Horizontal well critical rate is the maximum oil production rate that can be achieved from a horizontal well without causing water coning. Water coning is a phenomenon where water from the bottom of the reservoir moves upward and enters the wellbore, reducing the oil recovery and increasing the water production.
Giger and Karcher developed a correlation to estimate the horizontal well critical rate based on the reservoir and well parameters, such as the oil and water densities, the oil viscosity, the horizontal permeability, the vertical permeability, the well radius, the horizontal well length, the distance from the well to the water-oil contact, and the reservoir thickness. Their correlation is expressed as a mathematical formula that can be found in this paper.
The main idea behind their correlation is that the horizontal well critical rate depends on the balance between the gravity forces that keep the water-oil contact stable and the viscous forces that cause the water to move upward due to the pressure drawdown around the wellbore. The correlation also takes into account the effects of the horizontal well length, the distance from the well to the water-oil contact, and the anisotropy ratio (the ratio of the horizontal permeability to the vertical permeability) on the critical rate.
Basic Theory:
The Giger and Karcher method relates the critical rate (Qcrit) to the wellbore radius (rw), horizontal well length (Lh), and the viscosity of the reservoir fluid (μ).
![\[Q_{\text{crit}} = \frac{18.41 \cdot \mu \cdot L_h}{r_w^2}\]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-8df51d092055ec08f55b1ac529bf7bb6_l3.svg "Rendered by QuickLaTeX.com")
Procedures:
- Gather necessary data: reservoir fluid viscosity (μ), wellbore radius (rw), and horizontal well length (Lh).
- Plug the values into the Giger and Karcher formula to calculate Qcrit.
Excel Formulas:
Assuming the data is in cells B2 (fluid viscosity), B3 (wellbore radius), and B4 (horizontal well length), the Excel formula would be:
=18.41 * B2 * B4 / B3^2Comprehensive Explanation:
Let’s consider a scenario where a horizontal well has a fluid viscosity (μ) of 10 cP, a wellbore radius (rw) of 0.2 ft, and a horizontal well length (Lh) of 5000 ft.
Scenario:
- Reservoir fluid viscosity (μ): 10 cP
- Wellbore radius (rw): 0.2 ft
- Horizontal well length (Lh): 5000 ft
Excel Calculation:
In Excel, input the given values into cells B2, B3, and B4, and then use the formula mentioned above.
![\[Q_{\text{crit}} = \frac{18.41 \cdot 10 \cdot 5000}{0.2^2} \approx 2,302,500 \, \text{ft}^3/\text{day}\]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-96793e4dc6414e469f5a01587f219c37_l3.svg "Rendered by QuickLaTeX.com")
MATLAB Comparison:
For comparison, the same calculation can be done in MATLAB using the following script:
% Input data
mu = 10; % cP
rw = 0.2; % ft
Lh = 5000; % ft
% Giger and Karcher formula
Qcrit = (18.41 * mu * Lh) / rw^2;
disp(['Critical Rate (MATLAB): ', num2str(Qcrit), ' ft^3/day']);
Run this MATLAB script to obtain the critical rate, which should match the Excel result.
