Lion Share

home *** CD-ROM | disk | FTP | other *** search

/ Lion Share / lionsharecd.iso / dos_misc / crest500.zip / CREST.DOC < prev next >

Wrap

Text File | 1991-09-06 | 45KB | 1,077 lines

.ft e10 .pn 0 DOCUMENTATION ON CREST: CHEMICAL REACTIONS AND EQUILIBRIUM THERMODYNAMICS VERSION 5.00 developed by Dudley J. Benton August 10, 1991 .pa .pn 1 _CONTENTS_ Page Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Running the Program . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Interpreting the Output . . . . . . . . . . . . . . . . . . . . . . . . . 8 Defining Elements and Compounds . . . . . . . . . . . . . . . . . . . . . 8 Creating a Plot of Mole Fraction . . . . . . . . . . . . . . . . . . . . . 10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Appendix 1 Listing of Error Messages . . . . . . . . . . . . . . . . . . . 13 Appendix 2 Listing of Data File CREST.GAS . . . . . . . . . . . . . . . . Appendix 3 Listing of Data File CREST.AQU . . . . . . . . . . . . . . . . Appendix 4 Sample Program Output . . . . . . . . . . . . . . . . . . . . . Appendix 5 Program OXMOLES (computes combustion products vs. moles oxygen) Appendix 6 Program FINDENTH (computes enthalpy of combustion products vs. T) Appendix 7 Sample Plots of Computed Mole Fraction vs. Temperature . . . . .pa _INTRODUCTION_ CREST is an interactive computer program designed to solve chemical reactions using equilibrium thermodynamics. CREST can handle elements, compounds, and ions. CREST can compute the thermodynamic properties of the elements, compounds, and ions at a given state or it can compute the equilibrium composition of the products of a reaction involving these. CREST solves the simultaneous dissociation reactions implied by a reaction automatically. It is not necessary to specify all of the possible dissociation reactions, CREST will handle them for you. CREST can handle many elements and compounds (currently set at 32 elements and 128 compounds). Each compound can be composed of several elements (currently set at 16). CREST can handle complex reactions (currently set at 128 reactants and 128 products). Each of the dissociation species counts as a product of the reaction. CREST can solve any number of independent reactions although it will only solve one at a time. Simultaneous, dependent reactions should be specified as one reaction. Eventually, the capability of multiple sequential reactions will be added (maybe Version 6). You can specify the reaction to be solved interactively or in a data file. You can have any number of data files. CREST will allow you to interactively specify under what conditions (ie. temperature and pressure) you want the thermodynamic properties evaluated and the constraints on the reaction (ie. constant pressure or volume and specified temperature or heat transfer). CREST will also allow you to interactively change the molar fractions of the reactants. Elements and compounds are defined in a database file (cf. CREST.GAS and CREST.AQU) which cannot be altered by CREST. Any elements or compounds that appear in your reaction must be defined in the database before running the program. You can get a list of the available substances by selecting the appropriate command from the main menu or from the built-in full-screen editor. Additions to and modifications of the substances in the database will be covered in the section "DEFINING ELEMENTS AND COMPOUNDS." Throughout this manual and within the program, optional parameters are indicated by brackets, []. For example, the command B[atch]= can be given as Batch=, Batc=, Bat=, Ba=, or B=. If you use more than the first letter, it must be spelled correctly and must not have any trailing extraneous characters. Case (upper/lower) is immaterial. You can have several database files. Two are supplied (CREST.GAS and CREST.AQU). To access a different database file just specify it in the run command: CREST D[atabase]=CREST.AQU or select the appropriate option in the main menu. If none is provided, a file extension of ".DAT" will be assumed and the file is not found without any extension. CREST works in either English or SI units. The English units include the lb-mole (pound-mole), the BTU, degrees Rankine, and psia (pounds per square inch absolute). The SI units include the gm-mole, Joule, degrees Kelvin, and atmosphere. The units for each quantity are given by the program when listing results. You can select the units from the run command by adding U[nits]=S[I] or U[nits]=E[nglish]. English is the default. .pa _RUNNING THE PROGRAM_ Do not attempt to run CREST from BASIC. On a PC you should be in DOS with the DOS prompt. To run CREST just type CREST and hit Enter. CREST will offer you a menu like the following... Compute properties --> compute U,H,S,G for a given T,P Database ------------> select another or list current database Edit reaction -------> display or modify the reaction File reaction -------> save the current reaction in a disk file Graph ---------------> solve a series of reactions and plot results Print=ON/OFF --------> begin/quit listing results to printer Read reaction -------> open existing disk file and read contents Solve reaction ------> determine equilibrium composition of products Units=English/SI ----> select units for input/output use ^v then Enter to select or Esc to exit You may select any of these by touching a single key corresponding to the first upper case character in the menu line or by moving the cursor/highlight to the desired line with the arrow keys or mouse and then tap the Enter key. If the menu entries begin with numbers (0-9) instead of upper case letters (which is the case with the plot menu), then select using the numbers. If you have a Microsoft compatible mouse, then the left button can be used for Yes and the right button can be used for No or Esc. If you want to interrupt the program during a long series of calculations then tap the space bar and wait a few seconds. This will abort the current task. If you have a mouse, the same thing can be accomplished by depressing both buttons at the same time. If you wish to exit CREST, follow the instructions which appear on the screen. Essentially, a few taps on the Esc key will get you out. If you want the results to be printed select Print>ON from the main menu. . You can later stop printing by selecting Printer>OFF. Note that Ctrl-PrtSc will not work with CREST, nor will standard output device re-direct (CREST >PRN). If you want to spool the output to a file instead of the printer, then use the run command: S[pool]=spoolfile.ext. The spool file must not already exist to avoid unintentional overwriting. If you use the S[pool]= command, then CREST will automatically set Printer>ON. If you use the command S[pool]=PRN, then CREST will send the output to the printer as usual; but it will also turn Print>ON. This is a useful when running in the unattended mode (ie., from a batch file or spawned by another program). You can also specify the reaction file in the run command with the R[eaction]=file.ext. If no file extension is given and the file is not found without an extension, then CREST will assume .REA for the extension. You can also specify the database file in the run command with the D[atabase]=file.ext. If no file extension is given and the file is not found without an extension, then CREST will assume .DAT for the extension. You can run CREST interactively or unattended. In order to run in the unattended mode, you must use either the B[atch] or P[lot] run commands. The B[atch] command has several configurations as listed below, where: Tr=temperature of the reactants (if zero --> 537R/273K) Tp=temperature of the products (if zero --> 537R/273K) Pr=pressure of the reactants (if zero --> 14.7psia/1atm) Pp=pressure of the products (if zero --> 14.7psia/1atm) Q=heat transfer B[atch]=100:200 <--- here Tr=Tp=100, Pr=Pp=200 this will compute and list the properties, then exit B[atch]=P[ressure]:T[emperature]:100:200:300 <--- here P tells CREST to assume constant pressure (open system), T means specified temperature of the products (ie., compute the heat transfer), Tr=100, Pr=200, Tp=300 B[atch]=V[olume]:T[emperature]:100:200:300 <--- here V tells CREST to assume constant volume (closed system), T means specified temperature of the products (ie., compute the heat transfer), Tr=100, Pr=200, Tp=300 B[atch]=P[ressure]:Q:100:200:300 <--- here P tells CREST to assume constant pressure (open system), T means specified temperature of the products (ie., compute the heat transfer), Tr=100, Pr=200, Tp=300 B[atch]=V[olume]:Q:100:200:300 <--- here V tells CREST to assume constant volume (closed system), T means specified temperature of the products (ie., compute the heat transfer), Tr=100, Pr=200, Tp=300 The P[lot] command also has several configurations, where: Tp1=initial temperature of products Tp2=final temperature of products dTp=step size (ie., do from Tp1 to Tp2 in steps of dTp) device=graphics device - must be one of the following: =CRT (CGA/EGA/VGA/HGA automatically selected by hardware) =80 (HI-80 printer/plotter) =7240 (HP-7240 printer/plotter) =7470 (HP-7470 2-pen plotter) =7475 (HP-7475 6-pen plotter) =7550 (HP-7550 8-pen plotter) =Star (Star dot matrix printer) =Epson (Epson dot matrix printer) =IBM (IBM dot matrix printer) =Laser (HP LaserJet) log=either L for log Y-axis (moles) or omit for linear Y-axis P[lot]=P[ressure]:100:200:300:400:500:device:log <--- here P tells CREST to assume constant pressure (open system), Tr=100, Pr=100, Tp1=300, dTp=400, Tp2=500 P[lot]=V[olume]:100:200:300:400:500:device:log <--- here V tells CREST to assume constant volume (closed system), Tr=100, Pr=100, Tp1=300, dTp=400, Tp2=500 These run commands can be combined in any order. If either B[atch] or P[lot] are specified, then CREST will run in unattended mode, otherwise CREST will run in the interactive mode. Do not specify both the B[atch] and P[lot] commands. Two program (including source code in C) are provided which illustrate the potential uses of the CREST unattended mode when spawning it as a process from another program. The first of these is OXMOLES which uses CREST to compute the products of combustion at constant temperature and pressure but with varying moles of oxygen. The second is FINDENTH which uses CREST to compute the enthalpy of combustion products with varying temperature. Listings of these codes and sample results can be found in the Appendices. _Computing Thermodynamic Properties_ There is a default reaction which is loaded into the 50 line reaction data buffer. This happens to be the dissociation of water into hydrogen, oxygen, and hydroxl. You can examine this reaction by selecting menu option to edit reaction. CREST will list the reaction and some help information. To solve the reaction you must first return to the main menu. This is accomplished by pressing F10. The menu should reappear. Now select the menu option to Compute thermodynamic properties. CREST will run through a checking procedure and then look through the database for the elements and compounds. It does this once every time you change the reaction. CREST lists some information while it is checking your reaction. You need not be concerned if it flies by too fast to read. You only need to read it if you have made a mistake, in which case CREST will pause so you can read it. It just throws the information on the screen in the event that it encounters an error so that it will be there if you need it. After a few seconds you should see a header listing the units and symbols and a prompt to enter the temperature (T) and pressure (P). If you enter a zero for either temperature or pressure CREST will assume the standard reference values which are 537R/237K and 14.696psia/1atm. After you type these values (try 1000 14.7) hit Enter and CREST should list the internal energy (U/RTo), enthalpy (H/RTo), entropy (S/R), and Gibbs free energy (G/RTo) for each reactant and product under the specified conditions. The same prompt will return and you can do this as many times as you like. To return to the main menu just hit blank Enter. If you select this option, CREST will assume an equal number of moles for each product (as these are unknown without first solving for the equilibrium. If CREST takes more than one second to compute the properties, you probably don't have a math coprocessor in your PC. CREST will work even if you don't have one; but I must warn you that there is a speed difference of a factor of 30 to 120! Should you try to solve a long reaction without a math coprocessor, I suggest you get a good book to read while you wait. Note that if you don't know if you have a coprocessor and the program seems to be taking forever to run, you can interrupt it at any time by striking the spacebar or clicking both mouse keys at once. _Solving a Reaction_ Now to solve the reaction select menu option to Solve a reaction. If you haven't changed the reaction CREST will not go through the checking procedure again. You should see a header listing units and symbols and a prompt. CREST wants to know if you want to change the reactant mole fractions. That is, something like: C+O=CO C+2O=CO 2C+3O=CO You can change the coefficients in the equation as desired. If not, just respond with a N. Next you will be asked whether the reaction is constant pressure (open system, steady-state reaction, etc.) or constant volume (closed system, bomb calorimeter, etc.). Remember that for a closed system the conservation of energy is based on internal energy (U); whereas, for an open system it is based on the enthalpy (H). If you specify constant volume, CREST will compute the resulting pressure of the reactants. Then you will be asked whether you want to specify the final temperature of the products or the heat transfer (Q). If you specify the temperature of the products, CREST will compute the heat transfer per specified moles of reactants. If you specify the heat transfer, CREST will compute the temperature of the products. For example, a bomb calorimeter would be a constant volume, adiabatic (Q=0) reaction. An ideal furnace would be a constant pressure, adiabatic reaction. Of course, real furnaces lose both pressure and heat. You can specify the heat loss or addition, Q need not be zero. CREST will flash messages on the screen as it solves your reaction. These indicate such things as the number of simultaneous nonlinear equations that it is solving, the iteration number, temperature, pressure, and heat transfer. When these values and the mole fractions of the reactants "level-out" the iterations will stop and the results will be listed. You can enter as many temperatures and pressures as you like, then hit Enter to return to the constant pressure/constant volume prompt. If you want to change the reactant mole fractions just hit Esc. To get back to the main menu just hit Esc again. _Using the Edit Features_ CREST also has a built-in full screen editor. You get into edit mode by making the appropriate selection from the main menu. The reaction can take up to 50 lines. Each line can hold no more than 78 characters making the maximum length reaction 3900 characters. You can make whatever changes you want then exit to the main menu by pressing F10. Use F1 to list the elements and compounds in the database. Any lines in the stack that begin with an asterisk (*) will be ignored as comments. _Defining Reactions_ There can only be one reaction; but it can have many reactants and products. You can read a reaction from a file (try COAL) and save a reaction in a file (try MYREACT). You can have as many files containing reactions as you like. The reaction is defined by a group of elements and compounds followed by an equals (=) and another group of elements and compounds. The first group is the reactants and the second is the products. The mole fractions of the reactants need not be specified. You can interactively change this later. This is done by preceding the element or compound with a number (which may be a decimal fraction). The mole fraction of the products must not be specified (determination of the mole fraction of the products is the reason for running CREST in the first place). One of the important applications of chemical equilibrium analysis is to determine dissociation. Usually this requires specifying each of the dissociation reactions separately. This is not necessary with CREST. The combustion of one mole of carbon (C) with 1.5 mole of diatomic oxygen (Odia), would result in carbon, oxygen (O), diatomic oxygen, carbon monoxide (Cmonox), and carbon dioxide (Cdiox). This reaction could be represented in proper CREST syntax as: C+1.5Odia=C+O+Odia+Cmonox+Cdiox There are actually several reactions represented by the above equation. These are typically written as: C+Od<=>Cd+Od Cd<=>C+Co+O Co<=>C+O Od<=>O It is misleading to represent each dissociation reaction separately because they occur simultaneously and are interrelated. CREST solves all of the reactions simultaneously to give you an accurate representation of the actual chemical processes. Because CREST does all of this automatically, it reduces your chances of forgetting a crucial reaction as well as making the process much simpler than the classical approach. An example of a more complex reaction would be the combustion of coal... Coal+6.3Air+.2Cacarbonate=Ar+H+C+Smonox+Sdiox+Hdia+Ndia+Odia+Water+ Nmonox+Ndiox+Coal+Cdiox+Hydroxl+N+O+S+Cacarbonate+Cahydroxide+ Casulfide+Casulfite+Casulfate _Non-Ideal Behavior_ CREST is able to treat the reacting substances differently depending on what you tell it in the database and the reaction equation. There are five different groups of substances which can be specified in the database (more on databases later). These result in first order corrections to ideal behavior. The five groups are: 1 = ideal gas (Z=1.00, F=1.00) 2 = ideal gaseous ion (Z=1.00, F=1.00) 3 = ideal aqueous ion (Z=0.10, F=1.00) 4 = ideal liquid (Z=0.10, F=1.00) 5 = ideal dispursed solid (Z=0.01, F=0.10) where Z is the compressibility and F is the activity coefficient. Currently, Z and A are the same for groups 1&2 and 3&4, there may be a distinction in later versions. Higher order correction can be specified by the ! operator. If a substance is followed by a !, then it will be treated as a real substance. In the example below, only CO and CO2 are treated as real (non-ideal) substances. All of the rest will be treated as ideal gases. Methane + 2.5 Odia = O + Odia + H + Hdia + Ho + C + Cmonox! + Cdiox! If a ! is found before the first reactant (as illustrated below), then all of the reactants will be treated as real substances. ! Methane + 2.5 Odia = O + Odia + H + Hdia + Ho + C + Cmonox! + Cdiox! If a ! is found after the = and before the first product (as illustrated below) then all of the products will be treated as real substances. ! Methane + 2.5 Odia = ! O + Odia + H + Hdia + Ho + C + Cmonox + Cdiox Any real behavior is treated according to Redlich and Kwong's mixing rule. The temperature dependence of compressibility and activity coefficient is computed based on a modification of the method described by Fuller, which is in turn an improvement upon Soave's modification to the Redlich-Kwong equation of state. Because of the versatility which CREST offers in being able to select the way in which to treat each substance, it can be a powerful tool in learning how reactions will occur and what difference the assumption of ideal behavior makes in equilibrium calculations. _INTERPRETING THE OUTPUT_ CREST computes several quantities, among these are: temperature, pressure, internal energy, enthalpy, entropy, Gibbs free energy, heat (or energy) transfer, number of moles, and mole fraction. Temperature is in degrees Rankine or degrees Kelvin. Standard temperature is 537R or 237K. Pressure is in psia (pounds per square inch absolute) or atmospheres. Standard atmospheric pressure is 14.696 psia or 1 atm. Internal energy is in BTU/lb-mole or Joules/gm-mole. Enthalpy is in BTU/lb-mole or Joules/gm-mole and is the internal energy plus PV or ZRT. The enthalpy listed includes the enthalpy of formation. For ideal gases the difference between U/RTo and H/RTo will be one. For ideal liquids and solids these will be essentially the same. Entropy is in BTU/lb-mole/R or Joules/gm-mole/K and is referenced to absolute zero as required by the Third Law of Thermodynamics. Occasionally CREST will compute a negative entropy. Absolute entropy can never be negative. This is a problem that arises from having a relationship for specific heat which is not accurate over the range of temperatures. The Gibbs and Helmholtz free energies are defined by: G = H - TS or G/RTo = H/RTo - TS/RTo A = U - TS or A/RTo = U/RTo - TS/RTo and is a measure of the available or useful energy (although not a true measure as is availability). These have the same units and reference as enthalpy and internal energy. Heat (or energy) transfer is defined as being to or from the reactants. It is important to understand the concept of a system boundary as defined in the thermodynamic sense. Here the system is the reactants and the surroundings is everything else. In a furnace for example, the furnace itself is not part of the system. Only the coal and air are in the system. Positive heat transfer would be energy added to the coal and air from the surroundings and negative heat transfer would be heat removed from the coal and air to the surroundings. Heat transfer has the units of BTU or Joules. _DEFINING ELEMENTS AND COMPOUNDS_ Any elements or compounds referenced in the reactions you intend to solve must be in the database file before running the program. I have supplied two in order to get you started. You may want to add more. You must have an editor of some type in order to make changes in the database file. If you are going to use a word processor (e.g. PC-WRITE or WordPerfect) be sure to treat the file as ASCII. When reading this next section it will be helpful to refer to the listing of CREST.GAS found in Appendix and CREST.AQU found in an Appendix. CREST allows you to define elements and compounds. Elements can't be composed of anything else whereas compounds must be composed of elements. It is necessary to distinguish between the two in order to determine the conservation equations. Elements and compounds are identified by syntax. The order in which you define them doesn't matter; but the syntax is critical. _Defining Elements_ CREST allows you to define your own elements or isotopes. Each must be identified by a unique 12-character symbol. The first character of the symbol must be an upper case letter (A-Z) and the rest can either be lower case letters (a-z), or blanks (e.g. H, He, N, Na, Calcium), or one of the following #$%&:;@^`{|}~ (H#, Ca~, Na^). You cannot use numbers or parentheses (e.g. H2 and H(2) are not permissible). You should note that hydrogen (H) is an element; but diatomic hydrogen (H) is a compound composed of two hydrogen atoms. In order to reference diatomic hydrogen in a reaction you must define the element hydrogen (H) AND the compound diatomic hydrogen (Hdia). Note that H2 for diatomic hydrogen or OH for hydroxyl is not permissible. Following the symbol defining an, element you must specify nine numbers. These are to be in standard free format. That is, they can be in any column and can have mixed floating-point, integer, and exponential notation. Again, see the appendix for examples. The first of these numbers is the enthalpy of formation in BTU/lb-mole. Most often the enthalpy of formation is given in kilocalories per gram-mole (why not kilogram-mole I have no idea). To convert to BTU/lb-mole multiply by 1800. Note that the enthalpy of formation of elements is zero by definition (except diatomic gases). The next number following the enthalpy of formation is the entropy at STP (standard temperature and pressure which is 537R/237K and 14.696 psia/1atm). This must have the units of BTU/lb-mole/R. This is usually given in gram-calories per degree C per gram-mole. No conversion is required in this case. The next three numbers define the constant pressure specific heat (Cp) in BTU/lb-mole/R. This is usually given in gram-calories per degree C per gram-mole. This also requires no conversion. Cp is defined by the following equation: Cp = C1 + C2*T + C3*T*T For constant specific heat C2 and C3 are set to zero. If Cp is given for various temperatures, you must first curve-fit the data in order to determine the constants in the above equation. The next number must be an integer between 1 and 5 indicating the substance groups listed in the previous section on Non-Ideal Behavior. The next two numbers are the critical temperature (degrees R) and pressure (psia). If you don't know the correct values, set it to and CREST will use an empirical formula to estimate these properties. The last number is the molecular weight. _Defining Compounds_ CREST allows you to define your own compounds. Just as for elements, each must be identified by a unique 12-character symbol. The elements composing the compound must follow immediately and be set off by square brackets []. The number of moles of each element per mole of the compound must follow each element (viz. H2O2 for two hydrogen and two oxygen). These can be free format real numbers and there can be any number of spaces. Elements can also be repeated (e.g. OHOH will be interpreted the same as H2O2). You might define coal using the following symbols: Coal[C.2H.75S.05] This would be Coal means coal and it is composed of 20% C, 75% H, and 5% S (mole fraction). COAL[etc.] is not permissible because there is no way of distinguishing this from 1 mole each of C, O, A, and L. Carbon monoxide as a compound could be defined as: Cmonox[CO] MEK (methyl-ethyl-ketone) could be defined by any of the following: Mek[CH3 CO C2H5] Mek[CHHHCOCCHHHHH] Mek[C4H8O] All are equivalent in CREST syntax. The enthalpy of formation, entropy at STP, specific heat, substance group and critical properties follow as with the elements. No molecular weight should be specified for compounds as this is computed based on the elements comprising the compound. _CREATING A PLOT OF MOLE FRACTION_ CREST will create several files in order to assist you in creating a plot of mole fraction as a function of temperature. These files are designed for use with my plot program TPLOT. CREST will run TPLOT for you and display the plots if TPLOT.EXE can be found in the current directory or along the path. If HPGL2PRN.COM is in the current directory or along the path, then CREST will also use it to convert plots created by TPLOT to dot matrix or LaserJet form. CREST will also let you edit the plot command file CREST.PLT if there is an ASCII editor in the current directory or along the path named EDITP.EXE or EDITP.COM (you must supply your own editor). CREST creates a plot command file named CREST.PLT and at least one data file containing the results of the equilibrium calculations. These files are named CREST0.OUT through CREST8.OUT. The reason for creating more than one file is because TPLOT (and most other programs for that matter) can only read some maximum number of columns (for TPLOT this is 200 characters). Because each product requires a space and 12 characters for the name or mole fraction in exponential notation, it is necessary to break this up into several files, each with no more than 15 products. CREST by default removes the plot output files when it is finished. If you want to keep them, then set an environment variable using the following command at the DOS prompt: SET CREST=O Remember that unless you rename the output files, should you run CREST again these will be overwritten. .pa REFERENCES Abbott, M. M., 1973, "Cubic Equations of State," _AIChE Journal_ (19:596-601). Benton, D. J., 1987, "FEAST: Fast Estimation of Thermodynamic and Transport Properties," a computer code available on the ASME/CIME Bulletinboard (608)233-3378. Benton, D. J., 1988, "CREST: Chemical Reactions and Equilibrium Statistical Thermodynamics," loc. cit. Benton, D. J., 1991, "Applications of a Hybrid Derivative-Free Algorithm for Locating Extrema," SIAM-SEAS, Cullowhee, NC. Benton, D. J., 1991, "Solution of Complex Thermochemical Equilibria in Symbolic Form," Proceedings of the ASME WAM. Chung, W. K., S. E. M. Hamam, and B. C.-Y. Lu, 1977, Letter to the Editor regarding paper by Fuller (1976), op. cit. 16:494-495. Cruise, D. R., 1964, "Notes on the Rapid Computation of Chemical Equilibria," _Journal of Physical Chemistry_ (68:3797-3802). Fletcher, R., 1987, _Practical Methods of Optimization_, John Wiley and Sons, New York, NY. Fuller, G. G., 1976, "A Modified Redlich-Kwong-Soave Equation of State Capable of Representing the Liquid State," _Ind. Eng. Chem. Fund._, 15:254-257. Liu, Y., M. Wimby, and U. Gren, 1989, "An Activity-Coefficient Model for Electrolyte Systems," _Computers in Chemical Engineering_ (13:405-410). More, J. J. and D. C. Sorensen, 1984, "Newton's Method," _Studies in Numerical_ _Analysis_, G. H. Golub, ed., The Mathematical Association of America, pp. 29-82. Ortega, J. M. and W. C. Rheinboldt, 1970, _Iterative Solution of Nonlinear_ _Equations in Several Variables_, Academic Press, New York. Pierce, F. J., 1968, _Microscopic Thermodynamics_, International Textbook Company, Scranton, Pennsylvania. Powell, M. J. D., 1977, "Restart Procedures for the Conjugate Gradient Method," _Mathematical Programming_, Vol. 12, pp. 241-254. Prausnitz, J. M., 1969, _Molecular Thermodynamics of Fluid-Phase Equilibrium_, Prentice-Hall, Englewood Cliffs, New Jersey. Redlich, O. and J. N. S. Kwong, 1949, "On the Thermodynamics of Solutions," _Chemical Review_ (44:233-244). Smith, W. R. and R. W. Missen, 1982, _Chemical Reaction Equilibrium Analysis:_ _Theory and Algorithms_, John Wiley and Sons, New York. Stadler, H. P., 1989, _Chemical Thermodynamics_, The Royal Society of Chemistry, Cambridge, U.K. (available in the U.S. through CRC Press). van Wylen, G. J. and R. E. Sonntag, 1973, _Fundamentals of Classical_ _Thermodynamics_, John Wiley and Sons, New York. Wagner, H. M., 1975, _Principles of Operations Research_, 2nd Ed., Prentice-Hall, Englewood Cliffs, New Jersey. White, W. B., S. M. Johnson, and G. B. Dantzig, 1958, "Chemical Equilibrium in Complex Mixtures," _Journal of Chemical Physics_ (28:751-755). Wylie, C. R., 1975, _Advanced Engineering Mathematics_, 4th Ed., McGraw-Hill, New York. .pa APPENDIX 1 LISTING OF ERROR MESSAGES .pa ERROR#1: read error You may have typed something in wrong, file is corrupt, or any other problem which would result in a file read error. ERROR#2: syntax error This may be due to incorrect characters, use of parentheses, misplaced +,=,[,] sign etc. A syntax error will also occur if something like the following is found: "++", "+!", or "2!H". ERROR#3: reaction has only one reactant and only one product There isn't a reaction to solve. ERROR#4: element does not appear on both sides of reaction This error occurs if an element appears on the left side of a reaction then it must also appear on the right side and vise versa. ERROR#5: reaction has no products This can be due to a missing "=" sign or nothing on the right hand side of the reaction. ERROR#6: unexpected EOF (end of file) CREST was looking for something else and didn't find it before encountering the end of data. Sometimes this error occurs when your reaction has no "=" sign in it or you have not specified a reaction. ERROR#7: too many elements (max=24) ERROR#8: redundant reactant/product The more than one occurrence of the same substance was found on the same side of the reaction, for example Air+Coal+Air=etc... ERROR#9: too many compounds (max=128) ERROR#10: reaction has no reactants This can be due to an extra "=" sign or nothing on the left hand side of the reaction. ERROR#11: undefined substance Every substance in the reaction must appear in the database as either an element or a compound. ERROR#12: unable to access database This can be due to it not existing (e.g., you spelled it wrong), not accessible (e.g., hidden or locked), too many files, or bad PATH= environment variable. ERROR#13: compound contains no elements Each compound name in the database must be followed with the elements which comprise the compound. These must be contained within brackets []. ERROR#14: undefined mole fraction You may have improper syntax resulting in CREST interpreting a negative or zero mole fraction. ERROR#15: unable to access data file Either the file does not exist, you typed the name in wrong, the disk drive is down, or the file is read protected. ERROR#16: reaction equations unstable This may be due to an "ill posed" reaction, extreme temperature or pressure limits, or unreasonable specific heats. ERROR#17: illegal file name You cannot use spool or reaction filenames that begin with either CREST or TPLOT. You can use data files that begin with either. In any case, never use a filename of TPLOT.OUT as this will be destroyed by any graphics operations. ERROR#18: compound contains too many elements (max=12) ERROR#19: reaction contains too many reactants (max=128) ERROR#20: reaction contains too many products (max=128) ERROR#21: break detected You must have hit a key while processing was in progress. ERROR#22: reaction contains no elements ERROR#23: reaction contains no compounds ERROR#24: more than 128 simultaneous equations The total number of simultaneous equations that must be solved in order to determine equilibrium is equal to the number of elements plus the number of products. The number of elements adds to this total; because conservation of these constitutes linear constraints which are implemented using Lagrange multipliers. A 128x128 matrix of single precision (REAL*4) variables is accessible through large memory addressing. Anything bigger than this requires huge memory addressing and greatly increases the overhead and subsequent runtime. For this reason, I don't even make this an option. You will just have to make do with 128. ERROR#25: unable to open plot data file CREST.OUT ERROR#26: write error involving plot data file CREST.OUT ERROR#27: unable to open plot command file CREST.PLT ERROR#28: write error involving plot command file CREST.PLT ERROR#29: illegal video mode... may be a hardware incompatibility Your CRT should be in CGA or monochrome mode depending on the hardware. Try setting the mode to "MODE CO80" if it is a CGA. If you have a CGA plasma or LCD display and can't tell the highlighted or color lines from each other, then try setting it to "MODE BW80". ERROR#30: insufficient available memory In order to solve the equations it is necessary to allocate a considerable amount of memory. Your machine does not have sufficient available memory to process the request. Either solve a smaller reaction or find another machine. ERROR#31: substance element/compound ambiguity This error will occur if a substance which appears in the reaction is found in the database as a compound and appears in itself or some other compound as an element. ERROR#32: undefined state code The state code must be 0-5 which indicates respectively the following states: unknown, gas, gaseous ion, aqueous ion, liquid, or dispersed solid. CREST does not handle precipitated solids which have a vanishing activity coefficient. .pa .pn 0 APPENDIX 2 LISTING OF DATA FILE CREST.GAS .pa .de .ad CREST.GAS .ee .pa APPENDIX 3 LISTING OF DATA FILE CREST.AQU .pa .de .ad CREST.AQU .ee .pa APPENDIX 4 SAMPLE PROGRAM OUTPUT .pa CREST/V5.00: Chemical Reactions and Equilibrium developed by Dudley J. Benton TVA Engineering Lab, Drawer E, Norris, TN, 37828 (615)632-1887 G.... Gibbs free energy [BTU/lb-mole] H.... enthalpy [BTU/lb-mole] S.... entropy [BTU/lb-mole/R] Q.... heat transfer [BTU] R.... gas constant [BTU/lb-mole/R] Po... reference pressure [14.7 psia] To... reference temperature [537R] Pr... pressure of reactants [psia] Tr... temperature of reactants [R] Pp... pressure of products [psia] Tp... temperature of products [R] F.... activity coefficient Z.... compressibility (Z=PV/RT) Y.... number of moles X.... mole fraction (X=Y/Ytotal) Date: 08/10/91 Time: 2112 database: CREST.AQU reaction: CEMENT.REA *********************************** REACTION *********************************** * aqueous reactions with cement and asbestos - use with database CREST.AQU * 1000Water .5Cdiox .00001Odia .1Tricaaloxide .1Casilicateb .1Cawollastoni .1Mgchrysotile .005Ca^^ .01Clmonox~ = Water Cldia Cdiox Hdia Odia Algibbsite Tricaaloxide Calcite Caoxide Casilicateb Cawollastoni Mghydroxide Mgchrysotile Sioquartz H^ Al^^^ Ca^^ Oh~ Cl~ Clmonox~ Ctriox~~ Hcarbonate~ Mg^^ ******************************************************************************** solving reaction elements=8, products=23, equations=31 iterations=164, seconds=35, dY=0.0001, dE=0.0001 Tr=580, Pr=14.7, Tp=580, Pp=14.7, Q/RTo=-33 (Isobaric) substance state Y X Z F H/RTo S/R G/RTo -------------------------------------------------------------------------------- Water lqd1000.0000000 0.9990859 0.10 1.00 -114.5 9.11 -124.4 Cdiox gas 0.5000000 0.0004995 1.00 1.00 -158.3 33.67 -194.6 Odia gas 0.0000100 0.0000000 1.00 1.00 0.3 43.36 -46.5 Tricaaloxide sol 0.1000000 0.0000999 0.01 0.10 -1444.5 27.63 -1474.4 Casilicateb sol 0.1000000 0.0000999 0.01 0.10 -929.1 17.48 -948.0 Cawollastoni sol 0.1000000 0.0000999 0.01 0.10 -658.4 11.57 -670.9 Mgchrysotile sol 0.1000000 0.0000999 0.01 0.10 -1757.5 30.08 -1790.0 Ca^^ aqu 0.0050000 0.0000050 0.10 1.00 -218.9 5.82 -225.1 Clmonox~ aqu 0.0100000 0.0000100 0.10 1.00 -43.2 16.55 -61.1 -------------------------------------------------------------------------------- reactants 1000.9149170 1.0000000 0.10 1.00 -115077.9 9133.90 -124943.2 ================================================================================ Water lqd 999.5754395 0.9987319 0.10 1.00 -114.5 9.11 -124.4 Cldia gas 0.0000000 0.0000000 1.00 1.00 0.3 61.67 -66.3 Cdiox gas 0.0003200 0.0000003 1.00 1.00 -158.3 41.03 -202.6 Hdia gas 0.0000000 0.0000000 1.00 1.00 0.3 44.79 -48.1 Odia gas 0.0000000 0.0000000 1.00 1.00 0.3 59.48 -64.0 Algibbsite sol 0.0999931 0.0000999 0.01 0.10 -1031.5 19.51 -1052.5 Tricaaloxide sol 0.0000000 0.0000000 0.01 0.10 -1444.5 30.16 -1477.1 Calcite sol 0.4803705 0.0004800 0.01 0.10 -485.8 12.70 -499.5 Caoxide sol 0.0000000 0.0000000 0.01 0.10 -255.7 8.44 -264.8 Casilicateb sol 0.0000000 0.0000000 0.01 0.10 -929.1 20.01 -950.7 Cawollastoni sol 0.0001326 0.0000001 0.01 0.10 -658.4 12.23 -671.6 Mghydroxide sol 0.0000000 0.0000000 0.01 0.10 -372.1 11.77 -384.8 Mgchrysotile sol 0.0999777 0.0000999 0.01 0.10 -1757.5 30.08 -1790.0 Sioquartz sol 0.1999004 0.0001997 0.01 0.10 -366.9 6.30 -373.7 H^ aqu 0.0000002 0.0000000 0.10 1.00 0.0 22.27 -24.1 Al^^^ aqu 0.0000000 0.0000000 0.10 1.00 -214.2 -4.16 -209.7 Ca^^ aqu 0.1245045 0.0001244 0.10 1.00 -218.9 2.60 -221.7 Oh~ aqu 0.2347642 0.0002346 0.10 1.00 -94.2 5.69 -100.3 Cl~ aqu 0.0100000 0.0000100 0.10 1.00 -67.4 18.31 -87.2 Clmonox~ aqu 0.0000000 0.0000000 0.10 1.00 -43.2 39.57 -85.9 Ctriox~~ aqu 0.0048516 0.0000048 0.10 1.00 -273.0 5.39 -278.8 Hcarbonate~ aqu 0.0144703 0.0000145 0.10 1.00 -279.0 22.12 -302.9 Mg^^ aqu 0.0000700 0.0000001 0.10 1.00 -188.2 -0.13 -188.1 -------------------------------------------------------------------------------- products 1000.8446655 1.0000000 0.10 1.00 -115110.8 9119.19 -124960.2 -------------------------------------------------------------------------------- difference -0.0702515 0.0000000 -0.00 -0.00 -32.9 -14.70 -17.0 .pa APPENDIX 5 PROGRAM OXMOLES (COMPUTES COMBUSTION PRODUCTS VS. MOLES OXYGEN) .pa .de .ad OXMOLES.C .ee .pa APPENDIX 6 PROGRAM FINDENTH (COMPUTES ENTHALPY OF COMBUSTION PRODUCTS VS. T) .pa .de .ad FINDENTH.C .ee .pa APPENDIX 7 SAMPLE PLOTS OF COMPUTED MOLE FRACTION VS. TEMPERATURE