Jawaharlal Nehru Technological University Hyderabad B.Tech IV NATURAL GAS HYDRATES AND COAL BED METHANE Previous Question Paper (July - 2021 - R16)

The K-factor method is a thermodynamic approach used to predict the conditions under which gas hydrates form by calculating the equilibrium ratio (K-value) of each component in the gas mixture. The K-value is defined as the ratio of the mole fraction of a component in the vapor phase (y) to its mole fraction in the hydrate phase (x), expressed as K = y/x.

The method relies on the principle that at hydrate equilibrium, the summation of the mole fractions of all components in the hydrate phase must equal unity (Σx = 1). Since x = y/K, the equilibrium condition is satisfied when Σ(y/K) = 1. The K-values are functions of temperature and pressure, typically derived from empirical charts or correlations specific to the hydrate structure (Structure I or II).

The calculation steps involve: 1) Assuming a temperature for a given pressure; 2) Determining the K-value for each component at that temperature and pressure from standard K-factor charts; 3) Calculating the sum Σ(y/K); 4) Iterating the temperature until the sum equals 1.0. A sketch of the K-factor chart would show log(K) on the y-axis against pressure on the x-axis, with individual curves for each gas component (methane, ethane, propane, etc.) showing a downward trend as pressure increases.

For pure methane at 1,000 psia, the hydrate formation temperature is approximately 65°F (18.3°C). This value is obtained from standard hydrate equilibrium curves for pure methane.

At this pressure and temperature, the coexisting phases are the gas phase and the solid hydrate phase. The composition of the gas phase is 100% methane (y = 1.0). The composition of the hydrate phase is defined by the hydrate structure; for methane (Structure I), the hydrate cage occupancy results in a theoretical composition of approximately 1 mole of methane to 5.75 moles of water, or roughly 14.8 mole percent methane in the hydrate lattice.

The water content of the gas at 1,000 psia and 65°F is determined using standard water content charts for natural gas. For pure methane at these conditions, the water content is approximately 85 lb/MMCF.