Energy Convers. Mgmt Vol. 26, No. 3/4, pp. 277-281, 1986 0196-8904/86 $3.00 + 0.00 Printed in Great Britain Pergamon Journals Ltd

DESIGN OF ELECTRIC POWER GENERATION SYSTEMS USING WASTE HEAT ENERGY

MASARU NAKAIWA, I SHIGETAKE KAWASAKI, I YUJI NAKA, 2 K A Z U Y O S H I B A B A 3 and TAKEICHIRO TAKAMATSU 3

~National Chemical Laboratory for Industry, Ibaraki 305, Japan 2Research Laboratory of Resources Utilization, Tokyo Institute of Technology, Yokohama 227, Japan

3Department of Chemical Engineering, Kyoto University, Kyoto 606, Japan

(Received 17 August 1985)

Abstract--The recent energy crisis forces engineers to take into account reduction of electricity consumption as well as heat energy consumption in industry. As it is very difficult to save the amount of electricity, they have tried to recover electric power using waste heat energies. In this paper, the possibilities of electric power recovery from waste heat energies are discussed based on the relationship between supply heat sources and demand heat sources in chemical process systems. In solving such problems, the following difficulties appear: calculation of maximum quantity of generated electric power, determination of a suitable working fluid and its temperatures in the Rankine cycle, and so on. The proposed method Can solve them using the temperature-enthalpy diagram and, furthermore, has the advantage of being able to design a final heat exchanger network with heat exchangers in a power plant by means of a synthesis method using the same diagram.

Rankine cycle Energy conservation Power generation System design Waste heat recovery Working fluid Temperature-enthalpy diagram

INTRODUCTION

The waves of energy conservation in chemical indus- tries have expanded quickly with increasing oil price. In many cases of saving energy, as engineers pay attention only to heat energy recovery, utility systems to produce electricity and steam in a chemical com- plex are hardly keeping the balance of the feasible production ratio of electricity to steam. For this reason, it is very difficult to drive energy conser- vation. Especially as the feasible range of the ratio in an existing utility system is almost fixed, reducing only steam supply is restricted. The transformation of waste heat energy into electric energy becomes necessary. For example, electric power generation has been already realized using the heat energy of flue gas or the heat energy removed from condensers in distillation systems. When recovering electric power from waste heat energies, if engineers take into account heat energies of supply and demand only within a narrow temperature range, the heat integra- tion in the whole system cannot be advanced, and it may happen that more fresh steam is required. So, it is necessary to make clear what amount of electric power can be generated from waste heat energies from the viewpoint of the total system.

One of the methods to design heat-integrated process systems is a beat-matching method using the heat availability diagram [I]. With this method, the maximum heat recovery can be obtained easily. Then, a procedure to synthesize the feasible heat exchanger networks under the condition of the

maximum heat recovery in the same diagram can be used sequentially [2]. There are very few researchers for development of generalized heat recovery methods which include electric power gener- ation systems using waste heat energies. Linnhoff [3] proposed an idea to combine an electric power plant with a heat-energy recovery system, but did not show a method to choose a good working fluid and to determine the size of an electric power plant.

REPRESENTATION OF RANKINE CYCLE

When generating electric power using low- temperature heat energy removed from main process systems, the Rankine cycle is generally used. This cycle consists of the following four processes:

I-2 Reversible adiabatic compression, 2-3-4 Reversible constant-pressure heat addition, 4-5 Reversible adiabatic expansion, 5--6-1 Reversible constant-pressure heat rejection.

Here, as the temperature increase in the !-2 process is very small it can be neglected.

Although there are many working fluids available to the Rankine cycle, in this paper, fluorocarbon 114 (1,2-dichloro- 1,1,2,2-tetrafluoroethane) and n -butane are considered for illustration of the proposed method. Their physical properties, the saturated vapor equation and the equation of state to calculate enthalpy and entropy, can be represented by Martin's

277

278 NAKAIWA et al.: ELECTRIC POWER GENERATION SYSTEMS

~/- (W~-wP) /H th (1)

/ • . .•"•'"

T

. .Y

Entholpy (kd/kg)

, , . . . . . . . . ... . ' •

Fig. I. Rankine cycle.

28o32O ' ! 3°° I , ... I o,. lo 20 3o 40 i: 50 i~ 6o ::70 ~.

i

l 260 O 005 01 0 5

( W t - W p ) / H ~

Fig. 2. Saturation temperature at condenser--cycle thermal efficiency diagram (fluorocarbon 114).

equations [4] for fluorocarbon 114 and by Kurnik's equations [5] for n-butane.

For these working fluids, using superheated vapor can hardly contribute the increment of electric power generation due to the physical characteristics for adiabatic expansion. The working fluids are heated to the state of saturated vapor and enter a turbine. A typical example of the Rankine cycle is shown in Fig. 1, where, T' c and T~, are the saturation tem- peratures corresponding to condenser pressure and heater pressure, respectively. Also, D, is the tem- perature difference between T' c and T~, ( = T'c x D,), and, H~,, H'c and W' mean the required heat energy, the removed heat energy and the generated work, respectively.

The Rankine cycle is usually evaluated by using the cycle thermal efficiency. The cycle thermal efficiency is defined as follows:

,7 = (w, - W,')/H',, (1)

where W p is the work supplied to a pump and can be calculated by using the flow rate and the pressures at T'c and T~,. We assume that the turbine efficiency is nearly equal to the pump efficiency. Accordingly, the cycle efficiency is a function of T'c, D, and the physical properties of the working fluid. The computational results for fluorocarbon 114 and n-butane are shown in Figs 2 and 3. On comparing the two figures, below 30 K of D,, n-butane has the maximum value of r/ within 260-320 K of T'c. In the same region, the value of r/ for fluorocarbon I14 is bigger than that of n-butane. The relation is reversed in 40-80 K of D, at about T'~ = 296 K.

In a practical sense, there are some restrictions on the operating conditions of a turbine. For example, as some fluorocarbons are decomposed in the high temperature range of T~,, the useful range should be limited, and so on [6].

In the following section, the size of power gener- ation plant with the Rankine cycle is obtained as follows: assume T~. and D, and choose a suitable working fluid with high cycle thermal efficiency. Then, calculate its specific latent heat, 2(T'~, D,) specific sensible heat, h(T~., D,), and generated

electric power per unit flow rate, w'. Finally, given the real heat energy H~,, the flow rate, F, and generated electric power W' can be obtained by

F = H~/[2(T' c, Dr) + h ( T ' c, Or)] (2)

W' = Fw'. (3)

ELECTRIC POWER RECOVERY

When inserting the Rankine cycle into a space bounded by a heat supply composite line (HSCL) and a heat demand composite line (HDCL) in the temperature--enthalpy diagram, the following four problems appear:

(i) the feasible region of the Rankine cycle, (ii) the choice of a suitable working fluid,

(iii) the maximum electric power recovery, (iv) synthesis of heat exchanger networks.

The first problem (i) relates to the relationship between both heat composite lines, and the problem (ii) can be solved by using the cycle thermal efficiency. The third problem is based on the relationship be- tween heat composite lines and characteristics of the Rankine cycle, and the last problem relates to heat

L o

320

300

280

260

\

I 0.05 0.1

( W t - W p ) / H h

0.15

Fig. 3. Saturation temperature at condenser---cycle thermal efficiency diagram (n-butane).

NAKAIWA et al.: ELECTRIC POWER GENERATION SYSTEMS 279

composite lines generated newly. We are considering each problem in detail as follows.

The feasible region of the Rankine cycle

A working fluid in the Rankine cycle receives heat energy, H~, from some heat supply sources, and heat energy H'c at the condensation temperature T'c flows to the heat demand sources. Here, the auxiliary heat composite lines are defined as follows: denoting the minimum approach temperature for a heat exchanger as Ata.r,~n, the auxiliary heat composite lines of heat supply and heat demand, AHSCL and AHDCL, mean the heat composite line below At,,mSn of the heat supply composite line and the heat composite line above Ata,,~. of the heat demand composite line, respectively. The Rankine cycle should be in the region bounded by AHSCL and HDCL (or, AHDCL and HSCL).

After generating electric power, as the enthalpy difference between the heat composite lines below T'c shortens by W', T'~ should be at least lower than the temperature of the heat demand composite line re- lated to the minimum approach temperature.

To shift the heat supply composite line below T' c to the fight gives the maximum possible electric power recovery WSD(T~). When the heat supply composite line shifts and contacts the auxiliary heat demand composite line at the point P, the shift stops there as shown in Fig. 4a. The shift distance corresponds to WSn(T~). Denoting the quantity of electric power generated by a turbine as W', the following condition should be satisfied:

W~°(r~) _> W' . (4)

A possible space to introduce an electric power plant can be checked using WS°(T'c). If W' is very small, an electric power generation plant may not be realized. Meanwhile, if there is no minimum approach temperature between the heat supply com- posite line and the auxiliary heat demand composite line in the temperature range below T~ as shown in Fig. 4b, WSO(T'c) is defined as the enthalpy difference between both ends of the composite lines.

i T;

HDCL

I wSO I

E~holpy

Fig. 4b. Definition of W so without pinch point.

The choice of a suitable working fluid

When T'c, D, and unit heat energy supplied to a working fluid, h~, are known, the cycle thermal efficiency is determined. After the calculation for the cycle thermal efficiency of each working fluid, work- ing fluids are put in order of high efficiency.

S l , 32 . . . . . . . . . S n .

If it is possible to apply Sl with the maximum value of the cycle thermal efficiency to the Rankine cycle, the maximum quantity of generated electric power can be obtained. So, it is easy to choose the best working fluid using diagrams such as Figs 2 and 3 or equations of physical properties.

Realization of the Rankine cycle

Assume that T~ and D, in the feasible temperature range are obtained in (i), design an electric power plant as shown with the broken line, 1-3-4-5-6 in Fig. 5. The broken lines, 1-3-4 and 5-6-1, mean the demand heat energy and the supply heat energy according to the power plant. Needless to say, the heat composite lines should be written in T~ < T _< T~,. The heat composite lines below T~ must be shifted to the point 1" and the point 1', respect- ively. Consequently, new composite lines, 5"-6'-1" for the heat supply composite line and 1'-3'-4' for the

HSCL .." Ata, min

/

'"/

E~a lpy

Fig. 4a. Definition of W sD with pinch at P.

_~o, mqn

~ . . . . ~AHSCL / . . .3 . . . . 3'4 / • /'---- / 4

t ,.: / . . . . . o, / 4 r" I I" 6'//..",.~ .'~ J l

Enthalpy

Fig. 5. Modification of heat supply composite line and heat demand composite line in introducing the Rankine cycle.

E.C.M, 26'3-4--8

280 NAKAIWA et al.: ELECTRIC POWER GENERATION SYSTEMS

heat demand composite line are shown in the same figure with the thick solid lines. Denoting the en- thalpy difference between the cross points where T = T'c and the auxiliary heat supply composite line, and T = T'~ and the heat demand composite line intersect, respectively, as H*, H* means the quantity of the possible heat supply energy. The degree of this enthalpy difference is affected by the flow rate of a working fluid. In other words, it is possible to utilize the heat energy, 5-6, as a heat source. This positive energy utilization must make a heat exchanger network system more complicated and increases the investment cost. According to this reason, it is reasonable to assume the enthalpy difference as the latent heat at T'~ in designing an electric power plant. Consequently, H* is indepen- dent of the flow rate.

Meanwhile, as W s~ is given in step (i) and working fluid S~ is already chosen in step (ii), the best cycle thermal efficiency is known. The possible heat energy H s°, which is different from H*(Tt~), can be calcu- lated by using W s°.

H s° = WS°/rl (T'~, D, :Si). (5)

The flow rate of the working fluid is determined by using H*(T$) or HSO(Tt~, D,:S~) as follows:

if H* (T'~) <_ HS°(T'~, D,:SJ,

o r

if

H max = H* (T'~) (6)

H*(Ttc) >- HS°(T'c, D,:Si),

H m"x = HS°(Tt c, D,:S~), (7)

where H m~ means the maximum heat energy supplied to the Rankine cycle. Putting H;, = H ~ for the best working fluid Sl, the flow rate can be calculated by equation (2). If the heat composite line, 1'-3'--4' does not cross the auxiliary heat supply composite line within T'~ < T < T~,, the flow rate for assumed values of T~ and D, is obtained. In the reverse case, the flow rate should be changed. In other words, assuming H~, below H ~"x, it is necessary to search for the flow rate which brings the composite line, 1'-3'--4' into contact with the auxiliary heat supply composite line as shown in Fig. 6. In this case of H~ < H m~, the quantity of generated electric power should be calculated for each working fluid in order of high efficiency. Once the point of contact can be found for working fluid S r the calculation is finished. Then, the optimal working fluid and the size of an introduced electric power plant are determined by comparing maximum networks generated for 1 to j working fluids with each other.

In this stage, the maximum power generation for assumed values of T~ and D' can be calculated. Finally, the optimal flow rate can be obtained so as to maximize the electric power generation with changing T t and D,. The above-mentioned procedure is shown in Fig. 7.

HSCL Ata, m~n

l "'Fg'* Ill

En~lpy Fig. 6. Calculation of flow rate in the case of H max > H~,.

The synthesis of heat exchanger networks

As the heat supply composite line and the heat demand composite line which include the Rankine cycle are established in step (iii), a new method to design heat exchanger networks can be easily applied here [2]. If synthesized networks are very compli- cated, we can simplify them by reducing the value of H m~. Thus, it is possible to investigate whether electric power plants can be introduced or not from the economical standpoint.

_q o.m. T:o 1

I Colculote wSD a~l /4*

Colculote ~l ( I , 4 to n} j -

; 0.,--m,°.'-- 1

I ColcuIole tt~e W t (T t , D t ) under the

condition H~ < H max on(:l the flow rote

No

Fig. 7. Flow chart of calculation procedure.

NAKAIWA et al.: ELECTRIC POWER GENERATION SYSTEMS 281

. . . . "

320 / / / ~.. . / /

: / /

i ," 2 ¢ 5

300 i ~ H t . ~ . ~

¢ I ' I 2 0 0 0 4 0 0 0

H (kW)

Fig. 8. Heat supply composite line and heat demand com- posite line for the example.

EXAMPLE

Consider the following example:

The heat composite lines at the low temperature consist of sensible heat energies as shown in Fig. 8. The excess heat energy W so is 2635 kW, and cool- ing water at 293.15K is provided. The minimum approach temperature, Ato.mi, is equal to 10 K. The feasible range of the saturation temperature T~ is from 303.15 to 386K. Fluorocarbon 114 and n- butane are prepared as a working fluid.

The initial values of T'c and D, were assumed as 303.15 K and 5 K, respectively. In order to clear the strategy of choosing the better working fluid, alterna- tions of a working fluid are shown in Fig. 9 based on ( W ' - W p) vs D, under the conditions of T'c= 303.15 K and 323.15 K. The marks with square and circle correspond to n-butane and fluorocarbon 114, respectively. Under the condition of T'c = 303.15 K, the chosen working fluid altered fluorocarbon 114 to n-butane at about D, = 33 K, and for T'c = 323.15 K only fluorocarbon 114 was chosen. The optimal solution was obtained at T'c = 303.15 K and D t =

56.3 K and used n-butane. The flow rate of n-butane, the work supplied to a pump and the generated work were 6.17 kg/s, 5.3 kW and 335.5 kW. In Fig. 8, the enthaipy difference, as shown with the solid line, 2-3-4, is H~, ( = 2636 kW), which is equal to H m~x in this case, and the line, 1-3-4, is a new heat demand composite line. The heat supply line, 1-5, corre- sponds to H'c ( = 2300 kW), which involves a small

300

200

I00

A n " butane

f 3 o fluorocorbon 114

Tct • 303.15

s "O" - O" ~ O.

e , / " "'Q

0 i" ~, S Q

d

Tc t • 323.15 K ~o

I I I I I I o lo 20 30 40 50 60

D t ( K )

Fig. 9. Alternation of selected working fluid.

7 0

amount of latent heat generated with adiabatic expansion.

CONCLUSION

A design method for an electric power generation plant using waste heat energies is proposed in this paper. Under the condition of the maximum heat energy recovery or specified heat energy recovery, this method utilizes sufficient temperature difference between the heat supply composite line and the heat demand composite line for electric power generation. With this method, the working fluid and maxi- mum feasible size of an introduced plant can be calculated by drawing the heat composite lines in the temperature--enthalpy diagram. Moreover, it is easy to apply a synthesis method for heat exchanger net- works inclusive of heat exchangers in power plants, sequentially, using both final composite lines.

REFERENCES

1. T. Umeda, J. Itoh and K. Shiroko. Preprint of 2nd PAChEC, Denver, 28 1979).

2. Y. Naka and T. Takamatsu, Preprint of CHEMCOMP '82, Antwerp (1982).

3. B. Linnhoff, Ph.D. thesis, University of Leeds (1979). 4. J. J. Martin, J. Chem. Engng Data 5, 334 (1960). 5. R. T. Kurnik and A. J. Barduhn, Desalination 22, 211

(1978). 6. M. Kawamura, Netsukanri to Kogai 29, 45 (1977).