Methane Hydrates (MHs) are a promising energy source abundantly available in nature. Understanding the complex processes of MH formation and dissociation is critical for the development of safe and efficient technologies for energy recovery. Many laboratory and numerical studies have investigated these processes using synthesized MH-bearing sediments. A near-universal issue encountered in these studies is the spatial heterogeneous hydrate distribution in the testing apparatus. In the absence of direct observations (e.g. using X-ray computed tomography) coupled with real time production data, the common assumption made in almost all numerical studies is a homogeneous distribution of the various phases. In an earlier study (Yin et al., 2018) that involved the numerical description of a set of experiments on MH-formation in sandy medium using the excess water method, we showed that spatially heterogeneous phase distribution is inevitable and significant. In the present study, we use as a starting point the results and observations at the end of the MH formation and seek to numerically reproduce the laboratory experiments of depressurization-induced dissociation of the spatially heterogeneous MH distribution. This numerical study faithfully reproduces the geometry of the laboratory apparatus, the initial and boundary conditions of the system, and the parameters of the dissociation stimulus, capturing accurately all stages of the experimental process. Using inverse modelling (history-matching) that minimized deviations between the experimental observations and numerical predictions, we determined the values of all the important flow, thermal, and kinetic parameters that control the system behaviour, which yielded simulation results that were in excellent agreement with the measurements of key monitored variables, i.e. pressure, temperature, cumulative production of gas and water over time. We determined that at the onset of depressurization (when the pressure drop - the driving force of dissociation - is at its maximum), the rate of MH dissociation approaches that of an equilibrium reaction and is limited by the heat transfer from the system surroundings. As the effect of depressurization declines over time, the dissociation reaction becomes kinetically limited despite significant heat inflows from the boundaries, which lead to localized temperature increases in the reactor.