1. (30 pts) The drawdown pressure at some time t1 is described by the following expression, where r is radiating from the wellbore, and Z is from the bottom of the formation. p(r,z) = (1 z)(100 r) What is the average pressure of this reservoir, if the reselvoir is bounded by z = [0,1] and r = [0,100]? Note that this is an injection well. (30 points) So far in class, we have derived the expression for pressure based on single-phase ow. However, single-phase ow is rarely the case in reality. Using a similar logic, develop expressions, similar to the diffusivity equation derived in class, that capture the effect of oil and water both owing in the reselvoir. You may assume that densities of the uids remain constant. Recall that Darcy's law states: kwA kDA qw : VP1 Clo : \"w #0 You do not need to solve the equations, only set them up, with the corresponding initial and boundary conditions. Hint: the total ow rate qt is the sum of the water ow rate and the oil ow rate, i.e., qt 2 qo + qw. VP