Fig. $4\mathrm{.}22-$Discretized $1$D reservoir in exercise $4.$ is$.$

$4\mathrm{.}13$ Consider the incompressible$-$fluid$-$flow problem in the $1$D po$-$

rous body shown in Fig. $4\mathrm{.}22($viscosity of the fluid is $2\mathrm{.}0$ cp $).$

If the well in Block $2$ is produced at a steady flow rate of $450$

STB$/$D and this rate creates a pressure distribution of $p_1=2,400$

psia, $p_2=800a,$ and $p_3=800a,$ what is the permeability of

this linear, homogeneous system?

What kind of boundary condition would you assign to the ex$-$

treme left end of the system? Quantify your answer.

If all the length dimensions of the Blocks $1,2,$ and $3$ are

doubled, what would the flow rate into the well be if the same pres$-$

sure distribution is assigned to the new system?

Assume that the viscosity of the fluid of Part $1$ is $4$ cp and the

wellblock pressure is maintained at $800$ psia. What would the well

flow rate and the pressures in Blocks $1$ and $3$ be if the extreme ends

of the system represent no$-$flow boundaries?