Understanding Communication between Compartments in Tight Gas Reservoirs using Excel and MATLAB

Communication between compartments in tight gas reservoirs means the flow of gas from one section of the reservoir to another through a common boundary or a connecting channel. This can affect the reservoir performance, pressure distribution, and gas recovery.

There are different methods to study the communication between compartments, such as analyzing reservoir extension, pressure communication, fluid similarity, top seal efficiency, and faults sealing. These methods use different types of data, such as geophysics, geology, production, and reservoir engineering.

One of the challenges in studying communication between compartments is to allocate the production from each compartment in a multi-layered commingled system. This means to determine how much gas each layer in each compartment contributes to the total production of a well. This can help to estimate the original gas in place (OGIP) and the flow parameters for each layer and compartment.

Another challenge is to model the gas transport in a dual-porosity tight gas reservoir, which consists of a matrix system and a fracture system. The matrix system is the main storage of gas, while the fracture system is the main conduit for gas flow. The gas transport in such a reservoir is influenced by the pressure difference between the matrix and the fracture, the gas adsorption and desorption, and the diffusion and convection processes.

Basic Theory:

In tight gas reservoirs, low permeability restricts fluid flow, leading to challenges in reservoir management. Darcy’s law governs fluid flow, and understanding inter-well communication involves factors like permeability, reservoir pressure, and the distance between wells.

Procedures:

Define Reservoir Properties:
- Permeability (k)
- Reservoir Pressure (P)
- Distance between Wells (L)
Calculate Transmissibility:
- Use Darcy’s law: $T = \frac{k \cdot A \cdot h}{\mu}$ , where $A$ is the cross-sectional area, $h$ is the reservoir thickness, and $\mu$ is fluid viscosity.
Determine Inter-well Flow:
- Inter-well flow (Q) is given by $Q = \frac{P_1 - P_2}{T}$ .
Excel Formulas:
- Transmissibility: =k * A * h / μ
- Inter-well Flow: =(P1 - P2) / T

Comprehensive Explanation:

Let’s consider a tight gas reservoir with the following properties:

Permeability (k): 0.1 mD
Reservoir Pressure (P): 5000 psi
Distance between Wells (L): 1000 ft
Cross-sectional Area (A): 500 ft²
Reservoir Thickness (h): 50 ft
Fluid Viscosity (μ): 2 cP

Scenario:

Two wells (Well 1 and Well 2) are 1000 ft apart. Well 1 has a pressure of 5000 psi, and Well 2 has a pressure of 4900 psi. Calculate the inter-well flow.

Excel Calculation:

Create an Excel table with the given properties.
Use the provided Excel formulas to calculate transmissibility and inter-well flow.

Property	Value
Permeability (k)	0.1 mD
Reservoir Pressure	5000 psi
Distance (L)	1000 ft
Cross-sectional Area	500 ft²
Reservoir Thickness	50 ft
Fluid Viscosity	2 cP

Transmissibility: =k * A * h / μ
Inter-well Flow: =(P1 - P2) / T

Excel Result:

Inter-well Flow = 5000 psi – 4900 psi / T

MATLAB Comparison:

Perform the same calculations in MATLAB using the mathematical expressions.


            % MATLAB script
            k = 0.1e-3; % permeability in mD
            A = 500; % cross-sectional area in ft²
            h = 50; % reservoir thickness in ft
            mu = 2; % fluid viscosity in cP
            P1 = 5000; % pressure in Well 1 in psi
            P2 = 4900; % pressure in Well 2 in psi

            T = k * A * h / mu;
            Q = (P1 - P2) / T;

MATLAB Result:

Inter-well Flow = Q