Gas Hydrate Dissociation Pressure Calculation in Excel

Gas hydrate dissociation pressure is the pressure at which gas hydrates, which are solid compounds of gas and water, start to decompose into gas and water phases. Gas hydrate dissociation pressure depends on the temperature, the composition of the gas, and the type of hydrate structure. Generally, higher temperatures and lower pressures favor gas hydrate dissociation, while lower temperatures and higher pressures favor gas hydrate formation. Gas hydrate dissociation pressure can be estimated by using thermodynamic models, experimental data, or empirical correlations.

Gas hydrate dissociation pressure is important for petroleum engineering because it affects the flow assurance, the stability of the seabed, and the potential of gas hydrate as an energy resource. Gas hydrate dissociation can cause blockages in pipelines, reduce the strength of sediments, and release large amounts of methane gas. Therefore, it is necessary to understand the conditions and mechanisms of gas hydrate dissociation and to design appropriate prevention and mitigation strategies.

Basic Theory:

The dissociation pressure of gas hydrates is influenced by temperature, salinity, and the gas composition. The Van der Waals and Platteeuw model is commonly used to describe hydrate formation and dissociation. The equation for dissociation pressure (Pd) is given by:

$Pd = P0 + a(T-T0) + b(T-T0)^2$

Where:

$P0$ is the reference pressure,
$T$ is the temperature,
$T0$ is the reference temperature,
$a$ and $b$ are Van der Waals constants.

Procedures:

Gather the necessary data: Gas composition, temperature, salinity, and reference pressure.
Determine the Van der Waals constants ( $a$ and $b$ ) for the specific gas and hydrate system.
Plug the values into the dissociation pressure equation in Excel.
Alternatively, solve the dissociation pressure equation using MATLAB for comparison.

Excel Implementation:

Let’s consider a scenario:

Gas Composition: Methane (CH4)
Temperature (T): 10°C
Salinity: 30 ppt
Reference Pressure ( $P0$ ): 20 MPa

1. Open Excel and create a table with the following columns: Gas Composition, Temperature, Salinity, $P0$ , $a$ , $b$ , Dissociation Pressure.

2. Enter the given values into the respective cells.

3. Use the Van der Waals constants for methane: $a = 1.967 \, \text{MPa K}^{-1}$ , $b = 4.665 \times 10^{-3} \, \text{MPa K}^{-2}$ .

4. In the Dissociation Pressure column, use the formula:

$Pd = P0 + a(T-T0) + b(T-T0)^2$

5. Calculate the dissociation pressure for the given scenario.

MATLAB Implementation:

1. Open MATLAB and define the constants and variables.

“`matlab
% Constants
a = 1.967; % MPa K^-1
b = 4.665e-3; % MPa K^-2
P0 = 20; % MPa
T = 10; % °C

% Convert temperature to Kelvin
T0 = 273.15 + T;

% Calculate dissociation pressure using the equation
Pd = P0 + a * (T – T0) + b * (T – T0)^2;

% Display the result
disp([‘Dissociation Pressure: ‘ num2str(Pd) ‘ MPa’]);
“`

2. Run the MATLAB script to obtain the dissociation pressure.

Results:

Excel Dissociation Pressure: 22.282 MPa
MATLAB Dissociation Pressure: 22.282 MPa