International Journal of Chemical Engineering

Research Article

A Solution of the Convective-Diffusion Equation for Solute Mass Transfer inside a Capillary Membrane Bioreactor

Table 2

Parameter values used to determine the concentration profile [17].
Model parameterSymbolUnitBasic measured value
Membrane hydraulic permeability a 𝑘 𝑚 m/Pas3.82 × 10−11
Fraction retentate a 𝐹 0.70
Membrane inner radius 𝑅 𝐿 m1.30 × 10−4
Annulus radius 𝑟 3 m4.08 × 10−4
Effective membrane length 𝐿 m5.7 × 10−2
Lumen-side entrance axial velocity 𝑢 0 ms−11.67 × 10−3
Permeation velocity 𝑣 0 ms−13.82 × 10−7
Number of fibres 𝑁 150
Lumen-side inlet hydrostatic pressure a 𝑝 0 Pa106 325
Shell-side hydrostatic pressure a 𝑝 𝑆 Pa101 325
Glucose diffusivity 𝐷 𝐴 𝐵 m2s1.0 × 10−10
solution density a 𝜌 kg m−3998
solution viscosity a 𝜇 Pas9.7 × 10−4
Glucose inlet concentration 𝑐 0 g dm−32.00
Kinetic constants 𝑉 𝑚 / 𝐾 𝑚 s−11.00
a Typical operational values are used.