Effective wellbore radius is a measure of how much the wellbore affects the flow of fluid from the reservoir to the surface. It is related to the skin factor, which is a dimensionless parameter that quantifies the additional pressure drop caused by the wellbore. A positive skin factor means that the wellbore impedes the flow, while a negative skin factor means that the wellbore enhances the flow.
Slant well productivity is the ratio of the flow rate of a slant well to the flow rate of a vertical well with the same reservoir properties and pressure drop. Slant wells are wells that are drilled at an angle to the vertical direction, and they can have higher productivity than vertical wells because they intersect more reservoir area.
Van der Vlis proposed a method to calculate the slant well productivity by using the concept of effective wellbore radius. He assumed that the slant well can be approximated by a horizontal well with a certain length and diameter, and that the flow in the reservoir is radial and isotropic. He derived an equation that relates the slant well productivity to the effective wellbore radius, the slant angle, the reservoir thickness, and the reservoir permeability.
The equation is too complex to explain without formulas, but the main idea is that the effective wellbore radius of a slant well depends on the slant angle and the reservoir thickness. The higher the slant angle, the smaller the effective wellbore radius, and the lower the slant well productivity. The thicker the reservoir, the larger the effective wellbore radius, and the higher the slant well productivity.
Basic Theory:
The van der Vlis method relies on considering the effect of inclination on the wellbore radius. It accounts for the deviation of the wellbore from vertical, providing a more accurate estimation of productivity. The effective wellbore radius (re) is determined based on the actual wellbore radius (r) and the inclination angle (i).
The formula for calculating the effective wellbore radius is given by:
re = r/cos(i)
Procedures:
- Gather Data:
- Wellbore radius (r): The actual radius of the wellbore.
- Inclination angle (i): The deviation of the wellbore from vertical.
- Calculate Effective Wellbore Radius in Excel:
- Create an Excel spreadsheet.
- Enter the wellbore radius (r) in one cell.
- Enter the inclination angle (i) in another cell.
- Use the formula re = r/cos(i) to calculate the effective wellbore radius.
- Scenario:
- Wellbore Radius (r): 5 inches
- Inclination Angle (i): 30 degrees
Detailed Example in Excel:
| A | B | |
|---|---|---|
| 1 | Wellbore Radius (r) | 5 |
| 2 | Inclination Angle (i) | 30 |
| 3 | Effective Wellbore Radius | =A2/COS(RADIANS(B2)) |
MATLAB Comparison:
% MATLAB Code
r = 5; % Wellbore Radius
i = 30; % Inclination Angle (degrees)
% Convert inclination angle to radians
i_rad = deg2rad(i);
% Calculate Effective Wellbore Radius
r_e = r / cos(i_rad);
% Display Result
fprintf('Effective Wellbore Radius: %.2f inches\n', r_e);
Result:
Effective Wellbore Radius: 5.77 inches (both in Excel and MATLAB)
