Oil and Gas Reservoir Simulation in Matlab with Gas injection sensitivity analysis

The description of the project is already given in the updated syllabus. Be sure to include the effect of gravity and capillary in your simulation code. The description below will guide you in developing and testing your simulator.

In this phase, you are required to document, test and critique all the work you have done in developing your three-dimensional, two-phase black-oil simulator. It is suggested that you provide the following in your report.

1. Describe in details, the equations you implemented in your simulator. These should be an update of the equations you derived in Homework 6. Explain and describe the equations you computed analytically, mainly by differentiation, and the part of the work computed numerically by the computer. Include equations for wells in the reservoir. Give a general description of the various well constraints used in reservoir simulation. Then describe the specific well constraints used in your simulator and how you compute the well rate or well pressure for that constraint.

2. Describe the structure and performance of your programs. You may use flow charts, pseudo codes or lists to describe the structure of your program. Highlight what you did to save computer memory and what you did to increase the computational speed of the algorithm. What trade-offs did you make between reducing memory consumption and increasing computational speed. Document the type and name of the solver that you use. Is it a direct solver or an iterative solver? What informed your choice of this solver? Are there situations in which any other solver may be more suitable for the simulation code?

3. Use the data given for this project to test run your simulator. Also perform sensitivity studies on some input parameters. You may compare your results with those obtained from Eclipse Reservoir Simulator. Document all observations using clear plots, maps, etc. Discuss the results obtained and draw appropriate conclusions from the results. Also document the time taken to run each simulation case on your computer. In this case, you need to give a description of the configuration of your processor, RAM, processor speed and any other components that affect the speed of computation.

Test Cases:

Case 1: Gasflood in a heterogeneous isotropic reservoir

Use the heterogeneous permeability field provided to test your codes. The file name is k50x50.txt. Assume that the reservoir is isotropic.

Case 2: Gasflood in a heterogeneous anisotropic reservoir

Use the heterogeneous permeability field provided to test your codes. The file name is k50x50.txt. Here the reservoir is anisotropic such that permeability in the y-direction is one-third of the value in the x-direction and that in the z-direction is one-sixth of the value in the x-direction.

Sensitivity Studies

You should study the effect of different well configurations on pressure response in the wells, GOR from producers, and cumulative oil recovery in the well/reservoir. You may also study the effect of BHP constraints on the performance of the reservoir and wells. You may study how different relative permeability functions affect the pressure and GOR at the wells. In this regard, you are advised to create function files for the fluid properties to allow simple modifications. E.g. you can create one function that computes and its derivatives with respect to the primary unknowns. Your main file will call this function file anytime you need these values.

You may also study how the discretizations in space and time affect the convergence of the Newton-Raphson iterations in each time step.

Reservoir Description

Parameter Value

Lx 20000 ft

Ly 25000 ft

Lz 250 ft

Initial porosity 0.25

Initial pressure 6000 psi

Simulation Parameters

Minimum BHP in the producer: 1200 psi

Maximum BHP in the injector: 8700 psi

Simulation time: 3 years.

Please use the attached well location and fluid property files.

Evner: Coding, Matlab and Mathematica, Petroleum Ingeniørarbejde, Programming

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