Critical Rate for Horizontal Wells in Edge-Water Drive Reservoir in Excel

The critical rate for horizontal wells in edge-water drive reservoirs is the maximum production rate that can be achieved without causing water to break through the well. It depends on several factors, such as the reservoir properties, the well geometry, the oil-water contact, and the presence of any barriers or interbeds.

Generally, the critical rate increases with the horizontal well length, the reservoir thickness, the oil viscosity, and the anisotropy ratio (the ratio of horizontal to vertical permeability). It decreases with the water viscosity, the water-oil density difference, and the distance from the well to the oil-water contact.

If there are impermeable barriers or low-permeability interbeds in the reservoir, they can increase the critical rate and delay the water breakthrough by creating additional flow resistance and reducing the water cresting effect. The size and location of the barriers or interbeds also affect the critical rate.

Basic Theory:

The critical rate is the maximum production rate at which a horizontal well can produce without experiencing water breakthrough. In edge-water drive reservoirs, water encroachment from the reservoir edges can significantly impact well performance. The critical rate is influenced by reservoir and fluid properties, wellbore characteristics, and the geometry of the well.

Procedures:

The critical rate can be estimated using the following formula:

$Q_c = \frac{{h_{\text{eff}} \cdot k_{h}}}{{\mu_{o} \cdot (P_{d} - P_{w})}}$

Where:

$Q_c$ is the critical rate (STB/D).
$h_{\text{eff}}$ is the effective reservoir thickness (ft).
$k_{h}$ is the horizontal permeability (md).
$\mu_{o}$ is the oil viscosity (cp).
$P_{d}$ is the reservoir pressure (psia).
$P_{w}$ is the wellbore pressure (psia).

Comprehensive Explanation:

Effective Reservoir Thickness ( $h_{\text{eff}}$ ):Calculate $h_{\text{eff}}$ by considering the net pay thickness and adjusting for the effects of vertical permeability.
Horizontal Permeability ( $k_{h}$ ):Determine the horizontal permeability of the reservoir, which can be obtained from well tests or reservoir simulation.
Oil Viscosity ( $\mu_{o}$ ):Determine the viscosity of the reservoir oil at reservoir conditions.
Reservoir Pressure ( $P_{d}$ ):Obtain the reservoir pressure from well tests or reservoir simulation.
Wellbore Pressure ( $P_{w}$ ):Calculate the wellbore pressure based on the production rate and wellbore pressure drop.

Scenario:

Consider a horizontal well in an edge-water drive reservoir with the following parameters:

$h_{\text{eff}} = 30$ ft
$k_{h} = 100$ md
$\mu_{o} = 2$ cp
$P_{d} = 2500$ psia
$P_{w} = 1000$ psia

Excel Calculation:

Create an Excel table with the given parameters and use the formula to calculate the critical rate.

Parameter	Value
$h_{\text{eff}}$	30 ft
$k_{h}$	100 md
$\mu_{o}$	2 cp
$P_{d}$	2500 psia
$P_{w}$	1000 psia

$Q_c = \frac{{30 \cdot 100}}{{2 \cdot (2500 - 1000)}}$

Excel Formula: = (30 * 100) / (2 * (2500 - 1000))

MATLAB Analysis:

In MATLAB, you can use the same formula with the given parameters to calculate the critical rate.


h_eff = 30;
k_h = 100;
mu_o = 2;
P_d = 2500;
P_w = 1000;

Q_c = (h_eff * k_h) / (mu_o * (P_d - P_w));
disp(['Critical Rate (STB/D): ', num2str(Q_c)]);

Result:

The critical rate for the given scenario is calculated as follows:

$Q_c = \frac{{30 \cdot 100}}{{2 \cdot (2500 - 1000)}} = 0.06 \, \text{STB/D}$

Therefore, the critical rate for the horizontal well in this scenario is 0.06 STB/D.

This Excel-based approach provides a practical and user-friendly way to estimate the critical rate for horizontal wells in edge-water drive reservoirs. The MATLAB analysis serves as a comparison tool, ensuring the accuracy and reliability of the calculations.