1. Numerical Solution (20\%) A long and narrow reservoir is approximated by a rectangular prism. A single well is drilled in the reservoir as a producer. The dimensions and well location are given. The reservoir has an open boundary at the left (x=0) and closed boundary at the right side (x=L). The fluid flow has reached steady state, and is defined by the following ODE and boundary conditions, and the well flowing pressure. Other parameters are: wellbore radius rw=0.25ft, fluid viscosity =1.0cp, formation volume factor B=1.25RB/STB, permeability k=50mD. a. Divide the reservoir into four simulation cells or blocks. Use x22p887.3kyzqpB(x2500)=0 the block-centered grid system for the four cells and Discretize p(x)x=0=2000 the ODE. Write 4 equations for i=1,2,3,4. b. Solve the equations for pressure at each pressure point c. Plot pressure vs. distance xpx=4000=0pwf=1000 d. Calculate the well flow rate q in STB/D