Calculate Activation energy

Activated permeation-model \( P_i = P_{0,i} \exp (-\frac{E_{P,i}}{RT}) \)

\(P_i\):permeance of i-th component \(\rm{[mol/(m^2 \ s \ Pa)]}\) \(P_{0,i}\): pre-exponential factor \(\rm{[mol/(m^2 \ s \ Pa)]}\) \(R\):gas constant \(\rm{[J \ mol^{-1} \ K^{-1}]}\)

\(E_p\):activation energy of permeation for the i-th component \(\rm{[J/ \ mol]}\) \(T\):absolute temperature \(\rm{[K]}\)

modified Gas Translation (GT)-model
\( P_i = \frac{k_{0,i}}{\sqrt{M_iRT}} \exp (-\frac{E_{P,i}}{RT}) \)

where
\( k_{0,i} = k_{0}(d_p - d_{i})^3 \), \( k_0 = \frac{\sqrt{2 \pi} N_p}{6 \tau L A_m} \)

\(P_i\):permeance of i-th component \(\rm{[mol/(m^2 \ s \ Pa)]}\) \(E_{p,i}\):activation energy of permeation for the i-th component \(\rm{[J/ \ mol]}\)

\(R\):gas constant \(\rm{[J \ mol^{-1} \ K^{-1}]}\) \(T\):absolute temperature \(\rm{[K]}\) \(k_{0,i}\):permeation constant for the i-th component [-]

\(d_p\):pore diameter \(\rm{[m]}\) \(d_i\):diameter of the i-th component \(\rm{[m]}\) \(k_0\):structural constant \(\rm{[m^3]}\) \(N_p\):number of pores [-]

\(\tau\):tortuosity [-] \(L\):membrane thickness \(\rm{[m]}\) \(A_m\):membrane area \(\rm{[m^2]}\) \(M_i\):Molecular weight of i-th component \(\rm{[kg \ mol^{-1}]}\)

Reference

Lee HR, Kanezashi M, Shimomura Y, Yoshioka T, Tsuru T. Evaluation and fabrication of pore‐size‐tuned silica membranes with tetraethoxydimethyl disiloxane for gas separation. AIChE J. 2011;57:2755–2765.

How to use this web

1. Please select "Model type"

2. Please select "Gas type" and "Molecular size"

3. Please input Experimental temperature \(\rm{[K]}\) and permeance \(\rm{[mol/(m^2 \ s \ Pa)]}\)

4. Please click the button

Model type Activated permeation model type GT-model type

Gas type
Molecular weight,\(M_i\) [g/mol]
Molecular size,\(d_i\) [nm]
Type of Molecular size

Calculate Activation energy and Stuructre parameter

Experimental temperature [K]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]











Activation energy,\(E_{p,i}\) [J/mol]
permeation constant,\(k_{0,i}\) [-]
R2[-]