//Method Name: getTransmissibility
//Objectives: calculating the transmissibility between two blocks
//Inputs: two variables of type "GridBlock", the value of the geometric factor and a variable of type "Phase"
public static double getTransmissibility(GridBlock block_1, GridBlock block_2, double geometric_factor, Phase phase)
{
GridBlock upstream_block;
double viscosity, FVF, Kr;
//Check for Inactive blocks
if (block_1.type == GridBlock.Type.Inactive || block_2.type == GridBlock.Type.Inactive)
{
return(0);
}
//Determine the upstream block
if (block_1.pressure >= block_2.pressure)
{
upstream_block = block_1;
}
else
{
upstream_block = block_2;
}
//Assign the values of viscosity, FVF and Kr according to the appropriate phase
if (phase == Phase.Oil)
{
viscosity = 2 / (1 / block_1.oil_viscosity + 1 / block_2.oil_viscosity);
FVF = 2 / (1 / block_1.Bo + 1 / block_2.Bo);
Kr = upstream_block.Kro;
}
else if (phase == Phase.Gas)
{
viscosity = 2 / (1 / block_1.gas_viscosity + 1 / block_2.gas_viscosity);
FVF = 2 / (1 / block_1.Bg + 1 / block_2.Bg);
Kr = upstream_block.Krg;
}
else
{
viscosity = 2 / (1 / block_1.water_viscosity + 1 / block_2.water_viscosity);
FVF = 2 / (1 / block_1.Bw + 1 / block_2.Bw);
//viscosity = upstream_block.water_viscosity;
//FVF = upstream_block.Bw;
Kr = upstream_block.Krw;
}
double T = geometric_factor * Kr / (viscosity * FVF);
return(T);
}
//Method Name: assignBlockOrdering_ActiveOnly
//Objectives: this method is used for each "active block only" in the grid to assign its numbering and the numbering of neighbouring blocks
//Inputs: a variable of type "GridBlock" that contains all the data of the block, a general counter of the loop, block counter, array of block coordinates, array of grid dimensions and an array of the natural ordering of the in-active blocks
//Ouputs: N/A. This is an internal method that calculates the numbering and assign it to the variable "block" that is passed to this method
private static void assignBlockOrdering_ActiveOnly(GridBlock block, int counter, int block_counter, int[] block_coordinates, int[] grid_diemnsions, int[] inactive_blocks)
{
int i, j, k;
i = block_coordinates[0]; j = block_coordinates[1]; k = block_coordinates[2];
int x, y, z;
x = grid_diemnsions[0]; y = grid_diemnsions[1]; z = grid_diemnsions[2];
block.counter = block_counter;
block.east_counter = getNextBlockCounter(Direction.East, block_counter, counter, inactive_blocks, grid_diemnsions, block_coordinates);
block.west_counter = getNextBlockCounter(Direction.West, block_counter, counter, inactive_blocks, grid_diemnsions, block_coordinates);
block.north_counter = getNextBlockCounter(Direction.North, block_counter, counter, inactive_blocks, grid_diemnsions, block_coordinates);
block.south_counter = getNextBlockCounter(Direction.South, block_counter, counter, inactive_blocks, grid_diemnsions, block_coordinates);
block.top_counter = getNextBlockCounter(Direction.Top, block_counter, counter, inactive_blocks, grid_diemnsions, block_coordinates);
block.bottom_counter = getNextBlockCounter(Direction.Bottom, block_counter, counter, inactive_blocks, grid_diemnsions, block_coordinates);
}
//Method Name: assignBlockOrdering_Natural
//Objectives: this method is used for each block "both active and in-active" in the grid to assign its numbering and the numbering of neighbouring blocks
//Inputs: a variable of type "GridBlock" that contains all the data of the block, a general counter of the loop, array of block coordinates, array of grid dimensions and an array of the natural ordering of the in-active blocks
//Ouputs: N/A. This is an internal method that calculates the numbering and assign it to the variable "block" that is passed to this method
private static void assignBlockOrdering_Natural(GridBlock block, int counter, int[] block_dimensions, int[] grid_diemnsions, int[] inactive_blocks)
{
int i, j, k;
i = block_dimensions[0]; j = block_dimensions[1]; k = block_dimensions[2];
int x, y, z;
x = grid_diemnsions[0]; y = grid_diemnsions[1]; z = grid_diemnsions[2];
block.counter = counter;
block.east_counter = i < (x - 1) ? counter + 1 : -1;
block.west_counter = i > 0 ? counter - 1 : -1;
block.north_counter = j < (y - 1) ? counter + x : -1;
block.south_counter = j > 0 ? counter - x : -1;
block.top_counter = k > 0 ? (k - 1) : -1;
block.bottom_counter = k < (z - 1) ? (k + 1) : -1;
}
//Homogeneous grid
public static double getGeometricFactor(GridBlock block, GridType type, Direction direction)
{
double area, length, permeability, G;
//Rectangular grid
if (type == GridType.Rectangular)
{
if (direction == Direction.x)
{
area = block.delta_y * block.h;
length = block.delta_x;
permeability = block.Kx;
}
else if (direction == Direction.y)
{
area = block.delta_x * block.h;
length = block.delta_y;
permeability = block.Ky;
}
else
{
area = block.delta_x * block.delta_y;
length = block.h;
permeability = block.Kz;
}
G = Bc * permeability * area / length;
return(G);
}
//Cylindrical grid
else
{
//To-Do: implement this method
return(0);
}
}
//Method Name: getGeometricFactor
//Objectives: calculate the geometric factor of the well if it is perfectly centred within a grid block
//Inputs: a variable of type "GridBlock"
//Outputs: the value of the geometric factor of the well
public static double getGeometricFactor(GridBlock block)
{
double r_equivalent;
double Kh;
if (block.delta_x == block.delta_y && block.Kx == block.Ky)
{
r_equivalent = 0.198 * block.delta_x;
}
else if (block.delta_x == block.delta_y)
{
r_equivalent = 0.14 * Math.Sqrt(Math.Pow(block.delta_x, 2) + Math.Pow(block.delta_y, 2));
}
else
{
r_equivalent = 0.28 * Math.Sqrt(Math.Sqrt(block.Ky / block.Kx) * Math.Pow(block.delta_x, 2) + Math.Sqrt(block.Kx / block.Ky) * Math.Pow(block.delta_y, 2)) / (Math.Pow((block.Ky / block.Kx), 0.25) + Math.Pow((block.Kx / block.Ky), 0.25));
}
Kh = Math.Sqrt(block.Kx * block.Ky);
double G = 2 * Math.PI * Bc * Kh * block.h / (Math.Log(r_equivalent / (block.rw / 12)) + block.skin);
return(G);
}
//Method Name: assignGridOrdering
//Objectives: gives each block in the grid a number according to the numbering scheme used
//Inputs: an array of the (x, y, z) grid dimensions and an array of the Inactive blocks numberings
//Ouputs: an array of GridBlocks that are given numbers according to the numbering scheme used
public static GridBlock[] assignGridOrdering(int[] grid_dimensions, int[] inactive_blocks, NumberingScheme scheme)
{
//variables to store the grid dimensions
int x, y, z;
//store the grid dimensions
x = grid_dimensions[0]; y = grid_dimensions[1]; z = grid_dimensions[2];
//an array to store a block's i, j and k coordinates within the grid according to the engineering notation
int[] block_coordinates = new int[3];
//A variable to store block's data
GridBlock block;
//A variable representing the grid array of blocks
GridBlock[] grid = new GridBlock[0];
if (scheme == NumberingScheme.All)
{
//Grid array size is equal to all the block "including in-active blocks"
grid = new GridBlock[x * y * z];
}
else if (scheme == NumberingScheme.Active_Only)
{
//Grid array size is equal to the number of active-only blocks
grid = new GridBlock[x * y * z - inactive_blocks.Length];
}
//A general loop counter
int counter = 0;
//A block counter
//This variable is used only with the "assignBlockOrdering_ActiveOnly" method to keep track of the number of active blocks added to the grid
int block_counter = 0;
//A loop to iterate over all the blocks in the grid according to the engineering notation
for (int k = 0; k < z; k++)
{
for (int j = 0; j < y; j++)
{
for (int i = 0; i < x; i++)
{
block = new GridBlock();
//assign the values of the block coordinates
block.x = i; block.y = j; block.z = k;
//set block type "either Inactive or normal"
if (inactive_blocks.Contains(counter))
{
block.type = GridBlock.Type.Inactive;
}
//set the block coordinates array that will be passed to other methods
block_coordinates[0] = i; block_coordinates[1] = j; block_coordinates[2] = k;
//###########################################################################################
if (scheme == NumberingScheme.All)
{
//Natural ordering for the entire grid "both active and in-active blocks"
RectangularBlockNumbering.assignBlockOrdering_Natural(block, counter, block_coordinates, grid_dimensions, inactive_blocks);
}
else if (scheme == NumberingScheme.Active_Only)
{
//Natural ordering for the grid "active blocks only"
if (block.type == GridBlock.Type.Inactive)
{
//increment the general loop counter and skip this block
counter += 1;
continue;
}
RectangularBlockNumbering.assignBlockOrdering_ActiveOnly(block, counter, block_counter, block_coordinates, grid_dimensions, inactive_blocks);
}
//###########################################################################################
//increment counter at the end of the loop
counter += 1;
//this statement adds the block to the grid array
grid[block_counter] = block;
//only increment block_counter when a block is added to the grid to keep track of how many blocks have been added
block_counter += 1;
}
}
}
return(grid);
}
public static double calculate_BHP(GridBlock block)
{
return(block.pressure - (block.well_flow_rate / block.well_transmissibility));
}