thermodynamics and the simulation engineer

Chemical Product and ProcessModeling

Volume 3, Issue 1 2008 Article 24

Thermodynamics and the Simulation Engineer

Marco A. Satyro∗

∗Virtual Materials Group, Inc., [email protected]

Copyright c©2008 The Berkeley Electronic Press. All rights reserved.

Thermodynamics and the SimulationEngineer∗

Marco A. Satyro

Abstract

In this paper a brief, commented introduction to thermodynamics highlighting its connectionswith the simulation of chemical processes is presented. With these connections established I pro-ceed to comment on current challenges faced by process and product modelers and conclude with apeek into the future of process and product design and the role of thermodynamics as the unifyingdiscipline for engineers.

KEYWORDS: thermocynamics, process simulation, simulation engineering, product and processdesign

∗The permission of Virtual Materials Group, Inc. to publish this work is gratefully acknowledged.The author is indebted to the kindness and patience of the editors due to delays in delivering themanuscript caused by work constraints.

Introduction It is a well-known fact that process simulators are heavily dependent on thermodynamics and physical property models. It is also well known that process simulators usually have large tomes of written documentation talking about physical properties and thermodynamics. Experience has shown me that at least these sections of manuals go mostly unread although the simulation results are completely dependent on the underlining thermodynamic models for phase equilibrium and physical property calculations as defined by the chosen property package.

Property packages are the workhorses of process and reservoir simulators and in a nutshell they are a collection of methods bounded by the first and second laws of thermodynamics and designed to solve a specific class of problems. Going deeper, the essence of a property package is its ability to determine the state of minimum free energy of a system, and when that is determined it must have the ability to compute physical and transport properties and provide an accurate accounting of mass as it distributes across different phases. For example, a set of components and chemical reactions and a couple of independent variables such as temperature and pressure define a chemical system. A properly constructed property package will then determine the number of phases at thermodynamic equilibrium, the amounts and compositions1 of each phase at equilibrium and physical properties of each phase. In actuality, thermodynamic related calculations consume the lion’s share of clock cycles during any non-trivial simulation and they govern the numbers and the quality of the numbers one obtains.

As process simulators have evolved, more and more sophistication has been built into unit operation models, graphical user interfaces and also thermodynamic models. One interesting shift that has happened over the years is a change in the knowledge background of engineers using simulators. When I started in this business close to 30 years ago, engineers using simulators would be quite proficient at programming, process engineering and thermodynamics (Chien and Null, 1972; Null, 1980). As engineering practice evolves, engineer’s interests also change and nowadays we have just as bright engineers, but with a rather different background. Most young engineers these days do little programming and they do not seem to see much chemistry or physical chemistry during their formative years. Thus good part of the engineering they learn comes from the ubiquitous use of simulation tools (Svrcek and Satyro, 2006)

1 Thermodynamic equilibrium here is applied on its broadest sense and the state of minimum free energy is sought not only by varying the amounts of moles chemical components in the phases due to diffusion but also compositional variations due to chemical reactions.

1

Satyro: Thermodynamics and the Simulation Engineer

Published by The Berkeley Electronic Press, 2008

Extensive use of simulators is not necessarily a bad thing; simulators are wonderful tools to teach natural gas and refinery technologies, heat integration, distillation and absorption and to boot simulators are great virtual laboratories. That said, simulation is not the real thing, and good users of process simulation are the ones who combine expert use of the computer tools with deep knowledge of the rudiments of chemical engineering – thermodynamics, physical chemistry, stoichiometry and reaction engineering. These rudiments were very well established more than half a century ago and they are the most valuable commodities today. Computers are notorious for generating a large amount of information, but sometimes that information does not make sense2.

Since most engineers being trained today are proficient users of simulators from the onset of their professional careers and will use them routinely throughout their professional lives, I think it is appropriate to use the term simulation engineer for the majority of process engineers today. Our objective is to take a high level tour of the field and we will stop to examine an interesting issue here and there. During the process we will stress fundamental points I believe are important for the intelligent use of process simulators.

It is important to stress that by necessity this is a biased paper since it is based on my experience helping engineers model gas plants, refineries, petrochemical and chemical complexes. Nevertheless, the same principles apply to many other interesting areas that use simulation like pharmaceutical synthesis, corrosion engineering and reservoir engineering.

Why Thermodynamics is Relevant for Simulation? Although we all state the fact that thermodynamics is important for process simulation, the fundamental reason has to do with a special feature of classical thermodynamics. Classical thermodynamics is a model free science and as such, it is not bound by the accuracy of specific models and theories. This way of looking at Nature provides us with a powerful tool because even though we may not be able to understand the details related to a specific fluid or process, classical thermodynamics allow us to write exact relationships between quantities of interest, and with these relationships (and experiments or models or as it is usually the case a combination of models and data) we can perform material and energy balances.

This power comes with strings attached. Perhaps the biggest issue with the framework provided by classical thermodynamics is the fact that implicitly we always assume processes to be reversible. We know that real processes are irreversible. These irreversibilities may come from different sources such as poorly designed equipment (such as in distillation trays that show large

2 John Prausnitz put it best: “The quality of a computer is speed, not intelligence.”

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Chemical Product and Process Modeling, Vol. 3 [2008], Iss. 1, Art. 24

http://www.bepress.com/cppm/vol3/iss1/24

entrainment or weeping) to energy dissipation coming from internal friction due to viscosity. The snag about trying to model thermodynamic processes taking into account irreversibilities is a question of ignorance. Bluntly stated, we usually do not know the minute details that are required to model a process taking into account dissipative forces, at least in a readily accessible and cheap way.

When performing simulations we are usually interested in making broad (but correct from the first and second laws point of view) statements related to the material and energy balances a real operating unit would exhibit, but we usually have rudimentary knowledge about the actual equipment being used (we may know the number of trays and reflux ratio of a certain tower, but may have only vague information about the tray geometry and performance curve of the reflux pump). Even if we had this information easily available, the appropriate computation of equipment performance invariably involves detailed fluid flow analysis, and although computational fluid dynamics is an important tool, one usually can not justify using such a sophisticated tool to complete the material balance for a simple separation system3.

Thus enters the reversibility assumption. If we assume that the processes can be represented as a reversible process, we then can use classical thermodynamics to provide us with the relationships we need to calculate material and energy balances. For example, when computing the duty for a condenser we can simply calculate the difference between the enthalpy at the outlet and inlet of the heat exchanger. The enthalpy is a thermodynamic property that can be defined by the specification of two state variables (for example temperature and pressure) and the composition of the fluid. With this we can calculate useful information that allows us to proceed with design work.

Naturally this came with a price. We do not know exactly how the equipment is going to perform in the field because we are not accounting for non-idealities such as pressure drops, heat losses, etc. In exchange we can do useful engineering work by making simple but judicious guesses about pressure drops, mass transfer efficiencies, mechanical efficiencies and the like.

This is, in essence, the reason why thermodynamics is such a basic ingredient of process simulation. Its formal structure allows is to draw exact relationships between variables and correlate and extend data in a precise and consistent manner. The assumption of reversibility is the key feature used to create these precise relationships, and the relationships of classical

3 One could be malicious here and mention that even if we knew the construction details of a certain piece of equipment and we could calculate the fluid flow phenomena accurately, this does not mean we actually are modeling the real plant. Stories abound where distillation trays collapse and are collected at the bottom of the tower during maintenance. I fondly recall a case where we found a fossilized owl inside an ethanol concentration tower and no computational sophistication could have taken that into account.

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thermodynamics allow us to write mathematical expressions for the phase equilibrium, chemical equilibrium and energy balance problems we encounter when we try to express the behavior of a chemical plant using mathematical models.

The use of this idealized, but precise framework allows us to move on with the analysis of complex chemical engineering problems in a formal way while adding an immense amount of order in the process. The removal of rate issues from the problem makes it solvable using a very small amount of information. For example computerized analysis of complex distillation problems are now routine (Rong and Turunen 2006 a,b), and an example is shown in figure 1.

Incidentally, a thermodynamic property that is important for the conceptual design of separation systems was discovered by the careful analysis of the differential equations that describe the structure of simple distillation systems (Ostwald, 1900; Schreinemakers, 1901; Doherty and Malone, 2001). This property is the residue curve map and it describes the structure of the separation space of mixtures and it has an especially strong significance for the design of extractive and azeotropic distillation. A closely related thermodynamic property is the distillation boundary present in a multi-component system. These boundaries divide the separation space into regions and tell us what types of separations are possible and impossible based on elementary information such as feed composition and desired operating pressure ranges. It is quite remarkable that by using the condition of thermodynamic equilibrium and simple models for the liquid phase so much is already known and can be efficiently used for screening of processes (Foucher et. al, 1991). Figure 2 shows a typical residue curve, distillation boundary and distillation regions for azeotropic distillation.

Property Package Fundamentals Now that we have a good idea of why classical thermodynamics is important for process simulation we proceed to examine how thermodynamics is used for the solution of material and energy balance problems. This is usually done using a computer construct called a property package. Property package is the generic term we use when we refer to a set of computer routines used to model the thermo-physical behavior of fluids. Property packages are designed to solve the following problems:

1. Determine the number of phases a fluid has when its global composition and two extra intensive variables (such as temperature, pressure, molar enthalpy, molar entropy or molar volume) are specified.

2. Determine the composition of each phase at equilibrium

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3. Determine the pressure, temperature and composition of each phase at equilibrium

4. Determine volume of each phase 5. Determine the molar enthalpy, entropy and heat capacity of each phase 6. Determine transport properties of each phase 7. Determine interfacial properties

You will notice that transport properties are really not thermodynamic

properties since they depend on rate processes (e.g. rate of momentum distribution as related to viscosity) but it is common to have these properties estimated by property packages due to their importance for equipment design (Ely, J.F. and Hanley, H.J.M, 1981).

The equilibrium problem Classical thermodynamics provides us with the tools needed for the precise mathematical formulation of thermodynamic equilibrium, and when we create a property package we usually start by writing the models that, when applied to this mathematical formulation, will give us in return useful numbers that describe some important characteristic of the system. We start with the combined form of the first and second laws of thermodynamics as shown by equation 1 (Prigogine and Defay, 1954).

...1 ,,,,,

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+−= ∑∑=

nr

jj

nVSj

nc

ii

nVSi

dUdnnUpdVTdSdU

kj

εε

ε

1

Equation 1 is the starting point for pretty much all arguments related to

phase equilibrium and it captures the heat transfer, mechanical work and diffusion phenomena as applied to a given system. It can be augmented to include gravitational, electrical, magnetic, surface effects due to external force fields as desired, but the idea is always the same – we want to express the energy content and mass content of a body based on fluxes that enter or leave it carrying mass and energy. At thermodynamic equilibrium the fluxes are zero and equation 1 give us, in principle, all the necessary tools we need to determine the equilibrium condition based on the value of a certain set of variables, in this case the entropy S, the volume V, the composition and the chemical reactions happening in the body.

The snag with equation 1 is related to its natural variables. It is an unfortunate fact that we do not have an “entropy meter” that could be used like a thermometer, and an alternative variable has to be sought for the solution of practical engineering problems. From a process engineering perspective, the best

5



variables are the ones easily measured, and those are usually the temperature and pressure of a system. Fortunately we have exact mathematical techniques that allow us to change the variables present in equation 1 by more convenient variables. This technique is called Legendre transform (Modell and Reid, 1974) and it is a procedure designed to replace the independent variable by its derivative without loss of information. When we apply this technique to equation 1 we get all the common expressions we are used to such as enthalpy, Helmholtz energy and Gibbs free energy expressed in different independent variable sets and completely equivalent from a mathematical perspective.

Although each of these expressions for the energy of a system is equivalent, the independent variable set is not. It just happens that the Gibbs free energy is the equivalent to equation 1 when the independent variables are temperature and pressure, and it is written as equation 2. The only difference between equations 1 and 2 is a reflection of our limitations as human beings. Nature “knows” what the state of equilibrium should be and always works towards it. We don’t and in order to try to figure it out we are bound by things we can measure.

...1 ,,,,,

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+−−= ∑∑=

nr

jj

npTj

nc

ii

npTi

dGdnnGVdpSdTdG

kj

εε

ε

2

Equation 2 is the starting point for the construction of virtually all process

engineering calculations and from a purely formal point of view we are done. We end up spending most of our time creating models for the free energy as functions of temperature, pressure and composition and solving the resulting equations for some equilibrium situation we are interested in.

Note that equation 2 provides us with a rather complete description of Nature. When a process has given up everything it can and it has exhausted its sources of temperature gradients we will have no heat fluxes across it (dT = 0), we will not be able to extract any mechanical work out of it due to movement of a phase (dp = 0), all mass transfer that could happen will have happened and no

compositional gradients will exist ( iallnG

i

,0=⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂ ) and all chemical reactions

that could happen will have happened to maximum possible extent

( jallGj

,0=⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂ε

). This static picture of Nature painted by classical

thermodynamics is its great achievement due to its precise mathematical formulation and generality. It is also its greatest handicap since rates are

6



convenient ignored, and introduces at a fundamental level the need for engineering knowledge by users of process simulation software.

You see, according to equation 2, when we mix hydrogen and oxygen at ambient conditions we will form water and release energy. This is an accurate statement and there’s no escaping to its conclusion as long as time is not important. Oxygen and hydrogen react at extremely slow rates and a bottle filled with these two gases will need eons in order for any water to form. A small spark or the addition of a catalyst will change the situation and allow the reaction to proceed at an appreciable rate and allow the mixture to fulfill its fate as predicted.

Thermodynamics, Process and Product Modeling The true power of thermodynamics is expressed when equation 2 is combined with a good empirical model for phase equilibrium and physical property estimation. There are many successful examples of thermodynamic modeling applied to all types of chemical processes and the thermodynamics section of your favorite process simulator will provide you with an inventory of useful thermodynamic methods that have found their way into mainstream process modeling. Instead of looking at an encyclopedic listing of successful thermodynamic models, we will look at the main features of a successful class of model that provides the thermodynamic background for the modeling of processes of an important industrial segment – natural gas and oil processing.

Thermodynamics of Hydrocarbon Systems To a great extent, our economy is a hydrocarbon based economy and in a quiet and unassuming manner, this industry is shaped by equation 2 and simple but very successful thermodynamic models that allow engineers to play the whole gamut – conceptual design, design, detailed design, optimization, control design and operator training – with confidence. This engineering success depends on two simple observations:

1 Real molecules, in average, attract each other 2 Real molecules can not be compressed forever

The actual explanation for observation 1 is quite involved (Parsegian, 2006)

and can be achieved in a satisfactory manner only if we resort to a quantum mechanical interpretation of molecular electrical field averages. For our purposes it suffices to acknowledge that this is an experimental feature of Nature. Observation 2 is more easily understood and is related to the fact that, to a first approximation, molecules have a definitive size and therefore infinite compression is not possible.

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Using these two observations, scientists have been working on the creation of models for fluids for hundreds of years, and these models can be expressed conceptually by equation 3.

( )xVTfp r,,= 3

Equation 3 is what is called an equation of state and it is a model designed to be plugged into equation 2 and in turn provide us with a compact description of Nature. Before we proceed, did you ever ask yourself why equation 3 is written that way? Mathematically we could just as easily write equation 4.

),,( xPTgV r= 4

Equation 4 is in a form ideal for chemical engineers since usually pressure

and temperature are their bread and butter coordinates, it is kind of surprising to see that equations of state are usually not cast in this form. A moment of reflection shows that pressure and temperature are indeed convenient coordinates, but they do not uniquely define the state of a saturated system. If you imagine a pot of water boiling at one atmosphere pressure, the temperature will be 100 degrees centigrade, but we have two physically possible densities for the system, one corresponding to a saturated vapor and another corresponding to a saturated liquid. Equation 4 can provide one of the volumes, but not both. Equation 3 on the other hand can model this phenomenon since two different values of volume can correspond to a single pressure, in this case the vapor pressure of water at the normal boiling temperature. This is illustrated in figure 3 and is a basic structural characteristic of industrially useful equations of state.

The simplest mathematical structure that accommodates observations 1 and 2 and allows the prediction of liquid-vapor phase equilibrium was initially proposed by van der Waals in 1873 (Rowlinson, 1988) and is expressed by equation 5.

2Va

bVRTp −−

= 5

Equation 5 is the essence of gas processing modeling thermodynamics and it

captures all the essential phenomena that are important for process modeling. When combined with equation 2 it can be used for the computation of phase equilibrium, it provides values for phase volumes and it also allows the prediction of critical points, cricondentherms and cricondenbars thus providing engineers with an useful map of the thermodynamic space for the design of gas processing facilities. Naturally, the structure provided by equation 5 captures the basic

8



physics of simple fluids, but it is highly simplified, and as written it is not accurate enough for technical work. By judicious use of empiricism, industrial strength equations of state can be constructed by noting that three boundary conditions should be met:

1 Critical temperatures and pressures for individual components must be modeled accurately

2 Individual component vapor pressures must be modeled accurately 3 Individual component liquid densities must be modeled accurately

An example of simple equation of state with these characteristics is the

Advanced Peng-Robinson model (Virtual Materials Group, 2004) where equation 5 is modified to equation 6.

( ))()( bVbbVV

TabV

RTp c

−++−

−=

α 6

When the equation of state is cast as described by equation 6 the term ac is

determined using the individual component critical pressure and temperature thus ensuring exact representation of the critical temperature and pressure (the critical volume is estimated and usually not very accurate and therefore estimated by the model). The function α is an empirical function of temperature and its parameters are determined to provide optimal representation of individual component vapor pressures. In some instances these parameters can be generalized as a function of molecular parameters (most commonly the acentric factor for hydrocarbons and non-polar substances) and a simple prescription for handling undefined components such as oil fractions can be quickly constructed.

Usually simple cubic equations of state can not represent liquid volumes accurately because they overestimate the critical compressibility of fluids and consequently liquid densities are underestimated. There’s a voluminous amount of literature about this (Patel and Teja, 1982; Trebble and Bishnoi, 1986) but a simple way to skirt the issue is to define an empirical parameter called the volume translation (Peneloux et. al, 1982) where the volume calculated by equation 6 is shifted by a constant computed to match the liquid density exactly at some convenient condition (in gas processing and refining this is usually at 1 atm and 60 F) and the prescription for the equation of state is completed by equation 7.

δ+=VVt 7

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The next step is to extend the model from pure components to mixtures. This is another subject that is extensively covered in the technical literature and many good ideas as well as not so good ones have been published. For our purposes it suffices to say that many hydrocarbon systems can be effectively modeled for engineering design using remarkably simple mixing rules. Mixing rules for cubic equations of state is another subject that has an immense volume of literature attached to it. Here we simply state that effective modeling for hydrocarbon systems can be achieved using the mixing rules derived by van der Waals using simple physical arguments and summarized in modern form by equations 8 and 9.

( )∑∑= =

−=nc

i

nc

jijjiji kxxaaa

1 11 8

∑=

=nc

iiibxb

1 9

The interaction parameter term kij in equation 8 accounts for the imperfect

adherence to the energy field of a van der Waals fluid when compared to the energy field of a real fluid and they can be generalized for hydrocarbons and also hydrocarbons and important inorganic gases such as carbon dioxide nitrogen and hydrogen. Judicious usage of interaction parameters also allows the modeling of water and hydrocarbon mixtures to a reasonable degree of accuracy4. Figure 4 illustrates how well these simple models can represent complex, polar molecules (Virtual Materials Group, 2004). Figure 5 illustrates the effectiveness of this simple, semi-empirical solution to the natural gas modeling problem (Cota et al, 2007).

Before we proceed, it is instructive to examine equation 6 in conjunction to equation 2. By applying Legendre transformations on equation 2 and assuming that no chemical reactions happen in the system we can express equation 2 in a form where temperature and volume are the independent variables. When we do that we have a different5 expression for the system energy using volume and

4 It is important to qualify this statement. Equation 8 implies a single interaction parameter per binary pair, and this means that only one side of the mutual solubility curve can be modeled using this type of simplistic model. In practice this corresponds to us having to choose on modeling accurate solubilities of water in hydrocarbons or vice versa. The common practice is to model the solubility of water in hydrocarbon and predict the solubility of hydrocarbon in water. This usually means that the solubility of hydrocarbon in the water phase is grossly underestimated and has significant impact on the simulation of water purification and disposal systems. 5 We stress here. Different but completely equivalent to internal energy or Gibbs free energy. We just have a different set of independent variables.

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temperature as independent variables. This form is called the Helmholtz energy and it is shown in equation 10 (Shaw and Satyro, 2006).

ii nVTi

dnnUpdVSdTdA

j

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+−−=,,

10

Assuming a system of constant composition and taking the volume partial

derivative with respect to the volume at constant temperature we have equation 11.

TVAp ⎟⎠⎞

⎜⎝⎛∂∂

−= 11

Thus we can plug into equation 10 the equation of state and we can calculate differences between Helmholtz energies at different volumes via integration of equation 10 as suggested by equation 12.

∫−=ΔV

V

pdVA0

12

Using standard thermodynamic relationships you can show that equation 13 holds.

VTSS ⎟⎠⎞

⎜⎝⎛∂Δ∂

−=Δ 13

Therefore, as long as we can establish a reference point for the integration of equations 12 and 13 and our model for p is reliable, we can calculate thermodynamic properties such as enthalpies and free energies and these in turn are the basis for energy balances and equilibrium reactor calculations performed by simulators. For example, we can write the enthalpy as equation 14.

( )10 −+Δ+Δ+= ZRTSTAHH 14

And the calculation is complete when H0 is defined. It is common to use the ideal gas state as the reference state for fluid phase calculations. At this hypothetical state molecules behave like non-interacting hard points. They have no volume, they generate no potential fields and their collisions are perfectly

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elastic. Thus the energy content depends only on the average kinetic, rotational and vibrational energies of individual molecules and it is a function of temperature only. This is conveniently expressed using equation 15.

∫=T

TpdTCH

0

00 15

In equation 15 we have a reference temperature for integration and this is

an arbitrary choice, although careful choice slightly simplifies chemical reactor modeling6. In a nutshell, by combining the fundamental equation 2, a model for the Helmholtz energy, equation 11 (or if you feel more comfortable a model for fluid pressure, equations such as 6) and the ability do calculate a reference state for the integration of the energy equation 12 we are in business and a self-contained description of reality is available for efficient simulations of fluid systems. This is the essence of a property package and now it should be clear that they come from a well defined procedure bounded by thermodynamic principles. With it we can compute the number of phases at equilibrium, their compositions, densities, enthalpies and so on7.

The salient feature with the approach outlined here is really equation 11. It tells us that we can create Helmholtz energy models that are suited to a specific problem and then we can use the same framework to compute physical properties perform phase equilibrium calculations and compute material and energy balances of interest. For example, this infrastructure supports complex equations of state developed for accurate representation of important substances like water and industrial gases (Lemmon et. al, 2002). It also supports equations of state designed to better capture the molecular behavior of fluids such as SAFT (Chapman, 1990).

More recently, equations of state more complex than cubics, but simple enough for automated parameter determination have been proposed (Span and Wagner 2003 a,b,c). These equations provide an accurate representation of the Helmholtz energy surface and better qualitative description of volumetric

6 It is common to use the ideal gas enthalpy of formation at 25 C and 1 atm as the reference point for the evaluation of ideal has enthalpies. This simplifies the equations for modeling reactors but adds the complication of having to have (or have estimation methods) for ideal gas enthalpies of formation of all components in a simulation. This can be particularly troublesome when dealing with oil pseudo-components. 7 This is a convenient point to remind the reader that solving in principle and solving efficiently and reliably are two different things. The efficient computation of phase equilibrium is usually done using flash algorithms and this is a skillful combination of thermodynamics, mathematics, numerical methods and individual talent (Michelsen, 1982ab; Nghiem, Li and Heidemann, 1985).

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properties than achievable with cubics and it is expected that they will play a significant role in the natural gas processing industry in the next decade.

It is evident that the construction of complex models will always partly rely on quality physical property data. The last five years has seen a significant development in this area, and notable advances are the SOURCE database (Frenkel et. al, 2001) maintained by the Thermodynamics Research Center at the National Institute of Standards and Technology and the Thermo Data Engine (Frenkel et. al, 2005), also maintained by TRC’s group. TDE allows on evaluation of physical property on demand, creation of complex equations of state and last but not least immediate validation of the results as shown in figure 6.

The quality of the predictions from simple equations of state for natural gas processing is so good, and the model reliability is so high that this class of industry can be modeled accurately from the well bore down to the tail gas cleaning stage, and derivative works such as on-line monitoring are now common place (Sitter et al, 2006).

Thermodynamics and Statistical Mechanics The previous section briefly examined the structure of property packages from a thermodynamic perspective and how a simple model can be used for the modeling of an entire industry. Thus the requirements for a good model with industrial significance boil down to two observations:

1 The model needs to provide a good description of the Helmholtz energy of a fluid or fluid mixture

2 The model must include a way of calculating a reference state

This is usually how we leave the problem at undergraduate level and this is also usually the level users interact with process simulation tools. There’s nothing wrong with this and lots of solid and creative engineering work is done using models like cubics. That said, I always have an intellectually unsatisfying experience with reference states and the empirical (albeit brilliant) shape of van der Waals type equations of state.

The remedy for the lack of satisfaction8 comes from statistical mechanics. In essence, statistical mechanics concern itself with the interactions of a very large number of particles and the properties of the system emerge as average properties of these very many interacting particles. Statistical mechanics started with Maxwell and Boltzmann and it is now a well developed tool used in classical and quantum physics. The neat thing about statistical mechanics is that it provides a

8 As Mick Jagger said “you can get no satisfaction”. But statistical mechanics provides a pleasant stop gap.

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natural connection between microscopic and macroscopic properties, and equations of state can be created in a methodical way. This ability of creating models taking into account molecular interactions is important and allows systematic modeling of systems currently hard or impossible to model using simpler tools like surface phenomena and folding phenomena in complex molecules. This has obvious implications in protein molecule modeling and no so obvious in the processing of bitumen as we will see shortly. Statistical mechanics pinnacle is equation 16, and as Richard Feynman noted many years ago (Feynman, 1972) it is all “downhill from here” by creating applications or uphill to derive the fundamental expression.

QRTA ln−= 16 Q is the partition function of the system and it encodes all the different ways a system can dispose of its energy, and if you combine equation 16 with equation 11 you can get an immediate connection between microscopic phenomena as described by the partition function and classical thermodynamics. It is common to factor the partition function into one part that deals with energy associated with movement and another part that deals with internal molecular interactions that include vibration, rotation and electronic transitions9. When you factor these contributions to the energy of the system the partition function is expressed as equation 17.

!3

int

NZQQ NΛ

= 17

The Qint term describes the internal movements inside a molecule with Z is

usually called the configurational partition function and describes the translational movement of molecules. In general the movement is a function of the position since potential energies are in action and Z is expressed, in general, by equation 18.

9 This is a useful, but not quite correct assumption. Imagine long, polyatomic molecules colliding. It is clear that collisions will induce internal movements in the molecules after a collision and the factoring of translation and intermolecular phenomena is not entirely rigorous. That said, this is usually a good starting point. A remarkable thing with statistical mechanics is that by using very simple models we can get reasonable answers. Sometime ago someone told me that statistical mechanics is the science of getting reasonable answers from unreasonable assumptions. Be that is as it may, it is neat to see how much insight on complex problems we can get by imagining interacting balls, springs and potential energies.

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NkTU

N dqehN

Z 33 ...

!1

∫ ∫−

= 18

What is important from a modeling perspective is that by separating the

partition function into one section that depends on internal motion and another part that depends in external interactions we can devote attention in describing the structure of a molecule separately from the task of modeling the interactions between molecules. For example, if we concentrate on systems where the potential energy in the fluid is zero we can model ideal gas properties of complex molecules and accurately determine important properties such as ideal has heat capacities that in turn can be used for the modeling of real systems by providing the reference state for the computation of enthalpies as we saw before. On the other hand, we can dedicate our attention to the modeling of potential energies between molecules and derive new equations of state. It is significant that statistical mechanics can be used to create equations of state for any aggregation state of matter such as gases, liquids, solids, and complex interactions between not only molecules but also the substract in the background. This has important repercussions on the modeling of surface phenomena and semiconductor materials properties.

For example, by careful choice of intermolecular potential and internal movement we can reconstruct the van der Waals equation. This technique is also useful for the construction of new equations of state or activity coefficient models as shown elegantly by Sandler and co-workers (Sandler et al, 1986).

A last thought related to this bridge between macroscopic and microscopic phenomena. The partition function formulation is completely general and can be extended to quantum phenomena. Therefore, a consistent formal structure connecting the dimensions usually explored by chemical engineers and dimensions explored by physicists exists. As we move towards the processing of more exotic materials or processing at more extreme conditions of temperature we will see a significant interplay between physics and engineering. Albeit at its infancy, ultra cold chemistry related to Bose-Einstein condensates is being developed. At these extreme conditions, atoms can be manipulated, moved and separated using light – optical tweezers (Boyer et. al, 2006). It is quite possible that this will find its way into mainstream life through quantum computers. If this is to come into being engineers will have to be involved for the creation of large scale processing facilities and readily available predictions for the physical properties of such materials will be necessary.

This type of molecular manipulation also opens some interesting opportunities for the development of new catalysts, or catalyst based processes. Recently Horn and coworkers (Horn et. at, 2006) show that molecules that are illuminated by laser pulses with duration considerably shorter than their rotational

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period undergo alignment immediately after the pulse quits. This in turn can be used for the creation of aligned systems of molecules in gas phase, and even the remote possibility of aligning gas molecules and collimate them into catalyst sites presents incredible economic potential related to increased yields for kinetically controlled processes.

Process Economics Thermodynamics play the key role in the economic evaluation of processes that involve usage of energy. Simply put, thermodynamics establish the base line for reversible processes. Since we know that no real process is reversible, the study of reversible processes tells us the very best that can be obtained and therefore establishes an absolute and impartial basis for the creation, evaluation and ranking of processes. It is true that much can be done in optimizing kinetic parameters in processes and that many processes operate optimally from an economical perspective when driven into conditions away from what would be optimal from thermodynamic equilibrium due to kinetic constraints10. That said, if we did not have an absolute scale to measure the efficiency of processes we would be at the mercy of belief and not science. Thermodynamics is the provider of this absolute scale and the guardian against ill founded belief. In a nutshell, thermodynamics forces us to be honest. Without its guiding principles applicable to any natural process we would be forced to deal with a virtually endless need for experimental evidence when studying new processes and proposing new solutions.

It is amusing to see how this fundamental characteristic of thermodynamics has made its way into mainstream thought and is used in economics. For example, important issues nowadays are related to creating processes that are optimal from an economic point of view taking into account ecological effects. For example, Barbiroli (Barbiroli, 2006) wrote an interesting article on eco-efficiency where a key point is the definition of a “state of bliss” which is the “highest ideal condition in any choice”. The only way of objective studying these conditions is through the usage of limits imposed by thermodynamics.

Talking about environmentally important issues, thermodynamics plays a key role in the most important current issue related to the environment – carbon dioxide. From an orthodox point of view thermodynamics provides assistance in the optimization of combustion processes and in turn in the optimization of the 10 The production of ammonia and synthetic fuels are interesting case studies related to this. Perhaps more interesting is to study the influence of these processes in the economic history of the world. It is sobering for technically minded people to see the type of immense impact chemical technologies have on the world. Two highly recommended reads are Tooze’s (Tooze, 2006) and Levi’s (Levi and Debenedeti, 2006) books.

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useable energy per pound of fuel consumed. Thermodynamics also provides the basic framework for the analysis of non-conventional processes such as fuel cells and hydrogen based solutions. Steeneveldt and coworkers (Steeneveld et. al, 2006) provide an interesting overview on processes for the capture and storage of carbon dioxide which are convenient summarized in figure 7.

It is interesting to note that one of the most important processes for carbon dioxide removal is alkanolamine based processes. These processes are interesting for several reasons. From a thermodynamic point of view they involve a series of modeling techniques. It starts with the usage of equation 2 as the unifying principle, which is then fleshed out by experimentally determined equilibrium constants for the ionic acid-base reactions in aqueous phase. This is complemented by rigorous physics used to describe the limiting activity coefficients for ions in the aqueous phase and topped off by statistical mechanical based equations for activity coefficients, necessary to bring the model predictions in line with experimental measurements within error ranges acceptable for process design.

The interesting feature of this type of process is that it is not thermodynamically controlled, but rather, the kinetics of absorption of carbon dioxide and hydrogen sulfide are of fundamental importance for the designer, and these features are not described by the thermodynamic model. Therefore we supplement the model with the necessary kinetic information related to the carbon dioxide and hydrogen sulfide and in turn this information makes its way into the equations that describe the material and energy balances of distillation towers in the form of efficiencies11. A sample illustration in how different the carbon dioxide and hydrogen sulfide efficiencies are in a typical amine sweetening unit is shown in figure 8. Alternatively, models using first principle mass transfer models are available (Krishnamurthy and Taylor, 1985; Taylor and Krishna, 1993) where the material and energy balances are solved simultaneously with mass transfer rate expressions. Although this class of model does not require efficiencies or equivalent HETP values, it does require mass and heat transfer coefficients for the particular type of tray or packing being used. Its main advantages over simpler efficiency based models lie of its ability of predicting more accurate temperature profiles where vapor and liquid phases are not at equilibrium and rigorous integration of the material and energy balance for the simulation of packed towers. Rate based models have evolved considerably over the years and a state of

11 The kinetics of carbon dioxide absorption is very different from the kinetics of hydrogen sulfide absorption. Carbon dioxide reacts much more slowly than hydrogen sulfide with alkanolamines and therefore the amount of carbon dioxide absorbed in the amine solution per unit of time is much less than what could be absorbed from a purely thermodynamic point of view. The efficiency of carbon dioxide absorption is low and this can be used for the creation of all types of processes that remove hydrogen sulfide preferentially from a gas stream.

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the art implementation is provided by Taylor and co-workers (Taylor et al, 1994) and is also available in several commercial products such as Aspen’s RATEFRAC (Aspen Technology, 1994) and PROTREAT (Sulfur Experts, 2008).

A series of fascinating problems related to the modeling and optimization of this class of processes is related to thermodynamic irreversibilities. The basic idea of this type of process is to absorb the acid gases using a solution of alkanolamine in an absorber at high pressure and then drive the acid-base equilibrium back by heating up the solution rich in acid gases at low pressures. This works in general quite well, but there are other chemicals in the gas other than carbon dioxide and hydrogen sulfide such as nitrogen oxides, sulfur oxides and hydrogen chloride. These chemicals react with the alkanolamines forming stable salts that can not be decomposed via heating in the amine regeneration tower and the gas absorption capability of the amine solution decreases with time.

Another interesting issue to be explored has its roots on purely thermodynamic grounds. Since it takes lots of energy to bring aqueous solutions to boil in the amine regeneration step, why not replace the solvent by a solvent that can be more easily boiled off such as methanol? This is an idea being explored by Park and co-workers (Park et. al, 2006), and it is amenable to the same principles used for the thermodynamic modeling of aqueous solutions of alkanolamines and consequent design, optimization and comparison of alternative processes and finally informed decision related to the economic deployment of such alternative carbon dioxide and gas sweetening processed.

Process Optimization and Process Integration Process optimization and process integration methodologies go hand in hand with the thermodynamic model of the chemicals of interest as well as empirical knowledge from the engineer performing the optimization studies. Failure to accept the roles of empiricism and fundamental thermodynamic relationships is doomed to produce large case studies with little substance combined with significant doses of embarrassment. Over the years I have had the chance to collect my fair share of horror stories and I will not bother you with an encyclopedic listing. But I will tell you one of my favorites – distillation design by 10. This is a true story – and I saw it repeated many times with slight variations. Someone was designing a distillation tower to separate a certain mixture. The distillation algorithm would not converge and I was called to help diagnose what was going on. The mixture being separated had an azeotrope – it was not an exotic mixture or anything and the data was readily available in a standard handbook – and the tower layout looked strange to me so I asked the designer how he was going about designing the tower. To my absolute dismay the tower was being designed like this:

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1 Set the number of trays to 10 2 Put the feed in the middle 3 Set the reflux to 3 and the distillate flow corresponding to the desired

recovery 4 Run the simulation 5 If the simulation converged great 6 If tower did not converge then increase the number of trays by 10,

place the feed in the middle and run the simulation again until it converged.

I know it sounds like I am making this up but it is true – I saw it12. The

designer had several papers published and is an expert in the process. The problem is, there was no way that the approach would work because there was an azeotrope in the tower and the desired specification was impossible. No matter how many trays were added to the tower, the thermodynamic model built into the simulator would steadfastly refuse to allow the second law of thermodynamics to be broken. I solved the problem using pencil and paper in an hour or so and graphical techniques chemical engineers learn in undergraduate distillation courses and then used the simulator to polish the results. Similar situations happened several times, including one where a scientist kept asking me if the azeotrope problem would not go away if he kept increasing the size of the equipment he intended to use to separate the mixture in question.

It sounds amusing, but it is in reality quite tragic. In the heat of the battle folks rely on computerized tools as if they were some kind of substitute for thinking. Simulators are certainly great thinking aides, but they are not able to think for anyone, and this is perhaps the most important point I would like to get across in the paper. Deep understanding of the fundamentals of chemical engineering, chemistry, physics and physical-chemistry are your best guarantee for a successful career in chemical engineering. As tools grow in complexity, understanding of the basics grows in importance because you must be able to spot non-sense, either coming from the simulator or as a consequence of poor choices or poor thermodynamic modeling. I am a true believer that simulation engineers should also be conceptual engineers where they express their talent by exercising creative thinking buttressed by knowledge of basic science.

In my experience, the most fruitful advice for process optimizers and integrators is that before they embark on significant work involving computers that they spend the time understanding the basic chemistry of the process and ask

12 Mike Malone from the University of Massachusetts put it best. When having lunch a while ago we were talking about conceptual design and some of the new techniques he and Mike Doherty were developing. I will never forget Mike looking at me and saying something like “You know Marco, if the only tool you have is a hammer soon enough all problems look like nails”.

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themselves how good the thermodynamic model is and have a clear understanding of the limitations of such model. You see, this is the ideal moment for seeding the field with useful documentation about the model, clearly state assumptions, list experimental data used to define the model and report areas where the data is faulty, incomplete or of questionable quality. Moving forward, this opportunity offered by the time used to create the thermodynamic model allows us to ask good questions about the process such as what could be kinetically limited constraints, what are potential side products, what are potential regulatory issues we may have, what are potential alternative solvents, etc. It is impossible to place a truly comprehensive list of questions since problems will always be different and you, the designer, will always know better. What is important is to build this questioning behavior in your thinking process and make the most of the time you have to think about the fundamentals of your process. After you are satisfied with your basic understanding of the physics and chemistry of the process then simulators are wonderful tools that allow you to piece together your ideas and get your design done reliably, effectively and conscientiously.

Current and Future Research Important problems involving thermodynamics abound and opportunities for fruitful research appear virtually everywhere. I will not even try to provide an encyclopedic13 listing of opportunities since you can get these by simply cracking up any chemical engineering, chemistry, and physics or economics magazine. Instead I would like to mention two opportunities separated by a vast chasm of application. They illustrate extreme aspects of the art but intersect at a fundamental thermodynamic modeling interface.

Volumetric behavior of bitumen and solvent mixtures We can think of bitumen as a widely known thing since references to it are present in the Bible and by rights we should know quite a bit about it. This is not quite the case. Bitumen is a complex class of hydrocarbon mixtures that involve light and heavy organic molecules. The most important operation related to bitumen processing is how to get it out of the rock and get the hydrocarbon materials to processing plants. A couple of basic questions we need to be answered when designing facilities, are what is the density of the fluids being processed and when I mix fluids does the temperature go up or down? When we look at facilities that are processing thousands of tons of material per hour these questions translate into large capital investment and energy costs.

One would suppose that we can answer these questions quickly and reliably, especially if we could have a few more points on the distillation curve

13 It may sound as if I do not like encyclopedias. Nothing could be farther from the truth.

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and a better characterization of the heavy end. Mahan and co-workers (2006) measured the excess volumes of mixtures of heavy residues and paraffins used to simulate industrial plants using naphtha as a solvent. Since bitumen is processed in different ways depending on how it is extracted, but blended when fed to the upgrading facility, measurements were conducted in different ways. Some mixtures were produced at a certain temperature and then heated to a desired temperature. Some mixtures were first heated and then mixed and then moved to the desired temperature.

From a conventional thermodynamic perspective, the measured excess volumes should be identical within some measurement error. After all we all know that if we are careful and patient enough we should get pretty close to thermodynamic equilibrium and therefore the measurement of physical properties should be independent of the path of measurement. Not only the results are different depending on how the mixtures are prepared, they are qualitative opposite to one another as shown in figure 9. A definitive interpretation for these results is not yet available, but a couple of ideas come to mind. The first is that some kind of polymorphism may happen depending on the thermal history of the material, akin to the protein folding of complex molecules that result in a molecular shape change and therefore the volumetric behavior is different. A second thought is that the approach to equilibrium is so slow that even after several days no significant changes can be detected in the lab and much longer equilibration times are necessary.

If this is the case the residence times of these materials in the plant would suggest that we are not free to choose the way we perform experiments, but rather, we have to tailor experiments to mimic the way the plant is run because the mixing process is kinetically controlled. This fact is important for simulations, i.e., the way the process is conducted. This is not an alien concept when we are dealing with slow chemical reactions, but in this case we are perhaps considering an entry in a physical property handbook where, in order to make the measured properties relevant we have to specify that this is the excess volume for this bitumen and this solvent mimicking the thermal history of a certain processing technology.

This may be a necessary piece of information for the design of processing plants, but it does underline some significant lack of basic knowledge about what we are processing. The definitive answer to this conundrum is connected to finding ways of gathering a better understanding of the materials being processed, better understanding of the time constants involved in the process when compared to thermodynamically meaningful equilibration times and on top of this, how to perform these basic measurements in an efficient and cost effective way. Given the importance of energy producing technologies and its vast impact on the environment techniques for efficient hydrocarbon characterization and modeling for process design and optimization will only grow in importance.

Although not connected to bitumen processing, it is interesting to note that recycling provides a significant amount of hydrocarbon materials available for processing, and that there are significant opportunities related to process design and product design related to recycling. In order to explore these opportunities, thermodynamic modeling of polymeric materials after they are produced and subject to normal usage and finally discared will be important (Bai et. al, 2007).

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Statistical Mechanics and Process Engineering An important area of process engineering deals with interactions between molecules and surfaces such as adsorption and catalysis. For example, zeolite based surfaces can be used for separation of alkane isomers and recovery of valuable high octane chemical species, separation of aromatic isomers like xylenes, separation of sulfur compounds such as mercaptans and gas dehydration. In a related field, membranes can be used for separation of carbon dioxide from natural gas mixtures and creation of efficient separation processes for ethanol and water separations.

Contrary to conventional separation methods such as distillation and absorption where reliable thermodynamic models such as equations of state or activity coefficient based methods exist, surface based processes depend on interactions between substract and molecules. This is an area where classical thermodynamics has little to offer and statistical mechanical methods shine. If you recall equation 17, it encodes all the necessary structure to model the movement of molecules as well as interactions between molecules and any other source of potential energy such as the adsorbing substract. Since classical models are of little use, good part of the art related to surface chemistry deals with experiments trying to determine the molecule-substract interactions and summarize this experimental information in models that can be used for process design. An alternative way to go about solving this problem is based on the creation of models that take into account molecular and substract conformations and determination of molecule-substract interactions. This interesting approach is discussed in detail by Fuchs and coworkers (Fuchs et. al, 2006) and illustrated in figure 10.

The statistical mechanical tools can be used for virtually any molecular process and as we move towards more exotic materials such as organic metals, conductive liquids, ionic liquids, superconductors and conductive films the proper usage of modeling tools tempered with good understanding of the fundamentals of chemistry, physics and physical chemistry will be the differentiating factor between good and bad designs. This is poignantly demonstrated by Saito and Yoshida (Saito and Yoshida, 2007). The scientist who learns how to navigate the phase envelope of superconductive materials will have a good opportunity of designing the hot new commodity products of the next decade. Hand in hand with this, the engineer who can design the process that will bring these products to the mass market will change the world.

Integrating Thermodynamics into Processes, Products and Appliances A long time ago Arthur Clarke wrote that if technology is sufficiently advanced it is indistinguishable from magic. I think these days if technology is sufficiently

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advanced it is indistinguishable from an appliance. You see, my first computer had a 10 MB hard drive and I had lots of respect, care and tenderness towards it. If you are old enough you will recall a program called park that you had to run before moving your desktop. Today I have a 160 GB iPod that I simply toss around. Electronic storage technology is sufficiently advanced and therefore we treat it as just another appliance – we simply don’t care about it. We use it, very much like we use a pencil.

I do not think we have reached the point where fluid phase thermodynamics and flash calculation technology is advanced enough that we can consider it an appliance. But there are a few specific aspects of it where we are very close, and we at Virtual Materials Group are working on making the embedding of this technology in other applications a reality. For example, we now routinely use flash calculations and phase diagram tracing on-line to warn plant operators of potentially dangerous operating conditions when compressing sour gases or avoiding liquid dropping in retrograde conditions or creating ersatz sensors to provide operators with physical properties that can not be measured or telling refinery operators what’s the best way to operate units for changing feed stocks. This allow us to continuously learn new interesting twists and turns related to how thermodynamic models are used and how they must behave in real time applications (Sitter et. al, 2006). A sample of this type of thermodynamically based appliance is shown in figure 11.

Thermodynamics and Education By now it should be self-evident that thermodynamics is a rather pervasive discipline and it underlines the calculations performed by simulation programs and acts as the unifying force bring order to a significant amount of data collected in chemical and petroleum engineering. It should also be clear that mathematical prowess is not enough for efficient use of thermodynamics. Mathematical skill has to be tempered with empirical knowledge, and it is the combination of theory and data that makes thermodynamics a formidable tool.

The interplay between theory and empirical observation defines, in my opinion, how thermodynamics should be taught from a process engineering perspective. Unfortunately, in my experience the amount of theory and empiricism currently taught are not enough to allow recent graduates to work efficiently using modern process simulation tools. When I took chemical engineering in the early 1980’s we learned quite a bit of chemistry and more importantly physical-chemistry. I do not recall very complex labs, but we did perform experiments and somehow we did learn some rudiments about the behavior of fluids. My limited experience lecturing shows that students nowadays are just as bright and hardworking as I recall from my student years, but many students lack empirical knowledge. Perhaps this happens because chemical engineers are not taught as much physical-chemistry as previous generations were taught. A simple example should suffice. Recently in one graduate level examination I asked for students to comment on the accuracy of a simple activity

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coefficient model when applied to ethanol and water mixtures. The model incorrectly predicted that ethanol and water would phase split at 25 C and 1 atmosphere pressure. My students could perform the necessary mathematics to find out that the model would predict phase splitting and they had no problems computing the phase fractions and phase compositions.

But they did have problems commenting on the accuracy of the model. In this particular occasion I even had a student mentioning that he did not have time to go to the library to look for liquid-liquid equilibrium data for ethanol and water solutions. This lack of (basic) empirical knowledge seems to be making an insidious penetration in the educational process. Since in thermodynamics we still need a degree of empirical knowledge for effective usage of tools and models, it seems to me that students would benefit quite a bit by having a more extensive training in physical-chemistry.

Naturally, we do not want to create a situation where we are only reliant on empirical information. On the contrary, models are getting better all the time thanks for advancements in theory and in the available experimental databases available for determining model parameters. That said, it is always useful to have a certain amount of empirical information in your mind to help you judge the quality of computer models before embarking on a large simulation project. Sometimes this will avoid embarrassment. Sometimes it will motivate you to look for more data, more applicable to the conditions of the problem at hand or perhaps discard the thermodynamic model you originally intended to use.

I think that we should train the best conceptual engineers we can, and part of the art related to this task is learning when to be critical of results coming from computerized tools, how to refine models and how to do this in a time and resource sensible manner.

In conclusion Thermodynamics provides the underlining logical principle that allow us to collect, interpret and organize experimental data. This same logical principle allows us to draw exact relationships between quantities without the need for a molecular model. These relationships are derived from the first and second laws of thermodynamics and although axiomatic, these two laws seem to apply to every natural process at any scale. Combined with this logical structure, educated use of empiricism allows us to create useful models that can be used to calculate material and energy balances and design equipment, processes and new products. Some of the most successful models currently used owe their origin to theories created in the 19th century and are a testament to how far a simple theory can be taken as long as its development is done sensibly using basic engineering principles. A formal structure in the form of statistical mechanics can be used for the creation of new equations of state and models for the interactions of molecules

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and substract and combined with the logical structure provided by classical thermodynamics and software it will play a key role in the development of new processes and products of relevance for the 21st century.

Nomenclature a attractive coefficient for cubic equations of state A Helmholtz energy b covolume for cubic equations of state Cp isobaric heat capacity f some function g some function G Gibbs free energy h Planck’s constant H enthalpy k interaction parameter, Boltzman constant N number of particles n number of moles P Pressure q generalized position Q Partition function R gas constant S Entropy T Absolute temperature U Internal energy, potential energy x mole fraction vector V Volume Z compressibility factor, configurational partition function

Subscripts i component index j reaction index or component index t volume translated variable 0 reference state

Greek Letters Δ difference δ volume translation factor ε reaction extent Λ de Broglie wave number

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Figure 1 Petlyuk towers provide a highly integrated environment for separation using distillation with a single reboiler and condenser with savings between 20 and 50% when compared to a standard arrangement using multiple towers. Rong and Turunen (Rong and Turunen, 2006) show that this type of tower provides a unique thermodynamic equivalent side column structure and provide a rational procedure for tackling a combinatorial problem.

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Figure 2 Residue curves and distillation boundaries are thermodynamic properties defined by vapor-liquid equilibrium, simple models for the liquid phase and differential equations describing simple batch distillation. Note that the distillation boundary separates two different regimes for the distillation depending on the overall feed. One where the bottoms is rich in benzene and another where the bottoms is rich in n-propanol. In both cases the distillate is rich in i-propanol and benzene azeotrope.

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Figure 3 The structure of Nature is such that equations of state explicit in temperature and volume are more useful than equations of state explicit on pressure and temperature due to phase equilibrium phenomena. Note that the saturation pressures for the vapor or liquid steam are the same at the same temperature but the phase volumes are quite different. Curves calculated using VMGSim (Virtual Materials Group, Inc., 2007)

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Figure 4 Note that polar substances can also be modeled and important aspects of processing such as dehydration and hydrate depression can also be simulated and optimized (Virtual Materials Group, Inc., 2004)

Glycols Vapor Pressure Prediction

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0 100 200 300 400

Temperature (°C)

Vapo

r Pre

ssur

e

EG DEG TEG

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Figure 5 Simple but sensible flow sheet modeling in action. Properly tuned cubic equations of state together with reaction models for sweetening and sulfur processing can be used to model entire processes.

Gas Gathering APR for Natural Gas

MDEA Plant Amine Package

TEG Dehydration APR for Natural Gas

Claus Plant Claus Package

NLG Recovery APR for Natural Gas

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Figure 6 Typical results calculated using NIST’s Thermo Data Engine. Note the detailed quality information provided by uncertainty values for each experimental data point. Experimental data is for water thermal conductivity as a function of temperature and pressure (Frenkel et al, 2004)

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Figure 7 Fuel / carbon dioxide sequestration (adapted from Steeneveld et. al, 2006)

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Figure 8 DEA sweetening plant absorption tower simulation showing the tray efficiencies in absorber for H2S and CO2. Note that the efficiencies of carbon dioxide and hydrogen sulfide are very different from 1 and reflect kinetic effects that can not be predicted by classical thermodynamics. Also observe the maximum in temperature caused by the acid-base chemical reactions on the trays. Results from VMGSim (Virtual Materials Group, Inc., 2007)

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Excess Volumes for solvent / Athabasca Bitumen Vaccum Bottoms at 25 C

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0 0.2 0.4 0.6 0.8 1

Mass Fraction ABVB

Exce

ss V

olum

e, c

m3/

g

preparedannealed

Figure 9 Different excess volumes are measured depending on how the heavy hydrocarbon and solvent sample was prepared, based on data from Mahan et al, 2006.

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Water adsorption on Na52 fausjite

0

50

100

150

200

250

300

0 500 1000 1500 2000 2500 3000

Pressure, Pa

Num

ber o

f wat

er m

olec

ules

ads

orbe

d pe

r m

icro

cm

3

ExperimentSimulation

Figure 10 Adsorption of water in Na52Y fausjite at 300 K, based on data from Fuchs et. al, 2006

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Figure 11 On-line monitoring of sour gas compressor trains. Note that for optimal operation the temperature after the compressor intercooler has to be always above the gas dew point and therefore the intercooler temperature after stage 4 is not feasible. Based on data from Sitter et al, 2006.

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