role of viscosity in the accurate prediction of...
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ROLE OF VISCOSITY IN THE ACCURATE PREDICTION OF
SOURCE-TERMS FOR HIGH MOLECULAR WEIGHT
SUBSTANCES
A Thesis
by
IRFAN YUSUF SHAIKH
Submitted to the Office of Graduate Studies of Texas ARM University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
August 1999
Major Subject: Chemical Fngineering
ROLE OF VISCOSITY IN THE ACCURATE PREDICTION OF
SOURCE-TERMS FOR HIGH MOLECULAR WEIGHT
SUBSTANCES
A Thesis
by
IRFAN YUSUF SHAIKH
Submitted to the Office of Graduate Studies of Texas A&M University
In partial fulfillment of the requirements for the degree of
MASTER OF SCKNCE
Approved as to style and content by:
M. am Mannan
(Chair of Committee) Kenneth R. Hall
( ember)
John P. Wag ' r (Member)
ayford G. Anthony
(Head of Department)
August 1999
Major Subject: Chemical Engineering
ABSTRACT
Role of Viscosity in the Accurate Prediction of Source-Terms for High Molecular
Weight Substances. (August 1999)
Irfan Yusuf Shaikh, B. S. , Texas A@M University
Chair of Advisory Committee: Dr. M. Sam Mannan
This study shows that using better material property predictions results in better
source-term modeling for high molecular weight substances. Viscosity, density, and
enthalpy are used as a function of process variables, namely, temperature and pressure,
and mixing effects. The viscosity prediction uses an improvement on current predictions
by combining b-parameter and Modified Chung-Lce-Starling (MCLS) viscosity
predictions for the employed pseudo-mixtures.
The source-term model used is SPILLS. It is an established, publicly available
model, which has been incorporated into several proprietary dispersion modeling
packages. The model is modified to accommodate new material property relationships.
'I'he final results compared in this work are evaporation rates for pseudo-mixtures of
petroleum fractions. The results are compared to actual SPILLS model prediction. The
model is also compared using pentane with experimental evaporation data.
Currently, this work is valid for crude compositions and can be extended for
other materials that meet the new property prediction criterion. This work can also be
extended to other areas of source-term and dispersion modeling, namely, aerosol
entrainment, rainout predictions, and vapor cloud dispersion.
Dedicated to my parents,
Razia and Yusuf Shaikh
ACKNOWLEDGEMENTS
I would like to acknowledge the members of my committee for their suggestions
in this work; Dr. M. Sam Mannan for his continued support as my professor, advisor,
and committee chair, and Dr. Kenneth R. Hall and Dr. John P. Wagner for serving on my
committee.
I would also like to thank Dr. Dave Johnson and Mr. John Cornwell of Quest
Consultants for providing information on obtaining crude compositions. Others I would
like to thank include Mr. John Woodward of Wilf'red Baker Engineering for his helpful
insight, Ms. Donna Startz, Mr. Towanna Mann, and Mr. James Munnerlyn for all their
assistance associated with paperwork.
I v ould also like to thank my parents, Razia and Vusuf Shaikh for the myriad of
ways they have supported my efforts throughout my college career.
TABLE OF CONTENTS
Page
ABSTRACT .
DEDICATION . lv
ACKNOWLEDGEMENTS .
TABLE OF CONTENTS
v
vt
LIST OF FIGURES vt 1 1
LIST OF TABLES .
CHAPTER
tx
I INTRODUCTION
Background .
Previous Work
II MATERIAL PROPERTIES . 10
Pseudo-Mixtures . Properties
III DENSITY PREDICTIONS
10 ll
13
IV VISCOSITY PREDICTIONS 17
Effect of Carbon Dioxide on Viscosity Nitrogen Viscosity .
V SOURCE MODEL
19 20
21
Discharge Rate .
Enthalpy Enthalpy Correction Due to Pressure and Mixing Effects . .
Flashing .
Pool Spill Calculations
21 23 23 24 25
vu
CHAPTER
VI RESULTS AND DISCUSSION
Page
27
V CONCLUSIONS 36
Recommendations Extension of Model
NOMENCLATURE
36 37
39
Notation .
Subscripts Superscripts
LITERATURE CITED .
39 41 42
43
APPENDIX A EQUATIONS FOR ESTIMATING CRITICAL CONSTANTS . . . 47
APPENDIX B AIR PROPERTY EQUATIONS .
APPENDIX C SOURCE MODEL CALCULATIONS . . .
APPENDIX D VISUAL BASIC Sl JBROUTINES .
50
52
APPENDIX E SPILLS MODEL PRINTOUTS 62
VITA 64
LIST OF FIGURES
FIGURE
Density Comparison. .
Page
28
Viscosity Data Comparison at 310 K 30
Viscosity Data Comparison at 366 K 31
Viscosity Data Comparison at 450 K 32
Average Evaporation Rate vs Chemical Normal Boiling Point . . . 34
LIST OF TABLES
TABLE Page
Crude Pseudo-Mixture Compositions . 10
Critical Properties . .
Characterization Parameters for MPCS-MBWR Equation-of-State. . . 15
Regression Constants for Equations 21 to 25 18
Calculated B Parameter Values for Equations 21 to 25 . ,
Density Data Comparison 27
Comparison Based on Molecular Weight . . 28
Viscosity Data Comparison (mPa. s) 29
Effect of Deviation from Ideality for Enthalpy . . 33
10 Comparison of Evaporation Rates for Pseudo-Mixture with SPILLS
Model . 34
Comparison of Evaporation Rates for Pentane wtth Spill Data at
320K (in kg/m h) 35
CHAPTER I
INTRODUCTION
Background
The risk management program regulation promulgated recently by the U. S.
Environmental Protection Agency (EPA) requires regulated facilities to conduct off-site
consequence analyses (Vincent, 1976). This is for facilities that handle listed toxic or
flammable materials at or above specified threshold quantities. EPA's draft guidance
document includes look-up tables defining the impact of accidental releases. EPA also
allows the use of sophisticated dispersion models to determine dispersion distances. It
should be pointed out here that the EPA look-up tables are based on Gaussian equations
and as a result provide conservative dispersion distances. Also, the EPA look-up tables
are defined for v, orst case scenarios; meaning that criteria requires the most conservative
scenario, however remote the chances are of it happening. Other available models and
techniques vary in their accuracy because of different reasons. One reason is that
determination of realistic flow rates (source-terms) has a tremendous impact on the
accuracy of dispersion modeling for accidental release scenarios. Material released from
holes and cracks in tanks and pipes, from leaks in llanges, pumps, and valves, and a
large variety of other sources are poorly characterized. Source-term models represent
The AIChE. /onrna1 is used as a model for this thesis.
the material release process. In many cases, it is sufficient to analyze the release as one-
dimensional flow through an ideal hole with a generalized empirical discharge
coefficient based on geometry. However, most source models are constructed from
empirical or fundamental equations representing the physical and chemical processes
occurring during the release of materials. Sometimes, these models need to be modified
to fit a certain type of release scenario, and the results are only estimates since physical
properties of the material are not adequately characterized or completely understood. A
good example of this is to add a variable temperature-pressure dependent density
correlation into the utilized equation-of-state to better define the scenario.
For high-pressure systems where the fluid is processed above its normal boiling
point, a leak could well result in a jet stream of liquid flashing partially into vapor.
Small liquid droplets or aerosols might also form from the flashing process. This system
can then be transported by wind and other atmosphenc conditions, and can ignite.
The operating conditions are probably the most important part of the process. As
stated earlier, physical properties do characterize the design of the process and material
Used.
Heavy crude is used commonly in refining processes, where transportmg such
material involves large amounts of heat-transfer. The processes usually operate at high
temperatures and high pressures. A heat-transfer system, operating above its boiling
point can create an explosive situation if it develops a leak and releases fluid. A super-
heated liquid flashes to produce a vapor or mist. The consequences of not recognizing
the explosion hazard and thc conditions, which can create this, can be significant.
For this reason, this research project will focus on better defining heavy crude
using thermophysical-property relationships of viscosity and density into the model.
And the result of the simulated spill will be compared to field data obtained from
volatility experiments conducted by experiments done by Peter Kawamura and Donald
Mackay for University of Toronto (Kawamura and Mackay, 1987) and against an
unmodified SPILLS model.
Previous Work
The scope of this project is two-fold. The first step was to determine a realistic
viscosity-density model to better understand the material properties. The second step
was to modify an existing model to fit with these properties.
There has been a lot of previous work done in the area of estimating fluid
density. The density predictions for petroleum fractions have been extended from high
temperatures (up to 900'F) and high pressures (up to 3000 psia) for processes (Hwang et
al. , 1986). Some of the previous work include the Reidel equation and its modifications.
The equation is given by
p„= I+ 0. 85(l — T, )+ (1. 6916+ 0. 9846rii)(1 — T„j
where p, is the reduced density, T, is the reduced temperature and to is the acentric factor
(Hwang et al. , 1986).
Another equation commonly used is a form of Rackett equation. The general
form of the Rackett equation is
(2)
where Z~ corresponds closely to the critical compressibility factor and is a specified
constant for each fraction. These equations can be extended for pressure effects via
isothermal compressibility factor and Watson relationship (Hwang et al. , 1986; Reid et
al. , 1988).
The three-parameter corresponding states theory (3-PCS) can also be applied to
determine density of a predefined mixture of components, pseudo-mixture. The
methodology uses the concept of conformality (Brule and Starling, 1982). A reduced
property is said to be conformal with ihe same reduced property of a second fluid.
Z(&, . p, ), = Z(&;. p, )„ (3)
where I and II represent two different compounds. The 3-PCS methodology can be
applied with the Benedict-Webb-Rubin (BWR) equation of state to successfully
determine density over a wide range of temperatures and pressures for all compounds
that are applicable (Reid et al. , 1988).
There are several methods for the determination of the viscosity parameter that
have been developed in recent years. Although, all of these methods are empirical in
nature because no fundamental theory exists for the transport of liquids. This is
furthermore complicated by the fact that there is incomplete characterization of
penoleum mixtures involved. Liquid mixture viscosity data is usually presented in terms
of temperature, pressure, and composition. The generic base form of the relationship is
rf, = f (P, T, x, . ) (4)
The correlation function should have a good behavior for extrapolation. Linear
functional relations are best for this purpose. The correlation equation should also be
useful as a predictive tool.
There are two generic ways: one is to use only the properties of pure fluids, and
the other is to use not only the properties of pure liquids but also some information on
the liqutd mixtures. Onc of thc simplest representattons of viscosity over a wide region
of states is achieved in terms of temperature and density. One of the methods to
estimating viscosity is to plot residual viscosity, which is defined as viscosity at some
specific temperature and density minus its value at the same tempcraturc at zero density,
against density (Stephen and Lucas, 1979). This method is sul'ficient to obtain data for
all fluid states for which P-V-T data can be found. The results of this method are only
approximately valid at high densities and for wide temperature regions.
Generally increasing the pressure over a liquid results in an increase in viscosity.
This cffcct is more important at high rcduccd temperatures. According to Reid et al. , the
effect of pressure change may be estimated from
t7 1+ DIAP„ /2. 118)
t7 „1+ CruAP,
where tfsz — — viscosity of saturated liquid at vapor pressure, ruis the accntric factor, and
A, C, D are empirical correlations based on reduced temperature.
The viscosity of liquids decreases with increasing temperature. Brule et al.
(Brule et al, 1982), and Brule and Starling (Brule and Starling, 1982) give one of the
most common methods of estimation of viscosity. Both methods have a similar accuracy
for most non-polar compounds, but the Brule and Starling relation was developed
primarily for complex hydrocarbons, especially for high-molecular weight petroleum
products and coal-fluid polycyclic organic compounds. These relationships are also
sensitive to liquid density measurements. Either method can be incorporated for liquid
mixtures. Also, Brule and Starling relationship is in terms of process conditions like
pressure and temperature. Both methods use standard mixing rules incorporated into
their respective sets of equations. The Chung et al. method is a multi-parameter
corresponding-states expression. This method is extensively described by Reid,
Prausnitx, and Poling (Brule et al. , 1982; Reid et al. , 1988). Also, liquid viscosities are
very sensitive to the structures of the constituent molecules, and even mild association
effecls between components can often significantly affect the viscosity.
The Chung-Lee-Starling (CLS) viscosity correlation is a multi-parameter
corresponding-states expression. The CLS correlation employs the conformal-solution
model to represent the composition dependence of viscosity (Brule et al. , 1982). The
main equation is given below as
tl=tl, +E, Y +E, Y'IGN(Y)]e'" ' ' i GN(Y)
where ri, is the viscosity of isotropic reference fluid, and GN is a function of E, . The E
parameter is calculated as a function of y using the relation and universal constants a, and
b;, It is able to predict both high molecular weight paraffins, typical of petroleum, and
polycyclic organic compounds preponderant in shale oil and coal fluids. This equation
is quite analogous to 3-parameter corresponding states MBWR equations-of-state (Brule
et al. , 1982).
Another method commonly used is by looking at group contributions, which are
capable of making approximate predictions of properties for which only the molecular
structures may be known. A viscosity-activity coefficient model (UNIMOD) is an
example of this type of method (Cao et al. , 1993). The idea is similar to UNIQUAC
activity coefficient methods. A liquid mixture is described as a solution of groups and a
physical property of the mixture is the sum of contributions of all groups in the mixture.
One drawback to this method is its limitation to tertiary or 4-compound mixtures
because of the complexities in calculations involved with binary interaction parameters.
Another method uses a relationship between effective carbon number (ECN) and
parameter b in the one-parameter viscosity equation (Mchrotra, 1994):
Iog(p+ 0. 81) = 100(0. 0 IT) '
where b is a parameter which can be a function of boiling point, molecular weight and
critical properties. This method can be utilized effectively to extrapolate viscosities for
heavy hydrocarbons with reliability and can be extended to defined or undefined crude
oil mixtures via mixing rules for ECN. This is a reliable method for pseudo-mixtures as
there is data available using this method I'or pure hydrocarbons. This method can bc
extended to cover heavy hydrocarbons and also at high temperatures. Also, the method
has been shown that it can be extended to account for high pressure effects.
There has also been some previous research work done on source-term modeling.
Some of the most common models or types of models used are from specific type of
releases. For example, for liquid or two-phase jet &om a pressurized tank or pipe the
Bernoulli equation is recommended (Hanna and Strimaitis, 1989). The model assumes a
constant discharge coefficient and neglects any frictional losses. Also the model
assumes all flashing occurs downstream from the opening. The equation for discharge is
given by
g CpApi (2API pi +2gH) (8)
where Co is the discharge coefficient assumed to be it/(2+ii) = 0. 61, A = cross-sectional
area, and H is the depth of liquid in the tank above the hole.
Fauske-Epstein equation is also used in modeling sub-cooled liquids where AP is
the difference between storage pressure and vapor pressure in Eq. 8 (Hanna and
Strimaitis, 1989). For example, if the vapor pressure is greater than one atmosphere, and
the storage temperature is below the saturation temperature associated with storage
pressure then this modification is used.
EPA has recommended a set of dispersion models for application to releases, of
which, some of the most common source models available publicly, include SPILLS,
DEGADIS 2. 1, SLAB, and ALOHA. There are several proprietary models that do
source calculations also. PHAST and CANARY are two such examples. The SPILLS
model has been used for many years and been incorporated into several other models
(Fleischer, 1980). It contains empirical formulas for calculating the evaporative
emissions from liquid spills. The DEGADIS model, developed by the US Coast Guard,
has also been incorporated into several models and is used to calculate mainly dense-gas
slumping, transport, and dispersion analysis (Hanna et al. , 1991).
CHAPTER II
MATERIAL PROPERTIES
Pseudo-Mixtures
The first step is to define a compound to be used in this work. The pseudo-
compound utilized in this research was a product of actual fractional distillation data for
crude obtained from Quest Consultants, Inc. The fractional distillation data was for API
16 and API 25. 5 crude (Cornwell, 1999). The American Petroleum Institute (API) rates
crude by API gravity, ranging from 0 to 100 (GPAS, 1994). The mixture was cut-off to
ten most abundant components and their compositions. The compounds represcnttng
components of the mixture were chosen to match as closely as possible in molecular
weights and properties. They are listed in Table 1.
Table 1. Crude Pseudo-Mixture Com ositious No. Component
Data Utihzed API 25. 5 API 16
Com ounds Com ositions Com ositions
I 2 3 4 5 6 7 8 9 10 11
Nz
Cls COz C2s C3s C4s CSs C7s
CHs-200 CHs-300 CHB-400
Nz
CH4 COz CzHs CzHs
n-C4Hto
n-CsH)z n-CzHts C i4Hzs
Czo&z Cz9Hsz
0. 0007 0. 3518 0. 0153 0. 0887 0. 0702 0. 0548 0. 0346 0. 0647 0. 0733 0. 2459 0. 0000
0. 0092 0. 2741 0. 0035 0. 0256 0. 0335 0. 0337 0. 0326 0. 1473 0. 0000 0. 4185 0. 0220
Properties
The problem of characterization of compounds is the problem of correlation.
This means as a complex fluid increases in molecular weight the determination of
characterization parameters at the normal boiling point become less feasible. Therefore,
the properties for chemicals used in this research were gathered through various sources.
The critical properties used were obtained mostly through Perry's Handbook (Perry et
al. , 1986), the Properties of Gases and Liquids (Reid et al. , 1988), GPSA manual (GPSA,
1994a) and Starling and Brule (Brule et al. , 1982). The critical properties are listed in
Table 2.
Table 2. Critical Pro erties Comp. MW To T, P, V, p, y
[ mol] [K] [K] [bars] [cm'/mol] [mol/cm3]
N»
CH4
CO»
C»H»
C»H»
n-C4Hio
n-CsHi»
n-C7Hio
Ci4H»»
C»oH4»
CooHs»
28. 013 16. 043 44. 01 30. 07
44. 094 58. 124 72. 151 100. 205 198. 394 282. 556
382
77. 4 126. 2
111. 6 190. 4 194. 7 304. 1
184. 6 305. 4 231, 1 369. 8
272. 7 425. 2 309. 2 469. 7 371. 6 540. 3 526. 7 693 625 767 709 874
33. 9 46
73. 8
42. 5
38 33. 7
27. 4
14. 4 11. 1
11. 10
89. 8
99. 2 93. 9 148. 3
203 255 304 432 830
1227. 6 1552. 4
1. 11E-02 1. 01E-02 1. 06E-02 6. 74E-03 4 93E-03 3. 92E-03 3. 29E-03 2 31E-03 1. 20E-03 8. 15E-04 6. 44E-04
0 039 0 011 0. 239 0. 099 0. 153 0. 199 0. 251 0. 349 0. 581 0. 907 0. 915
0, 0263
0. 01289 0. 2093
0, 09623 0, 1538 0. 1991 0 253
0, 3499 0, 6364 0. 8853 0. 902
The critical properties that were not available through literature research were
calculated using equations given by Watanasiri et al. (1985). This was mainly done for
the last compound in Table 2. These correlations have been developed to estimate
critical constants, acentric factor, and dipole moment of model petroleum compounds
and other hydrocarbons. The equations used are based on molecular weight and specific
gravity. The equations used in this work are for T„V„P„cu, and dipole moment, p. .
Only significant terms are included in the final correlations. The equations are listed in
Appendix A.
CHAPTER III
DENSITY PREDICTIONS
The density of the pseudo-mixtures was determined using a multiparameter
corresponding-states (MPCS) correlation of petroleum fluid thermodynamic properties.
The MPCS, based on perturbation theory, gives relatively accurate predictions. For
polar compounds it gives slightly less accurate estimates (Brule et al. , 1982). But in
most cases, the results are sufficiently accurate to carry out constructive process design.
The equation-of-state used in this research is the Benedict-Webb-Rubin
(MBWR) equation cast with a conformal-solution model for mixture-properties. The
MBWR was selected because of its proven capability in accurately predicting
thermodynamic properties at relative reduced temperatures as low as T„= 0. 3 and
relative reduced densities as high as p, = 3 (Brule et al. , 1982). Therefore, the MPCS-
MBWR equation is indicated below as
Z 1 + p (E[ E T E3T + E4T E~~T )
+ p"'(F, — E, T' ' — E~„T" ')+ p"'(E, T' '+ E»T' ')
+ Es pe T ' (1+ E, p ) exp( — E4 p ) (9)
where p* is the reduced number density, T* is the reduced number temperature and E, is
a function of constants and orientation parameter. Thc equation, however, is restricted
to compounds it is capable of predicting accurately. All the components of the pscudo-
mixtures are within the limits,
The mixing rules used were based on MBWR equation-of-state. The
characterized parameters used for mixing rules are for molecular-size parameter, a;1,
molecular-energy parameter, e„, and orientation parameter, pi. The equations are as
follows:
(10)
(12)
The pair characterization parameters, era, ej, and )jj, are function ol' the pure-fluid
characterization parameters, a, c, and 7 of component i and j. The combining rules used
in this case are
(13)
(14)
where E„and f„j are the binary interaction parameters (BIPs). Thc BIPs are indicative of
dcvtations from ideal-solution behavior.
The parameters o, s, p+, T* and E are calculated from the following equations.
(16)
(17)
(18)
o' =0, 3189/p, (19)
E, =a, . +yb, (20)
where k is the Boltzmann constant. The values for these parameters, calculated for T =
317 K, are listed in Table 3 given below.
Table 3. Characterization Parameters for MPCS-MBWR E uation-of-State
Comp. Molecular Isotropic Reduced. Numbered.
Size, tr Fluid Force, s Temperature, T .
Nz CH4
COz
CzHo
CsHs
n-C4Hio
n-CsHiz
n-CzHio
Ci4Hzs
CzoI4z
CzoHsz
3. 0595 3. 1627 3. 1053 3. 6163 4. 0153 4, 3324 4. 5938 5. 1647 6. 4206 7. 3154 7. 9108
1. 31E-21 1. 98E-21 3. 16E-21 3. 17E-21 3. 84E-21 4. 42E-21 4. 88E-21 5. 61E-21 7. 20E-21 7. 97E-21 9. 08E-21
3. 99E+00 2. 65E+00 1. 66E+00 1. 65E+00 1. 36E+00 1. 18E+00 1. 07E+00 9. 32E-01 7. 27E-01
6. 57E-01 5. 76E-01
Eq. 9 is solved implicitly for reduced number density, p* and Z using an iterative
process where an initial value of Z = 1 is assumed and p~ is calculated based on ideal
gas equation. The value of p" is inserted into Eq. 9 and a new value of Z is calculated.
Thc process is repeated until values for Z and p~ converge. The values for density can
be seen in the results and discussion section of this work.
16
The density of nitrogen was also calculated separately. This time without the
mixing rules. The value of nitrogen density is needed in the viscosity calculation for
nitrogen.
CHAPTER IV
VISCOSITY PREDICTIONS
The main viscosity correlation used in this research for mixtures is based on the
work of Mehrotra (1994), and Orbey and Sandier (1993). The estimation of viscosity in
penoleum mixture simulations is an important problem. The first step in determination
of viscosity by the Effective Carbon Number method (ECN) is to separate the
hydrocarbons and non-hydrocarbon compounds. The ECN can only be used for
hydrocarbon fluids.
The generic form of the ECN equation is given by Eq. 7. The parameter b is
dependent on several properties of a compound including the ECN, T„Ts, and co.
Adding mixing rules to this equation can account for the pseudo-mixture. Eq. 21 is
obtained from Mehrotra (1994) and Eq. 22 to Eq. 25 are obtained from Mehrotra (1991a)
and are given below. The correlation equations werc predicted for pure hydrocarbon
fluids. The regression constants are listed in Table 4. The equations are as foflows:
b, = C, +, (ECN) + C, (ECN) ' '
b B0 + B~ [LogM]+ B, ' [LogM]
(21)
(22)
B, ' B, '
b, =BA+ '+ t
(23)
BD' +B) T + BiT (24)
b, = Bs +B, "m+B, m' (25)
18
Table 4. Regression Constants for E uations 21 to 25
21
23
25
Constant
Ct -5. 745 Cs 0. 616 Cs -40. 468 Bo' -1. 396 B i' -1. 4E+03 Bp' -2. 6E+05 B„" -15. 96 B, " 40. 19 Br" -49. 2
22
24
Constant
B, -66. 51 Bt 46. 64 Bt -9. 189 Bo' -28. 79 B&' 6. 08E-02 Bz' -3. 78E-05
The b, value is calculated for each hydrocarbon component and is given in Table 5.
Table 5. Calculated B Parameter Values for E uations 21 to 25
b (ECN) b w b (Tb b (Tc b (MW) CH4
C2H6 C3H8
n-C4H10 n-CSH12 n-C7H16 C14H28 C20H42 C29H52
-46. 213 -19. 626 -12. 856 -9. 9495 -8. 3732 -6. 7314 -4. 8919 -4. 3521 -3. 9299
-15. 524 -12. 463 -10. 963 -9. 9106 -8. 9720 -7. 9263 -9, 2176 -19. 982 -20. 378
-34. 344 -16. 347 -12. 118 -9. 8559 -8. 4950 -6. 9247 -4. 9072 -4. 2313 -3. 8262
-18. 592 -13. 759 -11. 490 -9. 8000 -8. 6000 -6. 9928 -4. 8293 -4. 4144 -4. 5461
-23. 644 -17. 647 -14. 663 -12. 825 -11. 572 -9. 9772 -7. 8587 -7. 3972 -7. 3461
Then the extension to pressure is applied. There is essentially a linear
relationship between the logarithm of ratio of viscosity at P to viscosity at 1 atm. The
range is from atmospheric pressure to 40 mPa. The relationship is given as follows:
p(T, P) = p(T)exp(M*P) (26)
where M is equivalent to 0. 98 x 10 kPa ' for hydrocarbons.
The equation for b; is used to calculate viscosity using Eq. 7 and combined with
the mixing rule given in Orbey and Sandier (1993). The equation is given as follows
1
p= exp, ' (27)
Finally, the viscosity results are combmcd with viscosities for carbon dioxide and
nitrogen. The results are provided in the results and discussions section of this thesis
using a linear correlation.
Effect of Carbon Dioxide on Viscosity
The main problem of predicting the effect of carbon dioxide viscosity is the state
of carbon dioxide when mixed with crude oil. It can be either pure carbon dioxide, a
dense fluid or a gas. Therefore, carbon dioxide has to be treated separately from the rest
ol' compounds. According to (Orbey and Sandier, 1993) viscosity correlation below
should be used for temperature range of 273 K to 500 K and pressures range from 0. 1
MPa to 50 MPa, when it. is used with a viscosity of the oil using a mixing rule. The
equation is given as follows:
p cps (T, P = 0. I mPa) = 0. 00 1 97 + 0. 000044T
Pcoz(T* P) = Pco, (T, P = 0. 1 mPa)+(0. 00602 — 1. 02 "10-'T) p
(28)
(29)
where ltco2 is for Pressures above atmosPheric and suPercritical temPeratures.
20
Nitrogen Viscosity
The viscosity of nitrogen is calculated by the Chung-Lee-Starling viscosity
correlation (CSM-3PCS-MCLS) which is Eq. 6 (Brule and Starling, 1982). Here, t)cs is
the Chapman-Enskog dilute viscosity and is represented by
26. 693(MT) Vce vt2(22)
(3o)
where the collision integral is calculated using the Leonard-Jones 12-6 potential model
and is given by
O' ' ' =/1/T* +C/e +Ele +RT*sin(ST*' — P) (31)
Equations for E(T*) and GN(Y) are given as follows
E(T*) = Es + E9 / T*+E, o / T*' (32)
and
GN(Y) =[E, (I — e "")/Y+E, Ge'" +E, G]/IE~E, +E, +E, ] (33)
where G is a function of Y and Y is the reduced number density (ttp'/6). G is given by
G = (1 — O. SY) /(1 — Y)' (34)
The calculated viscosity of nitrogen is combined with viscosities of other components
and is presented in the results and discussion section of this work.
CHAPTER IV
SOURCE MODEL
The source term model equations modified for use in this thesis are from the
SPILLS model (Fleischer, 1980). The SPILLS model was developed by Shell Research
and is an unsteady-state model representing the evaporation of a chemical spill. Thc
model is capable of atmospheric dispersion and can predict downwind concentrations as
a function of dme and distance (Fleischer, 1980). However, the scope of this research
limits the usage to source-term equations.
Discharge Rate
The discharge rate is based on thc Bcrnoulli equation. Thc friction term is not
neglected in this case as to stimulate more realistic results (de Nevers, 1991). The
equation is given below as
For the purpose of this research the initial velocity (u, ) is considered negligible. The
friction term is calculated using the Wood's approximation methodology given in de
Nevers (1991). This methodology uses the Reynold's Number (Ns, ) and the ratio of
roughness to diameter (dD). The roughness is assumed to be 0. 0018 for commercial
steel (de Nevers, 1991). This is a good approximation for pipes transporting heavy
crude and other hydrocarbons. The equation is given as
22
F =4(a+bNR. ) D 2
(36)
where
a = 0. 023 — +0. 132 (37)
(38)
and
c =1. 6 (39)
Eq. 34 and Eq. 35 are solved simultaneously 1'or u and F using an initial guess for u. The
discharge coefficient usually used in dtscharge models Co —— tt/(tt+2) is used to calculate
the velocity as shown below in Eq. 40 (Hannas and Strimaitis, 1989). And then F is
found from Eq. 36 and is used to calculate u from Eq. 36. The iterative process is
repeated until u and F values converge. The initial velocity guess equation is given as
(40)
From this the actual flow rate (Q = Aup) is calculated. "A" represents the cross-
sectional area. The diameter used here was set to 0. 5 inches.
23
The enthalpy calculation is based on heat capacity correlation. The enthalpy at
operating temperature subtracted by enthalpy at boiling point for the mixture gives the
heat released. The equation is given below as follows
Tb I ( cp cp cp cp ) b
(41)
where A, B, C, D are constants for mixtures based on composition
The heat of vaporization is calculated from Chen's equation given in Reid et al.
(1988). It is based on P„T„and Tb. The correlation is given below as
RT, T„, — 3. 958+1. 555 ln P, AH, , „ v(fp 1. 07 — Tb,
(42)
This empirical equation is capable of providing a good estimate of heat of vaporization.
This equation has been used to predict vapor pressures for petroleum fractions with
reasonable accuracy (Reid et al. , 1988). The properties used in this equation are for
pseudo-mixtures.
Enthalpy Correction Due to Pressure and Mixing Effects
The enthalpy correction accounts for deviations from enthalpy of fluid mixture to
enthalpy of a mixture (Holland, 1981). This is denoted below as:
H = H'+0 (43)
This deviation is based on effects of pressure and effects of interactions due to mixing
for enthalpy. Also, the enthalpy I-I, (P, T) of pure component i is related to its fugacity by
the well-known Maxwell relationships and stability criteria.
24
H, (P, T) — H, '(1, T) = — RT'I (44)
This relationship can be applied to mixtures as shown below
H(P, T, y, ) — H(1, T, y, ) = — RT [
' )
=Q (45) , (alog, f'i
P, M
The equation for Q was obtained from Holland and Anthony (1989). The equation for
Q is applied for mixing effects using mixing rules to find the fugacity of the mixture as
shown below
0= RT(Z — 1)+ — ' — 1 log„ (46)
where
cr= 1+m, 1— (47)
m, = 0. 48+ h574cu, — O. l76nr, ' (48)
A, B are defined according to the mixing rules given in Holland and Anthony (1989).
Flashing
Once the enthalpy correlations are established, the flashing fraction can be
determined from the generic equation given below:
AHrs + Qr',
AH, . „ (49)
25
where f is the ratio of liquid flashed to ambient as the pressure is reduced. This
determines the amount of liquid that would be spilled. All the liquid is considered
spilled as no aerosol entrainment is assumed here. To calculate aerosol entrainment in a
flashing process, a full-fledged near-field dispersion modeling has to be done on the
vapor cloud. One of the factors required in modeling aerosol, is the rate of change of the
vapor cloud's size.
Pool Spill Calculations
To get the evaporated amount, the pool length (or radius) must be calculated first.
The SPILLS model gives the pool length in terms of flow rate coming out and air-liquid
properties (Fleischer, 1980). Thc equation is given below as
0. 037D„, Ni%" p [v,
(50)
where u„, is the wind speed, D is the air-liquid diffusion parameter, v„„ is thc air
kinematic viscosity. All the properties of air are taken the same as given in the SPILLS
model and are given in Appendix B. The conductivity, k, viscosity, It, density, p, heat
capacity, cr, and thermal diffusivity, ct are functions of air temperature and taken at 1
atm.
Once the pool diameter is known, the pool area can be determined. Thus,
correlation for Sherwood number (Nss ) can be used to determine the mass transfer
26
coefficient, ks (Hannas and Strimaitis, 1989). The Eq. 51 gives the Nsa and Eq. 52 gives
the ks.
Nss = (51)
k, =D Ns„/d, (52)
Evaporation model in SPILLS model is determined, assuming mass transfer
occurs predominantly by forced convection over a flat plate. The mass transfer
coefficient is determined from Eq. 52, where it is a function of diameter, diffusion into
air, and Sherwood Number. The rate equation for convective mass transfer can be
expressed as
N = k, A(CI — C„) (53)
where N is the mass transfer rate in mol/s, and C, and Ci are initial and final chemical
concentrations into the air stream (Flmscher, 1980). C, is equal to zero. Converting the
equation into mass units,
n=k, Ap, (54)
where n is the mass transfer rate in kg/s. The liquid density is calculated from vapor
pressure and ambient temperature. The equation is given below as
P„„ p, = "M
RTn (55)
Therefore, the evaporation model equation ts obtained by combming Eq. 54 and Eq. 55.
Q„= k, A, , P „„„MW„ / RT„„, (56)
This equation is used for all slow evaporating pools of liquid spills.
27
CHAPTER V
RESULTS AND DISCUSSION
The density prediction method played an integral part in this work. The equation
used was MBWR, along with MPCS methodology. The experimental data used to
compare the density results were obtained from Hwang et al. (1986) and from Brule and
Starling (1982). The density methodology compares well with both mixture sets. The
Hwang et al. data is compared in Table 6 and Figure I, and the Brule and Starling data is
compared in Table 7.
Table6. Densit Data Com arison T [K] 273 300 340 380
Ex . -I[ cm] %AARD -II[ cm] %AARD 0. 720 0. 705 2. 08 0. 707 1. 79 0. 71 6 0. 688 3. 78 0. 690 3. 49 0. 683 0. 668 2. 20 0. 670 1. 90 0. 651 0. 632 2. 92 0. 634 2. 63
Brule and Starling (1982) give density data for different types of petroleum
reservoirs. The data is compared to both fractions based on molecular weight to see
percent difference in density ratios. The data compares relatively well. It should be
noted that although all crude compositions are different, the comparison in Table 7 is
intended to present how the pseudo-mixtures in this work compare to other crude.
Table 7. Com arison Based on Molecular Wei ht Crude Type Fraction I
MW -I [ cm % Diff. Crude Type 112 0. 705 Fraction 2
MW -II cm % Diff. 160 0. 707
Penn Wyoming Oklahoma
Iranian Iranian
123 0. 746 120 0. 764 121 0. 758 97 0. 719 119 0. 757
5. 50 7. 72 6. 98 1. 95 6. 86
Penn California Oklahoma
Arabian
153 0, 773 8. 77 162 0. 805 12. 41 148 0. 796 11. 41 159 0. 767 8. 13
08
0 75
07
~ 065
le
dl cj
06
~P dD tyt ~ Exp (Hweng 1986)
Pred Density 2
0 55
05 270 290 310 33D 370 390
Temperature [K]
Figure 1. Density Comparison.
29
The viscosity methodology is compared to a data set from Hwang et al. (1986).
The data is a function of both temperature and pressure and is given in Table 8 and
Figure 2, 3 and 4 for temperatures of 310K, 366K and 450K respectively.
Table 8. Viscosit Data Com arison (mPa. s) T (K) P (bar) Ex Crude Fraction 1 % AARD Fraction 2 % AARD
310
366
450
35 70 100 35 70 100 35 70 100
2. 88 2. 93 3. 50 1. 16 1. 21 1. 25 0. 50 0. 52 0. 55
2. 75 2. 77 2. 80 1. 08 1. 15 1. 17 0. 47 0. 47 0. 50
4. 5 5. 5
20. 0 6. 9 5. 0 6. 4 5. 8 9. 4 9. 1
2. 80 2. 82 2. 86 1. 12 1. 16 1. 18 0. 48 0. 48 0. 51
2. 8 3. 8 18. 3 3. 4 4. 1
5. 6 5. 0 8. 7 7. 3
30
3. 5
25 06 u
N
) 15
~ Exp (Herons 1966)
~Pied Fraclon1
~Pred Fraction 2
05
30 40 50 60 70 80 90 100 110
Pressure, bar
Figure 2. Viscosity Data Comparison at 310 K.
31
19
18
1. 7
91 15 0 O dl ) 14
!
~ Exp (tnwang 1986)
~Prad Fraction 1 ~ Prad Fracbon 2
13
12
30 40 50 60 70 60 90 I DD IID
Pressure, bar
Figure 3. Viscosity Data Comparison at 366 K.
32
1 OD
0. 90
D 60
e. u
0 70 43
0
, ~Prsd Pracrron1
060
050
0 40
30 40 50 60 70 60
Pressure, ber
90 110
Figure 4. Viscosity Data Comparison at 450 K.
33
The enthalpy results include a calculation for devianon from ideality. The values
for Q are given below in Table 9 as compared to the overall effect it has on the enthalpy
values. The effect of Q is minimal compared to constant pressure contribution. At this
temperature range and pressure range, the mixture behaves like an ideal solution.
Table 9. Effect of Deviation from Idealit for Enthal
317 K P 15 bar
AH (@&P)=
Q= DH=
% Effect
3. 2 x 10 -1. 7 x 10 3. 2 x 10 0. 000528
4. 4 x 10 J/mol -6. 4 x 10 J/mol
4. 4 x 10 J/mol 0. 00143
317 K P 50 bar
AH (@P)= Q=
AH= % Effect
3. 2 x 10 -4. 9 x 10 3 2 x 10 0. 001538
4. 3 x 10 J/mol -1. 3 x 10 J/mol
4. 3 x 10' J/mol
0. 003065
The average emissive evaporation rates of pseudo-mixtures were compared to the
predictions of SPILLS model. Both cases were run at same conditions. The conditions
were chosen for a hot summer day in Houston, TX. The model was run at 320K and 50
bars, set at 310K ambient temperature, D Class stabtlity and a wtnd speed of 10 m/s.
The predicted evaporation rates are at equilibrium with the surrounding, so no time ltmit
for pool formation was taken into consideration. See Appendix E for SPILL model runs.
Comparison is given in Table 10. The results are within 15%.
Table 10. Comparison of Evaporation Rates for Pseudo-Mixture with SPILLS Model
T= 320 K T~, = 310 K Eva oration (K s) S ill Area (m ) Eva oration (K m'hr)
Mixture I SPILLS Pred. % Diff
1. 90 2. 15 -13. 2 322 335 -4. 04 21. 2 23. 1 -8, 96
Mixture II SPILLS Pred. /o Diff
1. 88 2. 04 -8. 51 315 329 -4. 44 21. 5 22. 3 -3. 72
The evaporation rates of various hydrocarbons were plotted against their normal
boiling points (Cavanaugh, 1993). The pseudo-mixtures were added to that plot to show
a progressive correlation between the compounds. The results are show in Figure 5.
4 Propane
g 2O
E ol
al re 15
~ n-Butane
~ Mi xiure - I
~ Mixture - II
4 n-Pentane 4 n-Hexane
10
xt 4 n-Heptane
n-Octane n-Nonane
250 300 350
Normal aoiang Point (K)
400
Figure 5. Average Evaporation Rate Vs Chemical Normal Boiling Point.
The model was also run for one pure component, namely pentane. The reason
was to compare and evaluate the evaporation results against spill experiments done for
pentane. The data set was obtained from Kawamura and Mackay (1987). The spill
experiments were done for pentane at University of Toronto, Canada. The results of this
model are used to better stimulate actual pure compound releases, and then evaluate with
results for petroleum fractions. Also the comparison shows the flexibility of the model,
as it is able to handle between one to ten compounds. The results are show below in
Table 11.
Chemical
Table 11. Comparison of Evaporation Rates for Pentane with S ill Data at 320K in k m h
T (K) Exp. K-M Model This Work Pred '/o Diff. Pred. '/o Diff.
Pentane Pentane Pentane Pentane
274 10. 52 7. 22 278 6. 84 4. 19 280 8. 13 4 97 282 10. 41 6. 18
3 1. 4 6. 89 34. 5
38. 7 3. 82 44. 2 38. 9 4. 70 42. 2 40. 6 7. 05 32. 3
Ave. '/o Bias Abs. '/oDev.
37. 4 37. 4
38. 3
38. 3
36
CHAPTER VI
CONCLUSIONS
There are several conclusions based on the results of this work. First of all, this
work focuses on a new methodology to improve material properties to better predict
source-term results. The methodology includes improving density, viscosity, and
enthalpy correlations as they exist in the original SPILLS model and create a new
modified model. The results show predictions to be within 15% for evaporation data
compared to SPILLS model.
Recommendations
Onc of the main problems in doing source or dispersion calculations is that there
is very little experimental data to compare the results with. For dispersion modeling, the
data is limited to several major gaseous releases at specific conditions. The
rcproducibility of experiments has always been an issue since enormous logistic efforts,
including location and material quantity released, are required.
The source term model is the first step in determining dispersion results, which is
what is required ultimately. The source-term experimental data is even less sparse than
dispersion data. The data is mostly available for pool evaporation calculations, and for
pool evaporation experiments, the data seems to be focused on single component
systems.
37
There is also a definite need to collect data for the first step in source term
modeling, that is, the flashing process. This includes data for aerosol entrainment
modeling evaluation. In due course, aerosol formation is considered the most flammable
source of hazard in source term modeling. Therefore, there is a need to collect data for
fluids coming out at higher than ambient pressures and within their flammability limits,
so there can be a flashing process.
Other areas that need improvement are prediction techniques for heat of
vaporization. The AHv, r correlation is limited to low pressure situations. Another way
to approach that would be to derive an enthalpy correlation from the fundamental energy
balance accounting for liquid to vapor transfer in enthalpy.
Extension of Model
The model can also be applied to eventually predkcting aerosol. Eq. 57 best
describes a comprehensive breakdown of mass released from source term models.
(S7)
One criteria that is mcorporated into this model, but is not used is the cnteria for
estimating aerosol I'raction (Cavanaugh, 1993). This is based on the AIChE RELEASE
model as described in Cavanaugh (1993).
If Ts & Ta + 10, then f„„„~ —— 1. 0
If Ts & Ts, then f. „, „„~ — — 0. 0
If Tb & Ts & Tb + 10, then f„„„, , i = (Ts — Tb)710 (60)
38
The reason for not using this criteria is manifold. The criterion is only an
estimation technique based on linear interpolation without any experimental verification.
Also this limits the program into a Tb + 10' range for aerosol formation.
39
NOMENCLATURE
Notation
a Empirical Parameter
A Area, m'
or Empirical Constant for Various Equations
b Parameter Used in One-parameter Viscosity Correlation
or Empirical Parameter
B Parameter Used in b correlations for One-parameter Viscosity Correlation
or Empirical Constant for Various Equations
c Empirical Parameter
C Empirical Constant for Various Equations
D Diameter, m, in
or Empirical Constant for Various Equations
E Empirical Constant for Various Equations
ECN Effective Carbon Number
f Flashing Vapor Fraction
F Friction term in Energy Balance
G Empirical Function
GN Function of Y Used in MCLS Equation
H Enthalpy, J
or Mole/Mass Basis, J/mol, J/kg
40
k Boltzmann Constant, 1. 31 x 10 ' J/K
ks Mass Transfer Coefficient
I Liquid State
m Empirical Parameter
M Empirical Constant
MW Molecular Weight, g/mol
P Pressure, bar, Pa
Q Flow rate, kg/s, mol/s
R Ideal Gas Constant, 8. 314 J/mol K
t Time, s, hr
T Temperature, K, 'C, 'F
u Velocity, m/s'
v Vapor State
V Volume, cm, m, L 3 3
x Length, m
Y Function Used in MCLS Equation
Z Compressibility Factor
ct Empirical Parameter
Molecular-energy Parameter
or Roughness Factor
Orientation Parameter
Heat Capacity Deviation from Ideality, J/mol
O' ' ' Collision Integral
tl Viscosity, mPa. s, cP
p Density, kg/m, g/cm
tr Molecular-size Parameter
Binary Interaction Parameters
m Acentric Factor
Subscripts
air Air Properties
atm Atmosphere
b Boihng Point
c Critical
CE Chapman-Enskog Dilute Gas Viscosity
Cp Heat Capacity, I/mol K
D Used with Notation, C for Discharge Coefficient
e Effective Diameter, m
i, j Component Numbers
I Phase or Mixture One
II Phase or Mixture Two
g Gravity Constant, 9. 81 m/s
o Reference State
pool Pool Temperature, K
42
r Reduced
RA Rackett equation Compressibility Factor
Re Reynold's Number
Sc Schmidt Number
Sh Sherwood Number
SL Saturated Liquid
t Time in s, hr
vap Heat of Vaporization, J/mol
Superscripts
Reduced Number Property
Critical
Molecular Weight
Boiling Temperature
Acentric Factor
43
LITERATURE CITED
Beychok, M. R. , "Instantaneous Flow Rates Overstate Gas Release Determination, " Oil and Gas J„31, 80 (1997).
Bowen, P. J. and L. C. Shirvill, "Combustion Hazards Posed by the Pressurized Atomization of High-Flashpoint Liquids, " J. Loss Prev. Process Ind. , 7, 233 (1994).
Brule, M. R. and K E. Starling, "Application of Multiproperty Analysis in the Prediction of Complex-System Thermophysi cal Behavior, " AIChEAnnual Meeting, Los Angeles, November (1982),
Brule, M. R. , C. T. Lin, L. L. Lee, and K. E. Starling, "Multiparameter Corresponding- States Correlation of Coal-Fluid Thermodynamic Properties, " AICAE J. , 28, 616 (1982).
Cao, W. , K. Knudsen, A. Fredenslund, and P. Rasmussen, "Group-Contribution Viscosity Predictions of Liquid Mixtures Using UNIFAC-VLE Parameters, " Ind. Eng. Chem Res. , 32, 2088 (1993).
CAMRV Dispersion Model 1. 0, Quest Consultants Inc. , Norman, Oklahoma (1996).
Cavanaugh, T. A. , J. H. Siegell, and K. W. Steinberg, "Simulation of Vapor Emissions from Liquid Spills'*, J. Haz. Mat. , 38, 41 (1993).
Cornwell, J. , API 16 and API 25. 5 Data Sets, Quest Consultants, Norman, Oklahoma (1999).
Crowl, D. A. and J. F. Louvar, Chemical Process Safety: Fundamentals with
Applications, Prentice Hall, Englewood Cliffs, New Jersey (1990).
De Nevers, N. , Fluid Mechanics for Chemical Engineers, 2" ed. , McGraw-Hill, New York (1991).
Fleischer, M. T, SPILLS: An EvaporationtAir Dispersion Model for Chemical Spills on Land, Shell Development Company, Houston, Texas (1980).
Gas Processors Suppliers Association (GPSA), Engineering Data Book Volume I Sections 1-16, 10 ed. , Tulsa, Oklahoma (1994a).
Gas Processors Suppliers Association (GPSA), Engineering Data Book Vohtme II Sections 17-26, 10 ed. , Tulsa, Oklahoma (1994b).
44
Gray, J. A. , C. J. Brady, J. R. Cunningham, J. R. Freeman, and G. M. Wilson, "Thermophysical Properties of Coal Liquids 1. Selected Physical, Chemical, and
Thermodynamic Properties of Narrow Boiling Range Coal Liquids, " Ind. Eng. Chem. Process Des. Dev. , 22, 410 (1983).
Hanna, S. R. and P. J. Drivas, Guidelines for Use of Vapor Cloud Dispersion Models, AIChE Center for Chemical Process Safety, New York (1987).
Hanna, S. R. and D. G. Strimaitis, Workbook of Test Cases for Vapor Cloud Source Dispersion Models, AIChE Center for Chemical Process Safety, New York (1989).
Hanna, S. R. , D. G. Strimaitis, and J. C. Chang, "Evaluation of Fourteen Hazardous Gas Models with Ammonia and Hydrogen Fluoride Field Data, " J. Haz. Mat. , 26, 127 (1991).
Holder, J. A. , and J. A. Gray, "Thermophysical Properties of Coal Liquids 2. Correlating Coal Liquid Densities, " Ind. Eng. Chem. Process Des. Dev. , 22, 424 (1983).
Holditch, S. A. , B. M. Robinson, J. W. Ely, and Z. Rahim, "The Effect of Viscous Fluid
Properties on Excess Friction Pressures Measured During Hydraulic Fracture Treatments, " SPE Prod. Eng. , 2, 9 (1991).
Holland, C. D. , Fundamentals of Multicomponent Distillation, McGraw-Hill, New York
(1981).
Ilolland, C. D. , and R. G. Anthony, Fundamentals of Chemical Reaction Engineering, 2"— ed. , McGraw-Hill, New York (1989).
Hwang, S. C. , C. Tsonopoulos, and J. L. Heidman, Thermodynamic and Transport Properties of Coal Liquids, John Wiley k Sons, New York (1986).
Kawamura, P. I. and D. Mackay, "The Evaporation of Volatile Liquids, " J. Has. Mat. , 15, 343 (1987).
Lolley, C. S. , Compositional Changesin Heavy Oil
Steamflood
Simulator. Thesis. Texas AkM University, December (1995).
Mehrotra, A. K. , "A Generalized Viscosity Equation for Pure Heavy Hydrocarbons, " Ind. Eng. Chem. Res. , 30, 420 (1991a).
Mehrotra, A. K. , "Generalized One-Parameter Viscosity Equation for I, ight and Medium
Liquid Hydrocarbons, " Ind. Eng. Chem. Res. , 30, 1367 (1991b).
Mehrotra, A. K. , "Correlation and Prediction of the Viscosity of Pure Hydrocarbons, " Can. J. Chem. Eng. , 72, 554 (1994),
Mehrotra, A. K. , "Mixing Rules for Predicting the Viscosity of Bitumens Saturated with Pure Gases, " Can. J. Chem. Eng. , 70, 165 (1992).
Orbey, H. , and S. I. Sandier, "The Prediction of the Viscosity of Liquid Hydrocarbons and Their Mixtures as a Function of Temperature and Pressure, " Can. J. Chem Eng. , 71, 437 (1993).
Perry, J. H. , C. H. Chilton, and S. D. Kirkpatrick, Chemical Engineer 's Handbook, 4—
ed. , McGraw-Hill, New York (1963).
Post, L. , HGSYSTEM 3. 0: User 's Manual, Shell Research Limited, Chester, United Kingdom (1994).
Reid, R. C. , J. M. Prausnitz, and B. Poling, The Properties of Gases and Liquids, 4 ed. , McGraw-Hill, New York (1988).
Schmidt, P. F. , Fuel Oil Manual, 4'" ed. , Industrial Press, New York (1985).
Schmidt, Z. , D. R. Doty, P. B. Lukong, O. F. Fernandez, and J. P. Brill, "Hydrodynamic Model for Intermittent Gas Lifting of Viscous Oil, " J. Pet. Tech. , 3, 475 (1984).
Smith, J. M. and H. C. Van Ness, Introduction io Chemical Engineering Thermodynamics, 4 —" ed. , McGraw-Hill, New York (1987).
Stephen, K. and K. Lucas, Viscosity of Dense Fluids, Plenum Press, New York (1979).
U. S. EPA, RMP Off site Consequence Analysis Guidance, Research Triangle Park, North Carolina (1996).
Vincent, G. C. and W. B. Howard, "Hydrocarbon Mist Explosions — Prevention by Explosion Suppression, " AIChE Loss Prev. Symp. , 10, 286 (1976).
Watanasiri, M. R. Brule, and K. E. Starling, "Correlation of Phase-Separation Data for Coal-Conversion Systems, " AIChE J. , 28, 626 (1982).
Watanasiri, S. , V. H. Owens, and K. E. Starling, "Correlations for Estimating Critical Constants, Acentric Factor, and Dipole Moment for Undefined Coal-Fluid Fractions, *' Ind. Eng. Chem. Process Des. Dev. , 24, 294 (1985).
46
Wilson, G. M. , R. H. Johnston, S. C. Hwang, and C. Tsonopoulos, "Volatility of Coal Liquids at High Temperatures and Pressures, " Ind. Eng. Chem. Process Des. Dev. 20, 94 (1981).
Witlox, H. W. M. , and K. McFarlane, "Interfacing Dispersion Models in the HGS YSTEM Hazard-Assessment Package, " Atmos. Environ. , 28, 2947 (1994).
47
APPENDIX A
EQUATIONS FOR ESTIMATING CRITICAL CONSTANTS
(Reference: Watanasiri, et al. , 1985)
Critical Temperature,
ln(T, ) = — 0. 00093906T, + 0. 030950 ln(M(V) +1. 11067 ln(T, )
+ kBV(0. 078154SG ' ' — 0. 06106 1SG ' " — 0. 016943 SG) (A 1)
Critical Volume,
ln(V, ) = 80. 4479 — 129. 8038SG+ 63. 1750SG'
— 13. 1750SG'+1. 10108 1n(MlV)+42. 1958 1n(SG) (A2)
Critical Pressure,
ln(P, ) = 3. 95431+ 0. 70682(T, / V, . )
— 4 8400M1V/T, 0 15919Tb /M(V (A3)
Acentric Factor,
m = [0. 922170*10 ' T„+ 0. 507288Tb / MlV+ 382. 904 I MlV
+02420810 (Tb ISG) 02165b10 Tb bMTV+0. 1261b10 SG~M(V
+ 0. 1265*10 M)V' + 0. 2/016*10 ' SG* MlV' — 80. 6495T, "" / M(V
0 3780~10 Tb ISG ](Tb IM(V] (A4)
Reduced Dipole Moment,
/b' =100/b /(0. 5804897T„V, )"' (A5)
p = (ul/u4)+(u2*u3) (A6)
where
ul = (197. 933/MW+ 0. 039177M(V)V, /T, (A7)
u2 = 0. 318350*10 'V, +0. 956247*10 'T, — 0. 54790'10 'HVNP (A8)
u3 = — 1. 34634co + 0. 906609 ln(o)) (A9)
u4 = — 4. 85638 — 0. 013548M(V+0. 271949*10 'M/V +1. 04024 1n(M1V) (A10)
HVNP = — 10397. 5+46. 2681T, — 1373. 91T, ' +4595. 811n(T, ) (All)
49
APPENDIX B
AIR PROPERTY EQUATIONS
(Reference: Fleischer, 1980)
Absolute Viscosity,
1, 4587'" /r, poise =
T+B (B 1)
Thermal Conductivity,
6325xlQ 67'' k, ca//em — s — K =
T+245. 4x10 "" (B2)
Density (+~em ),
p =1, 293Q4x10 '"13. 5717 — Q. Q1729T+3. 676Q7x10 'T' — 2, 89775x10 'T') (B3)
Heat Capacity,
Cp, ca//g — K = 0. 0686042(3, 5915+7, 04474x10 'T+1, 39654x10 'T') (B4)
Thermal Diffusivity,
rr, cm' / sec = k / pCp (B5)
50
APPENDIX C
SOURCE MODEL CALCULATIONS
Model Breakdown
Fraction 1
T= 320 P= 50 P vap = 11. 4 Density = 6. 56E-01 density = 7. 10E-02 Viscosity = 6. 02E-04 2 = 1. 05E+00
Fraction 2 320 50
12. 1
4. 60E-01 7. 03E-02 6. 06E-04 1 05E+00
K
bar bar mol/m'
kg/m3 N*s/m
Calculation of Enthalpy as a Function of Temperature Cp = 1. 92E+05 2. 65E+05 J/mol K
DH (@P)= 3. 27E+07 4. 44E+07 J/mol
corr DH = -4. 76E+02 -1. 30E+03 J/mol
DH = 3. 27E+07 4. 44E+07 J/mol
Source/Orifice Area D = 0. 5 0. 5 in
0. 0127 0. 0127 m
6L= 1 1 m
AO = 0. 0001267 0. 00012668 m2
Discharge Coeffient vis = 6. 02E-04 den = 6. 56E-01 den = 7. 10E-02 velocity = 6 23E+00 Nre = 5. 98E+02 e = 1 BOE-03
6. 06E-04 4. 60E-01 7 03E-02 6. 20E+00 6 01E+02 1 BOE-03
N*s/m'
mol/m'
kg/m'
m/s
Flashing Process
Mass= 28 fraction = 0, 543
2. 8 0. 532
kg/s
Pool Length NSc = 2. 94E+04 Fraction Q 1. 2796 Dm = 1 OOE-04 L= 10. 12
2. 94E+04 1 3104 kg/s
1 OOE-04 m2/s 1001 m
les 310
1. 46E-05 110. 4
33. 4551 34 3. 5716787 -1. 73E-02 3. 68E-05 -2. 90E-08 1. 29E-03 1. 14E-03
3. 5915209 7. 04E-04 1. 40E-06
0. 0686042 2. 71E-01 6 33E-06
245. 4 12
6. 459 E-05 2. 1 0E-01 2. 94E+00
YIS = Aden =
B den =
C den D den den 0= den = A cp =
Bcp= Ccp= R= cp =
A cond =
B cond =
C cond =
cond =
diffusivity kin vis =
Air Propert T air= A vis =
B vis =
poise
g/cm3
cal/g-K
cal/cm-s-K cm2/sec m2/s
Evaporation Rate 7 pool =
Pool A=
R= u =
kin ws =
dla =
Nsh =
kg =
Qe= Q flux =
320 322
8. 314 10
2. 94E+00 10. 12
-17336. 01 -1. 71 E-01 -2. 1 5E+00 2. 31E+01
320 315
8. 314 10
2. 94E+00 10. 01
-17336. 178 -1. 73E-01 -2. 04E+00 2. 23E+01
K
m2 J/mol. K
m/s
m2/s m2/s
m/s
kg/s
kg/m2. h
APPENDIX D
VISUAL BASIC SUBROUTINES
Mixture Density MBWR Equation of State
Function Density(T, P, xl, x2, x3, x4, x5, x6, x7, x8, x9, x10, xi I) Dim i, j As Integer Dim x(1 To 11) As Single Dim Densitycij(1 To 11, 1 To 11), Densityci(1 To 11) As Single Dim sigmaij(1 To 11, I To 11), sigmai(1 To 11) As Single Dim eij(1 To 11, 1 To 11), ei(1 To 11) As Single Dim oij(1 To 11, I To 11), oi(1 To 11) As Single Dim Erlij(1 To 11, I To 11) Dim Er2ij(1 To 11, 1 To 11) x(1) = xl x(2) = x2 x(3) = x3 x(4) = x4 x(5) = x5 x(6) = x6 x(7) = x7 x(8) = x8 x(9) = x9 x(10) = x10 x(11) = xi 1
For i = I To 11 For j = I To 11 Densityci(i) = Worksheets("Mixing VB"). Cells(i + 6, 7). Value sigmai(i) = Worksheets("Mixing VB"). Cells(i + 6, 10). Value
ei(i) = Worksheets("Mixing VB"). Cells(i+ 6, 11). Value oi(i) = Worksheets("Mixing VB"). Cells(i+ 6, 11). Value Erl ij(i, j) = Worksheets("Mixing VB"). Cells(i + 22, j + 2). Value Er2ij(i, j) = Worksheets("Mixing VB"). Cells(i + 22, j + 2). Value Next j Next i
For i = I To 11 For j = I To 11 sigmaij(i, j) = Erlij(i, j) * (sigmai(i) * sigmai(j)) 0. 5
eij(i, j) = Er2ij(i, j) * (ei(i) * ei(j)) ~ 0. 5
oij(i, j) = 0. 5 * (oi(i) + oi(j)) Next j
Next i For i = I To 11 For j = I To 11 sigmax = sigmax+ x(i) ~ x(j) ~ sigmaij(i, j) ~ 4. 5 ex = ex + x(i) ~ x(j) * eij(i, j) * sigmaij(i, j) ~ 4. 5 ox = ox+ x(i) * x(j) * oij(i, j) * sigmaij(i, j) 3. 5 Next j Next i
sigmax = sigmax ~ (I /4. 5) ex = ex ~ sigmax ~ 4. 5 ox = ox * sigmax ~ 3. 5 'CSM-3PCS-MBWR E parameters El = 1. 45907 + ox * 0. 32872 E2 = 4. 98813 + ox * -2. 64399 E3 = 2. 20704 + ox * 11. 3293 E4 = 4. 86121 + ox * 0 E5 = 4. 59311 + ox * 2. 79979 E6 = 5. 06707+ ox * 10. 3901 E7 = 11. 4871 + ox * 10. 373 E8 = 9. 22469 + ox * 20. 5388 E9 = 0. 094624 + ox " 2. 7601 E10 = 1. 48858+ ox * -3. 11349 El I = 0. 015273 + ox * 0. 18915 E12 = 3. 51486+ ox * 0. 9426 ' Iterate for density and Z R = 83. 14 'em~3*bar/mol ~K
k = 1. 3 IE-23 Z = 0. 333 5 Zguess = Z Density = P / (R * T) Tstar = k * T / ex densitystar = Density * sigmax ~ 3 Z = I + densitystar * (El — E2 / Tstar - E3 / Tstar ~ 3 +
E9/Tstarx4-Ell /Tstar 5)+ densitystar 2 * (E5- E6/ Tstar - E10/ Tstar 2) + densitystar ~ 5 * (E7/ Tstar + E12 / Tstar 2) + E8 * densitystar ~ 2 / Tstar 3 * (I + E4 * densitystar 2) * Exp(-E4 * densitystar 2)
Error = Abs(Zguess - Z) If Error &= 0. 001 Then Go To 10 GoTo 5 10 Density = P / (Z * R * T) Density =P/(Z * R * T) End Function
54
Pure Nitrogen Density (MBWR Equation of State)
Function DensityN2(T, P, x I) Dim Density As Single Dim sigma As Single Dim e As Single Dim o As Single Dim Erl As Single Dim Er2 As Single Density = Worksheets("Mixing VB"). Cells(7, 7). Value sigma = Worksheets("Mixing VB"). Cells(7, 10). Value e = Worksheets("Mixing VB"). Cells(7, 11). Value o = Worksheets("Mixing VB"). Cells(7, 11). Value Erl = 1
Er2 = 1
sigma = Erl * (sigma ' sigma) 0. 5 e = Er2 * (e * e) x 0. 5 o = 0. 5 * (o + o) sigmax = sigmax+ x * x * sigma 4. 5 ex = ex+ x ¹ x * e ' sigma x 4. 5 ox = ox + x ¹ x * o " sigma x 3. 5
sigmax = sigmax x (1 / 4. 5) ex = ex * sigmax 4. 5
ox = ox * sigmax 3. 5 'CSM-3PCS-MBWR E parameters El = 1. 45907+ ox " 0. 32872 E2 = 4. 98813 + ox ' -2. 64399 E3 = 2. 20704 + ox * 11. 3293 E4 = 4. 86121 + ox " 0 E5 = 4. 59311 + ox * 2. 79979 E6 = 5. 06707+ ox * 10. 3901 E7 = 11. 4871 + ox ¹ 10. 373 E8 = 9. 22469+ ox * 20. 5388 E9 = 0. 094624 + ox * 2. 7601 E10 = 1. 48858 + ox * -3. 11349 El 1 = 0. 015273 + ox * 0. 18915 E12 = 3. 51486 + ox * 0. 9426 ' Iterate for density and Z R = 83. 14 'cm~3¹bar/mol¹K k = 1. 31E-23 Z = 1. 1
5 Zguess = Z Density = P / (R " T) Tstar = k* T/ex
densitystar = Density * sigmax ~ 3 Z = I + densitystar * (El - E2/Tstar- E3/Tstar 3+
E9 / Tstar 4 - El I / Tstar 5) + densitystar 2 * (E5- E6 / Tstar - E10 / Tstar ~ 2) + densitystar ~ 5 * (E7 / Tstar + E12 / Tstar 2) + E8 * densitystar 2 / Tstar ~ 3 * (I + E4 * densitystar 2) * Exp(-E4 " densitystar ~ 2)
Error = Abs(Zguess — Z) If Error &= 0. 001 Then Go To 10 GoTo 5 10 DensityN2 = P /(Z * R* T) End Function
Viscosity for Nitrogen
* G)
GN *
Function ViscosityN2(T, P, DensityN2) MW = Worksheets("Mixing VB"). Cells(6, 3). Value Tc = Worksheets("Mixing VB"). Cells(6, 4). Value Pc = Worksheets("Mixing VB"). Cells(6, 5). Value Densityc = Worksheets("Mixing VB"). Cells(6, 7). Value gamma = Worksheets("Mixing VB"), Cells(6, 12). Value ' MCLS E Parameters EO = I - gamma ' 0. 2756 El = 17. 4499 + gamma * 34. 0631 E2 = -0. 000961125 + gamma * 0. 00723459 E3 = 51. 0431 + gamma * 169. 46 E4 = 4. 66798 - gamma ' 39. 9408 E5 = 3. 76241 + gamma * 56. 6234 E6 = -0. 605917 + gamma s 71. 1743 E7 = 21. 3818 - gamma * 2. 11014 E8 = 1. 00377 + gamma * 3. 13962 E9 = -0. 0777423 - gamma * 3. 58446 E10 = 0. 317523 + gamma * 1. 15995 ' MCLS Equation densitystar = 0. 3189 * DensityN2 / Densityc Tstar = 1. 2593 * T/ Tc YY = 3. 14 * dcnsitystar /6 G = (1 - 0. 5 * YY) / (1 - YY) ~ 3 GN = (El * (1 — e ~ (-E4 * YY)) / YY + E2 * G * e ~ (E5 * YY) + E3
/ (El ' E4+ E2 + E3) ETstar = E8 + E9 / Tstar + E I 0 / Tstar ~ 2 Ljones = 1. 16145 / Tstar 0. 14874 + 0. 52487 / e (0. 7732 * Tstar)
+ 2. 16178 / e (Tstar * 2. 43787) - 0. 0006435 * Tstar * Sin(18. 0323 * Tstar ~ -7. 27371 - P)
sigma = (0. 3189 * 1E+24 / (Densityc * 6. 02252E+23)) (1 / 3) viscosityce = 26. 693 * (MW * T) 0. 5 / Ljones / sigma 2 ViscosityN2 = EO * viscosityce * (1 / GN+ E6 " YY) + E7 * YY 2 *
e ET star End Function
57
Heat capacity Macro
Function Cp(T, Comp) '[J/mol*K] Dim cpA(l To 11), cpB(1 To 11), cpC(1 To 11), cpD(1 To 11) As Single Dim cpi(1 To 11) As Single For i = 1 To 11 cpA(i) = Worksheets("Mixing VB"). Cells(i + 56, 3). Value
cpB(i) = Worksheets("Mixing VB"). Cells(i + 56, 4). Value cpC(i) = Worksheets("Mixing VB"). Cells(i+ 56, 5). Value cpD(i) = Worksheets("Mixing VB"). Cells(i + 56, 6). Value Next i
For i =1 To 11
cpi(i) = cpA(i) + cpB(i) * T + cpC(i) * T ~ 2 + cpD(i) * T ~ 3 Next i
Cp = cpi(Comp) * 1000 End Function
Constant Pressure Enthalpy
Function Int Cp(T, Comp) '[J/mol "K] Dim cpA(1 To 11), cpB(1 To 11), cpC(l To 11), cpD(1 To 11) As Single Dim Int Cpi(1 To 11) As Single For i = I To 11 cpA(i) = Worksheets("Mixing VB"). Cells(i + 56, 3). Value cpB(i) = Worksheets("Mixing VB"). Cells(i + 56, 4). Value cpC(i) = Worksheets("Mixing VB"). Cells(i + 56, 5). Value cpD(i) = Worksheets("Mixing VB"). Cells(i + 56, 6). Value Next i
For i = I To 11 Int Cpi(i) = cpA(i) " T + (I / 2) * cpB(i) " T ~ 2 +
(I / 3) * cpC(i) * T ~ 3 + (1 /4) ~ cpD(i) * T ~ 4 Next i
Int Cp = Int Cpi(Comp) * 1000 End Function
Enthalpy Correction Macro
Function Omega(P, T, Z, yl, y2, y3, y4, y5, y6, y7, y8, y9, y10, yl I) Dim yi(l To 11) As Single Dim Tci(l To 11) As Single Dim Pci(1 To 11) As Single Dim Vci(1 To 11) As Single Dim Zci(1 To 11) As Single Dim wi(I To 11) As Single Dim kij(1 To 11, I To 11) As Single Dim ai(1 To 11), A(1 To 11) As Single Dim bi(1 To 11), B(1 To 11) As Single Dim mi(1 To 11), alpha(1 To 11), dalpha dT(1 To 11) As Single R = 83. 14 'cm 3 "bar/mol*K
yi(1) = yl yi(2) = y2
yi(3) = y3 yi(4) = y4 yi(5) = y5 yt(6) = y6 yi(7) = y7 yi(8) = yg
yi(9) = y9 yi(10) = y10 yi(11) = yl I
For i = 1 To 11 Tci(i) = Worksheets("Mixing VB"). Cells(i + 5, 4). Value Pci(i) = Worksheets("Mixing VB"). Cells(i + 5, 5). Value Vci(i) = Worksheets("Mixing VB"). Cells(i+ 5, 6). Value Zci(i) = Worksheets("Mixing VB"). Cells(i + 5, 8). Value wi(i) = Worksheets("Mixing VB"). Cells(i + 5, 9). Value Next i For i = 1 To 11 For j = 1 To 11 kij(i, j) = Worksheets("Mixing VB"). Cells(i + 22, j + 2). Value Next j Next i For i = 1 To 1] ai(i) = 0. 42747 * R ~ 2 ~ Tci(i) ~ 2 / Pci(i) mi(i) = 0. 48 + 1. 574 * wi(i) - 0. 176 * wi(i) 2 alpha(i) = (1 + mi(i) " (1 - (T / Tci(i)) 0. 5)) 2 dalpha dT(i) = mi(i) * T ~ (-1 / 2) * Tci(i) (-1 / 2) * (1 + mi(i) '
(1 - (T / Tci(i)) (1 / 2))) A(i) = ai(i) 0. 5 * alpha(i) 0. 5/(R* T) bi(i) = 0. 08664 * R ' Tci(i) / Pci(i) B(i) = bi(i) / (R ' T) Next i
60
Mixing Rules
For j = 1 To 11 For i = I To 11 alpha2 = alpha2 + yi(i) s alpha(i) dalpha dT2 = dalpha dT2+yi(i) * dalpha dT(i) AA2 = AA2 + yi(i) * yi(j) " A(i) 6 A(j) * (1 — kij(i, j)) BB = BB + yi(i) * B(i) Next i
Next j Omega = R* T" (Z - 1)+ R * T * AA2/BB s (T/ alpha2 * dalpha dT2 - 1) * Log(1+ BB*P/Z) Omega = Omega / 10 End Function
Discharge velocity calculations (SI units)
Function DischargeVel(NRe, Density, viscosity, L, e, D) ' ambient conditions Patm = 1470000 ' SI units P = P ~ 100000 ' SI units ' Initial velocity CD = 0. 611 vguess = CD ~ ((2 * P - Patm) / Density) ~ 0. 5 5 v = vguess ' Wood's approximation method ' e = roughness A = 0. 0235 * (e / D) ~ 0. 225 + 0. 1325 * (e / D) B = 22 * (e / D) ~ 0. 44 C = 1. 62 * (e / D) ~ 0. 134 Friction= 4" (A+ B *NRe (-C)) * L* v 2/D/2 v = (2 * (Friction+ (P - Patm) / Density)) ~ 0. 5 Error = Abs(vguess - v) If Error &= 0. 001 Then Go To 10 GoTo 5 10 DischargeVel = (2 * (Friction + (P - Patm) / Density)) 0. 5 End Function
APPENDIX E
SPILLS MODEL PRINTOUTS
SPILL input file TITLE Mixturel input file for SPILL
RESERVOIR TRES = 46. 9 PRES = 15. 0
VRES = 100. 0 MRES = 40. 0 *
* RESERVOIR DATA * Storage/reservoir temperature (C). * Reservoir (absolute) pressure (atm).
If -1. 0, SPILL uses the mixture saturation pressure assuming all compounds are in liquid
* state. User MUST specify SPECIES keyword to use this option.
* Reservoir volume (m3). Reservoir mass contents jtonnes).
GASDATA WATERPOL= 0. 0000 CPGAS = 72. 95 MMGAS = 44. 10 HEATGR = 32. 37 SPECIES = MIXTURE1
312. 9 — 6. 823
* J/MOLE/C KG/KMOLE
1. 0000 105. 0 1. 739
(pollutant = dry pollutant (aerosol), water] water in pollutant (mole fraction) specific 'neat of dry pollutant molecular mass of dry pollutant heat group (used for HEGADAS link only)
10 1. 7239E+04, 369. 9 , 51. 91 -2. 146 , — 1. 416 , 49. 10 , 586. 8
PIPE DEXIT = 0. 0127
* PIPE EXI'I — P) ANE (CHOKE-8'RUNT) CONDI TONS * (Effect ve) release orifice diameter (m).
AMBIENT CONDITIONS AIP, PRESS = 1. 00
* I'ollowing parameters between ambient atmo TATM = 36. 9 QSQLAR = 300. 0 EMISS =- 0. 8
* ATMOSPHERIC AMBIENT CONDITIONS Atmosphere pressure ar. release height (atm).
are used for calculation of heat transfer sphere and reservoir
* Atmosphere temperature (degC) Solar heat flux (directly from the sun) (W/m2)
* Emissi. vity of reservoir surface ( —
)
TERMINAT
TLST MLST LLST PLST RLST
— 1. 0 — 1. 0 — 1. 0 — 1. 0 — 1. 0
* RESERVOIR RELEASE TERMINATION CRITERIA SPILL ignores criteria set to — 1. 0
* Last required elapsed time after release start (s) Last required reservoir mass content (tonnes)
* Last required reservoir liquid molefraction (3) * Last required reservoir pressure (atm) * I, ast required reservoir mixture density (kg/m3)
STEADY STATE TIME EVAP AREA
22. 31 1. 905 332. 0
* Time ro * Average * Surface * Setting
Steady Stat. e jmin) emissive evaporation rate of pool(kg/s) area over whi. ch heat flux occurs (m2) AREA to 0. 0 set. heat transfer to 0. 0
SPILL input file =======================
TITLE Mixture2 input file for SPILL
RESERVOIR TRES PRES
VRE8 MRES
46. 9 15. 0
100. 0 40. 0
* RESERVOIR DATA * Storage/reservoir temperature (C).
Reservoir (absolute) pressure (atm). * If -1. 0, SPILL uses the mixture saturation
pressure assuming all compounds are in liquid * state.
User MUST specify SPECIES keyword to use this option.
* Reservoir volume (m3). * Reservoir mass contents (tonnes).
GASDATA WATERPOL= 0. 0000 CPGAS = 72. 95 MMGAS = 44. 10 HEATGR = 32. 37 SPECIES = MIXTURE2
323. 9 — 6. 925
J/MOLE/C * KG/KF)OLE
1. 0000 106. 7
1. 979
[pollutant = dry pollutant (aerosol), water) water in pollutant (mole fraction) specific heat of dry pollutant molecular mass of dry pollutant heat group (used for HEGADAS link only)
10 1. 9279K+04, 366. 4 , 43. 98 — 2. 647 , — 1. 416 , 46. 16 , 646. 8
PIPE DEXIT 0. 0127
* PIPE EXIT — PLANE (CHOKE-FRONT) CONDITIONS * (Effective) release orifice diameter (m).
AMBIENT CONDITIONS AIRPRESS = 1. 00
* Following parame * between ambient
TATM = 36. 9 QSOLAR = 300. 0 EMISS = 0. 8
* ATMOSPHERIC AMBIENT CONDITIONS * Ats:osphere pressure at release heigh) (atm).
ters are used for calculation of heat transfer atmosphere and reservoir
* Atmosphere temperature (degC) * Solar heat flux (directly rom (. he sun) (N/m2) * Emissivity of reservoir surface (
— )
TERMINAT
TLST MLST LLST PLST RLS'I'
— 1. 0 — 1. 0 — 1. 0 — 1. 0 -1. 0
RESERVOIR RELEASE TERMINATION CRITERIA SPILL ignores criteria set to — 1. 0
* Last required elapsed time after release start (s) * Last required reservoir mass content (tonnes) * Last required reservoir liquid molef action * Last recurred reservoir pressure (atm) * Last required reservoir m xture density (kg/m3)
STFADY STATE TINE = 23. 67 EVAP = 1. 892 AREA = 315. 0
* Time to * Average * Surface * Setting
Steady State (min) emiss ve evaporation rate of pool(kg/s) area over which heat flux occurs im2) AREA to 0. 0 set heat transfer to 0. 0
VITA
Irfan Yusuf Shaikh was born January 6'", 1974, in Karachi, Pakistan. He grew up
in Karachi, Pakistan and moved to Houston, Texas in 1989 where his family relocated.
He graduated from Northland Christian High School in 1992. Irfan received his B. S in
chemical engineering from Texas A&M University in 1996. He began his M. S.
program at Texas A&M University the field of Chemical Engineering in 1997. He has
worked for a couple of professional internships related to field of study, namely at EQE
International in Houston, Texas and at Wilfred Baker Engineering in San Antonio,
Texas. He finished his M. S. in chemical engineering from Texas A&M in 1999.
Permanent Address
15118 Dawn Meadow
Houston, TX 77068
(281)-444-3110
Irfan Shaikh@hotmail. corn