## 4 Results and Discussion
values for modeling will provide a fair approximation only for temperatures below and fairly close to the CO\({}_{2}\) phase transition temperature, as illustrated in Figures 6-9. As noted previously, heat transport in aqueous systems is faster than mass transport by an order of two or three, which is a well-known fact verified by several of our earlier publications on hydrate phase transitions [21; 22]. It is therefore disappointing that so many kinetic theories are based on heat transport models rather than the associated mass transport limitations. The following profile (Figure 10) is based on data obtained from the molecular modeling of interfaces typical for CH\({}_{4}\) and CO\({}_{2}\) hydrates [39; 40; 41]. Recently, a number of experimental studies have studied the use of CO\({}_{2}\) with limited admixture of N\({}_{2}\) intended to both avoid the blocking of pores by newly formed CO\({}_{2}\) hydrate and to increase the flow permeability of the injection gas at the same time (see for instance [PERSON] [24], [PERSON] et al. [43], and [PERSON] [44]). Figure 10: Calculated heat transport rates through hydrate/liquid water interface as a function of liquid-side diffusivity coefficient in Equation (10). Upper curve is for D liquid in Equation (10) equal to \(1\times 10^{-07}\) m\({}^{2}\)/s (top), \(1\times 10^{-08}\) m\({}^{2}\)/s, \(1\times 10^{-09}\) m\({}^{2}\)/s, \(1\times 10^{-10}\) m\({}^{2}\)/s, \(1\times 10^{-11}\) m\({}^{2}\)/s (bottom). Absolute minimum heat transport rate is \(1.4\times 10^{-10}\) kJ/(m \(\times\) s), \(1.4\times 10^{-11}\) kJ/(m \(\times\) s), \(1.4\times 10^{-12}\) kJ/(m \(\times\) s), \(1.4\times 10^{-13}\) kJ/(m \(\times\) s), and \(1.4\times 10^{-14}\) kJ/(m \(\times\) s) for the same curves. Figure 1.0 Enthalpies of hydrate formation in kJ/mol hydrate former as function of pressure. The bottom solid curve is pure CO\({}_{2}\) hydrate; the middle one is 10 mol % N\({}_{2}\) in the CO\({}_{2}\)/N\({}_{2}\) mix; the top solid curve is for 20 mol % N\({}_{2}\). As illustrated in Figure 5, the heat of hydrate formation enthalpy varies along the hydrate stability limit. At 273.16 K and 14.19 bars, the calculated value amounted to \(-\)67.8 kJ/mol CO\({}_{2}\), with the corresponding value at 290 K and 403 bars equal to \(-\)58.5 kJ/mol CO\({}_{2}\). Inserting the former value as the enthalpy of hydrate formation in Equation (9), and the profiles in Figures 2 and 3 in Equation (12), one can find the limiting heat transport rate. These calculations are illustrated in Figure 10 below for five different values of diffusivity on the liquid side of the interface (in Equation (10)) for the most rate limiting portions of the interface. Heat cannot be transported faster than it moves across the rate-limiting sections, with many dynamic changes related to the mass and heat transport drastically changing the mass and heat transport rates. As an example, the calculated heat transport rates corresponding to the distance of 6 A from the liquid side would be four orders of magnitude higher than the values used Figure 1.1 On the other hand, the heat conduction coefficient of 0.57 W/(m\(\cdot\)K) (see Table 2), i.e., 5.7 \(\times\) 10\({}^{-4}\) kJ/(m\(\cdot\)s\(\cdot\)K), will still translate into heat transfer orders of magnitude faster than the mass transport-controlled rates on the left-hand side of Equation (9). The heat transport models along the lines presented here can be incorporated into simple kinetic models such as the classical nucleation theory (CNT) for use in hydrate phase transition modeling at the pore level in reservoir simulation. Yet, other applications are kinetic extensions of our hydrate risk evaluation models (see, for instance, [24; 25]). In this work, we have shown that mass transport through hydrate/liquid water interface is very slow. This issue is likely to limit hydrate film growth, and this may interfere the balance between distribution of released heat and temperature increase in surroundings. This may lead to partial re-dissociation of the hydrate film.