## 1 Introduction
It would require far too much space to review all the various methods used in experiments and pilot-plant tests for CH\({}_{4}\) hydrate production. We have three decades of experience in experiments on CO\({}_{2}\)/CH\({}_{4}\) exchange, and there is a plethora of literature already available on the topic. Similarly, there are numerous publications devoted to pressure reduction and studies of other methods. The focus in this work is mainly on the best way to model the phase transition thermodynamics and its associated kinetics. An important issue here is the need for a theoretically based model platform that accounts for all the implicit dynamic contributions to the phase transition. In order to accomplish this, we apply a fairly simple kinetic model based on theoretical considerations [7]. Yet, another important requirement to satisfy is a consistent thermodynamic model to describe the enthalpy changes taking place in hydrate phase transitions. With temperature, pressure, and concentrations as independent thermodynamic variables, Gibbs free energy will be the thermodynamic function determining phase stability. We need our models for enthalpy changes to be consistent with those for the Gibbs free energy. Another area where hydrate phase transition dynamics become relevant is the transport of CO\({}_{2}\) in pipelines, which is a routine process in offshore Norway and many places around the world. Given the high pipeline pressures and low seafloor temperatures on the seafloor (typically below 6 \({}^{\circ}\)C), residual water present in the CO\({}_{2}\) stream may drop out either via condensation in bulk or adsorption on rusty pipeline walls and subsequently form a hydrate. Hydrate formation on small droplets liquid water will involve a dynamic balance between the driving force for hydrate formation (Gibbs free energy) and the transport of released heat through the insulating CO\({}_{2}\) fluid surrounding the forming hydrate core. Hydrate formation on liquid water films adsorbed on the rusty walls will also involve the need to get rid of formation heat. While the liquid water and the pipeline wall will act as efficient heat conductors, pipeline insulation and the \"bulk\" CO\({}_{2}\) stream will hinder heat transport. The examples presented above present just a few samples of practical scenarios involving implicit coupling between phase transition dynamics and heat transport dynamics. Theoretical physics provides a number of platforms suitable for modeling phase transition dynamics. Common to all of them is the implicit coupling between the mass transport dynamics characterizing the phase transition, the thermodynamics control (a function of Gibbs free energy change), and the heat transport. The main focus of this work was to review some of the more recent and popular models applied to study hydrate phase transition dynamics in terms of actual kinetic rate limiting factors. Our secondary objective was to shed more light on the connection between nanoscale transition dynamics and hydrodynamic flow (which happens across a thin interface of 1-1.5 nm). Our third objective was related to the need for thermodynamic consistency. Many models describing enthalpy changes related to hydrate phase transitions are disconnected from the formal thermodynamic coupling between phase transition thermodynamics (Gibbs free energy changes) and the enthalpy changes related to heat transport requirements. The paper is organized as follows. Section 2 provides an overview of popular models used to describe hydrate formation and dissociation dynamics in terms of characteristic transition properties. In Section 3, we outline a theoretical concept to serve as a basis for alternative kinetic models comprehensively accounting for implicit coupling between mass transport, heat transport, and thermodynamic control. It is important to point out here that the model we used is just an example chosen for illustration purposes.