Application of the Stefan Problem to the Modelling the Decomposition of a Gas Hydrate Pipeline Plug
Creators: name: Bentum, Emmanuel
Publisher: name: Graduate Studies
Year: 2017
Subjects: subject: Education--Mathematics
subject: Physics
subject: Stefan
subject: Method of Lines
subject: Fourier's Heat law

description: This study deals with the application of the Stefan problem to modelling dissociation of hydrate plug in which the hydrates were formed from a gas mixture. In the previous attempt to simulate the decomposition of a hydrate pipeline plug, the hydrates have always been assumed to be pure methane, will lead to erroneous prediction for the rate of decomposition of a hydrate plug because the presence of even a small amount of ethane and or propane could drastically alter the three-phase equlibrium conditions for a gas hydrate formation. In the current study, the Stefan problem for heat conduction at a moving boundary is written in radial coordinates for the case of double sided-depressurization of a pipeline hydrate plug. The plug is assumed to have formed in the presence of various mixtures of methane and ethane, some of which formed structure I hydrates and some which formed structure II hydrates. The effect of the gas mixture composition, on the rate of hydrate plug decomposition is included by incorporating Giraldo and Clarke’s model, for the rate of decomposition of gas hydrates formed from a gas mixture, into one of the boundary conditions. In formulating the equations, it was assumed that the depressurization is always occurring at a pressure whose corresponding equilibrium temperature is greater than 273.15K, thus, there was no need to include an ice phase. The resulting partial differntial equation is highly non-linear and was solved by using the method of lines. At the time of writing,there were no publication available in which the method of lines had been applied to stefan problem in radial coordinates. A base case model was run, in which only heat conduction was considered. The base case scenario was able to satisfactorily model the experimental data from Peters et al. [1] with an Absolute Average deiviation (AAD) of 5%. The kinetic model was subsequently applied to the base case scenario and and it was found that the results were almost identical to those obtained without the kinetic term. From this, it was concluded that heat transfer controls the decomposition of the methane hydrate plug at the base case conditions. Subsequently, the model was used to simulate the decomposition of hydrate plugs formed from the mixtures of methane and ethane, some of which formed were sI hydrates and some formed were sII hydrates. Without the addition of the kinetic term there would be no means for including the composition of the gas mixture, in the heat transfer equations. A sensitivity analysis on the kinetic model was conducted. The geometric parameter which is related to the surface area was investigated and it was found out that by changing the ratio from 1 to 4 times varied very little indicating that the parameter was not very sensitive to the kinetic model. It was also observed that at pressures of 7.4MPa the rate of dissociation was heat controlled. However, when the pressure was lowered to 3.4MPa intrinsic kinetics became more predominant indicating a sharp difference between the heat transfer model and the kinetic model. At a temperature of 273.15K the model showed that the dissociation rate was only heat transfer controlled at a pressure of 7.8MPa. The Absolute Average Deviation (AAD) was less than 1%. However as the temperature was increased to 275.15K and eventually to 277.15K there was a sharp deviation from the kinetic model to the heat transfer model.