tailieunhanh - Mass Transfer in Multiphase Systems and its Applications Part 19

Tham khảo tài liệu 'mass transfer in multiphase systems and its applications part 19', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Mass Transfer through Catalytic Membrane Layer 709 The most hollow fiber configurations the ratio R L are very small less than 1 x 10-3 thus the inertial terms can be neglected Mondor Moresoli 1999 . Finally because the velocity gradients are smaller in the axial direction than in radial direction the axial stress terms can be neglected in the momentum equation. Thus the simplified form the momentum and the continuity equations are respectively given as 1 Õ du I r7 I r dr I dr dP dx 124 and du . 1 d ru - - _ 0 dx r dr The solute balance equation with constant diffusion coefficient ac de J a2C . 1 de . a2c II u -- - 2- dx dr I dr r dr dx 125 126 The J mass transfer rate presented should be inserted into the boundary condition given by eq. 2c of mass balance eq. 1a or eq. 126 thus this differential equation can be solved. In the case of membrane reactor or bioreactor the axial pressure gradient within the membrane is often negligible compared to the radial pressure gradient thus the first term in eq. 125 can often be neglected. When there is no change of volume of the fluid phase because the low convective permeation rate or the case of dilute fluid phase the mass balance equation given by eq. 126 should be taken into account during the mass transport calculation Piret Cooney 1991 . 7. Conclusion Mass transfer rate and in some cases the concentration distribution inside a membrane reactor were defined. Exact solutions of the mass transfer rate were given taking into account the external mass transfer resistance on the both sides of the catalytic membrane layer. The membrane is either intrinsically catalytic or catalytic particles are dispersed in the membrane matrix. For this letter case both pseudo-homogeneous model for nanometer sized particles and heterogeneous one for microsized catalyst particles have been presented. An analytical approaching solution was developed for cylindrical coordinate and or variable mass transport parameters as . diffusion coefficient