- Email: [email protected]
The effect of nonlinear investment function on the optimum structure of the petrochemical industry
Shorter
1588
Communications
c
8.0
talc exp tab 1 2 3
~CnlC [mPasl
t
tiD
related to component calculated value experimental value tabulated value related to component related to component related to component
C (Na,CO,)
1 (or H,O) 2 (or the basic solution 3 (or the basic solution
2) 3)
REFERENCES
5.0
A., Peev, G. and Elenkov, D., 1971, On the interfacial Verfahrensrechnik 5, area in floating bed contactors. 340-342. Kudra, T. and StrumiIio. C., 1975, Wymiana masy w procesie absorpcji z reakcja chemiczna w trbjfazowym zloiu fluidalnym. Ini. Chem. 5, 809-822. Palat?, Z., 1987, Viskozita vodn?ch roztokd NaOH/ Na,CO,. Chemick$ P&m. 37, 6&70. Skoczylas, A. and Szust, I., 1984, Determination of the effective interfacial area in gas-liquid systems in mechanical thin-layer apparatus. II. Limiting conditions for the application of the Danckwerts model and physico-chemical data required for design calculations. In?. Chem. Proc. 4, 729-743. Strumitto, C. and Kudra, T., 1977, Interfacial area in threephase fluidized beds. Gem. Engng Sci. 32, 229-232. Skubla. P., 198 1, Viscosity of binary and ternary liquid nonelectrolyte mixtures. Derivation of correlation equations. Coil. Czech. them. Commun. 46, 329-339. Timmermans, J., 1960, The Physico-chemical Constants of Einary Systems in Concentrafed Solutions 3. Interscience, New York. Wokniak, M. and Qstergaard, K., 1972, An investigation of mass transfer in a countercurrent three-phase fluidized bed. Chem. Engng Sci. 28, 167-171. Kosev,
4.0
3.0
2.0
1 .o 1.0
2.0
3.0
4.0
50
6.0
7.0
-
8.0
~,,pimPasl
Fig. 1. Comparison of experimental values of dynamic viscosity of aqueous NaOH/Na,CO, solutions with the values calculated from eq. (1).
P 4
ternary interaction density, kg m- 3 volume fraction
Subscripts A B
related to component related to component
PI23
ChenWaf Enginewing Scienre, Printed in Great Britain.
Vol.
coefficient,
44, No.
mPa s
A (H,O) B (NaOH)
7, pp. 1588-1591.
The effect of nonlinear
(Receioed
1989.
OXI 2509/89 83.CQ+O.O0 Q 1989 Pergamon Press ptc
investment function on the optimum petrochemical industry 3 October
1988; accepted
INTRODUCTION
There have been various attempts to model the intermediate chemicals industry. The philosophy for the development of a dynamic model of the intermediate chemicals industry has been presented (Rudd, 1975). Stadtherr and Rudd (1976, 1978) devised and expanded a static model of industrial development utilizing the criterion of minimum feedstock consumption. Stadtherr (1978), Afshar et al. (1981), Afshar and Rudd (1981) aind Rudd et al. (1981) extended the model for long-range planning studies, and contributed to the system analysis of the petrochemical industry by including price projections and technological developments. The structure of the industry satisfying the multiobjective criteria of minimum availability change, lost work and carbon consumption has been sought by Sophos et al. (1980). Multiobjective analysis has been extended by Afshar and Yang (1985) to determine the optimum structures for minimum
22 December
structure
of the
1988)
cost and least gross toxicity of chemical pro’duction. The relationship between short- and long-range development objectives are investigated by comparing the optimal system structures obtained with single- and multistep optimizations by Sokic and Stevancevic (1983). Most recently Sigurdsson and Rudd (1988ax) formulated a model that aids in studying the interactions in world trade of petrochemicals and its effect on individual petrochemicals worldwide. All of the above studies have assumed a linear variation of the investment cost with the plant capacity. Santiago et nl. (1986) assumed this variation to b-enonlinear (in the form of a power-law function). The nonlinearity can be obviated by a linearization procedure. Earlier, Jimenez et al. (1982) took into account a nonlinear investment fuqction in their study of the Mexican petrochemical Industry. The objective of the present study is to extend the integrated model developed by Rudd et ol. (1981) to cases for
Shorter Communications which the investment cost varies with the plant capacity in the form of a power-law function. The linearization procedure devised by Santiago et al. (1986) is adopted. A specific supply+lemand environment, price structure and cost data base is gssumed. THE
MODEL
AND
THE
DATA
function
cost =
5 P,F, + 5 CfXj i-1 i= 1 -
is minimized
2
t= 1
Hi(Q,-
IJ -= _ II3
BASE
The adopted model is the integrated model described in detail by Rudd et al. (1981). According to this model feedstocks enter the industry from a limited exogeneous supply, generally as by-products from the energy industries. These feedstocks enter a network of chemical processes to be converted to intermediate and final products. The model seeks out production capacities such that the objective
total production
1589
the first case the investment cost ofthe processes are assumed to vary linearly with the plant capacity. In the second case the investment cost of the processes is assumed to vary with the plant capacity in the form of a power-law function:
oil
(1)
subject to the constraints
xj (1 __
\A
K .
B/
K usually varies from 0.6 to 0.9 in the petrochemical industry. In our case K is taken to be 0.75. The variation of investment cost with the plant capacity in the form of eq. (6) introduces a nonlinearity to the objective function. In the present work the linearization method developed by Santiago et al. (1986) has been used to simplify the solution. The linearization method is essentially an iterative technique. Convergence on process capacities was obtained after seven iterations. During solution plant capacities of less than 10,000 tons/year were eliminated to simplify the problem. The structure of the industry with the linear objective function and the nonlinear one are shown in Ttible 2. Comparison of the results shown on Table 2 indicate the following:
M
Fi+
aiJXj=Qi
1 j=
(2)
I
F,
(3)
X,
(4)
Di< Qt.
(5)
In the above expressions Fi and Di are the quantities of feedstocks entering the process network and the demand quantities, respectively. Pi and Hi are chemical prices and heating value prices for chemical i, respectively. Cr represents utilities, investment, and labor-related costs as well as the fixed costs associated with the raw materials portion of the process such as catalysts. additives and fillers. Within the specified process capacity limits Bi and feedstock supply constraints Si, the model identifies processes to operate at levels Xi, such that chemicals are produced in quantities Qi_ aij are coefficients giving the amount of chemicals consumed or produced per unit production of processj. One has to note that any surplus chemicals, Qi--Di, are credited only for their heating value. Equations (1) (5) describe a linear programming problem. The problem is solved with TEMPO, which is a standard library package. The chemicals and processes, with one exception, are the ones given by Rudd et al. (1981). In the present study catalytic reforming of naphta to produce aromatics is included in the process list. Thus the model considers 131 chemicals and 183 processes. In the present study data related to the Turkish petrochemicals industry is utilized. The exogeneous demand for intermediate chemicals are given in Table 1. Heating value prices are those reported in Rudd et al. (1981) escalated to 1987 by utilizing the Nelson cost index. in the Coefficients aij and C: are the ones reported technology catalog by Rudd et al. (1981). The utility cost figures of 1977 are escalated to 1987 by using the domestic fuel oil price. The investment cost for each process is carried from 1977 to 1987 by the Marshall and Swift Equipment Cost Index. The yield and cost data for the catalytic reforming of naphta to produce aromatics are obtained from the industry (Kartal, 1988).
RESULTS
AND
DISCUSSION
In the present study it is assumed that only naphta is available as a major feedstock. Its price is obtained from the domestic suppliers as $l48/ton. Two cases are considered. In
(I) In the nonlinear case the total production cost of the industry is 16% larger. (2) The consumption of benzene by the industry is larger. The reason is that the reference plant capacity of process 37 (124,000 tons/year) is smaller than the selected plant capacity by the model (142,720 tons/year), and this causes a reduction in the investment cost coefficient in case 2. (3) The investment cost coefficient of the p-xylene-based dimethyl terephthaiate process 72 is higher than that of process 73. As a result the model prefers to produce all dimethyl terephthalate from process 73. (4) In the case of ethylene glycol the model again selects the process with a smaller cost coefficient. (5) The naphta-based hydrogen process is eliminated from the process list because of its smallcapacity. This leads to the acceptance of the sodium chloride based chlorine process (60) in the model to supply the required hydrogen for the production of cyclohexane (66). The reason for the production of vinyl chloride from ethylene (175) is the production of chlorine (60) in the model, since chlorine is one of the major raw materials of process 175. CONCLUSIONS
Major differences in the optimum structure of the petrochemicals industry occur when the investment cost is allowed to vary nonlinearly with the plant capacity in the form of a power-law function. For the specific problem studied in the
Table
1. Exogeneous
demand for intermediate Turkey
Chemical Acrylonitrile Benzene Butadiene Caprolactam Dimethyl terephthalate Ethylene Ethylene glycol Formaldehyde (100%) Phenol Phthalic anhydride Propylene (chemical grade) Styrene Terephthalic acid {fiber grade) Vinyl chloride
chemicals
Demand values (metric tons/year) 132,000 29,000 73,000 26,000 105,000 334,000 132,000 73,630 15,620 34,000 123,000 68,100 70,000 278,300
in
Shorter
1590 Table
2. Impact
of the nonlinear
Selected 15. 23. 33. 37. 38. 42. 56. 60. 65. 66. 72. 73. SO. 86. 92. 93. 94. 96. 99. 108. 113. 119. 130. 134. 141. 144. 146. 153. 154. 155. 161. 162. 165. 166. 175. 176. 177.
behavior
of the objective function (metric tons/year)’
process
Acetylene from naphtha Acrylonitrile from propylene Ammonia from naphtha Benzene from naphtha Benzene from toluene Butadiene from n-butylenes Caprolactam from cyclohexane Chlorine from sodium chloride Cumene from benzene Cyclohexane from benzene Dimethyl terephthalate from p-xylene Dimethyl terephthalate from terephthalic Ethylbenzene from benzene Ethylene from naphtha Ethylene dichloride from ethylene Ethylene glvcol from ethylene oxide Ethilene &co1 from ethilene Ethylene oxide from ethylene Formaldehyde from methanol Hydrogen from naphtha Isobutylene from butenes Isoprene
from
Communications
pentenes
t Process
numbers
refer to those given in Table
present work it is found that the production cost of the industry is 16% larger in the nonlinear case compared to the linear one. This is because the demand values for specific chemicals are rather low and some of the plant capacities are lower than those corresponding to the base case. TijRKER NURTEN
GijRKAN KARTAL
Department of Chemical Engineering Middle East Technical University 06531 Ankara, Turkey
REFERENCES Afshar, S. F., Maisel, D. S., Rudd, D. F., Trevino, A. A., and Yuan, W. W., 198 I, Advances in petrochemical technology assessment. Chem. Engng Sci. 36, 1487-1511. Afshar, S. F. and Rudd, D. F., 1981, The economic impact of new chemical technology. Chem. Engng Sci. 36,1421-1425. Afshar, S. F. and Yang, J. C., 1985, Designing the optimal
2 of Afshar
of the industry Nonlinear investment function case
59,867 132,000 71,094 118,441 2837 73,000 26,000
40,248 132,000 71,139 142,720
63,494 68,100
acid
structure
Linear investment function case
21,087 23,660 44,350 60,650 78,315 521,377 230,863 97,950 34,050 85,217 73,630 1855 74,188 63,958 126,294 29,945 15,620
acid
Methanol from carbon monoxide Methyl ethyl ketone from n-butylenes Phenol from cumene Phenol from benzene Phthalic anhydride from o-xylene Styrene from dehydrogenation of ethylbenzene Styrene with ethylbenzene by hydroperoxide Sulfuric acid from sulfur Synthesis Gas (Hz : CO = 3 : I) from coal Synthesis Gas (HZ : CO = 3 : 1) from residual oil Terephthalic acid, fiber grade from crude terephthalic Terephthalic acid crude from p-xylene Vinyl chloride from ethylene Vinyl chloride from ethylene dichloride Vinyl chloride from acetylene
on optimal
37,130 111,541 861 70,ooo 124,772
139,074 139,226
73,000 26,000 55,207 23,660 105,000 77,634 557,997 156,367 132,000 114,840 73,630 79,399
77,069 123,633 39,312 36,164 76,510 68,100 36,678 110,034 70,000 163,800 90.503 94,197 93,600
et al. (1981).
structure of the petrochemical industry for minimum cost and least gross toxicity of chemical production. Chem. Engng Sci. 40, 78 l-797. Jimenez, A., Rudd, D. F. and Meyer, R. R., 1982, A study of the development of the Mexican petrochemical Industry. Comput. &em. Engng 6, 219-229. Kartal, N., 1988, Modelling and planning the Turkish pctrochemical industry. MS. Thesis, Middle East Technical University, Ankara. Rudd, D. F., 1975, Modelling the development of the intermediate chemicals industry. Chem. Engng J. 9, l-20. Rudd, D. F., Afshar, D. F., Trevino, A. A. and Stadtherr, M. A., 1981, Petrochemical Technology Assessment. John Wiley, New York. Santiago, M. D., Iglesias, 0. A. and Paniagua, C. N., 1986, Optimal techncilogy paths for chemical industry production. Comput. them. Engng 10,421-431. Sigurdsson, M. and Rudd, D. F., 1988aq World-scale model predicts petrochemical trends: Parts 1, 2 & 3. Hydrocarb. Process. 67, No. 6: 9XB-98N; No. 7: 34E-34L; No. 8: 5OE-50L.
Shorter
Communications
Sokic, M. and Stevancevic, D., 1983, The optimal structure of the system of the petrochemical industry. Chem. Enyng Sci. 38. 265-273. Sophos, A., Rotstein, E. and Stephanopoulos, G., 1980, Multiobjective analysis in modeling the petrochemical industry. Chem. Engng Sci. 35, 2415-2426.
Chemical Enginecr~ny Science, Prmted an Great Bntain.
Vol. 44, No
7. pp.
1591bl593.
mass transfer? to rotating
INTRODUCTION
There is an increasing interest in electrochemical techniques for various applications in the chemical industry. One of the several steps involved in an electrochemical reaction is the transfer of a discharging ion/compound to the working electrode. When the mass transfer step is the slowest among the various steps, the rate of the electrochemical reaction is solely determined by the solid-liquid mass transfer rate. This situation is ofrelevence in both laboratory research work and industrial applications Cl, 23. In the former case, to obtain the intrinsic kinetics, the mass transfer resistance has to be eliminated. In industrial waste treatment (particularly removal of metals) the concentration of the (metal) ion is very small, giving rise to mass transfer control of the entire process. Laboratory as well as industrial applicationsemploy different types of rotating electrodes (such as disc and cylinder) as working electrodes in order to enhance solid-liquid mass transfer [I, 21. It is well known that standard impellers, like turbines, generate a much higher level of turbulence than the above type of electrodes. It will therefore be desirable to use these standard impellers in order to augment the mass transfer rate. There is considerable information available on solid-liquid mass transfer in mechar.ically agitated contactors C3,4], but practically no data are available in the literature on solid-liquid mass transfer 10 the impeller itself. It was therefore decided to determine the solid-liquid mass transfer coefficient for the following three types of 0.05 m dia standard turbine impellers: (1) four- and six-blade (2) four- and six-blade (3) four- and six-blade
disc turbines, 45” pitched turbines, curved turbines.
EXPERIMENTAL
A physical as well as a chemical dissolution method used to obtain the solid-liquid mass transfer coefficient. two systems employed were:
44:7-t
dissolution
in chromic
acid [4].
was The
GOO’~2509/89 $3.00+0.00 1989 Pergamon Press plc
impellers
publication 26 January
1989)
(2) benzoic acid dissolution solutions [S].
in water and aqueous glucose
Benzoic acid was coated on the above impellers by dip coating with molten henzoic acid and then finished with emery paper. A 0.15 m dia acrylic vessel was used and the speed of rotation was varied from 12.5 to 22.81 rev/s. The diffusivity of benzoic acid was varied by employing aqueous glucose solutions of different viscosities. The diffusivities of benzoic acid in the solutions were measured by the rotating disc method [6]_ The accuracy of the measured diffusivities was checked by comparing the value obtamed in pure water with the literature value at 30°C. The difference was less than 5%. The physical properties of the solutions used and the corresponding measured diffusivities are given in Table 1. The experiments were conducted in a batch mode. The volume of liquid used was such that it yielded a heightto-diameter ratio equal to one. The batch time varied from 240 to 300 s. An atomic absorption spectrophotometer was used to estimate copper in the chromate solution whereas benzoic acid was analysed by titrating a known sample volume against 0.01 N NaOH solution. Muss
transjer
correlation
It was proposed to develop a general correlation
for mass transfer to the impeller surface applicable to all the three impellers studied in the present work. Convective mass transfer in the impeller region is due to the relative motion of the impeller and the surrounding liquid. Thus the rotational Reynolds number may form a basis for a mass transfer correlation of the type: Sh =f(Re,
These impellers may be used in laboratory studies of electrochemical reactions. The data obtained and correlations developed can be used to predict the mass transfer step rate. Rotating impeller type electrochemical reactors can be used as a model equipment similar to the mechnically agitated reactor in gas-liquid systems.
CES
1978, A systems approach to assessing new technology. Chem. Engng Sci. 33, 921-922. and Rudd, D. F., 1976, Systems study of the industry. Chem. Engng Sci. 31, 1019-1028. and Rudd, D. F., 1978, Resource use by the industry. Chem. Engng Sci. 33,923-933.
1989.
Receiued6 June 1988; acceptedfor
copper
Stadtherr, M. A., petrochemical Stadtherr, M. A. petrochemical Stadtherr, M. A. petrochemical
0
Solid-liquid
(I)
1591
SC).
(1)
Similar correlations have been developed for the rotating cylinder electrode [S]. Figure 1 shows a plot of the Sherwood number against the impeller Reynolds number for the benzoic acid-water system for all the three impellers. It is evident that, regardless of the type of impeller, the variation in the Sherwood number with the Reynolds number is nearly s&me. This observation and the earlier successful correlation for the rotating cylinder electrode led us to seek the following type of correlation: Sh - 2 = a(Re)b(Scr.
(2)
In the above equation the limiting value for the Sherwood number (equal to two) for mass t 0 Isfer in a stagnant-infinite
1588
Communications
c
8.0
talc exp tab 1 2 3
~CnlC [mPasl
t
tiD
related to component calculated value experimental value tabulated value related to component related to component related to component
C (Na,CO,)
1 (or H,O) 2 (or the basic solution 3 (or the basic solution
2) 3)
REFERENCES
5.0
A., Peev, G. and Elenkov, D., 1971, On the interfacial Verfahrensrechnik 5, area in floating bed contactors. 340-342. Kudra, T. and StrumiIio. C., 1975, Wymiana masy w procesie absorpcji z reakcja chemiczna w trbjfazowym zloiu fluidalnym. Ini. Chem. 5, 809-822. Palat?, Z., 1987, Viskozita vodn?ch roztokd NaOH/ Na,CO,. Chemick$ P&m. 37, 6&70. Skoczylas, A. and Szust, I., 1984, Determination of the effective interfacial area in gas-liquid systems in mechanical thin-layer apparatus. II. Limiting conditions for the application of the Danckwerts model and physico-chemical data required for design calculations. In?. Chem. Proc. 4, 729-743. Strumitto, C. and Kudra, T., 1977, Interfacial area in threephase fluidized beds. Gem. Engng Sci. 32, 229-232. Skubla. P., 198 1, Viscosity of binary and ternary liquid nonelectrolyte mixtures. Derivation of correlation equations. Coil. Czech. them. Commun. 46, 329-339. Timmermans, J., 1960, The Physico-chemical Constants of Einary Systems in Concentrafed Solutions 3. Interscience, New York. Wokniak, M. and Qstergaard, K., 1972, An investigation of mass transfer in a countercurrent three-phase fluidized bed. Chem. Engng Sci. 28, 167-171. Kosev,
4.0
3.0
2.0
1 .o 1.0
2.0
3.0
4.0
50
6.0
7.0
-
8.0
~,,pimPasl
Fig. 1. Comparison of experimental values of dynamic viscosity of aqueous NaOH/Na,CO, solutions with the values calculated from eq. (1).
P 4
ternary interaction density, kg m- 3 volume fraction
Subscripts A B
related to component related to component
PI23
ChenWaf Enginewing Scienre, Printed in Great Britain.
Vol.
coefficient,
44, No.
mPa s
A (H,O) B (NaOH)
7, pp. 1588-1591.
The effect of nonlinear
(Receioed
1989.
OXI 2509/89 83.CQ+O.O0 Q 1989 Pergamon Press ptc
investment function on the optimum petrochemical industry 3 October
1988; accepted
INTRODUCTION
There have been various attempts to model the intermediate chemicals industry. The philosophy for the development of a dynamic model of the intermediate chemicals industry has been presented (Rudd, 1975). Stadtherr and Rudd (1976, 1978) devised and expanded a static model of industrial development utilizing the criterion of minimum feedstock consumption. Stadtherr (1978), Afshar et al. (1981), Afshar and Rudd (1981) aind Rudd et al. (1981) extended the model for long-range planning studies, and contributed to the system analysis of the petrochemical industry by including price projections and technological developments. The structure of the industry satisfying the multiobjective criteria of minimum availability change, lost work and carbon consumption has been sought by Sophos et al. (1980). Multiobjective analysis has been extended by Afshar and Yang (1985) to determine the optimum structures for minimum
22 December
structure
of the
1988)
cost and least gross toxicity of chemical pro’duction. The relationship between short- and long-range development objectives are investigated by comparing the optimal system structures obtained with single- and multistep optimizations by Sokic and Stevancevic (1983). Most recently Sigurdsson and Rudd (1988ax) formulated a model that aids in studying the interactions in world trade of petrochemicals and its effect on individual petrochemicals worldwide. All of the above studies have assumed a linear variation of the investment cost with the plant capacity. Santiago et nl. (1986) assumed this variation to b-enonlinear (in the form of a power-law function). The nonlinearity can be obviated by a linearization procedure. Earlier, Jimenez et al. (1982) took into account a nonlinear investment fuqction in their study of the Mexican petrochemical Industry. The objective of the present study is to extend the integrated model developed by Rudd et ol. (1981) to cases for
Shorter Communications which the investment cost varies with the plant capacity in the form of a power-law function. The linearization procedure devised by Santiago et al. (1986) is adopted. A specific supply+lemand environment, price structure and cost data base is gssumed. THE
MODEL
AND
THE
DATA
function
cost =
5 P,F, + 5 CfXj i-1 i= 1 -
is minimized
2
t= 1
Hi(Q,-
IJ -= _ II3
BASE
The adopted model is the integrated model described in detail by Rudd et al. (1981). According to this model feedstocks enter the industry from a limited exogeneous supply, generally as by-products from the energy industries. These feedstocks enter a network of chemical processes to be converted to intermediate and final products. The model seeks out production capacities such that the objective
total production
1589
the first case the investment cost ofthe processes are assumed to vary linearly with the plant capacity. In the second case the investment cost of the processes is assumed to vary with the plant capacity in the form of a power-law function:
oil
(1)
subject to the constraints
xj (1 __
\A
K .
B/
K usually varies from 0.6 to 0.9 in the petrochemical industry. In our case K is taken to be 0.75. The variation of investment cost with the plant capacity in the form of eq. (6) introduces a nonlinearity to the objective function. In the present work the linearization method developed by Santiago et al. (1986) has been used to simplify the solution. The linearization method is essentially an iterative technique. Convergence on process capacities was obtained after seven iterations. During solution plant capacities of less than 10,000 tons/year were eliminated to simplify the problem. The structure of the industry with the linear objective function and the nonlinear one are shown in Ttible 2. Comparison of the results shown on Table 2 indicate the following:
M
Fi+
aiJXj=Qi
1 j=
(2)
I
F,
(3)
X,
(4)
Di< Qt.
(5)
In the above expressions Fi and Di are the quantities of feedstocks entering the process network and the demand quantities, respectively. Pi and Hi are chemical prices and heating value prices for chemical i, respectively. Cr represents utilities, investment, and labor-related costs as well as the fixed costs associated with the raw materials portion of the process such as catalysts. additives and fillers. Within the specified process capacity limits Bi and feedstock supply constraints Si, the model identifies processes to operate at levels Xi, such that chemicals are produced in quantities Qi_ aij are coefficients giving the amount of chemicals consumed or produced per unit production of processj. One has to note that any surplus chemicals, Qi--Di, are credited only for their heating value. Equations (1) (5) describe a linear programming problem. The problem is solved with TEMPO, which is a standard library package. The chemicals and processes, with one exception, are the ones given by Rudd et al. (1981). In the present study catalytic reforming of naphta to produce aromatics is included in the process list. Thus the model considers 131 chemicals and 183 processes. In the present study data related to the Turkish petrochemicals industry is utilized. The exogeneous demand for intermediate chemicals are given in Table 1. Heating value prices are those reported in Rudd et al. (1981) escalated to 1987 by utilizing the Nelson cost index. in the Coefficients aij and C: are the ones reported technology catalog by Rudd et al. (1981). The utility cost figures of 1977 are escalated to 1987 by using the domestic fuel oil price. The investment cost for each process is carried from 1977 to 1987 by the Marshall and Swift Equipment Cost Index. The yield and cost data for the catalytic reforming of naphta to produce aromatics are obtained from the industry (Kartal, 1988).
RESULTS
AND
DISCUSSION
In the present study it is assumed that only naphta is available as a major feedstock. Its price is obtained from the domestic suppliers as $l48/ton. Two cases are considered. In
(I) In the nonlinear case the total production cost of the industry is 16% larger. (2) The consumption of benzene by the industry is larger. The reason is that the reference plant capacity of process 37 (124,000 tons/year) is smaller than the selected plant capacity by the model (142,720 tons/year), and this causes a reduction in the investment cost coefficient in case 2. (3) The investment cost coefficient of the p-xylene-based dimethyl terephthaiate process 72 is higher than that of process 73. As a result the model prefers to produce all dimethyl terephthalate from process 73. (4) In the case of ethylene glycol the model again selects the process with a smaller cost coefficient. (5) The naphta-based hydrogen process is eliminated from the process list because of its smallcapacity. This leads to the acceptance of the sodium chloride based chlorine process (60) in the model to supply the required hydrogen for the production of cyclohexane (66). The reason for the production of vinyl chloride from ethylene (175) is the production of chlorine (60) in the model, since chlorine is one of the major raw materials of process 175. CONCLUSIONS
Major differences in the optimum structure of the petrochemicals industry occur when the investment cost is allowed to vary nonlinearly with the plant capacity in the form of a power-law function. For the specific problem studied in the
Table
1. Exogeneous
demand for intermediate Turkey
Chemical Acrylonitrile Benzene Butadiene Caprolactam Dimethyl terephthalate Ethylene Ethylene glycol Formaldehyde (100%) Phenol Phthalic anhydride Propylene (chemical grade) Styrene Terephthalic acid {fiber grade) Vinyl chloride
chemicals
Demand values (metric tons/year) 132,000 29,000 73,000 26,000 105,000 334,000 132,000 73,630 15,620 34,000 123,000 68,100 70,000 278,300
in
Shorter
1590 Table
2. Impact
of the nonlinear
Selected 15. 23. 33. 37. 38. 42. 56. 60. 65. 66. 72. 73. SO. 86. 92. 93. 94. 96. 99. 108. 113. 119. 130. 134. 141. 144. 146. 153. 154. 155. 161. 162. 165. 166. 175. 176. 177.
behavior
of the objective function (metric tons/year)’
process
Acetylene from naphtha Acrylonitrile from propylene Ammonia from naphtha Benzene from naphtha Benzene from toluene Butadiene from n-butylenes Caprolactam from cyclohexane Chlorine from sodium chloride Cumene from benzene Cyclohexane from benzene Dimethyl terephthalate from p-xylene Dimethyl terephthalate from terephthalic Ethylbenzene from benzene Ethylene from naphtha Ethylene dichloride from ethylene Ethylene glvcol from ethylene oxide Ethilene &co1 from ethilene Ethylene oxide from ethylene Formaldehyde from methanol Hydrogen from naphtha Isobutylene from butenes Isoprene
from
Communications
pentenes
t Process
numbers
refer to those given in Table
present work it is found that the production cost of the industry is 16% larger in the nonlinear case compared to the linear one. This is because the demand values for specific chemicals are rather low and some of the plant capacities are lower than those corresponding to the base case. TijRKER NURTEN
GijRKAN KARTAL
Department of Chemical Engineering Middle East Technical University 06531 Ankara, Turkey
REFERENCES Afshar, S. F., Maisel, D. S., Rudd, D. F., Trevino, A. A., and Yuan, W. W., 198 I, Advances in petrochemical technology assessment. Chem. Engng Sci. 36, 1487-1511. Afshar, S. F. and Rudd, D. F., 1981, The economic impact of new chemical technology. Chem. Engng Sci. 36,1421-1425. Afshar, S. F. and Yang, J. C., 1985, Designing the optimal
2 of Afshar
of the industry Nonlinear investment function case
59,867 132,000 71,094 118,441 2837 73,000 26,000
40,248 132,000 71,139 142,720
63,494 68,100
acid
structure
Linear investment function case
21,087 23,660 44,350 60,650 78,315 521,377 230,863 97,950 34,050 85,217 73,630 1855 74,188 63,958 126,294 29,945 15,620
acid
Methanol from carbon monoxide Methyl ethyl ketone from n-butylenes Phenol from cumene Phenol from benzene Phthalic anhydride from o-xylene Styrene from dehydrogenation of ethylbenzene Styrene with ethylbenzene by hydroperoxide Sulfuric acid from sulfur Synthesis Gas (Hz : CO = 3 : I) from coal Synthesis Gas (HZ : CO = 3 : 1) from residual oil Terephthalic acid, fiber grade from crude terephthalic Terephthalic acid crude from p-xylene Vinyl chloride from ethylene Vinyl chloride from ethylene dichloride Vinyl chloride from acetylene
on optimal
37,130 111,541 861 70,ooo 124,772
139,074 139,226
73,000 26,000 55,207 23,660 105,000 77,634 557,997 156,367 132,000 114,840 73,630 79,399
77,069 123,633 39,312 36,164 76,510 68,100 36,678 110,034 70,000 163,800 90.503 94,197 93,600
et al. (1981).
structure of the petrochemical industry for minimum cost and least gross toxicity of chemical production. Chem. Engng Sci. 40, 78 l-797. Jimenez, A., Rudd, D. F. and Meyer, R. R., 1982, A study of the development of the Mexican petrochemical Industry. Comput. &em. Engng 6, 219-229. Kartal, N., 1988, Modelling and planning the Turkish pctrochemical industry. MS. Thesis, Middle East Technical University, Ankara. Rudd, D. F., 1975, Modelling the development of the intermediate chemicals industry. Chem. Engng J. 9, l-20. Rudd, D. F., Afshar, D. F., Trevino, A. A. and Stadtherr, M. A., 1981, Petrochemical Technology Assessment. John Wiley, New York. Santiago, M. D., Iglesias, 0. A. and Paniagua, C. N., 1986, Optimal techncilogy paths for chemical industry production. Comput. them. Engng 10,421-431. Sigurdsson, M. and Rudd, D. F., 1988aq World-scale model predicts petrochemical trends: Parts 1, 2 & 3. Hydrocarb. Process. 67, No. 6: 9XB-98N; No. 7: 34E-34L; No. 8: 5OE-50L.
Shorter
Communications
Sokic, M. and Stevancevic, D., 1983, The optimal structure of the system of the petrochemical industry. Chem. Enyng Sci. 38. 265-273. Sophos, A., Rotstein, E. and Stephanopoulos, G., 1980, Multiobjective analysis in modeling the petrochemical industry. Chem. Engng Sci. 35, 2415-2426.
Chemical Enginecr~ny Science, Prmted an Great Bntain.
Vol. 44, No
7. pp.
1591bl593.
mass transfer? to rotating
INTRODUCTION
There is an increasing interest in electrochemical techniques for various applications in the chemical industry. One of the several steps involved in an electrochemical reaction is the transfer of a discharging ion/compound to the working electrode. When the mass transfer step is the slowest among the various steps, the rate of the electrochemical reaction is solely determined by the solid-liquid mass transfer rate. This situation is ofrelevence in both laboratory research work and industrial applications Cl, 23. In the former case, to obtain the intrinsic kinetics, the mass transfer resistance has to be eliminated. In industrial waste treatment (particularly removal of metals) the concentration of the (metal) ion is very small, giving rise to mass transfer control of the entire process. Laboratory as well as industrial applicationsemploy different types of rotating electrodes (such as disc and cylinder) as working electrodes in order to enhance solid-liquid mass transfer [I, 21. It is well known that standard impellers, like turbines, generate a much higher level of turbulence than the above type of electrodes. It will therefore be desirable to use these standard impellers in order to augment the mass transfer rate. There is considerable information available on solid-liquid mass transfer in mechar.ically agitated contactors C3,4], but practically no data are available in the literature on solid-liquid mass transfer 10 the impeller itself. It was therefore decided to determine the solid-liquid mass transfer coefficient for the following three types of 0.05 m dia standard turbine impellers: (1) four- and six-blade (2) four- and six-blade (3) four- and six-blade
disc turbines, 45” pitched turbines, curved turbines.
EXPERIMENTAL
A physical as well as a chemical dissolution method used to obtain the solid-liquid mass transfer coefficient. two systems employed were:
44:7-t
dissolution
in chromic
acid [4].
was The
GOO’~2509/89 $3.00+0.00 1989 Pergamon Press plc
impellers
publication 26 January
1989)
(2) benzoic acid dissolution solutions [S].
in water and aqueous glucose
Benzoic acid was coated on the above impellers by dip coating with molten henzoic acid and then finished with emery paper. A 0.15 m dia acrylic vessel was used and the speed of rotation was varied from 12.5 to 22.81 rev/s. The diffusivity of benzoic acid was varied by employing aqueous glucose solutions of different viscosities. The diffusivities of benzoic acid in the solutions were measured by the rotating disc method [6]_ The accuracy of the measured diffusivities was checked by comparing the value obtamed in pure water with the literature value at 30°C. The difference was less than 5%. The physical properties of the solutions used and the corresponding measured diffusivities are given in Table 1. The experiments were conducted in a batch mode. The volume of liquid used was such that it yielded a heightto-diameter ratio equal to one. The batch time varied from 240 to 300 s. An atomic absorption spectrophotometer was used to estimate copper in the chromate solution whereas benzoic acid was analysed by titrating a known sample volume against 0.01 N NaOH solution. Muss
transjer
correlation
It was proposed to develop a general correlation
for mass transfer to the impeller surface applicable to all the three impellers studied in the present work. Convective mass transfer in the impeller region is due to the relative motion of the impeller and the surrounding liquid. Thus the rotational Reynolds number may form a basis for a mass transfer correlation of the type: Sh =f(Re,
These impellers may be used in laboratory studies of electrochemical reactions. The data obtained and correlations developed can be used to predict the mass transfer step rate. Rotating impeller type electrochemical reactors can be used as a model equipment similar to the mechnically agitated reactor in gas-liquid systems.
CES
1978, A systems approach to assessing new technology. Chem. Engng Sci. 33, 921-922. and Rudd, D. F., 1976, Systems study of the industry. Chem. Engng Sci. 31, 1019-1028. and Rudd, D. F., 1978, Resource use by the industry. Chem. Engng Sci. 33,923-933.
1989.
Receiued6 June 1988; acceptedfor
copper
Stadtherr, M. A., petrochemical Stadtherr, M. A. petrochemical Stadtherr, M. A. petrochemical
0
Solid-liquid
(I)
1591
SC).
(1)
Similar correlations have been developed for the rotating cylinder electrode [S]. Figure 1 shows a plot of the Sherwood number against the impeller Reynolds number for the benzoic acid-water system for all the three impellers. It is evident that, regardless of the type of impeller, the variation in the Sherwood number with the Reynolds number is nearly s&me. This observation and the earlier successful correlation for the rotating cylinder electrode led us to seek the following type of correlation: Sh - 2 = a(Re)b(Scr.
(2)
In the above equation the limiting value for the Sherwood number (equal to two) for mass t 0 Isfer in a stagnant-infinite