OS3A-7:BIVARIATE POPULATION BALANCE MODEL FOR HYDRATE FORMATION CONSIDERING MASS AND HEAT TRANSFER LIMITATIONS

Tatiana P. SAMPAIO 1, Frederico W. TAVARES 2, Paulo L. C. LAGE 3
1. Escola de Química (EQ), Universidade Federal do Rio de Janeiro, Brazil; 2. Escola de Química (EQ), Universidade Federal do Rio de Janeiro, Brazil; 3. Programa de Engenharia Química, COPPE, Universidade Federal do Rio de Janeiro, Brazil

    In this work, we proposed a bivariate population balance model for hydrate formation in a three phase agitated system using hydrate particle size and energy as distribution variables. The model is completed by the overall gas and liquid-phase energy and mass balances. The case studied considered a batch well mixed reactor with gas feed to keep a constant pressure and temperature control by a refrigeration jacket. The system was modeled using five distinct regions: the gas, liquid and solid phases and the gas-liquid and solid-liquid interfaces. The gas phase is composed exclusively by pure methane and the liquid-phase is composed by water and dissolved methane. The gas and liquid phases are assumed to be homogeneous and at thermal equilibrium. The gas-liquid interface is characterized by its area density where nucleation occurs at the three-phase equilibrium conditions. The nucleuses are assumed to be instantaneously transported to the liquid phase bulk. The energy produced during nucleation is also instantaneously transported to the liquid phase. The methane dissolution in the liquid phase from the gas-liquid interface is mass-transfer limited. The hydrate particle growth occurs at the conditions of the particle interface where particle temperature and methane concentration are obtained by combining the heat and mass transfer rates from the bulk phase and the solid-liquid equilibrium conditions at the particle surface. The energy liberated during growth is assumed to be absorbed by the hydrate particle itself. The solid phase is a polydisperse population of hydrate crystals that may have different temperatures and sizes. The particle temperatures are different among themselves and from the liquid-phase temperature. Besides nucleation and growth, particle aggregation and breakage were considered using models and parameters usually applied in crystallization problems. 

    The thermodynamic properties of the liquid and gas phases were evaluated from gamma-phi method using Henry’s law and the Peng-Robinson equation, respectively. Three-phase equilibrium was assumed at the solid interfaces and was described by the Parrish and Prausnitz model (Ind. & Eng. Chem. Process Design 11, 26-35, 1972). The heterogeneous nucleation model proposed by Kashchiev and Firoozabadi (J. Crystal Growth 241, 220-230, 2002) for lens-shaped cluster was applied considering the change in chemical potential due to hydrate formation. The population balance model was solved by using the Direct Quadrature Method of Moments (DQMoM) with two and three quadrature points, using selected bivariate moments for closure. The system of ordinary differential equations formed by the mass, energy and the bivariate moments of the population balance equation was solved using the Differential Algebraic System Solver in C (DASSLC). Results consist of the time evolution of the liquid-phase and particle temperatures, liquid and hydrate masses and methane concentration at liquid phase.