Pure Hydrate Phase Equilibria

Experimental data for hydrates of pure gases in contact with water are the most abundant, comprising of nearly 50% of all equilibrium hydrate-related data. 

Although a typical natural gas is mainly comprised of the first three normal paraffins, the phase equilibria of each component with water will differ from that of a natural gas with water. However, a comparison of predictions with data for methane, ethane, and propane simple gas hydrates is given as a basis for understanding the phase equilibria of water with binary and ternary mixtures of those gases. 

For example, at 278.2 K, hydrates form at a pressure of approximately 5 bar and dissociate upon pressurization at approximately 600 bar. A more detailed explanation of the pseudo-retrograde hydrate phenomena can be found in the binary hydrates section which follows. Note that the hydrate formation pressure of propane hydrates along the Aq-sII-V line at 277.6 K is predicted to be 4.3 bar. 

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For methane hydrate, the minimum water depth is 381 m in freshwater and upto 436 m in seawater, respectively, at 277 K. In the world s oceans at water depths greater than 600 m, the temperature is typically uniform at 277 K, due to the density maximum in seawater. Lower bottom water temperature exceptions can be found with strong subbottom currents from Antarctic and Arctic environments such as the north of Norway or Russia. Methane-phase equilibrium data in Chapter 6, indicate that 3.81 MPa are required to stabilize methane hydrates at 277.1 K. Using the rule of thumb 1 MPa = 100 m water, hydrates in pure water would be stable at depths greater than 381 m. 

The s-H hydrates have potential to become a better medium for natural-gas (mixed-gas of CH4 and impurities) storage and transportation . The s-H hydrates helped by CH4 can be generated under lower pressure condition than the pure CH4 hydrate. That is, we can handle the natural-gas hydrate (NGH) under more moderate condition by generating the s-H hydrate. The pressure reduction from pure help-gas hydrate depends largely on the kind of LGS. Some literatures reported that both the molecular size and the molecular shape of LGS have much effect on the equilibrium pressure of s-H hydrate. A lot of phase equilibrium data for the s-H hydrate systems are required to develop the effective storage and transportation system. 

Figure 1 shows the stability boundaries of s-H hydrates helped by CH4. The solid circle, open triangle, open circle, open diamond, open reverse-triangle, and solid reverse-triangle stand for the phase equilibria for the CH4+1,1-DMCH , CH4+MCH , CH4+c/ -1,2-DMCH CH4+MCP, CH4+c-Octane, and CH4+CW-1,4-DMCH s-H hydrate systems, respectively. The three-phase equilibrium data of pure CH4 hydrate are also plotted with solid square . The equilibrium pressures of s-H hydrates decrease from that of pure CH4 hydrate. The slope of stability boundary for each s-H hydrate system (the plot of In p vs. T is almost linear) is somewhat steeper than that of pure CH4 hydrate. As reported in the literatures , these equilibrium curves would cross at high temperature where the s-H hydrate is dissociated and the pure CH4 s-I hydrate is reconstructed. 

The pressure-temperature relations for the CH4 s-H hydrates were measured under four-phase equilibrium condition. The s-H hydrate formation was observed in the CH4+CI-DMCH, CH4+MCH, CH4+c-Octane, CH4+c >l,2-DMCH, CH4+c/ -l,4-DMCH and CH4+MCP systems. The equilibrium pressure of each s-H system increases in that order at isothermal condition and it is lower than that of pure CH4 s-I hydrate. The 1,1-DMCH molecule has the best molecular-size to fit the E-cage cavity and constructs the CH4 s-H hydrate at the lowest pressure in the all LGS of present study. 

Of particular interest to those in the natural gas industry is the phase diagram of hydrate systems in the presence of inhibitors. Fig. 3 shows the phase diagram for methane hydrates in the presence of methanol and a NaCl and KCl mixture. The solid line is the three-phase equilibrium curve for methane in pure water. As seen from Fig. 3, forming hydrates in the presence of either an alcohol or salt increases the pressure required for gas hydrate formation, at a given temperature. 

Fig. 1 Incipient hydrate forming conditions for pure methane. The solid line represents the three-phase equilibrium for either ice-hydrate-gas T < 273.15K), or liquid water-hydrate-gas (T > 273.15K). (View this art in color at www.dekker.com.)...

Pure solid + fluid phase equilibrium calculations are challenging but can, in principle, be modeled if the triple point of the pure solid and the enthalpy of fusion are known, the physical state of the solid does not change with temperature and pressure, and a chemical potential model (or equivalent), with known coefficients, for solid constituents is available. These conditions are rarely met even for simple mixtures and it is difficult to generalize multiphase behavior prediction results involving even well-defined solids. The presence of polymorphs, solid-solid transitions, and solid compounds provide additional modeling challenges, for example, ice, gas hydrates, and solid hydrocarbons all have multiple forms. 

Open circle and square are the critical (Kn2o) and triple points (TBacn) of pure components solid circles are the composition of liquid phases in critical equilibria N (L, = L2-G), M (L, = L2-S), p (L = G-S) and Q (L, = Lj-S) solid triangles are the composition of liquid phases in nonvariant equilibrium/, (L1-L2-G-S) soUdsquares are the composition of liquid and solid (hydrate) phases in the low-temperature part of equilibrium L-G-S, which ends in critical endpoint f . Heavy lines are the composition of liquid phases in monovariant equilibria L-G-S, L1-L2-G, L,-L2-S dashed lines show the composition of Uquid phases in the extension of the studied high-temperature part of three-phase curves L, = L2-S to the triple point of BaCb (L-G-S) dot-dashed lines are the critical curves L = G (Kh2oP) L, = L2 (NM and the curve originated in point Q ) dotted hue is the metastable part of the critical curve L, = L solid lines show the composition of liquid (fluid) phases in two-phase equihbria F1(L)-S and L1-L2 thin lines are the tie-lines. 

Equation (1) is readily recast in a form that is suitable for calculating the conditions for hydrate stability. Note that for a true three-phase equilibrium between water, hydrate and guest phases, the chemical potential of each individual species must be the same in all three phases. Thus must equal the chemical potential of water in its stable pure phased and we have that... 

The thermodynamic reaction equilibrium constant K, is only a function of temperature. In Equation 4.18, m, the activity of the guest in the vapor phase, is equal to the fugacity of the pure component divided by that at the standard state, normally 1 atm. The fugacity of the pure vapor is a function of temperature and pressure, and may be determined through the use of a fugacity coefficient. The method also assumes that an, the activity of the hydrate, is essentially constant at a given temperature regardless of the other phases present. 

Addition of a solute to the aqueous phase changes the D/H and 180/16Q ratios in the free water since newly formed hydration spheres selectively take hydrogen and oxygen isotopes. This in turn results in the change in the D/H and 0/" 0 ratios in the water vapor or the 0/ 0 ratio in the carbon dioxide in equilibrium with the free water, which is considered to have an energy state similar to pure water. 

Or, again, take the case of pure benzene on the one hand and a saturated solution of benzene in water on the other, both systems being at the same temperature A saturated solution of benzene is necessarily in equilibrium with pure liquid benzene itself because of the fact of saturation The conclusion to he drawn from the thermodynamic criterion considered is, that under these conditions, (8A)TV = o, and therefore, if we imagine one mole of benzene transferred from the pure benzene to the saturated solution, the work must be zero That is, there must be the same vapour pressure over the pure benzene as there is over its saturated solution in water, the vapour in each case being benzene vapour In the case of a hydrated salt on the one hand and the saturated solution of the salt on the other, the conditions are more complex We shall consider this point in Chap X in connection with the application of the Phase Rule to two component systems... 

InJthaxaae of a solution of common salt, however, we may have ice in contact with the solution at different temperatures and pressures. Further, it is possible to have a solution in equilibrium not only with anhydrous salt (NaCl), but also with the hydrated salt (NaCl, 2H2O), as well as with ice, and the question, therefore, arises Is it possible to state in a general manner the conditions under which such different systems can exist in equilibrium or to obtain some insight into the relations which exist between pure liquids and solutions As we shall learn, the Phase Rule enables us to give an answer to this question. 

Thinking it Through When partially soluble crystalline solids dissolve in pure water to form an aqueous solution, a dynamic equilibrium is established between the solid that separates into hydrated ions and the reforming of the solid phase from the hydrated ions. For silver chromate, this is the equilibrium reaction. 

In the current study we are mainly interested in describing the gas solubility in pure water, under two-phase equihbrium (H-Lw) conditions. Gases of interest to this study include methane and carbon dioxide, and we report results mainly for the case of methane. To this purpose we couple different published thermodynamic models that are based on (i) the van der Waals-Platteeuw (vdWP) theory [9, 10] from Statistical Thermodynamics to describe three-phase (H-Lw-V) equihbria, (ii) Equations of State (EoS) for fugacity calculations, and (iii) models of gas solubihty in the aqueous phase. The considered approach is described in detail by Tsimpanogiannis et al., [11]. The authors conducted an extensive review of experimental and theoretical studies related to the solubility of gases in the aqueous phase under hydrate equilibrium conditions. Here, we report additional results that were not included in the original publication. 

The definition of solubility permits the occurrence of a single solid phase which may be a pure anhydrous compound, a salt hydrate, a non-stoichiometric compound, or a solid mixture (or solid solution, or "mixed crystals"), and may be stable or metastable. As well, any number of solid phases consistent with the requirements of the phase rule may be present. Metastable solid phases are of widespread occurrence, and may appear as polymorphic (or allotropic) forms or crystal solvates whose rate of transition to more stable forms is very slow. Surface heterogeneity may also give rise to metastability, either when one solid precipitates on the surface of auiother, or if the size of the solid particles is sufficiently small that surface effects become important. In either case, the solid is not in stable equilibrium with the solution. See (21) for the modern formulation of the effect of particle size on solubility. The stability of a solid may also be affected by the atmosphere in which the system is equilibrated. 

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