Question #$1$ On Velocity Potential: Marks $=10+5=15$

In a reservoir as depicted in the figure on the right, oil flows in the x$-$direction $($i$.$e$.,$ towards East$)$ with a uniform flow velocity $\frac{q_w}{A}=1.$ To trace the oil flow in reservoir, a non$-$reactive tracer has been introduced to the formation through a well located at $(-1,0)$ with a flow rate per unit thickness $\frac{q_3}{h}=6,$ where $h$ is the formation thickness. The tracer movement in the reservoir is being monitored by an observation well located in $N*E$ area of the reservoir at $(1\mathrm{.}5,1\mathrm{.}5).$

a$)$ Derive an equation for the velocity potential for the tracer,

b$)$ Draw the velocity potential profile for the flow domain of the tracer, and

c$)$ Comment on your results

$$servoir Layout scnemat$$