1,720,983 research outputs found
Solution of population balance equations using the FCMOM
No full textThe FCMOM (Finite size domain Complete set of trial functions Method Of Moments) is an efficient numerical technique to solve population balance equations. It was presented and validated for spatially homogeneous [1,3] and inhomogeneous
conditions [2]. In this work, the general form of the FCMOM governing equations is presented which includes both the source terms and the terms accounting for spatially in-homogeneous conditions. Additionally, the role of the
spatial diffusion terms in the FCMOM technique is investigated both as far as the reconstruction of particle size distribution partial derivative with respect to the internal variable and as far as the effect of the particle diffusivity models on the speed of propagation of the disturbances
Solution of bivariate population balance equations using the FCMOM
No full textThe FCMOM (Finite size domain Complete set of trial functions Method Of Moments) is an efficient and accurate numerical technique to solve PBE (population balance equations) and was validated for monovariate PBE [Strumendo, M.; Arastoopour, H. Solution of PBE by MOM in Finite Size Domains. Chem. Eng. Sci. 2008, 63 (10), 2624]. In the present paper, the FCMOM is extended and used to solve
bivariate PBE. In the FCMOM, the method of moments is formulated in a finite domain of the internal coordinates and the particle distribution function is represented as a truncated series expansion by a complete system of orthonormal functions. In the extension to bivariate PBE, the capabilities of the FCMOM are maintained, particularly as far as the algorithm efficiency and the accuracy in the bivariate
particle distribution function reconstruction. The FCMOM was validated with the following bivariate applications: particle growth, particle dissolution, particle aggregation, and simultaneous aggregation and growth
Solution of population balance equations by the FCMOM for in-homogeneous systems
No full textThe FCMOM (finite size domain complete set of trial functions method of moments) is an efficient and
accurate numerical technique to solve monovariate and bivariate population balance equations. It was previously
formulated for homogeneous systems. In this paper, the FCMOM approach is extended to solve monovariate
population balance equations for inhomogeneous (spatially not uniform) systems. In the FCMOM, the method
of moments is formulated in a finite domain of the internal coordinates and the particle size distribution
function is represented as a truncated series expansion by a complete system of orthonormal functions. The
FCMOM is extended to inhomogeneous systems assuming that the particle-phase convective velocity is
independent of the internal variables (particle size). The method is illustrated by applications to particle diffusion
and to particle convection. In the case of particle convection, a gas-solid dilute flow in a pipe was simulated
and the FCMOM equations were coupled with the governing equations (mass and momentum balances) of
the gas phase
Solution of PBE by MOM in Finite Size Domains
No full textA new approach to solve PBE (Population Balance Equations), FCMOM (Finite size domain Complete set of trial functions Method Of Moments), is presented. The solution of the PBE is sought, instead of the [0,∞] range, in the finite interval between the minimum and maximum particle size; their evolution is tracked imposing moving boundaries conditions. After reformulating the PBE in the standard interval
[−1, 1], the size distribution function is represented as a series expansion by a complete system of orthonormal functions. Moments evolution equations are developed from the PBE in the interval [−1, 1]. The FCMOM is implemented through an efficient algorithm and provides the
solution of the PBE both in terms of the moments and in terms of the size distribution function. The FCMOM was validated with applications to particle growth (constant, linear, diffusion-controlled), simultaneous particle growth and nucleation, particle dissolution, particle aggregation
(constant, sum, product, Brownian kernels) and simultaneous particle aggregation and growth
Method of moments for the dilute granular flow of inelastic spheres
No full textSome peculiar features of granular materials (smooth, identical spheres) in rapid flow are the normal pressure
differences and the related anisotropy of the velocity distribution function f (1). Kinetic theories have been
proposed that account for the anisotropy, mostly based on a generalization of the Chapman-Enskog expansion
[N. Sela and I. Goldhirsch, J. Fluid Mech. 361, 41 (1998)]. In the present paper, we approach the problem
differently by means of the method of moments; previously, similar theories have been constructed for the
nearly elastic behavior of granular matter but were not able to predict the normal pressures differences. To
overcome these restrictions, we use as an approximation of the f (1) a truncated series expansion in Hermite
polynomials around the Maxwellian distribution function. We used the approximated f (1) to evaluate the
collisional source term and calculated all the resulting integrals; also, the difference in the mean velocity of the
two colliding particles has been taken into account. To simulate the granular flows, all the second-order
moment balances are considered together with the mass and momentum balances. In balance equations of the
Nth-order moments, the (N+1)th-order moments (and their derivatives) appear: we therefore introduced
closure equations to express them as functions of lower-order moments by a generalization of the ‘‘elementary
kinetic theory,’’ instead of the classical procedure of neglecting the (N+1)th-order moments and their derivatives.
We applied the model to the translational flow on an inclined chute obtaining the profiles of the solid
volumetric fraction, the mean velocity, and all the second-order moments. The theoretical results have been
compared with experimental data [E. Azanza, F. Chevoir, and P. Moucheront, J. Fluid Mech. 400, 199 (1999);
T. G. Drake, J. Fluid Mech. 225, 121 (1991)] and all the features of the flow are reflected by the model: the
decreasing exponential profile of the solid volumetric fraction, the parabolic shape of the mean velocity, the
constancy of the granular temperature and of its components. Besides, the model predicts the normal pressures
differences, typical of the granular materials
Application of a random pore model with distributed pore closure to the carbonation reaction
No full textSimulation of methane production from hydrates by depressurization and thermal stimulation
No full textRecently methane hydrates have attracted attention due to their large quantity on the earth and their potential as a
new resource of energy. This paper describes a one-dimensional mathematical model and numerical simulation of
methane hydrate dissociation in hydrate reserves by both depressurization and thermal stimulation using a onedimensional radial flow system (axisymmetric reservoir). A moving front that separates the hydrate reserve into
two zones is included in this model. A numerical coordinate transformation method was used to solve the moving
boundary problem. The partial differential equations were discretized into ordinary differential equations using the
method of lines. Our simulations showed that the moving front location and the gas flow rate production are
strong functions of the well pressure and reservoir temperature. The impermeable boundary condition at the reservoir results in very low temperature at the moving front and the formation of ice. The formation of ice, which plugs the
pore volume for the gas to flow, should be avoided. Compared with a stationary water phase model, our simulations showed that the assumption of a stationary water phase overpredicts the location of the moving front and the
dissociation temperature at the moving front and underpredicts the gas flow rate. The thermal stimulation using
constant temperature at the well method using a single well was found to have a limited effect on gas production
compared to gas production due to depressurization
Numerical simulation of methane production from a methane hydrate formation
No full textThis paper describes a one-dimensional model for hydrate dissociation in porous media by the depressurization
method. A moving boundary, which separates the total simulation zone into two zones, is used. The governing
equations consider the convective-conductive heat transfer and mass transfer in the gas and hydrate zones
together with the energy balance at the moving front. These equations were transformed into a new coordinate
system using a coordinate transformation method. The numerical method of lines was used to discretize the
governing equations after coordinate transformation. Distributions of temperature and pressure for different
well pressure and reservoir temperature are presented. The speed of the moving front and the gas production
rate were shown to be strong functions of the well pressure and the absolute permeability of the porous
media. Our simulations also showed that the assumption of stationary water phase, underpredicts gas production
and overpredicts the speed of the moving front
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