E. Saatdjian

Dynamics of natural gas adsorption storage systems employing activated carbon

Various aspects of the dynamics of natural gas adsorption storage systems employing activated carbon are studied theoretically. The fast charge of the storage system is the first subject addressed. Emphasis is given to thermal effects and hydrodynamics of flow through the carbon bed. In order to study the influence of diffusional resistances on charge dynamics, an intraparticle transport equation governed by a diffusion law is added to the computational model. Lastly, the slow discharge process and proposed solutions for reducing the adverse effect of the heat of adsorption on storage capacity, including in situ thermal energy storage, are discussed.

A simulation model of a high-capacity methane adsorptive storage system

A two-dimensional model is developed to describe the hydrodynamics, heat transfer and adsorption phenomena associated with the adsorptive storage of natural gas (NG) in cylindrical reservoirs. Intraparticle and film resistances to both heat and mass transfer are neglected. In the momentum equation, Erguns law is considered locally valid and is extended to two dimensions. These assumptions are fully justified in the paper. Numerical results are presented concerning the pressurization and blowdown of an ultra-lightweight 50 litre cylinder, commercially available for the storage of compressed NG, if it were filled with an activated carbon having a good adsorptive storage capacity. A simple formula is also proposed to predict the filling times for fast charges. The predicted temperature changes in the packed-bed are in good agreement with those reported in the literature for an experimental charge/discharge.

Charge dynamics of a methane adsorption storage system: Intraparticle diffusional effects

The charge of natural gas adsorption storage systems is studied numerically, With emphasis given to the impact on its dynamics of intraparticle diffusional resistances to mass transport. Besides adsorption kinetics and thermal effects, the simulation model takes into account both mass transport inside the adsorbent and hydrodynamics of flow through the packed bed. Numerical results are presented for change with methane of a 50 liter cylindrical reservoir, filled with hypothetical adsorbents with diffusional time constants in the range 10−3 s1D/Rp2 ≤ ∞. and with the adsorption equilibrium curve of a commercially available activated carbon with a good adsorptive storage capacity. An attempt is made to assemble the charge histories for different values ofD/Rp2 , in a single cure by using a modilied time scale.

Chaotic advection and heat transfer enhancement in Stokes flows

The heat transfer rate from a solid boundary to a highly viscous fluid can be enhanced significantly by a phenomenon which is called chaotic advection or Lagrangian turbulence. Although the flow is laminar and dominated by viscous forces, some fluid particle trajectories are chaotic due either to a suitable boundary displacement protocol or to a change in geometry. As in turbulent flow, the heat transfer rate enhancement between the boundary and the fluid is intimately linked to the mixing of fluid in the system. Chaotic advection in real Stokes flows, i.e. flows governed by viscous forces and that can be constructed experimentally, is reviewed in this paper. An emphasis is made on recent new results on 3-D time-periodic open flows which are particularly important in industry.

Natural Convection in a Porous, Horizontal Cylindrical Annulus

Natural conversion in a porous medium bounded by two horizontal cylinders is studied by solving the two-dimensional Boussinesq equations numerically. An accurate second-order, finite differenre scheme using an alternating direction method and successive underrelaxation is applied to a very fine grid. For a radius rato above 1.7 and for Rayleigh numbers above a critical value, a closed hysteresis loop (indicating two possible solutions depending on initial conditions) is observed

On the optimization of mixing protocol in a certain class of three-dimensional Stokes flows

Mixing in a special class of three-dimensional, non-inertial periodic flows is studied numerically. In the type of flow considered here, the cross-sectional velocity components are independent of the axial flow and the axial flow is independent of the axial coordinate. Using the eccentric helical annular mixer as a prototype, we consider the counter-rotating case with steady rotation of the outer cylinder and sinusoidal modulation of the inner one. Apart from the mixer geometry, the behavior of the system is governed by two dimensionless parameters obtained by scaling the cross-sectional stirring protocol with respect to the characteristic residence time of the fluid in the mixer. The first parameter is related to the average number of turns of the outer cylinder and the second one is related to the average number of modulation periods of the inner cylinder. The convection-diffusion equation is solved numerically, with temperature as a passive scalar, at high Peclet number. For a given three-dimensional mixer geometry and axial flow rate we show that there is an optimum modulation frequency for which the exit standard deviation of the temperature field is a minimum. Lagrangian simulations at infinite Peclet number and the use of other tools to study mixing, such as stretching calculations and tracer tracking methods, confirm that the optimized protocol does result in very effective mixing.

Natural convection in porous cylindrical annuli

Natural convection in a porous layer between two horizontal, concentric cylinders is investigated numerically by solving the 2‐D Darcy‐Boussinesq equations on a very fine grid. The parabolic‐elliptic system was solved by a second order finite difference scheme based on the implicit alternating direction method coupled with successive under relaxation. The calculations show that for radius ratios above 1.7, the functional relationship between the mean Nusselt number and the Rayleigh number exhibits a closed hysteresis loop associated with the transition from a two to a four cell flow pattern. For very small radius ratios, steady state regimes containing 2, 4, 6, and 8 cells are progressively obtained as the Rayleigh number is increased, but no hysteresis behaviour is observed. For a radius ratio of 2, the numerical results are in good agreement with the experimental data. Multi‐cellular regimes and hysteresis loops have also been reported in the literature for fluid annuli but some differences between the ...

On the numerical solution of partial differential equations with two spatial scales

Abstract A numerical solver developed for the solution of parabolic partial differential equations involving two spatial scales is presented. The equations are discretized using the finite volume method, and the resulting system of ordinary differential equations is solved using the stiff code DASSL. The solver has been implemented in the form of a collection of FORTRAN subroutines. The large sparse linear systems which occur during the solution process are solved by a direct efficient method based on a complete LU factorization. The method is fully described in the paper. The storage space needed by the algorithm is reduced by a factor of 3m 4 , m being the number of micro grid points, with respect to the standard LINPACK band solver. A comparison of the number of floating point operations involved in the different algorithms shows that this approach reduces the operation count for the factorization phase by a factor of about m, with respect to the LINPACK solver. For the substitution phase the improvement ratio is approximately equal to 3m 4 .

On the reduction of natural convection heat transfer in horizontal eccentric annuli containing saturated porous media

Studies numerically natural convection in a saturated porous medium bounded by two horizontal, isothermal eccentric cylinders by solving the governing two‐dimensional Darcy‐Boussinesq equations on a very fine grid for different values of the eccentricity e. For a radius ratio of 2 and e < 0.5, both a bicellular and a tetracellular flow patterns remain stable for moderate Rayleigh numbers. For e ≥ 0.5, the transition from one flow regime to the other occurs with one of the solutions losing stability. Suggests that in a real situation, insulation is more efficient if the eccentricity is set to the maximum value for which the four‐cell flow pattern is physically realizable than to the value that minimizes the heat transfer when the flow pattern is bicellular. The net gain with respect to a concentric insulation can be of the order of 10 per cent.

Heat Transfer in a Countercurrent, Gas–Solid, Packed Column

A theoretical model has been used, in conjunction with pressure drop and solid holdup data, to predict correctly the thermal efficiency of a countercurrent, gas-solid, packed heat exchanger. In the model, the ideal efficiency is multiplied by a ratio of particles in contact with the gas to the total amount of particles in the packed section. The Erugun equation is used to obtain both the effective packing porosity and the number of particles in contact with the gas. The results show that the model correctly gives the efficiency versus gas velocity curve for different packing heights and solids mass fluxes. The calculated and experimental velocities for which exchanger efficiency is a maximum are also in agreement.