Use of Ion Exchange Resins in Continuous Chromatography for Sugar Processing

Abstract

In this chapter, the use of ion exchange resins in continuous sugar process industry is reviewed. A particular focus is given to chromatographic methods and, in particular, to continuous annular chromatography and simulated moving-bed (SMB) apparatus. The use of ion exchange resins for the separation of a fructose and glucose mixture (by means of an SMB unit) and the separation into pure components of a ternary mixture of sugars (by means of a Pseudo-SMB technique) is detailed. The use of ion exchange resins in integrated reactors (separation in situ with reaction) is also addressed in this chapter, presenting several advantages of these promising intensified processes for the sugar industry.

Annexes

5.1.1 Annex (1)

The mathematical model approach, hereby used to simulate an SMB unit, represents it as a sequence of columns described by the usual system equations for an adsorptive fixed bed (each column $k$). All these columns are then linked by the so-called node equations, stated to each section $j$, making use of the equivalence between the interstitial velocity in the TMB and SMB, and thus one has for

$$ \begin{array}{l}\rm{Eluent (E) node}:{u}_{I}^{*}={u}_{IV}^{*}+{u}_{E}\\ \rm{Extract }(\rm{X})\rm{ node}:{u}_{II}^{*}={u}_{I}^{*}-{u}_{X}\\ \rm{Feed }(\rm{F})\rm{ node}:{u}_{III}^{*}={u}_{II}^{*}+{u}_{F}\\ \rm{Raffinate }(\rm{R})\rm{ node}:{u}_{IV}^{*}={u}_{III}^{*}-{u}_{R}\end{array}$$

Due to the switch of the inlet and outlet lines, the boundary conditions to a certain column are not constant during a whole cycle, but change after a period equal to the switching time. Since the model equations are set to each column $k$, the concentration of $i$ species at the beginning of each column $k$, ${C}_{{b}_{i,k}}^{0}$, must be recalculated for each switching time period following the next node mass balances:

$t=0$ to ${t}_{s}$:

$$ \begin{array}{llllll}{c}k=1:{{C}_{{b}_{i,{\displaystyle {\sum }_{j=I}^{IV}{n}_{j}}}}|}_{z=L}{}_{{\displaystyle {\sum }_{j=I}^{IV}{n}_{j}}}=\frac{{u}_{I}^{*}}{{u}_{IV}^{*}}{C}_{{b}_{i,1}}^{0}-\frac{{u}_{E}}{{u}_{IV}^{*}}{C}_{i}^{E}\\ k=2\\\rm{to}\\({n}_{I}+{n}_{II}):{{C}_{{b}_{i,\left(k-1\right)}}|}_{z={L}_{\left(k-1\right)}}={C}_{{b}_{i,k}}^{0}\\ k=({n}_{I}+{n}_{II}+1):{{C}_{{b}_{i,\left({n}_{I}+{n}_{II}\right)}}|}_{z={L}_{\left({n}_{I}+{n}_{II}\right)}}=\frac{{u}_{III}^{*}}{{u}_{II}^{*}}{C}_{{b}_{i,\left({n}_{I}+{n}_{II}+1\right)}}^{0}-\frac{{u}_{F}}{{u}_{II}^{*}}{C}_{i}^{F}\\ \rm{ }k=({n}_{I}+{n}_{II}+2)\\\rm{to}\\{\displaystyle {\sum }_{j=I}^{IV}{n}_{j}}:{{C}_{{b}_{i,\left(k-1\right)}}|}_{z={L}_{\left(k-1\right)}}={C}_{{b}_{i,k}}^{0}\rm{ }\end{array} $$

$t={t}_{s}$ to $2{t}_{s}$:

$$ \begin{array}{c}k=1: \\{ {C}_{{b}_{i,{\displaystyle {\sum }_{j=I}^{IV}{n}_{j}}}}|}_{z=L}{}_{{\displaystyle {\sum }_{j=I}^{IV}{n}_{j}}}={C}_{{b}_{i,1}}^{0}\\ k=2:\\{{C}_{{b}_{i,1}}|}_{z=L}{}_{1}=\frac{{u}_{I}^{*}}{{u}_{IV}^{*}}{C}_{{b}_{i,2}}^{0}-\frac{{u}_{E}}{{u}_{IV}^{*}}{C}_{i}^{E}\\ k=3\\\rm{to}\\({n}_{I}+{n}_{II}+1):\\\\{{C}_{{b}_{i,\left(k-1\right)}}|}_{z={L}_{\left(k-1\right)}}={C}_{{b}_{i,k}}^{0}\\ k=({n}_{I}+{n}_{II}+2):\\{{C}_{{b}_{i,\left({n}_{I}+{n}_{II}+1\right)}}|}_{z={L}_{\left({n}_{I}+{n}_{II}+1\right)}}=\frac{{u}_{III}^{*}}{{u}_{II}^{*}}{C}_{{b}_{i,\left({n}_{I}+{n}_{II}+2\right)}}^{0}-\frac{{u}_{F}}{{u}_{II}^{*}}{C}_{i}^{F}\\ k=({n}_{I}+{n}_{II}+3)\\\rm{to}\\{\displaystyle {\sum }_{j=I}^{IV}{n}_{j}}:\\{{C}_{{b}_{i,\left(k-1\right)}}|}_{z={L}_{\left(k-1\right)}}={C}_{{b}_{i,k}}^{0}\end{array} $$

This set of equations continues to progress in a similar way (shifting one column per ${t}_{s}$), until ${\displaystyle {\sum }_{j=I}^{IV}{n}_{j}}{t}_{s}$, repeating then from the first switch.

Considering the dimensionless variables $x=\frac{z}{{L}_{c}}$ and $\theta =\frac{t}{{t}_{s}}$, and a linear driving force (LDF) approximation [95] to the mass transfer (set in terms of the adsorbed phase in equilibrium with the bulk concentration and the average adsorbed phase concentration: ${a}_{i,k}\left({q}_{i,k}^{eq}-\langle {q}_{i,k}\rangle \right)$, where ${a}_{k}={k}_{LDF}{t}_{k}$), one can establish a set of mass balances equations for each species $i$ in each column $k$, in each section $j$, as follows for the bulk fluid phase:

$$ \frac{\partial {C}_{{b}_{i,k}}}{\partial q}={g}_{j}^{*}\left\{\frac{1}{P{e}_{j}^{*}}\frac{{\partial }^{2}{C}_{{b}_{i,k}}}{\partial {x}^{2}}-\frac{\partial {C}_{{b}_{i,k}}}{\partial x}-\frac{(1-{e}_{b})}{{e}_{b}}{a}_{i,k}\left({q}_{i,k}^{eq}-\langle {q}_{i,k}\rangle \right)\right\}$$

and for the mass balance in the particle,

$$ \frac{\partial \langle {q}_{i,k}\rangle }{\partial q}={g}_{j}^{*}{a}_{i,k}\left({q}_{i,k}^{eq}-\langle {q}_{i,k}\rangle \right) $$

with the respective initial:

$$ q=0:{C}_{{b}_{i,k}}(x,0)=\langle {q}_{i,k}(x,0)\rangle =0$$

and boundary conditions:

$$ \begin{array}{l}x=0:{C}_{b}{i,k}_{}={{C}_{{b}_{i,k}}|}_{x=0}-\frac{1}{P{e}_{j}^{*}}{\frac{\partial {C}_{{b}_{i,k}}}{\partial x}|}_{x=0}\\ \rm{}x=1:{\frac{\partial {C}_{{b}_{i,k}}}{\partial x}|}_{x=1}=0\end{array}$$

where ${g}_{j}^{*}=\frac{{u}_{j}^{*}}{{u}_{s}}$ is the ratio between SMB fluid and the solid interstitial velocities and $P{e}_{j}^{*}=\frac{{u}_{j}^{*}{L}_{c}}{{D}_{b}}$ the column Peclet number. As consequence, one obtains discontinuous solutions, reaching not a continuous steady state (SS) but a cyclic steady state (CSS).

5.1.1.1 Performance Parameters

The definitions of purity and recovery of these performance parameters, for the case of a binary mixture, are given below:

Purity (%) of the more retained (A) species in extract and the less retained one (B) in the raffinate streams, over a complete cycle (from $q$ to $q+{\displaystyle {\sum }_{j=I}^{IV}{n}_{j}}$):

$$ P{U}_{X}=\frac{{{\int }_{\theta}^{\theta+{ \sum _{j=I}^{IV}{n}_{j}}}{C}_{A}^{X}dq}}{{ {\int }_{\theta}^{\theta+{ \sum _{j=I}^{IV}{n}_{j}}}{C}_{A}^{X}d\theta}+{ {\int }_{\theta}^{\theta+{\displaystyle \sum _{j=I}^{IV}{n}_{j}}}{C}_{B}^{X}d\theta}}\rm{ } $$

$$ P{U}_{R}=\frac{{ {\int }_{\theta}^{\theta +{ \sum _{j=I}^{IV}{n}_{j}}}{C}_{B}^{R}d\theta}}{{ {\int }_{\theta}^{\theta +{ \sum _{j=I}^{IV}{n}_{j}}}{C}_{A}^{R}d\theta}+{ {\int }_{\theta}^{\theta+{\sum _{j=I}^{IV}{n}_{j}}}{C}_{B}^{R}d\theta}}$$

Recovery (%) of more retained (A) species in extract and the less retained one (B) in raffinate streams, again over a complete cycle:

$$ R{E}_{X}=\frac{{\displaystyle {\int }_{q}^{q+{\displaystyle \sum _{j=I}^{IV}{n}_{j}}}{C}_{A}^{X}dq·{Q}_{X}}}{{\displaystyle \sum _{j=I}^{IV}{n}_{j}{Q}_{F}{C}_{A}^{F}}}\rm{ }$$

$$ R{E}_{R}=\frac{{\displaystyle {\int }_{q}^{q+{\displaystyle \sum _{j=I}^{IV}{n}_{j}}}{C}_{B}^{R}dq·{Q}_{R}}}{{\displaystyle \sum _{j=I}^{IV}{n}_{j}{Q}_{F}{C}_{B}^{F}}}$$

5.1.2 Annex (2)

As mentioned before, the JO process (or Pseudo-SMB) is characterized by a discontinuous operating mode, mainly divided into two major steps. The mathematical model to simulate such process also replicates such discontinuity.

Step 1 (from 0 to ${t}_{Step1}$)

During step 1, the feeding is performed and the intermediary product is purged, as mentioned, before leading to the node balances:

$$ \begin{array}{l}\rm{Eluent (E) node}:{u}_{I}^{1*}={u}_{IV}^{1*}+{u}_{{E}_{1}}\\ \rm{Extract }(\rm{X})\rm{ node}:{u}_{II}^{1*}={u}_{I}^{1*}\\ \rm{Intermediary }(\rm{It}):{u}_{It}={u}_{II}^{1*}\\ \rm{Feed }(\rm{F})\rm{ node}:{u}_{III}^{1*}={u}_{F}\\ \rm{Raffinate }(\rm{R})\rm{ node}:{u}_{IV}^{1*}={u}_{III}^{1*}\end{array} $$

and for each species $i$:

$$ \begin{array}{l}j=I:{{C}_{{b}_{i},IV}|}_{x=1}=\frac{{u}_{I}^{1*}}{{u}_{IV}^{1*}}{C}_{{b}_{i,I}}^{0}-\frac{{u}_{E1}}{{u}_{IV}^{1*}}{C}_{i}^{E}\\ j=III:{C}_{{b}_{i,III}}^{0}={C}_{i}^{F}\\ j=II,IV:{{C}_{{b}_{i,(j-1)}}|}_{x=1}={C}_{i,j}^{0}\rm{ }\end{array} $$

with ${u}_{j}^{1*}$ representing interstitial velocity in section $j$during step 1.

Within each column, the concentration profiles are simulated by means of the well-known fixed-bed equations, initial and boundary conditions, similar to those expressed for the LDF approach for each column in the SMB modeling strategy (see Annex 1).

Step 2 (from ${t}_{Step1}$ to ${t}_{Step2}$)

In the second operation stage (step 2), one has the following nodes balances:

$$ \begin{array}{l}\rm{Eluent (E) node}:{u}_{I}^{2*}={u}_{IV}^{2*}+{u}_{{E}_{2}}\\ \rm{Extract (X) node}:{u}_{II}^{2*}={u}_{I}^{2*}-{u}_{X}\\ \rm{Feed}/\rm{Intermediary }(\rm{F}/\rm{It})\rm{ node}:{u}_{III}^{2*}={u}_{II}^{2*}\\ \rm{Raffinate }(\rm{R})\rm{ node}:{u}_{IV}^{2*}={u}_{III}^{2*}-{u}_{R}\end{array} $$

and for each species $i$:

$$ \begin{array}{l}j=I:{{C}_{{b}_{i},IV}|}_{x=1}=\frac{{u}_{I}^{2*}}{{u}_{IV}^{2*}}{C}_{{b}_{i,I}}^{0}-\frac{{u}_{E2}}{{u}_{IV}^{2*}}{C}_{i}^{E}\\ j=II,III,IV:{{C}_{{b}_{i,(j-1)}}|}_{x=1}={C}_{i,j}^{0}\rm{ }\end{array}$$

During step 2, similar mass balances and boundary conditions stated for the classical SMB unit (Annex 1) are used to simulate the operation of the Pseudo-SMB unit.

5.1.2.1 Performance Parameters (Pseudo-SMB)

The definitions of extract, intermediary, and raffinate purities ($P{U}_{X},P{U}_{It},P{U}_{R}$, %) and recovery at the extract, intermediary, and raffinate ports ($R{E}_{X},R{E}_{It},R{E}_{R}$, %) of the more intermediary and less retained components, respectively, are stated as follows:

Component A (during step 2):

$$ P{U}_{X}=\frac{{{\int }_{{t}_{Step1}}^{{t}_{Step2}}{C}_{{b}_{A}}^{X}d\theta}}{{{\int }_{{t}_{Step1}}^{{t}_{Step2}}{C}_{{b}_{A}}^{X}d\theta}+{{\int }_{{t}_{Step1}}^{{t}_{Step2}}{C}_{{b}_{B}}^{X}d\theta}+{{\int }_{{t}_{Step1}}^{{t}_{Step2}}{C}_{{b}_{C}}^{X}d\theta}}\rm{ }$$

$$ R{E}_{X}=\frac{{{\int }_{{t}_{Step1}}^{{t}_{Step2}}{C}_{{b}_{A}}^{X}d \theta \cdot{u}_{X}}}{{ {\int }_{\theta}^{\theta+{t}_{Step1}}{C}_{A}^{F}d \theta \cdot{u}_{F}}}$$

, during Step 2

Component B (during step 1):

$$ P{U}_{It}=\frac{{ {\int }_{\theta}^{\theta+{t}_{Step1}}{C}_{{b}_{A}}^{It}d\theta}}{{{\int }_{\theta}^{\theta+{t}_{Step1}}{C}_{{b}_{A}}^{It}d\theta}+{{\int }_{\theta}^{\theta+{t}_{Step1}}{C}_{{b}_{B}}^{It}d\theta}+{{\int }_{\theta}^{\theta+{t}_{Step1}}{C}_{{b}_{C}}^{It}d\theta}}\rm{}$$

$$ R{E}_{IT}=\frac{{{\int }_{\theta }^{\theta +{t}_{Step1}}{C}_{{b}_{B}}^{It}d\theta \cdot{u}_{It}}}{{ {\int }_{\theta }^{\theta +{t}_{Step1}}{C}_{B}^{F}d\theta \cdot{u}_{F}}} $$

Component C (during step 2):

$$ P{U}_{R}=\frac{{\displaystyle {\int }_{{t}_{Step1}}^{{t}_{Step2}}{C}_{{b}_{C}}^{R}d \theta}}{{{\int }_{{t}_{Step1}}^{{t}_{Step2}}{C}_{{b}_{A}}^{R}d \theta}+{ {\int}_{{t}_{Step1}}^{{t}_{Step2}}{C}_{{b}_{B}}^{R}d \theta}+{{\int }_{{t}_{Step1}}^{{t}_{Step2}}{C}_{{b}_{C}}^{R}d \theta}}\rm{ }$$

$$ R{E}_{R}=\frac{{ {\int }_{{t}_{Step1}}^{{t}_{Step2}}{C}_{{b}_{C}}^{R}d\theta \cdot{u}_{R}}}{{ {\int }_{\theta }^{\theta +{t}_{Step1}}{C}_{C}^{F}d\theta \cdot {u}_{F}}}$$