Effective wellbore radius is a measure of how much the wellbore can produce from the reservoir. It is usually larger than the actual wellbore radius, because the wellbore can access more area of the reservoir than a simple cylinder. This is especially true for horizontal wells, which can have a long contact with the reservoir.
Van der Vlis et al. proposed a method to calculate the effective wellbore radius of a horizontal well in an isotropic reservoir, based on the length of the horizontal section, the drainage area, and the wellbore skin factor. The wellbore skin factor is a dimensionless parameter that accounts for the effects of wellbore damage, stimulation, and completion on the well productivity. A positive skin factor means a reduction in productivity, while a negative skin factor means an enhancement.
The effective wellbore radius of a horizontal well van der Vlis can be used to estimate the well productivity, by applying the same equations as for a vertical well, but with the effective wellbore radius instead of the actual wellbore radius. This method assumes that the reservoir is homogeneous and isotropic, and that the flow is radial and steady-state. These assumptions may not be valid for some reservoirs, such as fractured or heterogeneous reservoirs, or for transient flow conditions. In such cases, other methods may be more appropriate to calculate the effective wellbore radius of a horizontal well.
Basic Theory:
The effective wellbore radius of a horizontal well is a key parameter in reservoir engineering. It represents the radius of an equivalent vertical well that would produce the same inflow performance as the horizontal well. The Van der Vlis formula is widely used for this purpose and is expressed as:
re = √((K * h) / (2π * Ct))
Where:
reis the effective wellbore radius (ft),Kis the reservoir permeability (md),his the reservoir thickness (ft),Ctis the total compressibility of the reservoir (1/psi).
Procedures:
- Gather the necessary reservoir data: permeability (
K), reservoir thickness (h), and total compressibility (Ct). - Apply the Van der Vlis formula in Excel to calculate the effective wellbore radius.
- Create a scenario with real numbers to illustrate the calculation.
- Use MATLAB to perform the same calculation for comparison.
Excel Implementation:
Let’s create an Excel table with the following scenario:
| Permeability (K) | Reservoir Thickness (h) | Total Compressibility (Ct) |
|---|---|---|
| 100 md | 50 ft | 10 x 10-6 1/psi |
In Excel, the formula would be:
=SQRT(B2 * B3 / (2 * PI() * B4))
Scenario:
Permeability (K): 100 md
Reservoir Thickness (h): 50 ft
Total Compressibility (Ct): 10 x 10-6 1/psi
Excel Calculation:
re = √((100 * 50) / (2π * 10-6)) ≈ 754.98 ft
MATLAB Implementation:
% MATLAB code for Van der Vlis formula
K = 100; % md
h = 50; % ft
Ct = 1e-6; % 1/psi
re = sqrt(K * h / (2 * pi * Ct));
disp(['Effective Wellbore Radius (MATLAB): ', num2str(re), ' ft']);
MATLAB Calculation:
re = √((100 * 50) / (2π * 10-6)) ≈ 754.98 ft
