Consider a well in a large, homogenous and isotropic reservoir. The well produced 100STB/D for 3 days, and was shut in for the next 1 day, produced 150 STB/D for the next 2 days, produced 50 STB/D for the next 1 day, and produced 200 STB/D for next 2 days .

a) Calculate and plot bottomhole pressure versus time in the reservoir for 9 days.

b) Calculate and plot pressure profile (pressure vs radius) in the reservoir at the end of 9 days.

B=1 RB/STB

μ_o=1 cP

h=10 ft

k=25 mD

φ=0.2

P_i=3000 psig

c_t = 10*10^-6 psi^-1

S=0

r_w = 1 ft.

Note 1: Please use field units to solve the pressure equations:

P(psia), q (STB/Day), k (mD), h (ft.), φ (fraction), μ (cP), c_t (psi^-1), r (ft.), t (hours), B_o (RB/STB).
 

P(r, t) = P - 141.2 q kh ( - 1/1 Bi (- 2 948 x ucer kt