FEM-Reservoir-Drainage-3D

Compares analytical/numerical results for the drainage of a single well. Modify the following variables to your liking.

It is written in Matlab, is self-contained, and no external dependencys.

Assumptions

• Incompressible Fluid
• Homogeneous Reservoir
• Neumann boundary (Reservoir side)
• Dirichlet boundary (Well side)

Modify Parameters

• Reservoir Depth, Area, and Volume (ft ; ft^2 ; ft^3)
• Reservoir Pressure (psi)
• Time and/or Iterations (days)
• Porosity (phi)
• Permeability (k)
• Compressibility (ct)
• Volume Flow (Q)
• Damage (hk)

Installation

Download package:

git clone https://github.com/FracThePermian/Reservoir-Simulation-Part-B

Navigate to folder from Matlab (~/Reservoir-Simulation-Part-B/) and run the Project_1_Main.m script.

Method and Materials

• The Finite Element Method (FEM) is an essential numerical tool for solving boundary value problems of PDE's.

Snippet of module that generates sparsity matrix

for i = 1:N  		                               %Generate sparsity matrix
    if i+NX <= N 
        T_diag = T_frac(i,i+NX,Ay,mu,Bw,dy);
        T(i,i+NX) = T(i,i+NX)-T_diag;
        T(i+NX,i) = T(i+NX,i)-T_diag;
    end
    
                                              % This is for diagonals toward the inside of sparsity
    if (mod(i,NX) ~= 0) && (i+1 <= N)  
        T_diag = T_frac(i,i+1,Ax,mu,Bw,dx);
        T(i,i+1) = T(i,i+1)-T_diag;
        T(i+1,i) = T(i+1,i)-T_diag;
    end
    T(i,i) = abs(sum(T(i,:)));                % Sum up every row on every iteration
    if BC(i) ~= 0                             % if and only if the boundary condition exists
        T(i,i) = T(i,i)+BC(i)*2*T_frac(i,i,Ax,mu,Bw,dx);
    end

Results

References

• Hughes, Thomas J. R.The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1987. Print.
• Kolukula, Siva. MatlabMesh Postprocessing. Net.

License

MIT