Hydrate Dissociation Model with Time Fractional Derivative

Abstract

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.