M. Shacham, M. B. Cutlip and M. Elly, " The Role of Physical Property Databases in Ch. E. Education", paper 148a, Presented at the 11AIChE Annual Meeting, Minneapolis, MN, Oct. 16-21, 2011

THE ROLE OF PHYSICAL PROPERTY DATABASES IN CH. E. EDUCATION

Mordechai Shacham, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Michael B. Cutlip, University of Connecticut, Storrs, CT

Michael Elly, Intel Corp., Qiryat Gat, Israel

Introduction

Numerical problem solving in Chemical Engineering typically requires a mathematical model of the problem along with physical and thermodynamic data and correlations (equations) of the chemical substances involved. The required pure compound properties are usually divided into constant properties and temperature and/or pressure dependent properties. In most ChE textbooks, the preparation of the mathematical model associated with a particular problem is typically emphasized. The property data required for solution of the problems are usually provided in tabular or graphical form in the appendix of the textbook and/or in a CD associated with the book (see for example, Felder and Rousseau, 2000 and Himmelblau and Riggs, 2004). Recently, various databases that contain extensive physical property data for a large number of compounds have become available. Typical examples are the DIPPR® database (Rowley et al., 2010) and the NIST database (http://webbook.nist.gov/chemistry/) databases. The use of the data available in these databases for problem solving has significant benefits over the use of the data provided in the textbooks. Some of the more important advantages are:

1. In current engineering practice, the databases are used as a principal source of property data and correlations. Thus it is important that students become experienced with the application of these sources during their educational programs.

2. The databases provide consistent sets of correlations for temperature-dependent properties enabling the use of solution techniques independent of the format in which the property data is provided. If temperature-dependent data are provided in tabular or graphical forms, for example, this prevents the use of standard numerical methods for problem solution, and data format dependent ad hoc solution techniques have to be used.

3. The data provided in databases are continuously updated with the new data as they become available. Property data in textbooks are often taken "as is" from references that may be as much as half a century old. The textbook data may be incorrect or even contradictory. It is important that students become accustomed to using reliable data.

4. The data available in the databases are evaluated and in cases when multiple values are available for the same property, one recommended value is selected by the database professionals. There may be very substantial differences between property values reported by different investigators. Brauner et al., 2005, for example mention the case of the melting point of 4-methyloctane for which the recommended value is 159.95 K while one reported experimental value is 219.62 K. The students must be made aware of the fact that several property values may be available and learn how to find and utilize the value with the highest confidence in its correctness.

5. The databases usually provide uncertainty values (upper limit on experimental error) which enable estimation of the uncertainty of the problem solution using error propagation analysis. An important goal of chemical engineering education is to impart to students that the numerical "solution" of a problem almost always has some associated uncertainty.

A convenient option for chemical engineering educators to incorporate the use of databases into their teaching has been integrated into the POLYMATH package. This widely-used computational tool for numerical problem solving now contains a "sample database" subset of the DIPPR© Database1. The "sample database" contains 34 constant properties and 16 temperature dependent property correlations for 112 compounds that are most frequently used in chemical engineering textbooks. A special interface POLYMATH Database Interface (PDI) now enables a convenient search of the sample database for selected compounds. The desired properties can be selected, and the data and correlations outputted in a format that can be copied and pasted directly into a computer code with all the significant figures given in the database. The formats that are currently supported are for POLYMATH2, MATLAB3 and Excel4. In the following example, the use of the POLYMATH interface to the DIPPR Database will be demonstrated for an adiabatic reactor design problem that will illustrate and highlight the database usage. Production of Acetic Anhydride – An Example Process models based on material and energy balances usually include some constant and temperature dependent data. A typical example of this type is presented by Fogler (1992). This example involves the vapor phase cracking of acetone to ketene and methane

CH3COCH3 → CH2CO + CH4 Acetone (A) → Ketene (B) + Methane (C)

as a key step in manufacturing acetic anhydride. The reaction is first order with respect to acetone (A) and the specific reaction rate can be expresses by

Tk

3422234.34)ln( −= (1)

where k is the specific reaction rate (1/s) and T is the temperature (K). It is desired to design a tubular reactor which yields 20% conversion. The case considered here involves adiabatic operation of the reactor, feed flow rate of FA0 = 8000 kg/hr acetone, inlet temperature of T0 = 1035 K and pressure P = 162 kPa. The mole balance equations for this system can be written

1 The Design Institute for Physical Properties and its acronym DIPPR® are registered trademarks of the American Institute of

Chemical Engineers (AIChE®) 2 POLYMATH is a product of POLYMATH Software, http://www.polymath-software.com

3 MATLAB is a trademark of The Math Works, Inc. http://www.mathworks.com

4 Excel is a trademark of the Microsoft Corporation, http://www.microsoft.com

AC

AB

AA r

dV

dFr

dV

dFr

dV

dF−=−== and; (2)

where FA, FB and FC are the molar flow rates (in mol/s) of compounds A, B and C, respectively, V is the volume (m3), and rA is the rate of the reaction mol/(m3*s) with respect to A:

AA kCr −= (3)

Here CA is the concentration of A (mol/m3) and it can be calculated using the ideal gas law.

( ) RT

P

FFF

FC

CBA

AA

++= (4)

The enthalpy balance equation yields

( ) ( )[ ]{ }PCCPBBPAA

QRRxA

CFCFCF

T∆HT∆Hr

dV

dT

++

+−−−=

0

(5)

where ( )RRx T∆H0 is the heat of the reaction at a reference temperature (TR, usually 25 ºC) and

∆HQ(T) is the enthalpy change that results when the temperature is raised from TR to some temperature T. CPA, CPB and CPC are the heat capacities (J/mol*K) of components A, B and C, respectively. Fogler (1992) rewrote these equations in terms of conversion (X = 1-FA/FA0) as the use of conversion enables obtaining graphical solution for the adiabatic case. Rewriting the mole balance equations in terms of the conversion yields:

0A

A

F

r

dV

dX −= (2A)

Since the flow-rates of the various compounds not calculated explicitly, Eq. 4 cannot be used for calculation of CA as it needs to be expressed in terms of the original concentration of A in the reactor feed CA0, the conversion in the reactor X, and the temperature change in the reactor relative to the feed temperature T0.

TX

TXCC A

A)1(

)1( 00

+

−−= (4A)

The use of the conversion requires revision of the enthalpy balance equation.

( ) ( )[ ]{ }( )PPAA

RPRRxA

CXCF

TTCTHr

dV

dT

∆+

−∆+∆−−−=

0

0

(5A)

where ∆CP is the overall change in the heat capacity per mol of A reacted. Solution of the Example Problem Using Traditional Techniques

Fogler (1992) used the Simpson graphical technique to find the volume of the reactor and the exit temperature for conversion of 20% of acetone data. Equations (2A), (3), (4A) and (5A) were used in the solution. Fogler (1992) provided standard heats of formation and 2nd order polynomial equations for calculating CP for the three compounds. As the example is based on Jeffrey’s (1964) publication, it is assumed that this publication is the source of the data used by Fogler. The set of equations and data (in POLYMATH format) as presented in the 3rd edition of the Fogler book is shown in Table 1. The row numbers shown in Table 1 are not part of the program; they were added as references for the explanations that follow. The model is in a compact form as many of the calculations were carried out separately. In line 3 the value of FA0 is given in (mol/s). The value of CA0 in mol/m3, calculated using the ideal gas law is shown in line 5. The equation for CPA is shown explicitly for compound A (in line 7) however for the rest of the compounds the equations are not shown and only the calculated expression for ∆CP is presented in line 8. The heats of formations of the individual compounds

are not shown either, only the resultant numerical value of ( )RRx T∆H0 is presented.

Figures 1 and 2 show the change of the conversion and temperature, respectively, in the tubular-flow adiabatic reactor as function of the reactor volume. The curves that were obtained by the model shown in Table 1 are marked as “Jeffrey’s data”. The conversion of 20% is obtained with the reactor volume V = 1.191 m3 and the exit temperature in this case is T = 937 K. Fogler (1992) obtained reactor volume of 1.27 m3 with the very same outlet temperature using Simpson graphical integration technique. Extracting Physical Properties from the DIPPR Database Using the POLYMATH Database Interface (PDI) The physical property data and correlations that needed for the enthalpy balance include heat of formation data and equations for calculating heat capacity and enthalpy values at temperature T for the reactant and the two products. Current, up to date data and equations for these properties can be found in the DIPPR database (Rowley et al., 2010). This database can be accessed through the POLYMATH Database Interface (PDI) software. The interface program enables searching the database for a particular compound, marking the desired properties and obtaining as output the necessary data and correlations in a format that can be copied and pasted directly into a computer code. The information that is provided by the interface program in the POLYMATH format is demonstrated in Table 2 for the properties of acetone that are required for the example problem. This table shows most of the information as provided by the interface when the POLYMATH format output is requested. The code that is generated by the interface program includes correlation equations, definition of constant values and comments. Lines 1-11 can be generated at once by selecting the desired “Compounds and Properties” and the “Basic Report.” The “Report Level” determines the amount of information that is to be included as comments. Lines 1 through 4 contain the information related to the heat of formation of acetone. In line 1, the full name of the property and the full name of the compound are shown (as a comment: text that starts with the “#” sign and ends with the end of the line). In line 2, the family of the compound and in line 3 its chemical formula are presented. In line 4, the property value related information is displayed. The units of the property and its uncertainty ( < 1% in this case) are included as comments. The variable into which the value of the property is

entered made up from the symbol of the property (HFOR in this case) and the chemical formula of the compound involved. The information provided for ideal gas heat capacity includes the full name of the property and the compound (line 5), the compound’s family (line 6) and its chemical formula (line 7). For temperature dependent properties DIPPR provides the information regarding range of validity for the temperature (line 8) and range of validity for the property (line 9). The ideal gas enthalpy and heat capacity (lines 10 – 11) deserve special discussion. In most cases DIPPR provides the coefficients for the Aly and Lee (1981) equation for this property. The integrated form of this equation, for calculating ideal gas enthalpy is considerably different than the heat capacity equation. For the benefit of the users, whenever the ideal gas heat capacity is requested by the user, the equation for ideal gas enthalpy is also included, as a comment (see line 10). Note that the enthalpy equation includes an integration constant Hcon. This constant depends on the standard state selected for the enthalpy calculation. For example, selecting as standard state pure gaseous component at 25 ºC (298.15 K) yields Hcon as ideal gas enthalpy at 298.15 K. This value has to be subtracted from the enthalpy of ideal gas at temperature T. Solution of the Example Problem Using Basic Model Variables and DIPPR Property Data The traditional solution technique that includes the use of “conversion” in the differential equations, requires extensive manipulation of the equations. This extra effort is not required when numerical solution techniques are used. Furthermore, in order to provide clear and complete documentation of the problem, it is preferable to include all the original data and variables in the model and carry out the calculations, even the simplest ones, with the computer model. The POLYMATH model for solution of the example problem, using these principles and data from the DIPPR database is shown in Table 3. For most of the variables the units are provided in forms of comments. The principal model equations are shown in lines 2-13. The mole balance equations (Eq. 2) are in lines 2-4 while the enthalpy balance equation (Eq 5) is in line 5. The notation ICP_C3H6O, ICP_C2H2_O and ICP_CH4 is used for representing CPA, CPB and CPC, respectively. The division by 1000 is used for converting the CP units from J/kmol*K (as provided by the DIPPR correlation) to J/mol *K for consistency with the mole balance equations. The variables rA (Eq. 3), CA (Eq. 4) and k are calculated in lines 6, 8, and 12,

respectively and the term: ( ) ( )T∆HT∆H QRRx +0 is calculated in line 13. The conversion X is not

required for the solution, using this formulation; however, it is calculated (in line 7) as the reactor volume is specified in terms of the desired conversion. In lines 15–33, the heat of formation data and the equations for calculating the heat capacity and enthalpy of the reactant and the products are presented. Only the information which is essential for the problem solution is shown. This includes the property values, units, upper limit on the uncertainty of the property values and temperature range of applicability of the correlation equations. The range of applicability is important in order to ensure that the solution of the problem does not require the use of one or more of the equations outside of their range of validity. The uncertainty level of the data is important in order to determine what size of “safety factor” has to be added to the calculated reactor volume, so that the desired conversion can be achieved even in the “worst case” situation. The problem specific constants, initial and final values are grouped together in lines 35-44. The inclusion of all the data and calculations needed for the problem solution and grouping

together the model equations, physical property data and problem specific data provide clear and complete documentation of the model. This in turn enables easy and efficient debugging, modification and extension of the model of the problem. The POLYMATH problem solution is obtained after the problem equations are automatically ordered just prior to the solution. The graphical solution obtained using the model presented in Table 3 is shown in Figures 1 and 2 (the curves marked as “DIPPR data”). Observe that the temperature and the conversion in the reactor are significantly lower in this case than when using the Jeffreys data. The volume required in order to achieve 20% conversion is 2.052 m3, thus the reactor size is larger by 72% than the size obtained using the Jeffreys data. The model shown in Table 1 cannot be used for locating the causes of difference because most of the original data was omitted, and it is necessary to consult the detailed description provided by Fogler (1992). It turns out that they main source of the difference is the heat of formation value of ketene which is provided by Jeffreys (-61.09 kJ/mol) and the one that provided by DIPPR (-47.5 kJ/mol). The source of the DIPPR heat of formation is Padley et al. (1986) where Jeffrey’s publication is from 1964. This demonstrates the importance of the use of the most up to date physical property data from reliable sources in process design calculations. Conclusions The example presented here demonstrates some of the advantages of the use of property databases and mathematical models that contain accurate and documented data typically needed in chemical engineering problem solving. This work demonstrates, in particular, that using physical property information from dated sources may lead to considerable errors in design. The inclusion of the original data in the model is shown to make the debugging, modification and extension of detailed modeling problems more easily accomplished. It is important for educators to introduce students to available and convenient problem solving tools. Additionally students should be exposed to:

• Use of consistent physical property data with documented uncertainty and range of applicability values, extracted from reliable property databases.

• Documentation of the problem, that includes a complete set of the original equations, property data and correlations and problem specific data, in the computer model, clearly marking the units and uncertainties of the variables and temperature range of applicability of the correlations.

References

1. Aly, F. A., and L. L. Lee, "Self-Consistent Equations for Calculating the Ideal Gas Heat Capacity Enthalpy, and Entropy". Fluid Phase Equilib. 6, 169 (1981)

2. Brauner, N., Shacham, M., Cholakov, G. St. and Stateva, R. P., “Property Prediction by Similarity of Molecular Structures – Practical Application and Consistency Analysis”, Chem. Eng. Sci. 60, 5458 – 5471 (2005)

3. Felder, R. M. and Rousseau, R. W., Elementary Principles of Chemical Processes,3rd

Ed, John Wiley & Sons, Inc, Hoboken, New-Jersey, 2000.

4. Fogler, H. S., Elements of Chemical Reaction Engineering, 2nd

Ed, Prentice Hall, Englewood Cliffs, New Jersey, 1992.

5. Himmelblau D. M., and Riggs, J. B., Basic principles and Calculations in Chemical Engineering, 7th

Ed., Prentice-Hall, Upper Saddle River, New-Jersey, 2004. 6. Jeffreys, G.V., A Problem in Chemical Engineering Design: The Manufacture of Acetic Anhydride, 2

nd

ed. (London: Institute of Chemical Engineers, 1964) 7. Pedley, J.B.; Naylor, R.D.; Kirby, S.P.; Thermochemical Data of Organic Compounds; Chapman and

Hall, London, 1986.

8. Rowley, R. L.; Wilding, W. V.; Oscarson, J. L.; Yang, Y.; Zundel, N. A., DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, (http//dippr.byu.edu), Brigham Young University, Provo, Utah, 2010.

Table 1. POLYMATH Solution of the Example Problem Using the Equations Presented by Fogler

(1992)

No. Equation/ # Comment

1 d(X) / d(V) = -ra/Fao

2 d(T) / d(V) = -ra*(-deltaH)/(Fao*(Cpa+X*delCp))

3 Fao = 38.3

4 To = 1035

5 Cao = 18.8

6 Tr = 298 # K

7 Cpa = 26.63+0.183*T-45.86*10^(-6)*T^2

8 delCp = 6.8-11.5*10^(-3)*T-3.81*10^(-6)*T^2

9 k = 8.2*10^14*exp(-34222/T)

10 ra = -k*Cao*(1-X)/(1+X)*To/T

11 deltaH = 80770+6.8*(T-Tr)-5.75*10^(-3)*(T^2-Tr^2)-1.27*10^(-6)*(T^3-Tr^3)

12 V(0) = 0

13 V(f) =1.191

14 X(0) = 0

15 T(0) = 1035

Table 2. Physical properties of acetone as obtained from the DIPPR database by the POLYMATH interface

No. Equation/ # Comment

1 # Enthalpy of Formation of Ideal gas at 298.15 K and 100000 Pa of ACETONE

2 # Compounds Family: KETONES

3 # Compounds Structure: CH3COCH3

4 HFOR_C3H6O = -215700000 # J/kmol (Uncertainty < 1%)

5 # Ideal Gas Heat Capacity of ACETONE

6 # Compounds Family: KETONES

7 # Compounds Structure: CH3COCH3

8 # Valid Temperature Range: 200K to 1500K

9 # Valid Value Range: 60487 to 188200 (J/kmol*K) 10 # HIG_C3H6O = 57040*T+163200*1607*coth(1607/T)-96800*731.5*tanh(731.5/T)

+HCON_C3H6O # J/kmol 11 ICP_C3H6O = 57040 + 163200 * (1607 / T / sinh(1607 / T)) ^ 2 + 96800 * (731.5 / T /

cosh(731.5 / T)) ^ 2 # J/kmol*K (Uncertainty < 1%)

Table 3. POLYMATH Solution of the Example Problem Using DIPPR Physical Properties

No. Equation/ # Comment

1 # Model equations

2 d(FA)/d(V) = rA

3 d(FB)/d(V) = -rA

4 d(FC)/d(V) = -rA

5 d(T)/d(V) = (-(deltaH)) * (-rA) / ((FA * ICP_C3H6O + FB * ICP_C2H2O + FC * ICP_CH4 )/1000)

6 rA = -k * CA

7 XA = (FA0 - FA) / FA0

8 CA = yA * P / (8.31 * T)

9 yA = FA / (FA + FB + FC)

10 yB = FB / (FA + FB + FC)

11 yC = FC / (FA + FB + FC)

12 k = 8.2E14 * exp(-34222 / T)

13 deltaH = (HFOR_C2H2O +HFOR_CH4 -HFOR_C3H6O+HIG_C2H2O +HIG_CH4 -HIG_C3H6O)/1000 #J/mol

14 #

15 # Thermodynamic data and correlations from the DIPPR database

16 # ACETONE

17 HFOR_C3H6O = -215700000 # J/kmol (Uncertainty < 1%)

18 HCON_C3H6O = 57040*Tref+163200*1607*coth(1607/Tref)-96800*731.5*tanh(731.5/Tref) # J/kmol

19 HIG_C3H6O = 57040*T+163200*1607*coth(1607/T)-96800*731.5*tanh(731.5/T)-HCON_C3H6O # J/kmol 20 # Valid Temperature Range:200K to 1500K 21 ICP_C3H6O = 57040 + 163200 * (1607 / T / sinh(1607 / T)) ^ 2 + 96800 * (731.5 / T / cosh(731.5 / T)) ^ 2 #

J/kmol*K (Uncertainty < 1%)

22 # KETENE

23 HFOR_C2H2O = -47500000 # J/kmol (Uncertainty < 5%)

24 HCON_C2H2O = 36940*Tref+68650*1490*coth(1490/Tref)-45240*640*tanh(640/Tref) # J/kmol

25 HIG_C2H2O = 36940*T+68650*1490*coth(1490/T)-45240*640*tanh(640/T)-HCON_C2H2O # J/kmol 26 # Valid Temperature Range:150K to 1500K 27 ICP_C2H2O = 36940 + 68650 * (1490 / T / sinh(1490 / T)) ^ 2 + 45240 * (640 / T / cosh(640 / T)) ^ 2 #

J/kmol*K (Uncertainty < 1%)

28 # METHANE

29 HFOR_CH4 = -74520000 # J/kmol (Uncertainty < 1%)

30 HCON_CH4 = 33298*Tref+79933*2086.9*coth(2086.9/Tref)-41602*991.96*tanh(991.96/Tref) # J/kmol

31 HIG_CH4 = 33298*T+79933*2086.9*coth(2086.9/T)-41602*991.96*tanh(991.96/T)-HCON_CH4 # J/kmol 32 # Valid Temperature Range: 50K to 1500K 33 ICP_CH4 = 33298 + 79933 * (2086.9 / T / sinh(2086.9 / T)) ^ 2 + 41602 * (991.96 / T / cosh(991.96 / T)) ^ 2 #

J/kmol*K (Uncertainty < 1%)

34 #

35 # Constants, initial and final values

36 Tref=298.15 #K

37 P = 162 * 1000 # Pa

38 FA0 = 38.3 # mol/m^3

39 FB(0) = 0

40 FA(0) = 38.3

41 FC(0) = 0

42 T(0) = 1035 #K

43 V(0) = 0

44 V(f) = 2.052 # m^3

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1 1.2

Volume (m^3)

Co

nvers

ion

(X

)Jeffreys data DIPPR data

Figure 1 – Conversion of acetone as function of reactor volume

920

940

960

980

1000

1020

1040

1060

0 0.2 0.4 0.6 0.8 1 1.2

Volume (m^3)

Tem

pera

ture

(K

)

Jeffreys data DIPPR data

Figure 2 – Temperature change in the reactor as function of volume