$@$r=r_w.$

Example Problem $1($Pressure Drawdown$)$

$q=135ST\frac{B}{D}$

$B_o=1\mathrm{.}02$

$r_w=0\mathrm{.}5ft$

$k=90mD$

$h=47ft$

$=0\mathrm{.}17$

$=13\mathrm{.}2cP$

$c_t=2\mathrm{.}0{10}^{-5}\frac{1}{}$

$p_i=3265g$

$A=40$acres

Estimate $p_{wf}$ after $15$ days and compare this estimate with analytical solution.

$($The problem is from Example $2\mathrm{.}1($p$.6)$ "Advances in Well Test Analysis" R$.$C$.$ Earlougher, Jr$.)$

Problem $2$: Using the reservoir simulator coded above $,($in Matlab$)$ simulate the bottomhole $($using Matlab$)$ flowing pressure

performances during the well tests shown on the next page and compare the

simulation results with analytical solutions.

Note that the analytical solution in the case of the infinitely acting reservoir is

approximated by $p_{wf}(t)=p_i-\frac{162\mathrm{.}6qB}{kh}(lo{g}_{10}(\frac{kt}{c_t{r}_w^2})-3\mathrm{.}23)$ in the field unit.

Example Problem $2($Two$-$Rate Flow Test$)$

$q_1=107ST\frac{B}{D}$ for $3$ hours

$q_2=46ST\frac{B}{D}$ for $22$ hours

$B_o=1\mathrm{.}5$

$r_w=0\mathrm{.}2ft$

$k=3\mathrm{.}0mD$

$h=59ft$

$=0\mathrm{.}06$

$=0\mathrm{.}6cP$

$c_t=9\mathrm{.}32{10}^{-5}\frac{1}{}$

$p_i=3548g$

Estimate $p_{wf}$ for $25$ hours and compare these simulated results with analytical

solution.

$($the problem is from Appendix E $()$p$.147)$ "Pressure Build up and Flow Test in Wells" Matthews & Russell $)$