PTE 508, Spring 2022 Project Two
Development of a 2-D, 2-Phase Simulator and Primary and Secondary Recovery Studies
离散作业代写 Rules to Complete the Project 1.Group study and discussions between students are allowed but each student must Discretize the PDE by himself/herself;
Rules to Complete the Project
1.Group study and discussions between students are allowed but each student must
- Discretize the PDE by himself/herself;
- Write his/her own computer codes to carry out all the calculations;
- Plot his/her own graphs;
- Write his/her own report.
2.A report is required for this project. Students must write the report following these guidelines:
- The report must be typed and printed on single-sided, letter-sized white paper.
- If one cannot type equations or symbols, use a black/blue pen to writeequations/symbols in the right places “neatly” and “cleanly.” Writings, marks and notes with pencils are not acceptable anywhere in the report.
- Bulk of the report must be printed in black; occasional color texts for highlights and emphasis are allowed. Also, use italic text sparsely.
- Each graph must have a title (caption) and labels for the horizontal and vertical axes.
- If several curves are plotted in the same graph, each curve must be labeled clearly. A curve must use a unique line style (color, thickness, solid, dashed, etc.) so the curve can be identified.
3.The report must be turned in on or before the due date, no exception.
Reservoir Schematics and Description 离散作业代写
A portion of a single layer oil reservoir is approximated by a square with side length Lx = Ly = 1100 ft, and the layer thickness is △z = 100ft ft. Porosity ∅ is pressure-dependent, and ∅= 0.20 measured at 1000 psia. Formation compressibility c∅ = 1.25 × 10−5 psi-1 is assumed to be constant. The reservoir is isotropic and homogeneous so permeability kx = ky = 10 mD for the whole reservoir. The reservoir is sealed, and has no flow at the four boundaries.
The reservoir initially contains oil and water only, so gas saturation Sg = 0. Oil saturation So = 0.70, and water saturation Sw = 0.30. Oil has a bubble point pressure pb = 1000 psia, and a constant viscosity μo = 5 cp. Water viscosity is also assumed constant, μw= 1 cp. Oil and water formation volume factors Bo and Bw are pressure-dependent, and their compressibilities are assumed constant above the oil bubble point: co= 1.75 × 10−5 psi-1 , and cw = 3.0 × 10−6 psi-1 . Bo = 1.25 RB/STB, and rw = 1.02 RB/STB, are measured at 1000 psia.
Five wells, A through E, are drilled in the reservoir. The well locations are given in a schematic diagram shown on the next page. The wells can serve as either producers or water injectors as described later. All fives wells have same data: wellbore radius Bw = 0.25 ft, skin factor S = 0 .
The well coordinates are: A=(550, 550), B=(50, 50), C=(1050, 50), D=(1050, 1050) E=(50, 1050). If the reservoir is divided into 11×11 equal size blocks, the five wells are located at the centers of 5 simulation cells, as shown above.
PDEs, Initial and Boundary Conditions, PVT and Relative Permeability Relations 离散作业代写
Calculate and plot Kro Sw and vs. in the same graph. (5 points)
Calculate and plot Bo, Bw , and ∅ vs. P=(1000, 3000) ; zoom in if needed. (5 points)
Use 2-D numerical simulation to study the reservoir.
Use IMPES method to solve the PDEs along with PVT and relative permeability curves.
Divide the formation into 11×11 equal-interval blocks to have 121 simulation cells. All five wells must be located at the centers of five simulation cells.
Use block-centered grid system to discretize the combined PDE derived in class: (20points)
i. Write the general discretized finite difference equations.
ii. Incorporate the no-flow boundary conditions at the four boundaries.
iii. Treat the production term implicitly and include the five wells in the discretized finite difference equations.
iv. Write the finite-difference equation for Cell 1, where Well-B is located, and for Cell 61 where Well-A is located.
v. Use Peaceman’s method to calculate productivity index Jw–oil & Jw -water for each well.
Write computer codes to program the PVT, Krw, Kro curves and the discretized finite-difference equations using MATLAB or any programming language (100 points)
- Use MATLAB sparse matrix to solve the finite difference equations for pressure
- Program and use the Gauss-Seidel iterative method if you don’t use MATLAB.
Perform “leakproof” tests: Set well rate to zero for all five wells by setting Jwoil = Jwwater = 0, and make a 100 day long simulation with Δt = 10 days. Debug your program until you pass the following tests: (20 points)
i. Pressure-”leakproof”: Pressure everywhere must remain unchanged (equal to the initial pressure).
ii. Saturation-”leakproof”: Oil saturation must remain unchanged.
Perform a “symmetric” test: (20 points)
i. Set well rate to 0 for wells B, C & D by setting Jwoil = Jwwater = 0;
ii. Set pwf= 1000 psia for well A;
iii. Make a 100-day long simulation with Δt = 10 days. The pressure distribution must be symmetric with respect to the center point ( x = 550, y = 550 ft).
iv. Plot p ( x, y, t =0) , p( x, y, 50) and p( x, y, 100) surface plots, and show the corresponding data in 3 tables.
Check material balance. Make a 100 day long simulation with Δt =10 days, and set all five wells as producers, pwf = 1000 psia . For each time step (20 points)
- Calculate cumulative production of the reservoir Vo, produced.
- Calculate oil in place, OIP
- (Vo , prod + OIP) == OIIP, error must be within 0.1% .
Conduct the following studies:
i. Primary Recovery Study, production without water injection:
1.Calculate Oil Initial in Place (OIIP) (5 points)
2.Make the five wells producers by setting flowing pressure pwf= 1000 psia.
3.Produce the reservoir with five wells until production rates become less than 10 STB/D for all wells.
1.Plot oil production rate vs. time of the five wells in the same graph. (5 points)
4.Calculate the cumulative production of the reservoir and calculate the recovery fraction: (10 points)
1.Plot cumulative production vs. time
2.Plot recovery fraction vs. time
5.Plot reservoir pressure distribution (surface plot) for t =0, 100, 200 , 300, 400 and 500 days , or end of production. (10 points)
ii. Secondary Recovery Study, production with water injection: (40 points)
- Repeat Steps 11-i-1 through 11-i-4
- Convert well-A into a water injection well by setting their flowing pressure Pwf = 3000 psia. Keep wells B-E as producers with pwf = 1000 psia.
- Run simulation until water cut in any of the four producers (B-E) is greater than 95% or simulation time=10,000 days, whichever comes first.
- Plot the oil saturation and pressure distributions when Well-A is converted into an injector, and at the end of the simulation. Also show the numerical value of oil saturation and So pressure p in tables.
- Calculate and plot the cumulative production from Wells A-E, and the reservoir recovery.
- Find water-breakthrough time when water cut in one of the four producers (B-E) is greater than 5%, and plot So and pressure distributions.
Write the final report to include the following items:
- PDEs with boundary conditions, PVT and Kro , Krw relations. (5 points)
- Discretization of the PDEs with boundary conditions (general form). (5 points)
- All the graphs and tables.
- Comparison and discussion of the Primary and Secondary Recovery results. (10 points)
- Observations, thoughts and suggestions about this project.
- Save the report as a single pdf file and use this format to name the file: PTE508-Spring-2022-Project2-Family-Name-Given-Name.pdf. Do not zip the file. Upload the pdf file to D2L dropbox before the due date and time. (10 points)
- You may zip all the MATLAB codes as a single file and upload it to D2L. (10 points)