Validation of pySembrane

The validation of the proposed pySembrane was established through a comparative analysis of the literature. The target system for validation was CO₂ separation from a gas mixture, with pySembrane applied across five distinct scenarios. Of these, three scenarios were compared against results from the Matlab-based ChemBrane program, while the reliability of the remaining two was assessed by comparing outcomes with published literature data. Table 1 shows the parameter settings employed in the five scenarios.

Table 1 Five validation scenarios.

	Scenario
Parameters	1	2	3	4	5
Temperature (T) [K]	308	308	308	298	315
Feed pressure (Pf) [bar]	35	35	15	5	20
Permeate pressure (Pp) [bar]	1	1	1	1	1
Feed flow (Ff) [mol/s]	0.35	0.35	0.35	4.46E-04	0.03
Sweep gas flow (Fsw) [mol/s]	.	.	.	2.01E-05	.
Feed CO2 composition (yf) [mol%]	10	10	10	40	20
Feed CH4 composition (yf) [mol%]	90	90	90	60	4
Feed H2 composition (yf) [mol%]	.	.	.	.	75
Feed CO composition (yf) [mol%]	.	.	.	.	1
CO2 permeance [mol/(m2 bar s)]	3.21E-04	3.21E-04	3.21E-04	8.41E-04	6.96E-06
CH4 permeance [mol/(m2 bar s)]	1.33E-05	1.33E-05	1.33E-05	1.32E-05	5.33E-07
H2 permeance [mol/(m2 bar s)]	.	.	.	.	1.60E-03
CO permeance [mol/(m2 bar s)]	.	.	.	.	6.67E-07
N2 permeance [mol/(m2 bar s)]	.	.	.	3.97E-05	.
Module diameter (dm) [m]	0.1	0.1	0.1	1.20E-02	0.1
Fiber outer diameter (do) [mm]	0.2	0.2	0.17	0.15	0.2
Fiber inner diameter (di) [mm]	0.25	0.25	0.12	0.2	0.25
Fiber length (L) [m]	0.6	0.6	1.5	0.3	0.6
Number of fibers (Nf)	60,000	60,000	60,000	106	60,000
Module configuration	COFS	CTFS	CTFS	CTFS	CTFS

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The validation results are presented in Fig. 1 and Table 2. In comparisons with ChemBrane, all scenarios—except for the permeate flow in scenario 3—showed errors below 5%, indicating a strong similarity. Notably, the permeate flow in scenario 3 displayed a 12.48% difference, because ChemBrane could not consider pressure drop in the system, unlike pySembrane. For Scenario 3, as the feed pressure decreases to 15 bar, the difference between the results of ChemBrane and pySembrane magnifies due to sensitivity to pressure drop. Additionally, while pySembrane exhibited an error exceeding 5% in scenario 4, the results closely align with those reported in the literature, as demonstrated in the Fig. 1 (b) and (c). This is because the measured value of permeate flow was too small, so the relative error reacts sensitively to little differences. On the other hand, in the overall comparison with the literature, the error was generally less than 5%. This finding highlights how pySembrane provides results consistent with previous research, demonstrating its reliability.

Fig. 1 (a) Validation error of each scenario compared with literature. Parity plots for (b) total flowrate and (c) purity of CO₂. The solid red line refers to the identity line, where each point on the line indicates equal values, therefore, the closer the points are to the line, the higher the accuracy.

Table 2 Comparison of pySembrane with ChemBrane and literature data.

	Permeate flow (mol/s)	Permeate CO2 purity (mol%)	Retentate flow (mol/s)	Retentate CH4 purity (mol%)
ChemBrane	0.03	59.12	0.32	94.77
pySembrane	0.0293	58.7256	0.3208	94.4371
Difference (%)	-2.28	-0.67	0.24	-0.35
ChemBrane	0.03	59.88	0.32	94.94
pySembrane	0.0298	59.4229	0.3203	94.5866
Difference (%)	-0.76	-0.76	0.09	-0.37
ChemBrane	0.02	56.72	0.33	92.92
pySembrane	0.0179	55.2064	0.3320	92.4568
Difference (%)	-12.53	-2.67	0.80	-0.50
Experiemental	4.464.E-05	54.40	4.219.E-04	63.30
pySembrane	4.6919.E-05	55.3833	4.1963.E-04	63.6336
Difference (%)	5.10	1.81	-0.54	0.53
Experiemental	0.007	11.50	0.023	5.16
pySembrane	0.0071	11.5206	0.0230	5.1683
Difference (%)	0.47	0.18	-0.11	0.16

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