Please help me out with this problem on task 2. thank you

 

PETE 2060 Fall 2016Project 2: Flow in a 1-D reservoir (Due on Monday 11/07/2016, 11:55pm)Consider slight compressible butconstant’fluid’propertyflow in undersaturated reservoir (i.e. pressureremains above bubble point) with no dip and wells represented as mass source/sink. Followinggoverning equation describes such flow in porous media:࠵±࠵!࠵±࠵±=࠵࠵±࠵࠵࠵!!࠵±࠵±+࠵Where the fluid density and rock porosity is described as:࠵=0.85 SG and࠵=0.15Define the total compressibility as࠵!=1.2࠵±²³´µ±¶µ(cf’ =’1 microsips andcR= 0.2 microsips) andassume that fluid viscosity is constant (= 3 cp) for your problem. All boundaries are no flow (i.e. settransmissibility coefficient to zero). Each grid block has the dimension of 100 ft X 100 ft (assume novariation in the third direction). Initial reservoir pressure MUST be hydrostatic with the first gridblockpressure set as the datum value of 3000 psia. Reference fluid density and rock porosity evaluated at3000 psia are 0.85 SG and 0.15.●: Producer Well -- Apply the average grid block pressure of 1500 psia in the grid block# 8 to model theproducer well. In other words, q can be set to zero in rest of the grid blocks.HINT: Convert into consistent units before you discretize the terms in governing equation. All unitconversions and definitions are available in any introductory textbook for petroleum engineering.P110 mD0.15P210 mD0.15P310 mD0.15P410 mD0.15P510 mD0.15P610 mD0.15P710 mD0.15P810 mD0.15●P910mD0.15P1010 mD0.15Task 1: Write a linear algebraic solver for N X N system for the gridblock pressures as unknowns.Task 2: Determine the transmissibility coefficients for your system and solve it. Present the results (i.e.pressure distribution in the reservoir) at three different time instances of 10, 30, and 90 days by solvingthe system of equations using time steps of 1, 2, and 3 days respectively.

Attachments:

• 1494303555-PETE 2060 Fall 2016 Project 2 - Simple 6 1.pdf