The hydrate dissociation is viewed as a phase change process in which hydrates transform from a solid phase into gas and liquid phase at a moving dissociation boundary. The boundary separates the dissociation zone containing gas and water from the undissociated zone containing the hydrates, leading to a density difference. Based on the assumption of a density difference between the dissociation zone and the hydrate zone, the authors propose a mathematical model to study hydrate dissociation under thermal stimulation in an infinite radially symmetrical reservoir. Analytical solutions to the temperature distribution are derived by using the self-similarity transformation. Considering the effect factors of the initial heated-water temperature and hydrate density, the authors conducted a thorough investigation of the temperature distribution and the location of the dissociation front for a sample hydrate reservoir. The results from our model show that the heated-water temperature and hydrate density exert significant influence on the hydrate dissociation. With the injection time unchanged, the dissociation distance tends to be increased as the heated-water temperature is increased, leading to a larger dissociation zone. Additionally, a smaller hydrate density can result in a larger dissociation distance. For hydrate thermal stimulation, a higher heated-water temperature and a lower hydrate density can lead to a larger dissociation distance with the injection time unchanged. As the hydrate dissociation proceeds, the dissociation rate is decreased.

In this paper, we shall investigate fractional partial differential equations with fractional moving boundary condition to study the dissociation of natural gas hydrate under heat injection. The moving boundary separates the hydrate reservoir into the dissociated zone and the hydrate one. By using the self-similar transformation and Wright function, we obtain the explicit solutions for two zones. We present simulations with steam and hot water injection and show the dissociation temperature in graphical mode from injection temperature to reservoir temperature with respect to the time, distance, and fractional order. Our analysis of fractional model turns out to be a successful generalization of the classical one; i.e., it can well describe the dissociation of natural gas hydrate and is theoretically consistent with the existing integer hydrate dissociation model. When the factional order tends to 1, the “limit solution” becomes the classical one.