Membrane Gas Separation

The Effect of Sweep Uniformity on Gas Dehydration Module Performance
335
to use of a product sweep in some cases. However, the changes in performance are modest 
and may not justify the purchase and maintenance of a vacuum pump. Metz et al. [16]
report measurements of the dependence of water permeability on water concentration. 
This dependence is important if boundary layer resistances to mass transfer are compa-
rable to or less than the membrane resistance. 
Pan [17] describes one of the fi rst attempts to evaluate the performance of a gas separa-
tion module for the separation of multicomponent mixtures. Pan ’ s analysis assumes the 
local permeate composition, that determines the partial pressure driving force for permea-
tion, is not equal to the bulk concentration of the permeate due to the membrane support 
resistance. Instead the composition within the membrane support is taken as the composi-
tion produced by cross - fl ow of the permeate through the support. Additionally, permeate 
pressure drop within the support is neglected. Kovvali et al. [18] propose a simplifi cation 
to Pan ’ s solution procedure by assuming a linear relationship between permeate and 
retentate mole fractions for suffi ciently small composition ranges. Chowdhury et al. [19]
obtain more accurate solutions by using a backward difference Adams - Moulton or Gear 
approximation for the governing differential equations. The resulting non - linear algebraic 
equations are solved with a modifi ed Powell hybrid algorithm that utilizes a fi nite differ-
ence approximation for the Jacobian. 
Coker et al. [20] avoid the assumption of a local permeate composition equal to the 
cross - fl ow composition by dividing a module into a series of N well - mixed stages and 
solving the Weller - Steiner equations [21] for each stage. If the stages are numbered from 
1 to N from the feed to the retentate product end, the retentate stream exiting stage i is 
the feed to stage i + 1. The permeate from stage i + 1 is sent to stage i as a sweep for 
countercurrent modules; for co - current modules, the permeate from stage i – 1 is used. 
This simplifi cation is equivalent to the use of fi rst - order fi nite differences to approximate 
the derivatives in the governing mass balances. Kaldis et al. [22] describe an alternative 
solution procedure in which the governing differential equations are approximated using 
an orthogonal collocation algorithm. 
Lemanski and Lipscomb
[23,24] 
describe solutions of the governing conservation 
of mass equations for fl ows throughout the lumen and shell regions of a module. The 
solution assumes the fl ows are equivalent to fl ow through an effective porous media 
and explicitly accounts for the infl uence of inlet and outlet port placement on perfor-
mance. Marriott et al. [25 – 27] also describe solutions to the governing conservation 
of mass, momentum, and energy equations for the fl ows within the lumen and shell 
regions. For countercurrent and co - current fl ows, the rigorous axis symmetric conserva-
tion equations are solved within the lumen of an individual fi bre – all fi bres are assumed 
identical. The lumen equations are coupled to the shell equations assuming uniform axial 
plug fl ow in the shell; fl uid distribution to and from lumen distribution manifolds is not 
considered. 
This work reports simulations of sweep distribution within the shell and its effect 
on module performance. Two types of simulations are considered: (1) simulations 
that assume the sweep fl ow around each fi bre is distributed in a Gaussian manner and 
(2) simulations that explicitly predict fl ow fi elds within the shell based on how the sweep 
gas is introduced. 
Predictions based on explicit calculation of the shell fl ow are in good agreement with 
those based a Gaussian sweep distribution using a standard deviation in sweep fl ow equal 

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336
Membrane Gas Separation
to
∼
20% of the average sweep fl ow rate. Surprisingly, sweep distribution has little effect 
on performance in both cases.