Crossflow Index in Petroleum Engineering in Excel

Crossflow index is a measure of the extent of interlayer crossflow in a layered reservoir. Interlayer crossflow occurs when fluid flows across the bedding plane from a low-permeability layer into an adjacent layer of higher permeability. This can affect the production and pressure behavior of a well, as well as the ultimate recovery of the reservoir.

Crossflow index is defined as the ratio of the total permeability-thickness product of the reservoir to the harmonic average of the permeability-thickness products of the individual layers. A higher crossflow index indicates a higher degree of crossflow and a more homogeneous-like behavior of the reservoir.

Crossflow index can be calculated from the porosity and permeability distributions of the reservoir layers, or estimated from the observed production and pressure data of a well. By comparing the actual performance of a well with the theoretical performance of a single-layer reservoir with the same pore volume and total permeability-thickness product, the occurrence of interlayer crossflow can be detected.

Interlayer crossflow can have both positive and negative effects on the performance of a well. On the positive side, crossflow can increase the sweep efficiency and the ultimate recovery of the reservoir, as the fluid from the low-permeability layers can be drained by the high-permeability layers. On the negative side, crossflow can cause early water or gas breakthrough, reduce the effective permeability of the reservoir, and increase the skin factor and pressure drop around the well.

Crossflow index is a useful parameter to evaluate the impact of crossflow on the reservoir behavior. It can also help in selecting the optimal completion and stimulation methods for a well, as well as designing the best production strategy for the reservoir.

Basic Theory:

Crossflow index is a dimensionless parameter used to quantify the degree of crossflow between different zones or layers in a reservoir. It is particularly relevant in horizontal wells where communication between layers can occur, impacting well performance. The formula for Crossflow Index (CFI) is given by:

$CFI = \frac{{h \cdot k}}{{\mu \cdot L}}$

Where:

$h$ is the net pay thickness (ft),
$k$ is the permeability of the reservoir (md),
$\mu$ is the viscosity of the reservoir fluid (cp),
$L$ is the length of the wellbore (ft).

Procedures:

Gather data: Collect data on net pay thickness ( $h$ ), permeability ( $k$ ), viscosity ( $\mu$ ), and wellbore length ( $L$ ).
Input data into Excel: Create a table in Excel with the collected data.
Apply the CFI formula: Use the formula to calculate the Crossflow Index for each reservoir layer.
Interpret results: Analyze the calculated CFI values to understand the degree of crossflow and its potential impact on well performance.

Explanation:

Consider a horizontal well with the following data:

Net pay thickness ( $h$ ): 50 ft
Permeability ( $k$ ): 200 md
Viscosity ( $\mu$ ): 5 cp
Wellbore length ( $L$ ): 1000 ft

Excel Table:

	Net Pay Thickness (ft)	Permeability (md)	Viscosity (cp)	Wellbore Length (ft)	Crossflow Index (CFI)
A	50	200	5	1000	=B2C2/(D2E2)

Excel Formula:

$\text{{CFI}} = \frac{{\text{{B2}} \times \text{{C2}}}}{{\text{{D2}} \times \text{{E2}}}}$

Calculation:

$\text{{CFI}} = \frac{{50 \times 200}}{{5 \times 1000}} = 2$

Interpretation:

A CFI value of 2 indicates a moderate degree of crossflow between reservoir layers.

MATLAB Solution:

In MATLAB, you can use the following script to calculate CFI:


% MATLAB script for Crossflow Index calculation
h = 50; % Net pay thickness (ft)
k = 200; % Permeability (md)
mu = 5; % Viscosity (cp)
L = 1000; % Wellbore length (ft)

CFI = (h * k) / (mu * L);

disp(['Crossflow Index (CFI) = ', num2str(CFI)]);

Result:

Running the MATLAB script yields a CFI value of 2, consistent with the Excel calculation.