doc/lyxFinal/howto-physprops.lyx

#LyX 1.4.1 created this file. For more info see http://www.lyx.org/
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\language english
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\use_amsmath 2
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\quotes_language english
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\tracking_changes false
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\end_header

\begin_body

\begin_layout Chapter
Multi-phase equilibrium
\begin_inset LatexCommand \index{equilibrium}

\end_inset

 libraries
\begin_inset LatexCommand \label{cha:physprops}

\end_inset

 
\end_layout

\begin_layout Standard
This chapter describes the models we provide to compute thermodynamic properties
\begin_inset LatexCommand \index{thermodynamic properties}

\end_inset

 for multi-phase
\begin_inset LatexCommand \index{multi-phase}

\end_inset

, multi-component
\begin_inset LatexCommand \index{multi-component}

\end_inset

 vapor/liquid mixtures
\begin_inset LatexCommand \index{vapor/liquid mixtures}

\end_inset

 where we assume equilibrium exists among co-existing phases.
 
\end_layout

\begin_layout Section
A description of the libraries
\end_layout

\begin_layout Standard
In this section we describe the three libraries, 
\family typewriter
phases.a4l
\family default
, 
\family typewriter
components.a4l
\family default
 and
\family typewriter
 thermodynamics.a4l
\family default
.
 These libraries contain many models, but the end user is only interested
 in a few of them.
 Our intention is that these few should be very simple to use, with the
 complexities buried inside the models.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
first the phase definitions
\end_layout

\end_inset

The first contains the models we use to define the phases we allow for a
 mixture (i.e., vapor, liquid, vapor/liquid, liquid/liquid and vapor/liquid/liquid
)
\begin_inset LatexCommand \ref{id:#id(pgfId-1010487)}

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Standard
It should be noted that, while the models will correctly set up the data
 structures for the liquid/liquid and vapor/liquid/liquid options, we do
 not really support these alternatives at this time.
\end_layout

\end_inset


\noun off
.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
then the components and their data
\end_layout

\end_inset

The second library contains the models having all the component physical
 properties for the components we include with ASCEND -- e.g., there are property
 values for heat capacity
\begin_inset LatexCommand \index{heat capacity}

\end_inset

, heat of vaporization
\begin_inset LatexCommand \index{heat of vaporization}

\end_inset

, accentric factor
\begin_inset LatexCommand \index{accentric factor}

\end_inset

 and so forth for water, methanol, carbon dioxide, etc.
 There is also the very extensive list of group contribution
\begin_inset LatexCommand \index{group contribution}

\end_inset

 data we need to use the UNIFAC
\begin_inset LatexCommand \index{UNIFAC}

\end_inset

 method.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
and finally the mixture thermodynamic models
\end_layout

\end_inset

The third provides the models we use to compute multi-component mixture
 thermodynamic properties for phases, such as ideal gas
\begin_inset LatexCommand \index{ideal gas}

\end_inset

, Pitzer
\begin_inset LatexCommand \index{Pitzer}

\end_inset

, UNIFAC, and Wilson
\begin_inset LatexCommand \index{Wilson}

\end_inset

.
 The final model in this library is the one to compute equilibrium conditions
 for multi-component, multi-phase systems.
 We provide both a constant relative volatility
\begin_inset LatexCommand \index{relative volatility}

\end_inset

 and a rigorous phase equilibrium model, with the ability to switch interactivel
y between which one to use.
 Thus one can first assume constant relative volatility to have a better
 chance to converge and then switch to the version that makes the chemical
 potential
\begin_inset LatexCommand \index{chemical potential}

\end_inset

 equal for a component in all phases.
\end_layout

\begin_layout Subsection
The 
\family typewriter
phases.a4l
\family default

\begin_inset LatexCommand \index{phases.a4l}

\end_inset

 library
\end_layout

\begin_layout Standard
\begin_inset Marginal
status open

\begin_layout Standard
need to create only instances of phases_data
\end_layout

\end_inset

The 
\family typewriter
Phases.a4l
\family default
 library, see Figure 
\begin_inset LatexCommand \ref{fig:physprops.phases.a4l}

\end_inset


\noun off
, has only one model in it, phases_data
\noun default

\begin_inset LatexCommand \index{phases\_data}

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Standard
In this and following figures, we represent each model as a rectangle.
 On the upper left is the name of the model.
 In 
\begin_inset LatexCommand \ref{fig:physprops.phases.a4l}

\end_inset


\noun on
Figure 1-1
\noun off
, the model is phases_data.
 On the left side we list in order the parameters for the model.
 These are shared objects
\begin_inset LatexCommand \index{shared objects}

\end_inset

 a model containing an instance of phases_data will pass to that instance.
 An example would bepd IS_A phases_data(V, 'Pitzer_vapor_mixture', 'none',
 'none')We list the parts defined locally within a model on the right side
 of the rectangle, including instances of models, atoms and sets.
 The slanted double-headed arrow indicates a set; thus, phases and other_phases
 are sets in phases_data.In 
\begin_inset LatexCommand \ref{fig:physprops.thermoLib}

\end_inset


\noun on
Figure 1-3
\noun off
 we show lines connecting a model, call it A, to a part within another model,
 call it B.part.
 The connection is to the sides of both.
 This type of connection says B.part is an instance of model A.
 We also show connections from the bottom of one model, call it C, to the
 top of another, call it D; with this connection we indicate that the lower
 model D is a refinement
\begin_inset LatexCommand \index{refinement}

\end_inset

 of the upper model C.
\end_layout

\end_inset


\noun off
.
 The user creates an instance of this model, specifying which phases are
 to exist for a stream or holdup and which thermodynamic model the system
 should use to compute mixture properties for each phase.
 Compiling this instance then sets up the data structures required to characteri
ze those phases for the system.
\end_layout

\begin_layout Standard
For example, suppose we want to model a flowsheet consisting of a single
 flash unit.
 Suppose further that we want to allow the feed to the flash unit to be
 vapor, liquid or vapor/liquid (i.e., 2 phase).
 The product streams from the flash unit will be a vapor phase mixture and
 a liquid phase mixture.
 We would define three instances of the phases_data model, one for each
 type of phase condition we wish to model.
 You can find the following statements in the model 
\family typewriter
testflashmodel
\family default

\begin_inset LatexCommand \index{testflashmodel}

\end_inset

 in the library 
\family typewriter
flash.a4l
\family default

\begin_inset LatexCommand \index{flash.a4l}

\end_inset

.
\end_layout

\begin_layout LyX-Code
pdV IS_A phases_data('V', 'ideal_vapor_mixture', 
\end_layout

\begin_layout LyX-Code
                     'none', 'none');
\end_layout

\begin_layout LyX-Code
pdL IS_A phases_data('L', 'none', 
\end_layout

\begin_layout LyX-Code
                     'UNIFAC_liquid_mixture', 'none');
\end_layout

\begin_layout LyX-Code
pdVL IS_A phases_data('VL', 'ideal_vapor_mixture',
\end_layout

\begin_layout LyX-Code
                      'UNIFAC_liquid_mixture','none');
\end_layout

\begin_layout Standard
When compiled, 
\family typewriter
pdV
\family default
, 
\family typewriter
pdL
\family default
 and 
\family typewriter
pdVL
\family default
 contain the data structures the thermodynamic models require to model a
 vapor, liquid and vapor/liquid stream
\begin_inset LatexCommand \index{stream}

\end_inset

 (or holdup
\begin_inset LatexCommand \index{holdup}

\end_inset

).
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
the phase indicators and types
\end_layout

\end_inset

The first parameter is a character that indicates the phase option desired
 - 
\family typewriter
'M'
\family default
, 
\family typewriter
'V'
\family default
, 
\family typewriter
'L'
\family default
, 
\family typewriter
'VL'
\family default
,
\family typewriter
 'LL'
\family default
 and 
\family typewriter
'VLL'
\family default
.
 
\family typewriter
'M'
\family default
 is for a material only stream (no thermodynamic properties are to be computed),
 
\family typewriter
'V'
\family default
 is for vapor and 
\family typewriter
'L'
\family default
 for liquid.
 This model always expects the user to supply in the last three parameters
 an ordered list giving the three single phase mixture models to be used:
 vapor, liquid1, liquid2.
 For a non-existent phase
\begin_inset LatexCommand \index{non-existent phase}

\end_inset

, the user should supply 'none' as the model.
 If there is only one liquid phase, liquid2 will not exist.
 The allowed models we can use to estimate multi-component phase mixture
 properties are in the third of the libraries we describe in this chapter,
 
\family typewriter
thermodynamics.a4l
\family default

\begin_inset LatexCommand \index{thermodynamics.a4l}

\end_inset

, which we discuss shortly in Section 
\begin_inset LatexCommand \ref{ssec:physprops.thermoLib}

\end_inset


\noun off
.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Standard

\noun off
\begin_inset Graphics
    filename howto-physpropsFig1.eps
    width 90col%

\end_inset


\end_layout

\begin_layout Caption
Phases.a4l
\begin_inset LatexCommand \index{Phases.a4l}

\end_inset

 models
\begin_inset LatexCommand \label{fig:physprops.phases.a4l}

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
The 
\family typewriter
components.a4l
\family default

\begin_inset LatexCommand \index{components.a4l}

\end_inset

 library
\end_layout

\begin_layout Standard
In this library (see Figure 
\begin_inset LatexCommand \ref{fig:physprops.components.a4l}

\end_inset


\noun off
) we provide the actual physical property data for the components supplied
 with ASCEND.
 The data we provide is that found in the tables at the back of Reid
\begin_inset LatexCommand \index{Reid}

\end_inset

, Prausnitz
\begin_inset LatexCommand \index{Prausnitz}

\end_inset

 and Poling
\begin_inset LatexCommand \index{Poling}

\end_inset

, The Properties of Vapors 
\noun default
&
\noun off
 Liquids, 4th Ed, McGraw-Hill
\begin_inset LatexCommand \index{McGraw-Hill}

\end_inset

, New York (1986).
 For a few of the components, we have also identified their UNIFAC groups
\begin_inset LatexCommand \index{UNIFAC groups}

\end_inset

.
 We include a few Wilson binary mixture parameters
\begin_inset LatexCommand \index{Wilson binary mixture parameters}

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
need to create only instances of components_data
\end_layout

\end_inset

The purpose of this library is similar to the 
\family typewriter
phases.a4l
\family default
 library.
 We wish to provide an easy-to-use model that will set up the data structures
 for the components in a mixture that the thermodynamic models will use
 when estimating mixture physical properties.
 All the user has to do is create an instance of the bottom-most model 
\family typewriter
components_data
\family default
, passing into it a list of the components in the mixture and the name of
 one of them which is to serve as the reference component.
 This model, having parts which are instances of the others present in this
 library, then compiles into the needed data structures.
\end_layout

\begin_layout Standard
An example of use is found in the model 
\family typewriter
testflashmodel
\family default
 in the library 
\family typewriter
flash.a4l
\family default

\begin_inset LatexCommand \index{flash.a4l}

\end_inset

:
\end_layout

\begin_layout LyX-Code
cd IS_A components_data(['n_pentane','n_hexane',
\end_layout

\begin_layout LyX-Code
                         'n_heptane'],'n_heptane');
\end_layout

\begin_layout Standard
When compiled 
\family typewriter
cd
\family default
 has in it a data structure containing the physical properties for the three
 species listed.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
reference component
\end_layout

\end_inset

The choice of which species to use as the reference component
\begin_inset LatexCommand \index{reference component}

\end_inset

 is up to the user.
 Usually a good choice is one that is plentiful in the mixture, but that
 need not be so.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Standard
\begin_inset Graphics
    filename howto-physpropsFig2.eps
    width 100col%

\end_inset


\end_layout

\begin_layout Caption
components.a4l
\begin_inset LatexCommand \index{components.a4l}

\end_inset

 models
\begin_inset LatexCommand \label{fig:physprops.components.a4l}

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
adding a new component
\end_layout

\end_inset

One can add more components to this library as follows:
\end_layout

\begin_layout Enumerate
add the name of the new component to the list of supported_components at
 the beginning of the model 
\family typewriter
td_thermodynamic_constants
\family default
 (part of the 
\family typewriter
WHERE
\family default
 statement that causes the system to output a diagnostic if someone subsequently
 misspells the name of a component)
\end_layout

\begin_layout Enumerate
add the component data as a 
\family typewriter
CASE
\family default
 to the 
\family typewriter
SELECT
\family default
 statement in
\family typewriter

\newline
td_thermodynamic_constants
\family default
 (for an example, look at how it is done for 'methanol')
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
adding UNIFAC group identifiers
\end_layout

\end_inset

Put the UNIFAC group identifiers
\begin_inset LatexCommand \index{UNIFAC group identifiers}

\end_inset

 for the new component into the set subgroups.
 To illustrate, this statement for methanol is:
\end_layout

\begin_layout LyX-Code
subgroups:== ['CH3', 'OH'];
\end_layout

\begin_layout Standard
You can find all the UNIFAC group identifiers possible in the model 
\family typewriter
UNIFAC_constants
\family default

\begin_inset LatexCommand \index{UNIFAC\_constants}

\end_inset

.
 Then fill in the vector 
\family typewriter
nu
\family default
 with a value for each of these groups (to indicate how many such groups
 are in the molecule).
 To illustrate, the values for methanol are:
\end_layout

\begin_layout LyX-Code
nu['CH3']:==1;
\end_layout

\begin_layout LyX-Code
nu['OH']:==1;
\end_layout

\begin_layout Standard
If you are entering the component without identifying its UNIFAC groups,
 then enter the subgroups statement and define it as empty -- i.e., write
\end_layout

\begin_layout LyX-Code
subgroups:== [ ];
\end_layout

\begin_layout Standard
There should then be no entry for nu (see the 
\family typewriter
CASE
\family default
 for hydrogen, for example).
 An activity coefficient estimated by the UNIFAC method will be unity for
 such a component.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
adding Wilson parameters
\end_layout

\end_inset

To add Wilson parameters
\begin_inset LatexCommand \index{Wilson parameters}

\end_inset

, first fill in the names of the other components for which you are adding
 data into the set 
\family typewriter
wilson_set
\family default
.
 For example, this set for methanol might be:
\end_layout

\begin_layout LyX-Code
wilson_set:== ['H2O','(CH3)2CO','CH3OH'];
\end_layout

\begin_layout Standard
Then fill in lambda and energy parameters into the arrays 
\family typewriter
lambda
\family default
 and 
\family typewriter
del_ip
\family default
, one for each of the other components.
 Again, to illustrate, these arrays for methanol would be:
\end_layout

\begin_layout LyX-Code
lambda['H2O']:==0.43045;
\end_layout

\begin_layout LyX-Code
lambda['(CH3)2CO']:==0.77204;
\end_layout

\begin_layout LyX-Code
lambda['CH3OH']:==1.0;
\end_layout

\begin_layout LyX-Code
del_ip['(CH3)2CO']:==2.6493E+002 {J/g_mole};
\end_layout

\begin_layout LyX-Code
del_ip['H2O']:==1.1944E+002 {J/g_mole};
\end_layout

\begin_layout LyX-Code
del_ip['CH3OH']:==0.0 {J/g_mole};
\end_layout

\begin_layout Standard
Finally for each of these other components, go to its 
\family typewriter
CASE
\family default
 statement, add the name of the new component to its wilson_set and then
 add statements to set the corresponding lambda and energy data.
 BEN, IS THIS RIGHT????If you are not adding any Wilson data, enter the
 statement:
\end_layout

\begin_layout LyX-Code
wilson_set:== [ ];
\end_layout

\begin_layout Subsection
The 
\family typewriter
thermodynamics.a4l
\family default

\begin_inset LatexCommand \index{thermodynamics.a4l}

\end_inset

 library
\begin_inset LatexCommand \label{ssec:physprops.thermoLib}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
create instances only of phase_partials and thermodynamics
\end_layout

\end_inset

Figure 
\begin_inset LatexCommand \ref{fig:physprops.thermoLib}

\end_inset


\noun off
 shows all the models in this library and how they are related to each other.
 There are two models in this library that the user has to worry about:
 
\family typewriter
\noun default
phase_partials
\family default
\noun off

\begin_inset LatexCommand \index{phase\_partials}

\end_inset

 and 
\family typewriter
\noun default
thermodynamics
\family default
\noun off
.
 The user creates one instance of thermodynamics for every stream or holdup
 in a process model.
 Each instance, when compiled has parts which are instances of the other
 models in this library and which are create the equations to compute the
 thermodynamic properties for a multi-component, multi-phase mixture.
\end_layout

\begin_layout Standard
However, the user must pass each instance of a thermodynamics model an array
 of instances of 
\family typewriter
phase_partials
\family default
, one for each phase in the mixture.
 One 
\family typewriter
phase_partials
\family default
 model must exist for each phase in each stream or holdup in the process
 model as it provides the equations modeling that phase.
 
\end_layout

\begin_layout Standard
\begin_inset Note Note
status collapsed

\begin_layout Standard
Need to explain UNIFAC, Pitzer etc, since these terms are not familiar to
 the Mechanical Engineer, and no details are provided as to which is appropriate
 for which types of problems.
\end_layout

\begin_layout Standard
Also, it would be useful to know how to model a homogenous two-phase stream
 of gas/liquid mixture of a single component.
\end_layout

\begin_layout Standard
Also, the documentation needs a 'hello world' example of how to use the
 properties correlation, eg how to compute the enthalpy of water at room
 temperature / atmospheric pressure.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Each of the models in the array of 
\family typewriter
phase_partials
\family default
 must be refined to be one of the possible models for computing properties
 for a single phase mixture, i.e., one of the models lying below the 
\family typewriter
phase_paritals
\family default
 model in Figure 
\begin_inset LatexCommand \ref{fig:physprops.thermoLib}

\end_inset


\noun off
: 
\family typewriter
\noun default
ideal_vapor_mixture
\family default
\noun off

\begin_inset LatexCommand \index{ideal\_vapor\_mixture}

\end_inset

, 
\family typewriter
\noun default
Pitzer_vapor_mixture
\family default
\noun off

\begin_inset LatexCommand \index{Pitzer\_vapor\_mixture}

\end_inset

, 
\family typewriter
\noun default
UNIFAC_liquid_mixture
\family default
\noun off

\begin_inset LatexCommand \index{UNIFAC\_liquid\_mixture}

\end_inset

 or 
\family typewriter
\noun default
Wilson_liquid_mixture
\family default
\noun off

\begin_inset LatexCommand \index{Wilson\_liquid\_mixture}

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Standard

\noun off
\begin_inset Graphics
    filename howto-physpropsFig3.eps
    lyxscale 50
    width 100col%

\end_inset


\end_layout

\begin_layout Caption
Models in thermodynamic.a4l
\begin_inset LatexCommand \label{fig:physprops.thermoLib}

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
The information in an instance of a 
\family typewriter
phases_data
\family default
 model allows us to construct this array of 
\family typewriter
phase_partials
\family default
.
 We extract the following code from the library 
\family typewriter
stream_holdup.a4l
\family default

\begin_inset LatexCommand \index{stream\_holdup.a4l}

\end_inset

 to illustrate how we have created such a model, given a 
\family typewriter
phases_data
\family default
 model.
\end_layout

\begin_layout LyX-Code
MODEL select_mixture_type
\begin_inset LatexCommand \index{select\_mixture\_type}

\end_inset

(
\end_layout

\begin_layout LyX-Code
    cd WILL_BE components_data;
\end_layout

\begin_layout LyX-Code
    type WILL_BE symbol_constant;
\end_layout

\begin_layout LyX-Code
) REFINES sh_base;
\end_layout

\begin_layout LyX-Code
phase IS_A phase_partials(cd);
\end_layout

\begin_layout LyX-Code
SELECT (type)
\end_layout

\begin_layout LyX-Code
CASE 'ideal_vapor_mixture':
\end_layout

\begin_layout LyX-Code
phase IS_REFINED_TO ideal_vapor_mixture(cd);
\end_layout

\begin_layout LyX-Code
CASE 'Pitzer_vapor_mixture':
\end_layout

\begin_layout LyX-Code
phase IS_REFINED_TO Pitzer_vapor_mixture(cd);
\end_layout

\begin_layout LyX-Code
CASE 'UNIFAC_liquid_mixture':
\end_layout

\begin_layout LyX-Code
phase IS_REFINED_TO UNIFAC_liquid_mixture(cd);
\end_layout

\begin_layout LyX-Code
CASE 'Wilson_liquid_mixture':
\end_layout

\begin_layout LyX-Code
phase IS_REFINED_TO Wilson_liquid_mixture(cd);
\end_layout

\begin_layout LyX-Code
OTHERWISE:
\end_layout

\begin_layout LyX-Code
END SELECT;
\end_layout

\begin_layout LyX-Code
boundwidth IS_A bound_width;
\end_layout

\begin_layout LyX-Code
...
\end_layout

\begin_layout LyX-Code
...
\end_layout

\begin_layout LyX-Code
...
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
END select_mixture_type;
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
MODEL stream( .......
\end_layout

\begin_layout LyX-Code
...
\end_layout

\begin_layout LyX-Code
...
\end_layout

\begin_layout LyX-Code
...
\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout LyX-Code
FOR j IN phases CREATE
\end_layout

\begin_layout LyX-Code
smt[j] IS_A select_mixture_type(cd, pd.phase_type[j]);
\end_layout

\begin_layout LyX-Code
END FOR;
\end_layout

\begin_layout LyX-Code
FOR j IN phases CREATE
\end_layout

\begin_layout LyX-Code
phase[j] ALIASES smt[j].phase;
\end_layout

\begin_layout LyX-Code
END FOR;
\end_layout

\begin_layout LyX-Code
state IS_A thermodynamics(cd, pd, phase, equilibrated);
\end_layout

\begin_layout LyX-Code
...
\end_layout

\begin_layout LyX-Code
...
\end_layout

\begin_layout LyX-Code
...
\end_layout

\begin_layout LyX-Code
...
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
cannot directly embed SELECT statements in FOR loops
\end_layout

\end_inset

We had to be a bit tricky, but we hope we have not been so devious that
 you cannot understand what we have done if we explain it to you here.
 Look first at the code we extracted from the model stream.
 The models 
\family typewriter
cd
\family default
 and 
\family typewriter
pd
\family default
 are instances of a 
\family typewriter
components_data
\family default
 and a 
\family typewriter
phases_data
\family default
 model respectively.
 If we look inside 
\family typewriter
pd
\family default
, we will find it contains an array called 
\family typewriter
phase_type
\family default
, with one entry for each phase that gives the type (name) of the model
 to be used to set up the equations for that phase.
 ASCEND does not allow 
\family typewriter
SELECT
\family default
 statements
\begin_inset LatexCommand \index{SELECT statements. embedded in FOR}

\end_inset

 to be embedded directly within a 
\family typewriter
FOR
\family default
 loop -- thus we need a bit of deviousness.
 For each phase j we create 
\family typewriter
smt[j]
\family default
 as an instance of a 
\family typewriter
select_mixture_type
\family default
 model.
 We parameterize the 
\family typewriter
select_mixture_type
\family default
 with the components data 
\family typewriter
cd
\family default
 and the type (name) 
\family typewriter
pd.phase_type[j]
\family default
 of the model to be used to generate its equations.
 Then we embed the select statement within the 
\family typewriter
select_mixture_type
\family default
 model, something ASCEND does allow.
\end_layout

\begin_layout Standard
The model 
\family typewriter
select_mixture_type
\family default
 appears first in this code.
 It uses the type (name) it is passed to select and then to instance the
 desired refinement of the 
\family typewriter
phase_partials
\family default
 model.
 
\end_layout

\begin_layout Standard
Returning to the code extracted from the flash model, the second 
\family typewriter
FOR
\family default
 loop creates the desired array by aliasing the array element 
\family typewriter
phase[j]
\family default
 with the phase model created within the corresponding 
\family typewriter
smt
\family default
 instance.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status open

\begin_layout Standard
disappearing phases
\begin_inset LatexCommand \index{disappearing phases}

\end_inset


\end_layout

\end_inset

The multi-phase model handles the case where a phase disappears by using
 a complementarity
\begin_inset LatexCommand \index{complementarity}

\end_inset

 formulation.
 This formulation relaxes the constraint for a phase that its mole fractions
 must sum to unity when it disappears.
 Thus the vapor/liquid model will correctly alter the model to handle the
 situation when the mixture becomes a superheated vapor or a subcooled liquid.
\end_layout

\begin_layout Standard
We are now ready to create an instance of a thermodynamics model.
 When compiled this instance contains all the equations needed to estimate
 the phase conditions for a multi-phase, multi-component mixture assuming
 equilibrium exists among the phases.
 The following line of code, extracted from the stream model referred to
 above, illustrates its use:
\end_layout

\begin_layout LyX-Code
state IS_A thermodynamics(cd, pd, phase, equilibrated);
\end_layout

\begin_layout Standard
where 
\family typewriter
cd
\family default
 is an instance of a 
\family typewriter
components_data model
\family default
, 
\family typewriter
pd
\family default
 of a 
\family typewriter
phases_data
\family default
 model, 
\family typewriter
phase
\family default
 an array of instances of 
\family typewriter
phase_partials
\family default
, and 
\family typewriter
equilibrated
\family default
 a 
\family typewriter
boolean
\family default
 variable.
 When 
\family typewriter
equilibrated
\family default
 is 
\family typewriter
FALSE
\family default
, the model will generate the equations assuming constant relative volatilities
 (the user must estimate these volatilities).
 When 
\family typewriter
TRUE
\family default
, the model generates the equations assuming the chemical potentials for
 a component are equal in all phases.
\end_layout

\begin_layout Section
Using the thermodynamics models
\end_layout

\begin_layout Standard
There are several libraries of models that use the libraries we have just
 described.
 The first library to examine is 
\family typewriter
stream_holdup.a4l
\family default
.
 This library contains steady-state models for a stream and a holdup.
 The following gives the parameter list for a user to create an instance
 of a stream.
\end_layout

\begin_layout Subsection
Streams
\begin_inset LatexCommand \index{streams}

\end_inset

 and holdups
\begin_inset LatexCommand \index{holdups}

\end_inset


\end_layout

\begin_layout LyX-Code
MODEL stream (
\end_layout

\begin_layout LyX-Code
    cd WILL_BE components_data;
\end_layout

\begin_layout LyX-Code
    pd WILL_BE phases_data;
\end_layout

\begin_layout LyX-Code
    equilibrated WILL_BE boolean;
\end_layout

\begin_layout LyX-Code
) REFINES sh_base;
\end_layout

\begin_layout Standard
The model 
\family typewriter
sh_base
\family default
 is a dummy model to tie all models into this library back to a common root
 model.
 The user need do nothing because of this refinement.
 What you should note is that all you need to do to create a stream is create
 a 
\family typewriter
components_data
\family default
 model and a 
\family typewriter
phases_data
\family default
 model.
 One supplies the boolean variable 
\family typewriter
equilibrated
\family default
 as a variable that one can set interactively or in a method or a script
 when running the model to decide how to model equilibrium, as we have discussed
 above.
 A holdup is equally as easy to model.
\end_layout

\begin_layout Subsection
Flash units
\begin_inset LatexCommand \index{flash units}

\end_inset

 and variants thereof
\end_layout

\begin_layout Standard
From streams and holdups, we can move on to unit operation models.
 The library 
\family typewriter
flash.a4l
\family default
 provide us with a flash model.
 The parameter list for the flash model is:
\end_layout

\begin_layout LyX-Code
MODEL vapor_liquid_flash
\begin_inset LatexCommand \index{vapor\_liquid\_flash}

\end_inset

(
\end_layout

\begin_layout LyX-Code
   Qin WILL_BE energy_rate;
\end_layout

\begin_layout LyX-Code
   equilibrated WILL_BE boolean;
\end_layout

\begin_layout LyX-Code
   feed WILL_BE stream;
\end_layout

\begin_layout LyX-Code
   vapout WILL_BE stream;
\end_layout

\begin_layout LyX-Code
   liqout WILL_BE stream;
\end_layout

\begin_layout LyX-Code
) WHERE (
\end_layout

\begin_layout LyX-Code
   feed, vapout, liqout WILL_NOT_BE_THE_SAME;
\end_layout

\begin_layout LyX-Code
   feed.cd, vapout.cd, liqout.cd WILL_BE_THE_SAME;
\end_layout

\begin_layout LyX-Code
   vapout.pd.phase_indicator == 'V';
\end_layout

\begin_layout LyX-Code
   liqout.pd.phase_indicator == 'L';
\end_layout

\begin_layout LyX-Code
   (feed.pd.phase_indicator IN ['V','L','VL','VLL']) == TRUE;
\end_layout

\begin_layout LyX-Code
) REFINES flash_base;
\end_layout

\begin_layout Standard
Again we see that to create a flash unit, we need to create the variable
 
\family typewriter
Qin
\family default
 for the heat input to the unit, a boolean 
\family typewriter
equilibrated
\family default
 and three streams, 
\family typewriter
feed
\family default
, 
\family typewriter
vapout
\family default
 and 
\family typewriter
liqout
\family default
.
 The three streams must all be different streams.
 They must have the same components in them.
 The stream 
\family typewriter
vapout
\family default
 must be a vapor stream and the stream 
\family typewriter
liqout
\family default
 a liquid stream.
 The 
\family typewriter
feed
\family default
 stream can be of any kind.
\end_layout

\begin_layout Standard
Hopefully with the above information, creating a flash unit should not now
 seem particularly difficult.
\end_layout

\begin_layout Standard
If you examine this library further, you will see it contains models which
 are variations of the flash unit for: 
\family typewriter
detailed_tray
\family default
, 
\family typewriter
tray
\family default
, 
\family typewriter
feed_tray
\family default
, 
\family typewriter
total_condenser
\family default
 and 
\family typewriter
simple_reboiler
\family default
.
\end_layout

\begin_layout Subsection
Distillation columns
\begin_inset LatexCommand \index{Distillation columns}

\end_inset


\end_layout

\begin_layout Standard
We provide two libraries that allow you to model distillation columns: 
\family typewriter
column.a4l
\family default

\begin_inset LatexCommand \index{column.a4l}

\end_inset

 and 
\family typewriter
collocation.a4l
\family default

\begin_inset LatexCommand \index{collocation.a4l}

\end_inset

.
 The library 
\family typewriter
column.a4l
\family default
 first models a tray stack and then a simple column using that model.
 A third model extracts the profiles for pressure, temperature, a parameter
 that indicates the deviation from constant molar overflow conditions, total
 vapor and liquid flows and component compositions against tray number.
 This information may then be used for plotting these profiles using the
 ASCEND plotting capability.
\end_layout

\begin_layout Standard
The library 
\family typewriter
collocation.a4l
\family default
 provides collocation models for simple columns.
 With collocation models, one models composition profiles as smooth functions
 of tray number in a column section.
 Columns with a large number of trays are modeled with relatively small
 collocation models.
 Also the number of trays becomes a continuous variable, aiding in optimization
 studies where the number of trays in each section is to be computed.
\end_layout

\begin_layout Subsection
Dynamic unit models
\end_layout

\begin_layout Standard
ASCEND contains models for simulating the dynamic behavior of units.
 Their use is described in Chapter 
\begin_inset LatexCommand \vref{cha:ivp}

\end_inset

.
\end_layout

\begin_layout Section
Discussion
\end_layout

\begin_layout Standard
We have presented a description of the libraries that allow one to model
 the equations providing thermodynamic properties for multi-component, multi-pha
se mixtures when one assume equilibrium exists among co-existing phases.
 With this description, we hope that these models become much less difficult
 to use.
 We end this chapter by describing other libraries that build on the property
 estimation libraries, models for streams and holdups, for flash units and
 variations thereof, and for columns.
\end_layout

\end_body
\end_document