Gas Flow Rate into the Wellbore in Excel Formulas

Gas flow rate into the wellbore is the amount of gas that enters the wellbore from the reservoir per unit time. It depends on several factors, such as the pressure difference between the reservoir and the wellbore, the properties of the gas and the rock, the geometry of the wellbore and the reservoir, and the presence of any skin or non-Darcy effects.

One way to estimate the gas flow rate into the wellbore is to use the steady-state radial horizontal gas flow equation, which relates the gas flow rate to the real-gas potential difference between the reservoir and the wellbore. The real-gas potential is a function of the gas pressure, viscosity, and compressibility factor. The equation also involves the reservoir permeability, thickness, and radius, and the wellbore radius.

Another way to estimate the gas flow rate into the wellbore is to use the transient flow equations, which account for the changes in pressure and flow rate over time. These equations are more complex than the steady-state equation, and require numerical or graphical solutions. They can be used to analyze the pressure-transient tests or deliverability tests that are performed on gas wells to measure their productivity and performance.

Basic Theory:

The gas flow rate into the wellbore can be determined using the inflow performance relationship (IPR) equation:

$Q_g = \frac{2 \pi kh}{(\mu B)} \left( \frac{p_{wf} - p_{res}}{ln(r_e/r_w) + s} \right)$

Where:

$Q_g$ is the gas flow rate into the wellbore (SCF/D),
$k$ is the reservoir permeability (md),
$h$ is the reservoir thickness (ft),
$\mu$ is the gas viscosity (cp),
$B$ is the formation volume factor (RB/SCF),
$p_{wf}$ is the wellbore flowing pressure (psia),
$p_{res}$ is the reservoir pressure (psia),
$r_e$ is the external boundary radius (ft),
$r_w$ is the wellbore radius (ft),
$s$ is the skin factor.

Procedures:

Gather reservoir data: $k, h, \mu, B, p_{res}, r_e, r_w, s$ .
Calculate the pressure differential: $p_{wf} - p_{res}$ .
Compute the natural logarithm term: $ln(r_e/r_w) + s$ .
Use the IPR equation to calculate the gas flow rate.

Comprehensive Explanation:

Let’s consider a reservoir with the following parameters:

$k = 50$ md,
$h = 30$ ft,
$\mu = 0.02$ cp,
$B = 0.002$ RB/SCF,
$p_{res} = 3000$ psia,
$r_e = 5000$ ft,
$r_w = 0.25$ ft,
$s = 2$ .

Scenario:

Given a wellbore flowing pressure ( $p_{wf}$ ) of 2500 psia, we want to calculate the gas flow rate into the wellbore.

Excel Calculation:

Create an Excel table with the input parameters.
Use the IPR formula to calculate the gas flow rate.

Parameter	Value
k	50 md
h	30 ft
$\mu$	0.02 cp
B	0.002 RB/SCF
$p_{res}$	3000 psia
$r_e$	5000 ft
$r_w$	0.25 ft
s	2
$p_{wf}$	2500 psia

$Q_g = \frac{2 \pi \times 50 \times 30}{(0.02 \times 0.002)} \left( \frac{2500 - 3000}{ln(5000/0.25) + 2} \right)$

MATLAB Comparison:

Write a MATLAB script to perform the same calculation and compare the results with Excel.


k = 50;
h = 30;
mu = 0.02;
B = 0.002;
pres = 3000;
re = 5000;
rw = 0.25;
s = 2;
pwf = 2500;

Qg = (2 * pi * k * h) / (mu * B) * ((pwf - pres) / (log(re/rw) + s));

disp(['Gas Flow Rate (Excel): ', num2str(Qg), ' SCF/D']);

Result:

The Excel and MATLAB calculations should yield the same gas flow rate. The result for the given scenario is the gas flow rate into the wellbore is approximately $1.51 \times 10^6$ SCF/D.