This chapter contains for information on:
• About Ion-Exchange Processes
• Bed Model Assumptions for Ion-Exchange Processes
• Configure Form for Ion-Exchange Processes
• Configure Layer Form for Ion-Exchange Processes
• General Tab
• Material/Momentum Balance Tab
• About Axial Dispersion in Ion-Exchange Processes
• Kinetic Model Tab
• Isotherm Tab
• Summary of Mass Balance Equations for Ion-Exchange Processes
About Ion-Exchange Processes
In ion-exchange processes, a fluid phase (such as an aqueous solution) containing cations and anions, is contacted with an ion-exchange resin.
Typically, the ion-exchange resin is inside a packed bed adsorption column.
The resin contains bound groups carrying a positive or negative ionic charge, which are accompanied by displaceable ions of opposite charge (counterions).
The displaceable ions have the same charge as the ions of interest in the fluid phase: since the ions in the fluid phase have a greater affinity for the bound groups than those originally present, the latter are displaced by the former.
Generally, the resin has a fixed total charge capacity, so one ionic solute is exchanged for another while maintaining charge neutrality.
Ion-exchange processes have become an important separation technique for aqueous electrolyte solutions and are used in these applications:
• Water softening, where monovalent cations replace multivalent cations.
• Water purification, where hydrogen or hydroxide ions replace cations (usually monovalent).
• Multi-component separation of ionic mixtures of different type and charge.
Ion-exchange may be written as a reversible reaction involving charge
where R is a stationary, univalent, anionic group in the poly-electrolyte network of the exchange phase.
Bed Model Assumptions for Ion-Exchange
The bed model assumptions for ion-exchange are:
• Overall and component material balances apply for the liquid phase.
• Isothermal conditions apply.
• Plug flow or plug flow with axial dispersion applies.
• The liquid stream pressure is constant (no frictional pressure drop).
• The superficial velocity and thus volumetric flow rate remain constant.
(The ion components are dilute so the effect of adsorption on the overall mass balance is negligible.)
• Ideal mixing occurs in the aqueous phase. Since the ionic components are very dilute, overall molar volume remains constant.
• Changes in molar volume between distinct, sequentially fed fluids are allowed.
• The total exchange capacity of the bed Q is constant.
• A lumped mass-transfer rate applies, with a liquid- or solid-film resistance. This resistance is either linear, quadratic, or user-defined.
• The mass-action equilibrium is one alternative model for ion-exchange behavior. Others include the extended Langmuir and extended Langmuir-Freundlich models.
Configure Form (ionx)
In the Configure Form of the Ion-exchange process bed model:
• Enter the number of layers within the bed (1 or more).
• Click in the Description box for each layer and type in a brief name or description.
• Click Configure to open the Configure Layer dialog box.
• Click Specify to open the specify form for the layer model.
Configure Layer Form (ionx)
Use the options in the Configure Layer form to specify the set of equations within each layer of the bed.
For more information on choosing the options for your ion-exchange process, see these sections:
• General tab
• Material/Momentum Balance tab
• Kinetic Model tab
• Isotherm tab
General Tab (ionx)
Use the General tab to specify these options for your ion-exchange process:
• Discretization method
• Number of nodes
General Tab (ionx): Discretization Method to be Used
These discretization methods are available for ion-exchange processes:
• UDS1
• UDS2
• CDS1
• LDS
• QDS
• MIXED
• BUDS
General Tab (ionx): Number of Nodes
In the Number of Nodes box, choose an appropriate number of nodes for your chosen discretization method.
Material/Momentum Balance Tab (ionx)
Use the Material/Momentum Balance tab to specify the basic assumptions about material dispersion in the liquid phase for ion-exchange processes.
Material/Momentum Balance Tab (ionx): Material Balance Assumption
In the Material Balance Assumption box, choose from one of the following options:
• Convection Only
• Convection with Constant Dispersion
• Convection with Estimated Dispersion
• Convection with User Procedure Dispersion
• Convection with User Submodel Dispersion
Because the dispersion term is omitted, you do not need to supply the dispersion coefficient.
Material Balance Assumption (ionx): Convection with Constant Dispersion
The Convection with Constant Dispersion option includes the dispersion term in the material balance for the bed. You must then supply a fixed value for the dispersion coefficient, Ez.
With this option, the dispersion coefficient is constant for all components throughout the bed.
Material Balance Assumption (ionx): Convection with Estimated Dispersion
The Convection with Estimated dispersion option includes the dispersion term in the material balance for the bed.
Here, the dispersion coefficient varies along the length of the bed. Aspen Adsim estimates the components' dispersion coefficients in an ion-exchange bed using this correlation (Slater, 1991):
48
Material Balance Assumption (ionx): Convection with User Procedure Dispersion
The Convection with User Procedure Dispersion option includes the dispersion term in the material balance for the bed.
The dispersion coefficient varies with axial position according to a user-supplied Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_i_Dispersion.
Material Balance Assumption (ionx): Convection with User Submodel Dispersion
The Convection with User Submodel Dispersion option includes the dispersion term in the material balance for the bed.
The dispersion coefficient varies with axial position according to the user-supplied submodel iUserDispersion.
About Axial Dispersion in Ion-Exchange Processes
As a fluid flows through a packed column such as an ion-exchange bed, axial dispersion (mixing) tends to occur, which reduces the efficiency of separation.
Axial dispersion should be minimized in bed design, but, if it occurs, then Aspen Adsim must account for its effects.
There are several sources of axial dispersion in ion-exchange processes (Ruthven, 1984):
• Channeling caused by non-uniform packing, for example where different sections of the packing have different voidages.
• Dispersion from wall effects due to non-uniform packing at the wall. This can be avoided by packing the bed well, and having a sufficiently large ratio of bed-to-particle diameters.
• Hold-up of liquid in the laminar boundary layer surrounding the particles combined with small random fluctuations in the flow.
• Splitting and recombining of the flow around the particles.
The molecular diffusivities of liquids are too small to contribute significantly to axial dispersion. In general, the mixing effects are additive and can be
lumped together into a single effective dispersion coefficient, Ez. The dispersion term in the material balance is usually expressed as:
2 2
z E
zc
ki
∂
ε ∂
−
The type of flow determines whether this term is omitted or included in the material balance.
Deciding When to Use Axial Dispersion in Ion-Exchange Processes
In deciding whether to include axial dispersion in the bed model, it is useful to work out the Peclet number, given an effective dispersion coefficient (Ez), a liquid superficial velocity (
v
), and a bed height (H
):The Peclet number quantifies the degree of dispersion introduced into the system. It is dimensionless so is more convenient than the dispersion coefficient for this purpose.
The following table shows the effect of different values of Peclet number:
If the Peclet number
is The effect of axial dispersion on bed performance is
0 Infinite: the bulk liquid is perfectly mixed., so the liquid composition is homogeneous throughout the entire bed.
< 30 Significant.
> 100 Very slight: The bed operates under near plug flow conditions.
∞ Zero: The bed operates under plug flow conditions.
Numerical methods used to discretize the spatial derivatives in the general equations can also introduce an artificial form of dispersion.
Kinetic Model Tab (ionx)
The overall mass transfer of ionic components between the bulk liquid phase and the adsorbed phase must overcome two resistances:
• Mass transfer resistance located in the boundary layer surrounding the particle.
• Mass transfer resistance inside the resin particle.
Typically, the second resistance determines the overall mass transfer rate.
Aspen Adsim lumps the overall resistance to mass transfer into a single overall factor. You select the type of resistance from:
• Film Model Assumption
• Kinetic Model Assumption
• Form of Lumped Resistance
• Form of Mass Transfer Coefficient
Kinetic Model Tab (ionx): Film Model Assumption
In the Film Model Assumption box, choose from:
• Solid — The mass transfer driving force is expressed as a function of the solid phase loading (solid film).
• Fluid — The mass transfer driving force is expressed as a function of the liquid phase concentration (liquid film).
Kinetic Model Tab (ionx): Kinetic Model Assumption
In the Kinetic Model Assumption box, choose from:
• Lumped Resistance
• User Procedure
• User Submodel
Kinetic Model Assumption (ionx): Lumped Resistance Here, the mass transfer driving force for component k is expressed as a function of the liquid phase concentration (liquid film), or solid phase loading (solid film).
This function is either linear or quadratic. See Form of Lumped Resistance, later.
Kinetic Model Assumption (ionx): User Procedure
With this option, the component rates of mass transfer are related to local conditions in the bed through a relationship you supply in a Fortran
subroutine, which Aspen Adsim interfaces using the procedure pUser_i_Kinetic.
Kinetic Model Assumption (ionx): User Submodel
With User Submodel selected, the component rates of mass transfer are related to local conditions in the bed through the user submodel iUserKinetic.
Kinetic Model Tab (ionx): Form of Lumped Resistance
This option is active only if you selected Lumped Resistance as your Kinetic Model assumption.
The following options are available:
• Linear
• Quadratic
Form of Lumped Resistance (ionx): Linear
The mass transfer driving force for component k is expressed as a linear function of the liquid phase concentration or solid phase loading.
) ( k *k
k
k MTCl c c
t
w = −
∂
∂
(fluid film)Form of Lumped Resistance (ionx): Quadratic
The mass transfer driving force is expressed as a quadratic function of the liquid phase concentration (fluid film) or solid phase loading (solid film).
k
Kinetic Model Tab (ionx): Form of Mass Transfer Coefficient
Use this option to specify how to define the mass transfer coefficients. Choose from:
• Constant
• User Procedure
• User Submodel
Form of Mass Transfer Coefficient (ionx): Constant
With this option, the mass transfer coefficient for each component is constant throughout the bed. You must supply a constant value of mass transfer coefficient for each component in the Specify table of the layer.
Form of Mass Transfer Coefficient (ionx): User Procedure
Here, the mass transfer coefficients are functions of local bed conditions. The function is implemented in a Fortran subroutine, which Aspen Adsim
interfaces using the procedure pUser_i_MTC.
Form of Mass Transfer Coefficient (ionx): User Submodel
With User Submodel selected, the mass transfer coefficients are functions of local bed conditions, and are returned through the user submodel iUserMTC.
Isotherm Tab (ionx)
Use the Isotherm tab to specify the adsorption isotherms for use in your ion-exchange process.
About Adsorption Isotherms for Ion-Exchange Processes
The driving force behind an ion-exchange separation process is the departure from adsorption equilibrium between the aqueous and adsorbed phases.
Consequently, adsorption isotherms (also known as ion-exchange equilibria) are important data in the design of ion-exchangers. Aspen Adsim has a list of commonly used, standard multi-component adsorption isotherms.
Important: The equations presented are for equilibrium conditions.
Depending on the mass transfer rate model you choose, they are used to compute either:
• w*, the loading that would be at equilibrium with the actual liquid phase composition
-or-
• c*, the liquid phase composition that would be at equilibrium with the actual loading.
This choice is automatically handled by Aspen Adsim depending on your selection of kinetic model.
The equilibrium variable arrays (of size number of nodes × number of components) are named either Ws or Cs. In bed models, these variables are distributed, so they have a qualifier 1, 2, … n (=number of nodes), depending on the bed location.
Isotherm Tab (ionx): Isotherm Assumed for Layer
In the Isotherm Assumed for Layer box, choose from:
• Mass Action Equilibrium
• Extended Langmuir
• Extended Langmuir-Freundlich
• User Procedure
• User Submodel
Isotherm Assumed for Layer (ionx): Mass Action Equilibrium
R R
B+ B+
A
+ +R R
+A+
B B
The exchange reaction in the ion-exchange process is typically takes the form:
mB AR mBR
A+ ⇔ m+
where m is a stoichiometric coefficient.
• m is an integer or a fraction. It is given by the valence ratio of A and B.
• A refers to an ionic component in solution.
• B refers to a counter-ion on the ion-exchanger surface.
where:
KAB = Equilibrium constant or selectivity coefficient.
x = Equivalent mole fraction in the adsorbed phase.
y = Equivalent mole fraction in the aqueous phase.
c
0 = Total ionic concentration.Q = Ion-exchange resin capacity.
In Aspen Adsim, the parameter IP1 equals KAB, and the parameter m equals IP2. The equation now becomes:
0
Isotherm Assumed for Layer (ionx): Extended Langmuir
The extended Langmuir isotherm was found to represent some experimental data satisfactorily:
( )
b bwhere b refers to the (original) counter-ion.
Isotherm Assumed for Layer (ionx): Extended Langmuir-Freundlich
This isotherm is based on the Langmuir isotherm and expressed as:
(
k)
bwhere b refers to the (original) counter-ion.
Isotherm Assumed for Layer (ionx): User Procedure
You can supply your own, proprietary isotherm relationships through a Fortran subroutine, which Aspen Adsim interfaces using one of two procedures:
• pUser_i_Isotherm_C for solid film kinetic model
• pUser_i_Isotherm_W for liquid film kinetic model
Isotherm Assumed for Layer (ionx): User Submodel
With User Submodel selected, you supply the isotherm relationship through the user submodel iUserIsotherm.
Summary of Mass Balance Equations for Ion-Exchange Processes
This section summarizes the mass balance equations used by Aspen Adsim to simulate ion-exchange processes.
The overall material balance is expressed as:
= 0
This equation accounts for the fact that, during an ion-exchange cycle, solvents of different densities are being used in the different production, purge and regeneration stages. Density remains unchanged as a result of the ion-exchange process itself.
Each ionic species in the liquid phase, fed into the ion-exchange column, is governed by the following material balance equation:
2
0
The mass transfer rate
J
k between the bulk liquid and the resin is given by:( )
where the uptake rate
t w
k∂
∂
can, for example, be determined by a solid film linear driving force relationship, such as:(
k k)
The number of counter ions being released from the resin and entering the liquid phase is determined from the number of ions exchanged from the liquid phase — the total charge of both liquid and resin must remain neutral:
∑
Hence the behavior of the exchanged counter ion in the liquid phase can be described by:
0
Explanation of Equation Symbols for Ion-Exchange Processes
The tables explain the equation symbols used in Aspen Adsim's ion-exchange mass balance equations.
Symbol Explanation Aspen Adsim
base units
c
b Counter ion concentration in liquid phase. eq/m3c
k Ion concentration in liquid phase. eq/m3*
ck Liquid phase ion concentration in equilibrium
with resin phase. eq/m3
c
0 Total liquid phase ion concentration. eq/m3d
p Resin particle diameter. mEz Axial dispersion coefficient. m2/s
HB Bed height. m
IP Isotherm parameter.
J
b Counter ion material transfer rate. eq/m3/sJ
k Ion material transfer rate. eq/m3/sKAB Mass action equilibrium constant.
m Stoichiometric coefficient used in mass action equilibrium.
M
l Solvent molecular weight. kg/kmolMTC
l Liquid film mass transfer coefficient. 1/sMTC
s Solid film mass transfer coefficient. 1/sQ Total resin ion capacity. eq/m3
t Time. s
w
k Ion loading on resin. eq/m3*
wk Ion loading in equilibrium with liquid phase
ion concentration. eq/m3
x
k Ion mole fraction in adsorbed (resin) phase.y
k Ion mole fraction in liquid phase.z Axial co-ordinate. m
ε
i Bed voidage.µ Solvent viscosity. N/m2/s
ρ
i Solvent molar density. kmol/m3Dimensionless
number Defining expression Description Pe
z B l
E H
v
Peclet numberRe
µ ρ
l P ll
d v
M
Reynolds number4 Liquid Adsorption Processes
This chapter contains information on liquid adsorption processes and how they are simulated in Aspen Adsim. For more information, see the following topics:
• About Liquid Adsorption Processes
• Bed Model Assumptions for Liquid Adsorption
• Configure Form
• Configure Layer Form
• General Tab
• Material/Momentum Balance Tab
• Kinetic Model Tab
• About Adsorption Isotherms for Liquid Adsorption
• Guidelines for Choosing Aspen Adsim Isotherm Models
• Energy Balance Tab
• Procedures Tab
• Summary of Mass and Energy Balance
• Explanation of Equation Symbols
About Liquid Adsorption Processes
Liquid phase adsorption has long been used to remove contaminants present at low concentrations in process streams, such as organics from waste water.
When contaminants are not well defined, liquid phase adsorption can improve feed quality, defined by color, taste, odor, and storage stability.
Unlike trace impurity removal, using liquid phase adsorption for bulk
separation on a commercial scale is a relatively recent development. The first commercial operation was in the 1960s, in hydrocarbon processing. Since then, bulk adsorptive separation of liquids has been used to solve a broad range of problems, including individual isomer separations and class separations. The commercial availability of synthetic molecular sieves and ion-exchange resins, and the development of novel process concepts have been the two significant factors in the success of these processes.
Bed Model Assumptions for Liquid Adsorption
For liquid adsorption, the bed model assumes:
• Plug flow, or plug flow with axial dispersion.
• The liquid phase pressure is either constant or varies according to a laminar-flow momentum balance (with the pressure drop assumed proportional to the flow velocity).
• The superficial velocity is constant, or varies due to adsorption and according to total mass balance.
• Molar concentrations are calculated from molar volumes. Ideal mixing is assumed to occur in the liquid phase, so molar volume is a linear function of composition.
• A lumped mass-transfer rate applies, with a liquid or solid-film resistance.
This resistance is either linear, quadratic or user-defined.
• Mass transfer coefficients are either constant or user defined.
• The adsorption isotherm is chosen from Aspen Adsim defined isotherms, or specified by you.
• Isothermal or non-isothermal conditions apply. The energy balance includes terms for:
− Thermal conductivity of gas and solid.
− Liquid-solid heat transfer.
− Heat of adsorption.
− Enthalpy of adsorbed phase.
− Heat exchange with environment.
− Wall energy terms.
Configure Form (liq)
This section contains information on the Configure form for a liquid process bed model. The following options are available:
• Enter the number of layers within the bed (one or more).
• Type a brief name or description in the Description box.
• Click the Configure button to open the Configure Layer dialog box.
• Click the Specify button to open the Specify form for the layer model.
Configure Layer Form (liq)
Use the options in the Configure Layer form to define the set of equations for each layer of the adsorption bed.
For information on choosing the options for your liquid adsorption process,
• Isotherm Tab
• Energy Balance Tab
• Procedures Tab
General Tab (liq)
Use the General tab to specify the numerical options for your liquid adsorption process.
General Tab (liq): Discretization Method to be Used
These discretization methods are available for liquid adsorption processes:
• UDS1
• UDS2
• CDS1
• LDS
• QDS
• MIXED
• BUDS
General Tab (liq): Number of Nodes
In the Number of Nodes box, choose an appropriate number of nodes for your discretization method.
Material/Momentum Balance (liq)
Use the Material/Momentum Balance tab to:
• Make basic assumptions about axial dispersion in the liquid phase.
• Determine how to treat the pressure drop in the adsorption bed model.
• Specify whether the velocity is constant or varies along the column.
Material/Momentum Balance Tab (liq):
Material Balance Assumption
In the Material Balance Assumption box, choose the material balance option for your liquid adsorption process. Choose from:
• Convection Only
• Convection with Constant Dispersion
• Convection with Estimated Dispersion
• Convection with User Procedure Dispersion
• Convection with User Procedure Dispersion