Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 19-30 Campbell, J. S. Ind. Eng. Chem. Process Des. Dev 1070, 9 , 588. Carberry, J. J. Catel. Rev. 1070, 3 , 61. Carberry, J. J. ”Chemical and Catalytic Reaction Engineering”; McGraw-HIII: New-York, 1976; p 217. Huiburt, H. M.; Srini Vasan, C. D. AIChE J . 1061, 7 , 143. Kiier, K.; Chatikavanu. V.; Herman, R. G.; Simmons, G. W. J . Catal. 1082, .74. . , 343. - .-. Leonov, V. E.; Karabaev, M. M.; Tsybina, E. N.; Petrishcheva. G. S. Kinet. Katal. 1073. 14. 970. M a r s , J. Ind.’Eng: Chem. ProcessDes. Dev. 1071, 1 0 , 541. Moe, J. M. Chem. €ng. Prog. 1082, 58, 33. Plno, P.; Mazzanti, G.: Pasquon, I. Chim. Ind. (Mllan) 1053, 35, Natta. 0.; 705. Natta, G.; Mazzanti, G.; Pasquon, I. Chim. Ind. (Milan) 1055, 3 7 , 1015.
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Pasquon, I . Chim. Ind. (Mlan)1060, 42, 352. Ruggeri, D.; Vaccari, A.; Trifir6, F.; Gtwrardl, P.; Del Piero, G.; Notari, 6.; Manara, G. 3rd International Congr. “Sclentiflc Bases for the Preparation of Catalysts”, Louvaln-Le Neuve, Oct 1982. Santacesaria, E.; Morbideiii, M.; C a r 6 S. Chem. Eng. Sci. 1081, 36, 909. Soave, G. Chem. Eng. Scl. 1072, 27, 1197. Treybal, R. E. “Mass Transfer Operations”, 3rd ed.; McGraw-Hill: New York, 1975; p 75. Van Herwijnen, T.; De Jong, W. A. J . Catal. 1080, 63, 83.
Received for review July 8, 1982 Revised manuscript received December 29, 1983 Accepted January 18, 1984
Synthesis of Optimal Heat and Power Supply Systems for Energy Conservation Masatoshl Nishlo, Ichiro Koshljlma, Katsuo Shlroko, and Tomlo Umeda Chiyo& Chemical Engineering 8 Construction Co., Ltd., Tsurumi, Yokohama, Japan
The synthesis problem of energy supply systems includes the selection of proper heating and power generating
units a s well a s energy integration. Such problems have been generally formulated as a linear programming (LP) problem. The structural analysis of the problem and solutions will be focussed on rather than merely solved. As a practical consideration for preliminary selection of technologies, a problem regarding the selection of heating devices such a s electric heaters, furnaces, steam heaters, or heaters with a heating medium under given loads is defined a s a synthesis problem of optimal heat and power supply systems and formulated into an LP form with an objective function of minimum fuel. The results of analysis of the LP problem clarify essential structures of heat and power supply systems under arbitrary heat and power demands.
Introduction A number of studies on energy conservation have been made by the process industries in the wake of the need to save energy. For example, aiming a t effective use of energy, energy management and saving have been strengthened, efficiency of equipment has been improved, and an increase in overall efficiency has been sought by means of an appropriate combination of equipment. When an energy conservation project is carried out, economics is an important factor that dominates whether the project should be carried out or not. It is expected to have a rational way of preliminary choice of energy conservation technologies. There are a variety of ways to utilize heat and power for process industries that consume great amounts of energy. Various methods for efficient use of heat and power have been applied ranging from the energy consuming system where process systems are the central part to the energy supply system where a steam-power system is the central part. Efforts a t energy utilization have been made independently from each other in individual subsystems, namely, process systems and steam-power systems. Among them are studies in energy conservation technologies for process systems (Umeda et al., 1978; Umeda and Shiroko; 1980, Umeda et al., 1981) and the steam-power system (Nishio et al., 1980). Nishio et al. (1982) have presented a method for an optimal use of steam and power through the coordination of process systems and the steam-power system. In that paper a qualitative approach has been proposed for the coordination problem on energy use and practical candidates of energy conservation technologies 0196-4305/85/1124-0019$01.50/0
to be chosen have been shown based on necessary steam and power demands. On the other hand, Nishio et al. (1981) have taken up the problem of determining an optimal structure for fuel supply systems as an example of a quantitative approach for the energy coordination problem. The problem has been formulated in terms of an LP form and general feasible solutions have been derived on the basis of heat and power demands. The motivation of this approach has been described in detail. Some explanation is repeated later in this paper. Furthermore, Nishio et al. (1983) have modified the formulation of the same problem, obtained general optimal solutions, and proved them to be optimal. This paper expands upon the previous paper in determining a structure for an optimal supply system of heat and power. First, the problem is formulated as an LP problem, and next general optimal solutions are derived by applying the method for solution given in the previous paper (Nishio et al., 1984). Finally, numerical studies are carried out as to the effects of steam header pressure level, i.e., high and medium pressure levels which are design parameters for problem, to determine the optimal system structure. Problem Formulation In general a number of heating loads are required to generate fine products in process industries where various types of heating devices are employed, depending on the extent of the heating loads as well as the heating levels. While there are cases where furnaces or electric heaters are used for a heating load at a high temperature level, and steam heaters or heaters with heating mediums such as hot oil used for heating loads at medium temperature levels, 0 1984 American Chemical Society
20
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 1, 1985
there exists a problem of choice with respect to heating devices so long as heating requirements such as heating loads and heating levels are satisfied. Whether furnaces, electric heaters, or steam heaters should be employed shall not be determined solely by comparing equipment efficiency independently, but from an overall viewpoint taking into account a total energy balance including a balance between heat, power, and process steam demands. In this problem of determining a structure for an optimal supply system of heat and power, the following devices of heating and power generation are considered possible system elements: furnaces, steam heaters, and electric heaters for heating, and back-pressure turbines and condensing turbines for power generation. For the purpose of a preliminary choice of these technologies, running costs are usually dominant rather than fixed costs in evaluating an economic factor on energy conservation projects. Therefore, a linear programming problem with an objective function of minimizing fuel consumption is formulated as follows.
4 Furnace
___.
I,-.
3M+1
E Xi
minimize
(1)
j=l
Figure 1. Energy flow diagram.
< VFit ?Ti,
0
TEi, ?Tj, ?c
< 1.0, x i 2 0
where eq 2,3, and 4 are supply-demand relationships for heat with each heating level, process injection steam with each heating level, and power, respectively. vTi, Ri, and vFi may be defined as follows. ho - hi VTi = VMVb (5) ho - ~ B F W
Also, vTj and Rj can be defined by replacing i in eq 5 and 6 with J . In the case of using heating mediums it is possible to deal with heaters by accounting for overall thermal efficiency of the heater including indirect thermal efficiency in place of 9Fi in eq 2. The caae often seen in chemical industries is chosen as a typical example of eq 1-4 as shown in Figure 1 and formulated as follows.
xi + x~+ x 3 + x4 + x 5 + x 6
yx$.?& subject to
VFlXi
1 ~ 2 x 2
+ R~?ITIX~ + VE1x7 2 (1 - fi)Q (9) R211~2X4+ 7 ~ 2 x 2 8 fiQ (10) R2VT2X5
TTlX3
< VFlt
H - x7
(11)
2
+ ‘IT2X4 + ‘ITZX5 + Tcx6 0
(8)
-x 8
VF2, VTl? 1T2, Vc, TEl, 1732
xi,
..e,
x 8
(12)
< l.0
10
General optimal solutions for arbitrary conditions and
alternative feasible solutions will be derived for the chosen case in the next section. Method for Problem Solving and Solutions Although it is possible to solve eq 1-4 by an LP technique under given conditions that determine coefficients in eq 2-4 and heat and power demands that define right-hand-side of eq 2-4, optimal solutions have to be obtained every time when different conditions are provided. While parametric studies using MPSX of IBM would give us optimal solutions systematically for a given set of different conditions, they are only specific optimal results, and above all, the approach using the LP code does not provide alternative feasible solutions other than optimal solutions. The method which was proposed in a previous paper (Nishio et ai., 1984) can be useful for a problem with a comparatively small number of variables, say, less than ten variables subject to several constraints in the sense that it can bring general optimal solutions for arbitrary conditions and provide alternative feasible solutions at the same time. First, feasible solutions are derived for the problem defined in eq 8 to 12. Secondly, they are arranged in accordance with the feasible regions based on heat and power demands. Thirdly, general optimal solutions are obtained as a result of the ordered arrangement of feasible solutions. General Feasible Solutions. A certain set of combinations of basic variables can be obtained for the problem defined in eq 8-12 by making use of an obvious property of LP solution (that is, the optimal solutions are found a t the intersections of constraints) and by examining the possible combinations of variables from heat and power system designs. Those combinations of variables which involve those of optimal solutions are given in Table I, where the first column sequentially indicates the solution number and the first row shows the variables X1 through Xs. Only variables with flag 1are to be chosen as bases for solution. Once
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 1, 1985
Table I. Set of Combination of Independent Variables soln no. x1 x2 nS x4 x5 x7 xg 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
E
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 1
1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1
0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1
a combination set of variables is determined, a set of feasible solutions can be derived by solving simultaneous eq 9-12, using each combination of variables as basic variables. Table I1 shows the results that were solved based on Table I. The set of solutions can be optimal but it remains unknown at present as to under what conditions they become optimal. Analysis of General Feasible Solutions Based on Energy Demands. By examining the regions in which each feasible solution holds, the following nine points are found to be cut-points which define the feasible regions for the soiutions.
Scheme I 1.
2.
PI
p2
p 3
p 4
p5
p6
p7
p0
p9
f l
p2
P3
f4
f 5
p 7
f6
f0
P 9
P2
f 3
P4
P7
f 5
f 6
Pe
f 9
p2
p3
p4
p7
f5
P0
P6
p9
p1
p2
p4
p3
p 7
f5
p8
p6
f9
I p1
f2
f4
p 7
p3
f5
f0
p6
f9
1 pt 1
p4
p2
p7
p3
p5
P8
p 6
f9
pl
p4
p7
p2
p 3
f5
P0
p6
p 9
p1
p4
p7
p2
PS
p3
P0
p6
f9
pl I
p4
f7
p2
PS
f 0
p 3
f6
f9
I I
P1 p1
RzW &W
4. I 5. 6.
7. 8.
I
9. I 10.
R2 E2
+
+
R2w
-w -w *w
-
&W
*
R2w
R27E2
sequence 1 f
< b,;
sequence 2
b, I f < b2;
sequence 3
b2 If
sequence 4 b3 f
bl =
RlR2 + (Rl + R217F2
< b,;
< b4; b4 =
R2 b3 = R1+ R2
VElVE2
R2 + 7E2 + (TE1 + VE2)R2
seauence 5
sequence 10
P, = R ' ( 1 - f)Q H R1 R2 P g = -(I - f ) Q + fQ H R1
-
If each cubpoint value is compared other than the relations which obviously hold, i.e., P1< P2 < P3,P5;P1 < P4< P5, P,; P, < Pa; P I < P5 < P6 < Pa< P9, there exist the ten arrangements (see Scheme I) with increasing order of magnitude from the left to the right. The ten sequences in Scheme I hold in the following regions which are arranged in terms o f f value.
b7 If
R2 < b,; b8 = VEl
= H - -fQ
. R2W . &W
3. 1
sequence 8
P4
21
b, 5
+ R2
f
Now, the relation between R2Wand cut-points Pi (i = 1-9) that define the feasible regions for the solutions can be represented by the relation between power to be generated and power that can be generated, as shown in Table 111. The relation shown a t P I in Table I11 implies that it is possible to supply the additional power needed when electric heaters are employed for both heat demands a t medium and low heat levels. This power is generated while supplying steam demands for process uses. Accordingly, more power can be generated than demanded including that for electric heaters in the region where R2Wis less
22
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 1, 1985 0 00-
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