Consider single$-$phase fluid flow in the $2$D horizontal reservoir as shown in the figure below. A well located in gridblock $7$ produces at a rate of $4000$ STB$/$D$.$ All gridblocks have $x=250ft,y=300ft,h=100ft,k_x=270md,$ and $k_y=220md.$ The FVF and viscosity of the flowing fluid are $1R\frac{B}{S}TB$ and $2\mathrm{.}0cp,$ respectively. The reservoir south boundary is maintained at $3000$ psia, the reservoir west boundary is sealed off to flow, the reservoir east boundary is kept at a constant pressure gradient of $0\mathrm{.}1\frac{}{f}t,$ and the reservoir loses fluid across its north boundary at a rate of $500$ STB$/$D$.$ Write the flow equations for gridblocks $1,4,9$ and $12,$ where each gridblock falls on two reservoir boundaries.