Thermal dispersion in a porous medium

Publisher Summary This chapter focuses on two idealized patterns (of all possible flow patterns), plug flow and back-mix flow. Plug flow assumes that fluid moves through the vessel “in single file” with no overtaking or mixing with earlier or later entering fluid. Back-mix flow assumes that the fluid in the equipment is perfectly mixed and uniform in composition throughout the vessel. All patterns of flow other than plug and back-mix flow may be called nonideal flow patterns because for these the design methods are not nearly as straightforward as those for the two ideal flow patterns. The treatment of nonideal flow patterns discussed in the chapter divides naturally into two parts: flow of single fluids and flow of two fluids. The main emphasis falls on the nonideal flow of single fluids through process equipment. Conversion in a reactor with nonideal flow can be determined either directly from tracer information or by use of flow models. The distribution of residence times gives information on how long various elements of fluid spend in the reactor but not on the detailed exchange of matter within and among the elements. The exact nature of the surrounding molecules is of no importance. Thus, the distribution of residence times yields sufficient information for the prediction of the average concentration in the reactor effluent. Because of a lack of applications, conversion expressions for two region models have not been developed for homogeneous systems. For heterogeneous systems, the appropriate expressions can be found in the works of the individual investigators.

Patterns of Flow in Chemical Process Vessels

Combustion and gasification of coals in fixed-beds

https://hal.archives-ouvertes.fr/hal-02594054/document

A review on experience feedback and numerical modeling of packed-bed thermal energy storage systems

In this paper, a one-dimensional model of countercurrent fixed-bed coal gasification is developed, and results are compared to experimental data from commercial-scale gasifiers. The steady-state model considers separate gas and solid temperatures, axially variable solid and gas flow rates, variable bed void fraction, coal drying, devolatilization based on chemical functional group composition, oxidation and gasification of char, and partial equilibrium in the gas phase. Generalized treatment of gas-phase chemistry and accounting for variable bed void fraction were necessary to predict realistic axial temperature and pressure profiles in an atmospheric fixed-bed gasifier. Model evaluation includes sensitivity of axial temperature profiles to model options, model parameters and operational parameters. Model predictions agree reasonably well with experimental temperature and pressure profile data for gasification of eight coal types ranging from lignite to bituminous. The relative importance of char oxidation resistances to bulk film diffusion, ash diffusion, and chemical reaction is identified.

Modeling fixed-bed coal gasifiers

Experiments of heat and mass transfer from the tube wall to the fluids flowing through the packed beds were carried out separately. In heat transfer air was used as the fluid, and several kinds of solid particles with low and high thermal conductivities were investigated to determine effective thermal conductivities and wall heat transfer coefficients. In mass transfer the dissolution rate of the coated material on the inner wall of the packed tube to the water stream was measured, and wall mass transfer coefficients were analyzed. It was found that a close similarity exists between the JH and JD factor for the wall coefficients in the turbulent-flow region.

Heat and mass transfer from wall to fluid in packed beds

Mass transfer rates from solid particles to water in packed bed were measured for spherical and cylindrical β-naphthol particles.Data at low water velocities show that Sh tends to approach 2.0 with decrease of Rep, as shown in Fig. 2. The effect of Sc on Sh was examined and plotted as in Fig. 4. It was found that Sh-2 was proportional to Sc1/3.The present data and the previonsly published data of other investigators for spherical and cylind rical particles are shown in Fig. 5. The solid lines drawn in the figure correspond to the equations:(3)(4)The data for flakes11) and broken solids4), which are shown in fig. 6 for the experimental range of Rep>1, agree with the results obtained from Equations (3) and (4).

Mass Transfer from Particles to Fluid in Packed Beds

乱流撹拌装置の起動の際の撹拌トルクおよび吐出流量の時間的変化を直接測定して, これらの記録と液体の流動状態の時間的変化を記録した映画とを対照して調べた結果, 撹拌羽根が起動する際は, 動力の大部分が, インペラーから乱れた吐出流が発生する際に消費されることが判明した。このことから, 正逆あるいは断続回転によって, パッフルなし撹拌構の混合時間が短縮できるであろうとの予想を得, この予想は混合時間対動力消費の測定結果により裏付けられた。

Adsorption Separation of Liquid by means of Parametric Pumping

本研究は反応系での触媒内有効拡散係数 (DeR) と非反応の物理拡散系での有効拡散係数 (DeD) との本質的な相異について検討したものである。触媒が広い細孔分布を有するとき, 反応系で有効な平均細孔半径より, 非反応系のそれのほうが圧倒的に大きいことを明らかにし, また, DeR<DeDなること, および細孔分布が分っているときDeR, DeDの推算法を提案し, また有効拡散係数の推算値と実測値との比較を示した。

Effective Diffusivity in Catalyst Pellets

In a cylindrical packed tube heated under the uniform wall temperature, the partial differential equation for the temperature in the steady state is given by Eq. (1).However, when no chemical reaction takes place, Eq. (1)reduces to Eq. (1') with the assumption thatCp G is uniform over the cross section and ke, r and ke, z are uniform within the bed.The solutions can be obtained by applying the finite Hankel transform with respect to. In case of semi-infinite cylinder, Eq. (2) representing the boundary condition at the bed inlet and Eq. (3) representing the boundary condition at the inside wall surface, are applied to Eq. (1'). The solution is given by Eqs. (6) and (7), where ξi is the root of Eq. (4). On the other hand, in case of finite cylinder, Eq. (10) which stands for the bed outlet condition should be employed together with Eqs. (2) and (3), in solving Eq. (1'). The solution is shown by Eqs. (6) and (11).The temperature at the center axis of the packed tube tc and the mixed-mean temperature over the cross section tm are represented by Eqs. (8) and (9), respectively, which are modified forms of Eq. (6).However the solution for the temperature distribution in the finite cylinder will be valid for any value of δ, Eq. (11) is nearly equal to Eq. (7) when δ is less than 30 or so.The value of δ is smaller than 10 for the usual packed beds14), consequently, it may be concluded that Eqs. (6) and (7) are applicable enough, regarding the packed bed as the semi-infinite cylinder.In case the flow-rate is relatively high, k becomes small, and then Eqs. (6) and (7) are nearly equal to Eq. (13) obtained by Maeda et al4) and Marshall et al1), in which equation the axial heat conduction is neglected. But it should be pointed that Eqs. (6) and (7) serve as a good solution for the low flow-rate range, because k is not so small in this range.When chemical reaction approximated by q=q0·exp[-αl] takes place, the temperature distribution is reprerented by Eq. (14), assuming the packed bed as the semi-infinite cylinder.

https://www.jstage.jst.go.jp/article/kakoronbunshu1953/23/3/23_3_161/_pdf

Noriaki Wakao

Papers

Heat and mass transfer from wall to fluid in packed beds

Mass Transfer from Particles to Fluid in Packed Beds

Adsorption Separation of Liquid by means of Parametric Pumping

Effective Diffusivity in Catalyst Pellets

Theoretical Temperature Distribution in Packed Bed