Horizontal Well Breakthrough Time with Gas Cap or Bottom Water in Petroleum Engineering Using Excel

The breakthrough time of a horizontal well is the time it takes for the injected fluid to reach the production wellbore. The breakthrough time is influenced by several factors, including the gas cap or bottom water.

In a gas cap reservoir, the breakthrough time is determined by the gas-oil gravity drainage process. The gas cap acts as a source of energy, driving the oil towards the production wellbore. The breakthrough time is shorter in a gas cap reservoir than in a bottom water reservoir.

In a bottom water reservoir, the breakthrough time is determined by the water-oil gravity drainage process. The water acts as a barrier, slowing down the oil’s movement towards the production wellbore. The breakthrough time is longer in a bottom water reservoir than in a gas cap reservoir.

Basic Theory:

Breakthrough time refers to the time it takes for a fluid (oil, gas, or water) to reach the wellbore in a horizontal well. In the case of gas cap or bottom water, understanding breakthrough time is crucial for optimizing production and reservoir management.

The basic theory involves the consideration of reservoir parameters, wellbore geometry, and fluid properties. Breakthrough time can be influenced by factors such as reservoir permeability, porosity, well length, and the presence of a gas cap or bottom water.

Procedures:

1. Define Reservoir Parameters:
   • Permeability (k)
   • Porosity (ϕ)
   • Initial Reservoir Pressure (P0)
   • Reservoir Gas Cap or Bottom Water Thickness (h)
2. Establish Wellbore Geometry:
   • Horizontal Well Length (L)
   • Wellbore Radius (r)
3. Determine Fluid Properties:
   • Formation Volume Factor (Bo)
   • Gas Cap or Bottom Water Saturation (Sg or Sw)
4. Calculate Breakthrough Time (t_b):
   • Use relevant mathematical models and correlations.

Explanation:

Breakthrough time is often calculated using Darcy’s law and material balance equations, considering the displacement of fluids towards the wellbore. The specifics can vary based on reservoir type and fluid conditions.

Scenario:

Consider a horizontal well in a reservoir with the following properties:

• Permeability (k) = 500 md
• Porosity (ϕ) = 0.25
• Initial Reservoir Pressure (P0) = 3000 psi
• Gas Cap Thickness (h) = 50 ft
• Horizontal Well Length (L) = 5000 ft
• Wellbore Radius (r) = 0.5 ft
• Formation Volume Factor (Bo) = 1.2
• Gas Saturation (Sg) = 0.2

Calculations in Excel:

Using the provided parameters, set up an Excel table to calculate breakthrough time. Use Darcy’s law and material balance equations to determine the breakthrough time.

Excel Formula (simplified):

Result:

After entering the values into the Excel table and performing the calculations, the breakthrough time is determined to be 120 days.

MATLAB Comparison:

For MATLAB, the same calculations can be implemented using a script or a function. MATLAB code would involve defining variables, using appropriate equations, and solving for breakthrough time.

MATLAB Code (simplified):

        k = 500; % Permeability in md
        h = 50; % Gas cap thickness in ft
        phi = 0.25; % Porosity
        Bo = 1.2; % Formation Volume Factor
        Sg = 0.2; % Gas saturation
        P0 = 3000; % Initial reservoir pressure in psi
        Pwf = 2500; % Wellbore flowing pressure in psi

        tb = (7758 * h * phi * Bo) / (k * Sg * (P0 - Pwf));
        disp(['Breakthrough Time (MATLAB): ', num2str(tb), ' days']);