Mass Transport in a Microchannel Bioreactor With a Porous Wall

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Xiao Bing Chen ◽  
Yi Sui ◽  
Heow Pueh Lee ◽  
Hui Xing Bai ◽  
Peng Yu ◽  
...  

A two-dimensional flow model has been developed to simulate mass transport in a microchannel bioreactor with a porous wall. A two-domain approach, based on the finite volume method, was implemented. For the fluid part, the governing equation used was the Navier–Stokes equation; for the porous medium region, the generalized Darcy–Brinkman–Forchheimer extended model was used. For the porous-fluid interface, a stress jump condition was enforced with a continuity of normal stress, and the mass interfacial conditions were continuities of mass and mass flux. Two parameters were defined to characterize the mass transports in the fluid and porous regions. The porous Damkohler number is the ratio of consumption to diffusion of the substrates in the porous medium. The fluid Damkohler number is the ratio of the substrate consumption in the porous medium to the substrate convection in the fluid region. The concentration results were found to be well correlated by the use of a reaction-convection distance parameter, which incorporated the effects of axial distance, substrate consumption, and convection. The reactor efficiency reduced with reaction-convection distance parameter because of reduced reaction (or flux), and smaller local effectiveness factor due to the lower concentration in Michaelis–Menten type reactions. The reactor was more effective, and hence, more efficient with the smaller porous Damkohler number. The generalized results could find applications for the design of bioreactors with a porous wall.

2011 ◽  
Vol 110-116 ◽  
pp. 3489-3494
Author(s):  
Hong Tong Low ◽  
Xiao Bing Chen ◽  
Peng Yu ◽  
Sony Winoto

A two-dimensional flow model, incorporating mass transport, has been developed to simulate flow in a microchannel bioreactor with a porous wall. A two-domain method was implemented which was based on finite volume method. For the porous-fluid interface, a stress jump condition was used with continuity of normal stress; and the mass interfacial conditions were continuities of mass and mass flux. Two parameters are defined to characterize the mass transports in the fluid and porous regions. The porous Damkohler number is the ratio of consumption to diffusion of the substrates in the porous medium. The fluid Damkohler number is the ratio of substrate consumption in the porous medium to substrate convection in the fluid region. The concentration results are found to be well correlated by the use of a reaction-convection distance parameter which incorporates the effects of axial distance, substrate consumption and convection.


2014 ◽  
Vol 44 (2) ◽  
pp. 149-157
Author(s):  
A. M. RASHAD

 A boundary-layer analysis is presented for the natural convec tion boundary layer flow about a sphere embedded in a porous medium filled with a nanofluid using Brinkman-ForchheimerDarcy extended model. The model used for the nanofluid incorporates the ef fects of Brownian motion and thermophoresis. The governing partial differential equa tions are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity, temperature, and nanoparticles volume fraction profiles as well as the local skin-friction coefficient, local Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.


1982 ◽  
Vol 22 (01) ◽  
pp. 141-150 ◽  
Author(s):  
Muhammad I. Kabir ◽  
Larry W. Lake ◽  
Robert S. Schechter

Abstract In-situ leach mining for uranium is an emerging technology. Currently, the selection of a well pattern designed to recover mineral values is governed primarily by arguments based on hydrological considerations. The effects of well pattern and well spacing on uranium recovery and oxidant utilization are considered in this paper. As expected, formation permeability heterogeneities and anisotropies are found to be important issues requiring careful consideration, however, it also is shown that chemical factors cannot be ignored. In particular, it is shown that the oxidant efficiency and the produced uranium solution concentrations are sensitive to the presence of other minerals competing with uranium for oxidant. If the Damkohler number for competing minerals, which measures the speed of the reaction, exceeds that for uranium, the competing mineral will have to be oxidized completely to recover a large proportion of the uranium. If the Damkohler number is smaller, it may be possible to achieve considerable selectivity for uranium by adjusting the well spacing. It also is shown that the oxidant efficiency is generally highest for well patterns that give streamlines of roughly equal length and that there is a minimum distance between injection and production wells to utilize oxidant most advantageously. Introduction In-situ solution mining is a process whereby uranium is recovered from permeable sandstone bodies by injecting and producing a leach solution through an array of wells penetrating the mineralized zone. It appears to have broad application and in many situations offers both economic and environmental advantages. The processes may be classified generally as acid or alkaline, but the general features of both are the same. The insoluble uranium in the mineralized zone is in the +4 state of oxidation. To be mobilized, the uranium must be oxidized to the +6 state and complexed either with sulfate in the case of acid leaching or carbonate in the case of alkaline leaching to form highly soluble uranyl sulfates or carbonates. The leach solutions, therefore, contain an oxidant (oxygen, hydrogen peroxide, ferric cations, sodium hyperchlorite, etc.) together with a complexing agent (anion). The choice of leach solution depends on a number of factors including selectivity and injectivity. For example, formations containing more than 1 wt% carbonates are not likely to be candidates for acid leaching because of the large acid requirement and because of permeability loss due to precipitation of calcium sulfate. It is the purpose of this paper to consider the technical factors (as opposed to economic) that govern the choice of well pattern to be used for leaching. The discussion is structured so that the conclusions apply to both alkaline and acid lixiviants and to any oxidant, although an occasional reference to a particular oxidant may appear. Considerable use is made of the computer simulator previously reported. The computational details are available in that paper. A number of factors that pertain to the selection of a well pattern are considered. It is shown that the effectiveness of the oxidant - i.e., the uranium recovered per unit of oxidant injected - is related to the well pattern, to the reaction rates, and to the permeability variations, especially if the formation is anisotropic. Furthermore, the spacing between wells is related to reactions with oxidizable minerals that compete for oxidant. These considerations can be quantified to some extent by studying linear systems. Linear Flow Systems SPEJ P. 132^


1987 ◽  
Vol 60 (1) ◽  
pp. 140-158 ◽  
Author(s):  
Dancheng Kong ◽  
James L. White ◽  
Frederick C. Weissert ◽  
Nobuyuki Nakajima

Abstract A fundamental study on curing of rubber compounds in molds is presented. We have measured the thermal conductivity of a range of rubber compounds determining the influence of carbon black, other fillers, and oil. The heats of reaction associated with the curing kinetics of model compounds were measured. A mathematical model is proposed to predict the temperature profiles for curing a reactive slab. This involves inclusion of an energy generation rate, which depends on time and temperature. This is expressed through a Damkohler number. Solutions of the heat conduction equation are interpreted in terms of the Fourier number and the Damkohler number. Calculations are carried out using experimentally determined thermal conductivities and curing kinetics. Thick parts are shown to heat up more slowly (associated with the Fourier number) and to show greater overshoots of cure temperature (associated with the Damkohler number).


Author(s):  
K. R. V. Manikantachari ◽  
Scott Martin ◽  
Ramees K. Rahman ◽  
Carlos Velez ◽  
Subith Vasu

Abstract A counterflow diffusion flame for supercritical CO2 combustion is investigated at various CO2 dilution levels and pressures by accounting for real gas effects into both thermal and transport properties. The UCF 1.1 24-species mechanism is used to account the chemistry. The nature of important nonpremixed combustion characteristics such as Prandtl number, thermal diffusivity, Lewis number, stoichiometric scalar dissipation rate, flame thickness, and Damköhler number are investigated with respect to CO2 dilution and pressure. The results show that the aforementioned parameters are influenced by both dilution and pressure; the dilution effect is more dominant. Further, the result shows that Prandtl number increases with CO2 dilution and at 90% CO2 dilution, the difference between the Prandtl number of the inlet jets and the flame is minimal. Also, the common assumption of unity Lewis number in the theory and modeling of nonpremixed combustion does not hold reasonable for sCO2 applications due to large difference of Lewis number across the flame and the Lewis number on the flame drop significantly with an increase in the CO2 dilution. An interesting relation between Lewis number and CO2 dilution is observed. The Lewis number of species drops by 15% when increasing the CO2 dilution by 30%. Increasing the CO2 dilution increases both the flow and chemical timescales; however, chemical timescale increases faster than the flow timescales. The magnitudes of the Damköhler number signify the need to consider finite rate chemistry for sCO2 applications. Further, the Damköhler numbers at 90% sCO2 dilution are very small; hence, laminar flamelet assumptions in turbulent combustion simulations are not physically correct for this application. Also, it is observed that the Damköhler number drops nonlinearly with increasing CO2 dilution in the oxidizer stream. This is a very important observation for the operation of sCO2 combustors. Further, the flame thickness is found to increase with CO2 dilution and reduce with pressure.


Author(s):  
Bassem H. Ramadan

The effect of the Damkohler number (Da) and non-unity Lewis number on a two-dimensional, steady, laminar diffusion flame anchored by a dividing plate in a rectangular channel was considered. The governing equations were solved numerically, using the SIMPLE and ADI schemes. The results for non-unity Lewis number were compared with those for a unity Lewis number, and Da a was also varied in order to determine their effect on the flame structure. The results show that an increase in the Da causes the flame to exist closer to the trailing edge of the divider and to increase the reactivity. A non-unity Lewis number creates a non-symmetrical flame by forcing the flame to exist on the fuel side.


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