An Enhanced Sherwood Number to Model the Hydrogen Transport in Membrane Steam Reformers

Abstract

It is well known that membrane reactors are inherently two-dimensional systems in which species concentrations vary as a consequence of both the reaction and permeation across the membrane, which occurs in the direction perpendicular to that of the main gas flow. Recently, an expression for an enhanced Sherwood number was developed to describe the hydrogen concentration gradients arising in methane steam-reforming membrane reactors as a consequence of the combined effect of hydrogen production, dispersion, and permeation. Here, the analysis is developed in further detail with the aim of (i) assessing the validity of the simplifying assumptions made when developing the 1D model and (ii) identifying the operating conditions under which it is possible to employ the 1D model with the enhanced Sherwood number.

Keywords: 2D model; concentration gradients; hydrogen; membrane reactors.

Figure 1

Hydrogen recovery, $$R_h$$, vs. pressure for a reactor operating with $$Da=1$$, $$Pe=100$$, and $$\gamma$$ values of 1 (triangles) and 3 (circles).

Figure 2

Ratio between the radial and axial components of velocity at 0.1, 10, 20, 30, 40, 50, 60, 70, 80, and 90% of the reactor length evaluated for γ = 5, Da = 1, and (a) Pe = 20, P = 1 atm (b) Pe = 20, P = 10 atm, (c) Pe = 50, P = 1 atm, (d) Pe = 50, P = 10 atm, (e) Pe = 100, P = 1 atm, and (f) Pe = 100, P = 10 atm.

Figure 3

Hydrogen recovery vs. pressure evaluated through the full 2D model (solid lines) and 1D model with enhanced Sherwood number (dashed lines) at $$Da=5$$, $$\gamma =5$$, and $$Pe$$ values of 20, 30, 40, 50, 70, and 100.

Figure 4

Comparison of hydrogen recovery vs. pressure evaluated through the full 2D model (solid line) and 1D model (dashed lines) with the enhanced Sherwood number (dashed lines) and the 1D model with fixed values of $$Sh$$ of 3.66 and 7.75 at $$Da=5$$, $$\gamma =5$$, and $$Pe=50$$.