The Effects of Quartic Term Mathematical Model on The Concentration Profile of Fixed Bed Gas Adsorber

The need for a reliable mathematical model depicting the process inside a column adsorber has become a requisite in designing an effective gas adsorber. Even though this task can be done by using commercial software, it is still important to get an understanding of how the entire process happens. In this paper, we discuss a new way to approximate the concentration profile inside the porous solids. It is an extension of the work of Liaw et al., who adopted a parabolic (i.e., quadratic) profile, which is a function of pellet radius while retaining the spherical symmetry. We extend their work by adding the quartic term. The inclusion of this new term still preserves the form of linear driving force approximation with some correction to Glueckauf’s parameter (i.e., the effective diffusivity coefficient). The addition of the correction will affect the breakthrough curve so that it affects the saturation time. In the binary system of hydrogen/methane discussed in this study, we found that a negative correction to the diffusivity coefficient will make the saturation happen earlier compared to that of the parabolic case, and vice versa. This study may help us design an efficient gas purifier, in particular when we set out for the regeneration of the adsorbent.Keywords: activated carbon; effective diffusivity coefficient; hydrogen; linear driving force; methane; parabolic profile A B S T R A KKebutuhan model matematis yang dapat menggambarkan proses penyerapan dalam kolom adsorpsi telah menjadi kebutuhan yang tak terelakkan dewasa ini. Walaupun kini telah tersedia berbagai perangkat lunak komersial, namun tidak dapat dipungkiri bahwa memahami bagaimana proses tersebut terjadi tetap menjadi suatu hal yang berguna. Paper ini bertujuan untuk menampilkan cara baru dalam pemodelan konsentrasi adsorbat di dalam adsorben padat berpori. Kami memperluas metode yang dikembangkan Liaw et al. dengan menambahkan suku pangkat empat (kuartik). Penambahan ini akan mengoreksi koefisien difusivitas efektif dari persamaan linear driving force (LDF). Koreksi yang bernilai negatif, misalnya, akan mengurangi nilai koefisien difusivitas tersebut sehingga akan menghambat kemampuan adsorpsi. Hasil perhitungan kami pada sistem biner hidrogen/ metana menunjukkan bahwa suatu koreksi bernilai negatif dapat menyebabkan saturasi berlangsung lebih cepat dari kasus profil parabolik. Begitu pula sebaliknya, koreksi positif akan menambah daya adsorpsi sehingga saturasi dapat diperlambat. Studi ini kami harapkan dapat diterapkan untuk mendesain suatu kolom adsorpsi yang efisien, terutama dalam perencanaan proses regenerasi adsorben.Kata kunci: hidrogen; karbon aktif; koefisien difusivitas efektif; linear driving force; metana; profil parabolik

Exact equivalence at cyclic steady state between isothermal diffusion and linear driving force models for linear adsorption systems

To match the dynamics of a linear driving force model and the diffusion equation is of great practical importance in the design and optimization of adsorption separation processes. A frequency response analysis is applied to show that it is not possible to arrive at an equivalence based on a single parameter. Using this as the basis, a universal equivalence for the linear problem is constructed and closed form analytical expressions for the two parameters are derived for the sphere and slab geometries. The two parameters represent the increased effective mass transfer coefficient and a reduction in the active volume of the particle, both corresponding to the internal concentration profiles of the diffusion equation at cyclic steady state.