Aspen Adsim

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Aspen Adsim

2004.1

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Who Should Read this Guide

This guide contains reference information for use by experienced users of the Aspen Adsim application.

The guide also describes the following Aspen Adsim features: • Numerical methods for solving the partial differential equations. • Estimation module.

• Cyclic Organizer.

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General Information

This section provides Copyright details and lists any other documentation related to the Aspen Adsim 2004.1 release.

Copyright

Version: 2004.1 April 2005

subsidiaries, affiliates, and suppliers. All rights reserved. This Software is a proprietary product of Aspen Technology, Inc., its applicable subsidiaries, affiliates and suppliers and may be used only under agreement with AspenTech.

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All other brand and product names are trademarks or registered trademarks of their respective companies.

This document is intended as a guide to using AspenTech's software. This documentation contains AspenTech proprietary and confidential information and may not be disclosed, used, or copied without the prior consent of

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Technical Support

Online Technical Support

Center

AspenTech customers with a valid license and software maintenance agreement can register to access the Online Technical Support Center at: http://support.aspentech.com

You use the Online Technical Support Center to: • Access current product documentation.

• Search for technical tips, solutions, and frequently asked questions (FAQs).

• Search for and download application examples.

• Search for and download service packs and product updates. • Submit and track technical issues.

• Search for and review known limitations. • Send suggestions.

Registered users can also subscribe to our Technical Support

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• Technical advisories. • Product updates.

• Service Pack announcements. • Product release announcements.

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Phone and E-mail

Customer support is also available by phone, fax, and e-mail for customers who have a current support contract for their product(s). Toll-free charges are listed where available; otherwise local and international rates apply.

For the most up-to-date phone listings; please see the Online Technical Support Center at:

http://support.aspentech.com

Support Centers Operating Hours

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Introducing Aspen Adsim

Aspen Adsim simulates gas processes with adsorption only, or adsorptive reaction gas processes where both reaction and adsorption occur

simultaneously.

Gas-phase adsorption is widely used for the large-scale purification or bulk separation of air, natural gas, chemicals and petrochemicals.

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1 Gas Adsorption Processes

This chapter contains information on: • About Gas Adsorption Processes.

• Bed Model Assumptions for Gas Adsorption Processes. • About Aspen Adsim Bed Models.

• Configure Form. • Configure Layer Form. • General Tab.

• Material/Momentum Balance Tab. • Kinetic Model Tab.

• Isotherm Tab. • Energy Balance Tab. • Reaction Tab.

• Procedure Tab.

• Summary of Mass and Energy Balance Equations. • Explanation of Equation Symbols.

About Gas Adsorption

Processes

Gas-phase adsorption is widely used for the large-scale purification or bulk separation of air, natural gas, chemicals and petrochemicals, where it is often better to use gas-phase adsorption rather than the older unit operations of distillation and absorption.

Adsorbent attracts molecules from the gas, removing the molecules from the gas phase and concentrate on the surface of the adsorbent. Many process concepts have been developed to allow:

• Efficient contact of feed gas mixtures with adsorbent to carry out desired separations.

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For gas phase applications, most commercial adsorbents are pellets, beads, or other granular shapes, typically about 1.5 to 3.2 mm in diameter. These adsorbents are usually packed into fixed beds through which the gaseous feed mixtures are passed. Normally, the process is cyclic. When the bed capacity is exhausted, the feed flow is stopped to finish the loading step of the process. The bed is then treated to remove the adsorbed molecules in separate regeneration steps, then the cycle is repeated.

Gas phase adsorption processes have seen a growth in both variety and scale, especially since 1970. This is due mainly to improvements in adsorbents, for example the discovery of porous adsorbents with a large surface area, such as zeolites. These advances have encouraged parallel inventions of new process concepts. Increasingly, the development of new applications requires close cooperation in adsorbent design and process cycle development and optimization.

Bed Model Assumptions for Gas

Adsorption Processes

Aspen Adsim simulates gas processes with adsorption only, or adsorptive reaction gas processes where both reaction and adsorption occur

simultaneously.

For gas processes, the bed model makes the following assumptions: • Isothermal or non-isothermal conditions apply. Terms in the energy

balances include:

− Thermal conductivity of gas and thermal conductivity of solid. − Compression.

− Gas-solid heat transfer. − Heat of adsorption.

− Enthalpy of adsorbed phase. − Heat exchange with environment. − Wall energy terms.

− Enthalpy of mixing is negligible.

• Plug flow or plug flow with axial dispersion occurs.

• The system is fully mixed in the radial direction. Alternatively, radial dispersion and thermal conduction are used to account for radial material and temperature distributions.

• The gas phase is ideal or non-ideal, the non-ideal behavior needing a compressibility factor.

• Gas phase pressure is either constant (with velocity either constant, or varying according to mass balance and only applicable for breakthrough simulations), or the pressure varies according to a laminar or turbulent flow momentum balance.

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• Mass transfer is described using a lumped overall resistance, or by a model that accounts separately for micropore and macropore effects. The driving force is based on a liquid or solid film, and is either linear,

quadratic, or user-specified. Mass transfer coefficients are either constant, or vary with local conditions. A limited rigorous particle material balance functionality is provided.

• Adsorption isotherms are either applicable for single or multi-component adsorption. IAS theory can be used for pure component isotherms.

About Aspen Adsim's Bed

Models

The table shows the classifications of adsorption bed models:

Name Type

Model type Flow setter under compressible flow conditions.

Flow type Reversible. Time dependency Dynamic.

Reversible models handle forward or reverse flow in the bed. They contain dummy variables associated with the input and output streams.

The adsorption bed models are usually flow setters, but within the bed they can be both flow setters and pressure setters. This is because they determine internal pressure profiles and gas velocity profiles, provided the general compressible flow model is used.

The nature of the process and its operating conditions determine the type of model to use. For example, a bulk separation process such as producing oxygen-rich gas from air requires a different model to that for a purification process for removing trace impurities.

The adsorption column models use a set of partial differential equations to represent the momentum, heat, and material balances across the column. You can add further relationships, which are specific to the various options.

Bed Model Ports

Bed models contain an input and an output port. Each port has associated variables that correspond to the material connection stream variables, and which allow for reversible flow.

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Configure Form (Gas)

On the Configure form of the bed model:

1 Enter the number of layers within the bed (one or more). 2 Enter the bed type: Vertical, Horizontal or Radial.

See Configure Form for Gas Process Bed Model, later.

3 For vertical beds only, define the spatial dimensions of the bed model: 1-D or 2-D.

See Configure Form for Gas Process Bed Model: Spatial Dimensions, later. 4 For vertical and horizontal beds, specify whether an internal heat

exchanger is present.

See Configure Form for Gas Process Bed Model: Internal Heat, and See Configure Form for Gas Process Bed Model: Spatial Dimensions, later. 5 In the Description box for each layer, type a brief name or description. 6 Click Configure to open the

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Configure Layer Form (gas) dialog box.

7 Click Specify to open the Specify form for the layer model.

Configure Form (gas): Bed Type

To choose the bed type:

• In the Bed Type box, choose vertical, horizontal or radial bed orientation.

Vertical Bed Type

Typically, you use a vertical orientation for an adsorption bed. Vertical

columns prevent variation in flow width because the flow is along the column axis.

Horizontal Bed Type

Occasionally, you may need to choose horizontal orientation, for example, when a vertical bed may cause fluidization of the bed. Horizontal beds allow a much greater inflow area, keeping gas superficial velocities below the

fluidization velocity.

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L

H

_0,1

H

_B,1

H

_0,2

H

_B,2

D

_B

z

W(z)

Layer 1

Layer 2

The effective width W(z) of the bed is given as:

(

)

[

]

0.5

4 )

(

z

D

z

W

=

_B

−

Where: B

D

= Column diameter

z = Height of adsorbent above column base

The effective cross-sectional flow area of the bed is the product of the width and the total horizontal length of the bed, that is, W(z)L.

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Radial Bed Type

Use a radial bed type when the flow through the bed is in the radial direction, from a central core to the outer circumference of the packed bed.

Product Feed Adsorbent Layer 1 Inner Core Bed Shell Adsorbent Layer 2

The volumes of the central core and the bed shell are the dead volumes of the column. The positive radial co-ordinate runs from the center of the bed to the outer circumference.

Configure Form (gas): Spatial

Dimensions

If you select a vertical bed type, you need to specify either one- or two-dimensional spatial discretization:

• One-dimensional discretization — Spatial derivatives are evaluated in axial (flow) direction only.

• Two dimensional discretization — Second order spatial derivatives are evaluated in both the axial and radial direction, allowing the calculation of radial composition and temperature distributions.

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Configure Form (gas): Internal Heat

Exchanger

The adsorption columns used in some temperature swing adsorption

processes are equipped with internal heat exchangers to improve adsorbent regeneration. Aspen Adsim can simulate this configuration through the following sub-options:

• None, that is, no heat exchanger • 1-Phase, internal

• 1-Phase, jacket

• Steam-Water, internal • Steam-Water, jacket

The heat exchanger operates either as a jacket encircling the adsorption column or is integrated into the packed bed of the adsorbent. The heat exchange medium remains in the phase it is supplied in, or is condensed in order to use its heat of evaporation to heat the bed.

Heat Exchange Jacket

Internal Heat Exchanger

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Configure Layer Form (gas)

Use the options in the Configure Layer Form to specify the bed layers. The form has the following tabs:

• General tab

• Material/Momentum Balance tab • Kinetic Model tab

• Isotherm Tab • Energy Balance tab • Reaction tab

• Procedures tab

General Tab (gas)

Use the General tab to specify the numerical options for solving the partial differential equations, and to select the gas model assumption.

General Tab (gas): Discretization

Method to be used

These discretization methods are available for gas phase adsorption processes: • UDS1 • UDS2 • CDS1 • CDS2 • LDS • QDS • MIXED • Flux Limiter • BUDS • FROMM

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General Tab (gas): Number of Nodes

In the Number of Nodes box, choose an appropriate number of axial nodes for your chosen discretization method.

General Tab (gas): Number of Radial

Nodes

The Number of Radial Nodes option is available only if you selected a vertical bed with a 2-D spatial dimension.

Choose an appropriate number of radial nodes. The derivatives in the

component material balances and the gas phase energy balances are second order in radial co-ordinates, and are approximated by central differences.

General Tab (gas): Flux Limiter to be

used

If flux limiter is your discretization method, choose from: • van Leer

• OSPRE • SMART

General Tab (gas): Gas Model

Assumption

Gas flowing through the packed bed can be ideal or non-ideal. The gas model defines the relationship between pressure, temperature and molar density:

g g

T

R

Z

P

=

ρ

(overall) or i g i

Z

R

T

c

Py

=

(component) Where: P = Pressure Z = Compressibility factor

R = Universal gas constant

g

T

= Gas phase temperature

g

ρ

= Molar gas phase density

i

y

= Mole fraction of component i

i

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In the Gas Model Assumption box, choose from: • Ideal Gas Law (where Z=1)

• Fixed Compressibility (where Z is constant)

• User Procedure Compressibility (where Z is supplied through a user Fortran subroutine interfaced by the procedure pUser_g_Compressibility, or calculated using a selected physical properties package)

• User Submodel Compressibility (where Z is supplied through the user submodel gUserCompressibility)

Material/Momentum Balance

Tab (gas)

Use the Material/Momentum Balance tab to specify the material and momentum balances, and the 2-D dispersive properties.

About Axial Dispersion in Gas

Adsorption Processes

As a fluid flows through a packed column, axial mixing tends to occur. This reduces the efficiency of separation so should be minimized in column design. However, if axial dispersion occurs, the model must account for its effects. In gases, there are three main sources of axial dispersion:

• From wall effects, due to non-uniformity of packing either at the wall (wall effects) or in the core section of the packing (channeling). You can avoid this type of dispersion by having a sufficiently large ratio of bed-to-particle diameters.

• From molecular diffusion effects.

• From turbulent mixing effects arising from the splitting and recombining of flows around the adsorbent particles.

In general, the molecular diffusion and turbulent mixing effect are additive and proportional to the second order spatial concentration derivative, so they can be lumped together into a single effective dispersion coefficient,

E

_i. The dispersion term in the material balance is typically expressed as:

2 2

z

c

E

k zk i

_∂

∂

ε

−

Where:

ε

= Interparticle voidage

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It is useful to work out the Peclet number Pe using a dispersion coefficient (effective bulk diffusivity

E

_z), typical bed velocities (

ν

_g), and bed height (

H

_b):

Pe

v H

E

g _b z

=

The Peclet number quantifies the degree of dispersion introduced into the system. It is dimensionless so is more convenient to use for this purpose than the dispersion coefficient.

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 gas is perfectly mixed and the gas is homogeneous through the entire bed.

< 30 Significant.

> 100 Very slight: The bed operates under near plug flow conditions.

∞ Zero: The bed operates under plug flow conditions.

Note: The numerical methods used to model the spatial derivatives in the general equations can also introduce an artificial form of dispersion.

Material/Momentum Balance Tab

(gas): Material Balance Assumption

The Material Balance Assumption option is available unless you previously chose vertical bed and two-dimensional bed discretization. Choose from these options:

• Convection Only

• Convection with Constant Dispersion • Convection with Estimated Dispersion • Convection with User Submodel Dispersion • Convection with User Procedure Dispersion

Material Balance Assumption (gas): Convection Only

The Convection Only option drops the dispersion term from the material balance, so the model represents plug flow with a zero dispersion coefficient (infinite Peclet number). Because the dispersion term is missing, you need not supply the dispersion coefficient.

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Material Balance Assumption (gas): Convection with Constant Dispersion

The Convection with Constant Dispersion option assumes that the dispersion coefficient is constant for all components throughout the bed. You supply its value.

Material Balance Assumption (gas): Convection with Estimated Dispersion

The Convection with Estimated Dispersion option assumes that the dispersion coefficient varies along the length of the bed. Aspen Adsim estimates the values during the simulation.

Aspen Adsim estimates the components' dispersion coefficients using the following correlation, (Kast, 1988):













+

=

p g mk i i p g mk zk

r

v

D

r

v

D

E

2

49 .

9

1

73 .

0 ε

ε

Where: g

ν

= Gas velocity mk

D

= Molecular diffusivity zk

E

= Axial dispersion coefficient

i

ε

p

r

= Particle radius

Material Balance Assumption (gas): Convection with User Submodel Dispersion

If you choose Convection with User Submodel Dispersion, the (varying) dispersion coefficient is estimated using the user submodel gUserDispersion.

Material Balance Assumption (gas): Convection with User Procedure Dispersion

If you choose Convection with User Procedure Dispersion, the (varying)

dispersion coefficient is estimated through a user-supplied Fortran subroutine, which Aspen Adsim interfaces through the procedure pUser_g_Dispersion.

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Material/Momentum Balance Tab

(gas): Momentum Balance Assumption

Use the Momentum Balance Assumption box to specify how the adsorption bed layer model treats gas velocity and pressure. Base your choice on the plant operating conditions and the envisaged scope of the simulation (constant pressure models are only applicable for breakthrough investigations).

Choose from:

Constant pressure options—The bed is driven by gas superficial velocity and the pressure is assumed constant in the bed. The bed is velocity-driven, and no momentum balance is needed. These models are applicable only for breakthrough investigations.

The constant pressure options are: • Constant Pressure and Velocity

• Constant Pressure with Varying Velocity

Pressure driven options—The velocity is related to the overall or internal pressure gradients. In such cases, velocity and pressure gradient are related through a momentum balance. The pressure-drop relationships apply to local conditions inside the bed, so the momentum equations for entire beds can be used to determine local pressure gradients. No simplifying assumptions are made regarding the gas densities, gas velocities, or pressures.

The pressure driven options are: • Darcy's Law

• Karman-Kozeny Equation • Burke-Plummer Equation • Ergun Equation

Momentum Balance Assumption (gas): Constant Pressure and Velocity

Use the Constant Pressure and Velocity option only when using a simple flowsheet to simulate the breakthrough behavior of an adsorption column. The gas velocity and pressure are constant along the bed, whilst the gas density is essentially constant along the bed. These assumptions are valid only when dealing with the removal of trace components from a bulk carrier gas.

Momentum Balance Assumption (gas): Constant Pressure with Varying Velocity

Use the Constant Pressure with Varying Velocity option only when using a simple flowsheet to simulate the breakthrough behavior of an adsorption column.

Gas density is constant along the bed, so the pressure does not vary axially. Superficial velocity varies along the bed due to the rate at which the gas is adsorbed onto the solid, or desorbed from it.

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This option is applicable to bulk separation applications, in which case the axial velocity profile is determined by an overall material balance rather than an axial pressure gradient.

Momentum Balance Assumption (gas): Darcy's Law

Use this option to apply a linear relationship between the gas superficial velocity and the pressure gradient at a particular point in a bed.

Darcy's law states that pressure drop is directly proportional to flow rate. You have to set the proportionality constant. The relationship is given as:

g p

K

z

P

_ν

∂

₌

₋

Where: p

K

= Darcy’s law proportionality constant

g

ν

= Gas velocity

Momentum Balance Assumption (gas): Karman-Kozeny Equation

Choose this option to use the Karman-Kozeny equation to relate velocity to pressure drop. This is the laminar component of the Ergun equation:

(

)

g i p i

_v

r

z

P

3 2 2 3

2 )

1 (

10

5 .

1 ε

ψ

ε

µ

∂

−

×

−

=

−

For details of the Karman-Kozeny model see Bird et al. (1960). Where:

ψ = Shape factor

µ = Dynamic gas viscosity

Momentum Balance Assumption (gas): Burke-Plummer Equation

This option uses the Burke-Plummer equation to relate velocity to pressure gradient: 2 3 5

2 )

1 (

10

75 .

1

_g i p i g

v

r

M

z

P

ψε

ε

ρ

∂

−

×

−

=

− Where: M = Molecular weight

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Momentum Balance Assumption (gas): Ergun Equation

This option uses the Ergun equation, which combines the description of pressure drops by the Karman-Kozeny equation for laminar flow and the Burke-Plummer equation for turbulent flow.

(

)



_









₋

×

+

−

×

−

=

− − 2 3 5 3 2 2 3

2 )

1 (

10

75 .

1

2 )

1 (

10

5 .

1

g i p i g g i p i

_v

r

M

v

r

z

P

ψε

ε

ρ

µ

ε

ψ

ε

∂

It is valid for both laminar and turbulent flow, and is the most popular option. For details of the Ergun model, see Bird et al. (1960).

Set Variables for Pressure-Drop Options (gas)

This table shows the variables you need to specify for the pressure drop options:

Equation Symbol Variable Definition

p

K

Kp Proportionality constant ψ Sfac Sphericity p

r

Rp Particle radius i

ε

Ei Interparticle voidage

Material/Momentum Balance Tab

(gas): 2-D Dispersive Properties

The 2-D Dispersive Properties option is available only if you selected vertical bed and two-dimensional discretization. The axial dispersion is calculated from: 2 2

z

c

E

k zk i

_∂

∂

ε

−

Additionally, a radial dispersion term is also evaluated:













∂

−

r

c

r

E

k rk i

_∂

∂

ε

1

If you later specify the process as non-isothermal, equivalent dispersive terms are evaluated for the gas and solid phase energy balances. Namely: • Gas phase thermal conduction in axial direction: ₂

2

z

T

k

_gz g i

_∂

∂

−

ε

• Gas phase thermal conduction in radial direction:

_











∂

−

r

T

r

k

g gr i

1 ε

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• Solid phase thermal conduction in axial direction: ₂ 2

z

T

k

s sz

_∂

∂

−

• Solid phase thermal conduction in radial direction:













∂

−

r

T

r

k

s sr

1

Choose from: • Fixed • Estimated

2-D Dispersive Properties (gas): Fixed

Choose this option if the dispersive properties are constant throughout the packed bed. You must supply values for:

•

E

_zk: The dispersion coefficient of component k for the axial direction. •

E

_rk: The dispersion coefficient of component k for the radial direction. For non-isothermal operation, you must give values for the following thermal conductivities:

•

k

_g: The effective thermal conductivity of the gas phase. •

k

_s: The effective thermal conductivity of the solid phase.

2-D Dispersive Properties (gas): Estimated

Choose this option when variables such as pressure, temperature and velocity are changing significantly through the column. These variables influence the values of dispersion coefficients and thermal conductivities.

The axial dispersion coefficient is estimated using the following correlation, (Kast, 1988):













+

=

p g mk i i p g mk zk

r

v

D

r

v

D

E

2

49 .

9

1

73 .

0 ε

ε

Where: g

ν

= Gas Velocity mk

D

= Molecular diffusivity of component k

zk

E

= Axial dispersion coefficient of component k

i

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The radial dispersion coefficient is evaluated according to (Carberry, 1976):

4

g p rk

v

r

E

=

Where: rk

E

= Radial dispersion coefficient of component k

Assuming the analogy between mass and heat transfer is valid, the effective gas phase thermal conductivity in the axial direction is:

(

)

∑

=

nc i i i z pg g gz

C

E

y

k

1 ,

ρ

Where: gz

k

= Effective gas phase thermal conductivity in axial direction

g

ρ

= Molar gas density

pg

C

= Molar specific heat capacity at constant volume

The effective gas phase thermal conductivity in the radial direction comprises a static and a dynamic contribution (Froment and Bischoff, 1990). The two contributions are additive. Assuming the validity of the analogy between heat and mass transfer, the dynamic contribution to the effective radial gas phase thermal conductivity is:

(

)

∑

=

nc k k rk pg g i dyn gr

C

E

y

k

1

ρ

ε

Where: dyn gr

k

= Dynamic contribution to the effective gas phase thermal conductivity in radial direction

As the adsorbent (a solid) is not in motion, it has no dynamic contribution to its effective thermal conductivity in the radial direction.

(36)

The static contribution of the gas phase effective thermal conductivity in the radial direction is:

(

g p rg

)

i stat gr

k

r

k

=

ε

+

β

2 α

Where:

0 .

1 =

β

= Factor

(

)

3 3

100

1

2

1

10

227 .

0 











−

+

×

=

−

T

p

rg

ε

α

= Radiation contribution p = Emissivity g

k

= Thermal conductivity of the gas.

The total effective radial gas phase thermal conductivity is now given by:

stat gr dyn gr gr

k

=

+

The effective radial solid phase thermal conductivity comes from:

(

)

s p rs g i stat sr sr

k

r

k

_γ

α

φ

ε

β

+

−

=

2

1

Where: 3 3

100

2

10

227 .

0 











−

×

=

−

T

p

rs

α

= Radiation contribution

28 .

0 =

φ

= Function of the packing density

3

2 =

γ

= Factor

s

k

= Thermal conductivity of the solid

Aspen Adsim assumes that the effective solid thermal conductivity in the axial direction is not a function of any process variables, so

k

_s is constant through the simulation.

(37)

Kinetic Model Tab (gas)

Use the Kinetic Model tab to specify the model kinetics, such as resistances, diffusivities and mass transfer coefficients.

Kinetic Model Tab (gas): Film Model

Assumption

In the Film Model Assumption box, choose from:

• Solid, where the mass transfer driving force is expressed as a function of the solid phase loading.

• Fluid, where the mass transfer driving force is expressed as a function of the gas phase concentration.

Kinetic Model Tab (gas): Kinetic Model

Assumption

Typically, several mass transfer resistances occur in gas phase adsorption processes:

• Mass transfer resistance between the bulk gas phase and the gas-solid interface.

• Mass transfer resistance due to the porous structure of the adsorbent. In cases where the adsorbent has two distinct pore size regions, such as macropores and micropores, the resistance can be subdivided to account separately for each region.

You can consider mass transfer resistances in one these ways:

• Lumped Resistance  Separate mass transfer resistances are lumped as a single overall factor, or one resistance dominates all others.

• Micro & Macro Pore  The effects of the individual resistances to mass transfer in the micro- and macropores can be accounted for individually. • Particle MB  Where all components are adsorbed and the adsorbent has

a homogenous pore structure, you can use a rigorous particle material balance to determine the loading profile inside the adsorbent.

• Particle MB 2  Where inert components are present, or the radial gas phase concentration profiles in the pores of the adsorbent particles are to be accounted for in addition to the loading profiles. The adsorbent should possess a homogenous pore structure. This option performs a rigorous particle material balance for both the adsorbed and the gas phases.

(38)

In the Kinetic Model Assumption box, choose from these options: • Lumped Resistance

• Micro and Macro Pore Effects • Particle MB

• Particle MB 2 • User Procedure • User Submodel

Kinetic Model Assumption (gas): Lumped Resistance

Here, the separate resistances to mass transfer is lumped as a single overall factor, or one mass transfer resistance dominates the others.

Kinetic Model Assumption (gas): Micro and Macro Pore Effects

Two concentration gradients greatly affect the diffusion rate: • Within the pores of the solid.

• Within the void spaces between the particles (that is, within the crystallines).

Under practical conditions in gas separation, pore diffusion limits the overall mass transfer rate between the bulk flow and the internal surface of a

particle. This gives importance to the effect of pore diffusion on the dynamics of absorbers.

The following table shows the difference between modeling macropore and micropore resistance in composite and uniform adsorbents:

Pore structure Example(s) Micropore

diffusional resistance

Macropore diffusional resistance

Uniform Activated carbon alumina silica molecular sieve carbon

High Negligible

Composite Zeolites High High

When modeling adsorbents with uniform pore structure, you can usually discount any macropore diffusional resistance. However, when modeling composite adsorbents, both resistances can be significant and should be accounted for.

Qualitatively, a higher pore diffusion rate results in a sharper and steeper concentration wave front, giving a better separation. Quantitative prediction of behavior requires the simultaneous solution of the mass balance within the particle, as well as for the bulk flow in the bed.

(39)

Where:

s

ρ

= Adsorbent bulk density

i

w

= Loading of component i due to adsorption

i ads

J

_, = Mass transfer rate of component i

• If you know the concentration profile within the particle, you can make considerable savings in numerical computation because integration along the radial distance in the particle is no longer necessary. Several

researchers have recently shown that profiles obtained by exact numerical solutions of both Pressure Swing and Thermal Swing Adsorption processes are usually parabolic in shape, so you can model pore diffusion by

assuming a parabolic concentration profile within the particle.

The model developed for particle diffusion accounts for both interparticle (macropore) and intraparticle (micorpore) diffusion effects. The model assumes that material flows first from the bulk gas to the macropores (crystallines), and then from the macropores to the solid surface via the micropores:

r

P

2r

c

Interpellet

porosity

Micropore

Bulk Gas Macropore _SurfaceSolid

Bulk:

c

bk

, ε

B

, w

bk

Macropores:

w

msk

, c

msk

Interpellet

Voidage: ε

i

Pellet

(macroparticle)

Intrapellet

Porosity ε

P

Solid

Microporous

Particles: w

k

, c

k

c

bk

, ε

B

, w

bk

c

msk

, (1-ε

i

) ε

P

, w

msk

ε

i

c

k

, w

k

*

The material balance model assumes that:

• Radial concentration profile within the particle is parabolic. • Concentration profile within the particle is radially symmetric. • Radial dispersion is negligible.

(40)

Gas Phase

The component balance in the bulk gas phase is of the form:

( )

₍

₁

₎

₍

₁

₎

₌

₀

∂

−

+

∂

−

+

∂

+

∂

t

c

t

w

t

c

z

v

c

_msk p i k s p bk B g bk

_ε

_ρ

_ε

[Convection] + [accumulation] + [mass transfer (accumulation) to micropore] + [mass transfer (accumulation) to macropore]

In the given example, the gas phase material balance is written for a convection only situation in a vertical, one-dimensional adsorption layer.

Macropore (Crystalline)

The material balance in the macropore is given as: Fluid Film Model:

(

i

)

p msk

(

p

)

s k

K

mac

(

c

bk

c

msk

)

t

w

t

c

₌

₋

∂

−

+

∂

−

ε

1 ε

ρ

1

[accumulation] + [mass transfer to micropore] = [rate of mass transfer from bulk gas]

Solid Film Model:

(

₁

)

(

₁

)

(

₁

)

(

* *

)

msk bk mac s p k s p msk p i

K

w

t

w

t

c

−

=

∂

−

+

∂

−

ε

ρ

ε

ρ

Micropore (Particle)

Fluid Film Model:

(

₁

)

(

*

)

k msk mic k s p

K

c

t

w

−

=

∂

−

ε

ρ

[accumulation] = [rate of mass transfer from macropore] Solid Film Model:

(

p

)

s k

(

p

)

s

K

mic

(

w

sk

w

k

)

t

w

−

=

∂

−

₁

*

1 ε

ρ

ε

ρ

[accumulation] = [rate of mass transfer from macropore]

Specifying Particle Resistance Coefficients

If you choose Micro & Macro Pore Effects, you must specify the values of the macropore and micropore resistances:

K

_mac and

K

_mic. The following options are available in the Form of Mass Transfer Coefficient field.

(41)

Constant

This option forces the particle resistance coefficients to be constant throughout the bed. Set the coefficients in the variable arrays Kmac and Kmic.

The macropore constant

K

_mac is given by:

2

0 .

15

P efP mac

r

D

K

=

Where: efP

D

= Component diffusivities in macropores

p

r

= Particle radius

The micropore constant

K

_mic is given by:

2

0 .

15

c efc mic

r

D

K

=

Where: efc

D

= Component diffusivities in micropores

c

r

= Microparticle radius

Estimated

This option uses a submodel in which Aspen Adsim automatically estimates the coefficients.

User Procedure

If you choose this option, the bed model is written so that the component rates of mass transfer are related to local conditions in the bed through the procedure type pUser_g_Kinetic.

)

,

(

_g _i _s _i _g i

_f

_T

_P

_c

_T

_w

_v

t

w =

∂

Note: Langmuir adsorption kinetics is quite a popular option, and can be applied with such a procedure.

User Submodel

(42)

Kinetic Model Assumption (gas): Particle MB

This option determines the loading and gas phase concentration profiles inside an adsorbent particle, by rigorously solving the particle material balance for both phases. For this to work, the following conditions must be met: • Adsorbent has a uniform pore structure.

• Effective gas phase diffusion coefficient is calculated from the molecular and the Knudsen diffusion coefficients.

• Effective diffusivities for the gas and adsorbed phase are independent of the location inside the particle.

The Particle Material Balance option considers two mass transfer resistances: • The intraparticle mass transfer resistance, which is the diffusional

resistance inside the particle pore structure, caused by both gas and adsorbed phase diffusion.

• The interparticle mass transfer resistance, which is the resistance to mass transfer posed by the boundary layer between particle surface and bulk gas.

(43)

r

_p

Bulk

Gas

Boundary

Layer

Adsorbent

Particle (Uniform

Pore Structure)

c

_i

c

_i

*

w

_i

*

w

_i

(r)

0

=

∂

= r i

r

w

J

_i p r r i

r

w

=

∂

(

)

(

*

)

i i f r r i ei s i

a

k

c

r

w

D

a

J

p

−

ε

−

=

∂

ρ

=

1

The particle material balance is expressed as:

0

2

2 2

=













∂

+

∂

−

∂

r

w

r

w

r

D

t

w

_k _k ek k Where: k

w

= Loading ek

D

= Effective adsorbed phase diffusion coefficient

r = Radial particle co-ordinate

The effective diffusion coefficient is assumed constant throughout the particle. It is calculated from the particle location inside the adsorber (axial and radial column co-ordinate) using the procedure pUser_g_De or submodel

(44)

The boundary conditions for this partial differential equation come from both the symmetry condition at r=0:

0

=

∂

= r i

r

w

and the material flux through the boundary layer at

r

=

r

_p:

(

₁

)

(

*

)

k k fk i r r k ek s

_r

a

k

c

w

D

a

p

−

=

∂

=

ε

ρ

Where:

a = Specific particle surface

s

ρ

= Bulk density of solid

i

ε

fk

k

= Boundary layer mass transfer coefficient

k

c

= Gas phase concentration

*

k

c

= Interface gas phase concentration

The gas phase composition and the loading are coupled by the condition that thermodynamic equilibrium has been achieved at the interface between gas phase and particle:

( )

* * i eq r r i i

w

f

c

w

p

=

₌ Where: eq

f

= Isotherm equation * i

w

= Loading at

r

=

r

_p

The boundary layer mass transfer coefficient is expressed using the following Sherwood number correlation:

6 . 0 3 / 1

1 .

1

2 Sc

Re

Sh

_i

=

+

_i Where: mi p fi i

_D

r

k

Sh

=

2

= Sherwood number

Sc

=

µ

= Schmidt number

(45)

mi

D

= Mean molecular diffusion coefficient

µ = Gas phase dynamic viscosity

g

ρ

= Molar gas phase density

M = Mean molecular weight

g

ν

= Superficial velocity

Kinetic Model Assumption (gas): Particle MB 2

This option determines the loading and gas phase concentration profiles inside an adsorbent particle, by rigorously solving the particle material balance for both phases. For this to work:

• Adsorbent has a uniform pore structure.

• Effective gas phase diffusion coefficient is calculated from the molecular and the Knudsen diffusion coefficients.

• Effective diffusivities for gas and adsorbed phase are independent of the location inside the particle.

The Particle Material Balance 2 option considers two mass transfer resistances:

• The intraparticle mass transfer resistance, which is the diffusional resistance inside the particle pore structure, caused by both gas and adsorbed phase diffusion.

• The interparticle mass transfer resistance, which is the resistance to mass transfer posed by the boundary layer between particle surface and bulk gas.

Aspen Adsim

Aspen Adsim

2004.1

Who Should Read this Guide

General Information

Copyright

Related Documentation

Technical Support

Online Technical Support

Center

Phone and E-mail

Contents

Introducing Aspen Adsim

1 Gas Adsorption Processes

About Gas Adsorption

Processes

Bed Model Assumptions for Gas

Adsorption Processes

About Aspen Adsim's Bed

Models

Bed Model Ports

Configure Form (Gas)

Configure Form (gas): Bed Type

L

H

H

H

H

D

z

W(z)

Layer 1

Layer 2

(

)

[

]

4

)

(

z

z

D

z

W

=

−

D

Configure Form (gas): Spatial

Dimensions

Configure Form (gas): Internal Heat

Exchanger

Configure Layer Form (gas)

General Tab (gas)

General Tab (gas): Discretization

Method to be used

General Tab (gas): Number of Nodes

General Tab (gas): Number of Radial

Nodes

General Tab (gas): Flux Limiter to be

used

General Tab (gas): Gas Model

Assumption

T

R

Z

P

=

ρ

Z

R

T

c

Py

=

T

ρ

y

Material/Momentum Balance

Tab (gas)

_∂

_ν

₌

₋

_v