Thermodynamics: Second Law Analysis - American Chemical Society

11 Economic Selection of a Venturi Scrubber PETER J. PETIT

Downloaded by CORNELL UNIV on September 22, 2016 | http://pubs.acs.org Publication Date: May 28, 1980 | doi: 10.1021/bk-1980-0122.ch011

Coal Gasification Systems Operation, Allis-Chalmers Corporation, Milwaukee, WI 53201

Selecting a vendor is a task which is frequently encountered in the chemical process industries. Several quotations are soli c i t e d from different vendors on the same system or piece of equipment, with the intent of awarding the sale to the vendor having the most attractive combination of performance and cost. If performance does not vary significantly from quote to quote, the task is reduced to determining which alternative represents the lowest total (capital plus operating) cost. There is usually little problem in obtaining capital costs from the vendors, but operating costs are often more d i f f i c u l t to establish. This is particularly true if the equipment u t i l i z e s an unconventional form of "fuel" (such as steam, waste heat or a pressure drop) instead of or in conjunction with the more common fuels (such as coal, oil, or e l e c t r i c i t y ) . Not only can it be more d i f f i c u l t to price accurately the unconventional fuels, but also variations in the rate at which these fuels are used may have significant impact on the flows and balances in the rest of the plant, of which the equipment is to be a part. The traditional means for assessing operating cost involves the use of a perperty called energy, the obvious strategy being to determine a "cost per unit energy" for each form of fuel, which can then be applied to the flow rate of that fuel. Though this strategy works well in the more straightforward cases, there is one major flaw in its logic which can lead to errors in more complicated problems: Energy does not define a substance's value as a fuel. For example, a unit of e l e c t r i c a l energy can potentially do more "work" than a unit of low temperature steam energy, and a unit of energy in a i r at ambient temperature, pressure and humidity can do nothing. At the same price per unit energy, e l e c t r i c i t y is the best bargain of the three. What property, if not energy, imparts fuel value to a substance? The answer is available energy. Available energy is any form of potential energy (thermal, chemical, e l e c t r i c a l , etc.) residing in a substance which is notinequilibrium with the

O-8412-0541-8/80/47-122-187$05.00/0 © 1980 American Chemical Society Gaggioli; Thermodynamics: Second Law Analysis ACS Symposium Series; American Chemical Society: Washington, DC, 1980.


188

THERMODYNAMICS: SECOND LAW ANALYSIS

environment, measuring the substance's c a p a c i t y t o d r i v e proc e s s e s — t o perform u s e f u l "work." ("Potential energy" is used here in a broader sense than the t r a d i t i o n a l concept o f energy a s s o c i a t e d w i t h a conservative force f i e l d . ) T h i s paper addresses the problem o f choosing between two vendors who have submitted q u o t a t i o n s on a v e n t u r i scrubber and cyclone combination which will be used in a l a r g e p l a n t t o clean a p r e s s u r i z e d gas stream. The method o f economic a n a l y s i s employed here is based on the concept o f a v a i l a b l e energy, which is rooted in the second law o f thermodynamics, r a t h e r than on energy, which is a f i r s t law concept. When energy is used to assess o p e r a t i n g costs in t h i s type o f problem, it g e n e r a l l y becomes necessary t o c a r r y out a d e t a i l e d energy balance t o assess c o r r e c t l y the e f f e c t on p l a n t o p e r a t i n g cost o f switching from one vendor's equipment t o another. In large o r complicated systems where t h i s is i m p r a c t i c a l , c o r r e c t i o n s ( e f f i c i e n c i e s ) are sometimes employed which p u t all energy u n i t s on an "equivalent" b a s i s . U n f o r t u n a t e l y , t h i s l a s t method is prone t o e r r o r and m i s i n t e r p r e t a t i o n . In t h i s paper, the p r o p e r t y c a l l e d a v a i l a b l e energy will be used t o assess o p e r a t i n g c o s t s . Because a v a i l a b l e energy does define a substance's p o t e n t i a l value as a f u e l , no c o r r e c t i o n s are needed when the consumption o f one f u e l is compared t o that o f another. F o r example, one u n i t o f steam a v a i l a b l e energy s e r v i n g to " f u e l " a t u r b i n e is f u l l y e q u i v a l e n t t o one u n i t o f e l e c t r i c a l a v a i l a b l e energy d e l i v e r e d t o an e l e c t r i c motor. Extensive treatments on the meaning and methodology o f a v a i l able energy have been presented in s e v e r a l other papers U-\7) The emphasis here will be p l a c e d on i l l u s t r a t i n g another example of the a p p l i c a t i o n o f a v a i l a b l e energy c o s t i n g a n a l y s i s t o a r e a l - l i f e problem. A p p l i c a t i o n o f A v a i l a b l e Energy Methodology t o Vendor Problem

Selection

The f o l l o w i n g is a case study in the a p p l i c a t i o n o f second law a n a l y s i s to problems in which choices between a l t e r n a t i v e concepts must be made on the b a s i s o f o v e r a l l economics. Quotes from two vendors were obtained on a v e n t u r i scrubber and cyclone combination, s i m i l a r t o t h a t shown in Figure 1, t o be used f o r c l e a n i n g a p r e s s u r i z e d gas stream. The information from the quotes is contained in Table I. From the information p r e s e n t ed it is not immediately c l e a r which equipment would be the bett e r choice. A s u p e r f i c i a l look a t the t a b l e might lead to the c o n c l u s i o n that Unit A is p r e f e r a b l e : I t s i n i t i a l cost is l e s s and the operating costs a s s o c i a t e d with pump power will be l e s s . A f t e r f u r t h e r o b s e r v a t i o n , however, it is r e a l i z e d that there is an o p e r a t i n g cost a s s o c i a t e d with the pressure drop o f the gas flowing through system A; " f u e l " must be s u p p l i e d somewhere in the system in order t o compensate f o r t h i s . Should other matters be

Gaggioli; Thermodynamics: Second Law Analysis ACS Symposium Series; American Chemical Society: Washington, DC, 1980.


PETIT

Venturi

Scrubber

GAS INLET

SHAFT POWER

MAKEUP WATER

SPRAY PUMP

Figure 1.

Combination venturi scrubber and cyclone for gas cleaning



190

TABLE I. INFORMATION CONTAINED IN VENDOR QUOTES ON VENTURI SCRUBBER AND CYCLONE UNITS


System Cost Cleaning E f f i c i e n c y F i r s t Law E f f i c i e n c y

Vendor A

Vendor Β

$8000 97. 0% 98. 7%

$9000 97.0% 98.9%

Scrubber Pressure Drop 55.1 kPa Spray Pump Power 0.15 kW Gas Flow Rate : kg/hr Inlet 24,755 Exit 24,765 Gas Temperature: °C Inlet 37.8 Exit 36.1 I n l e t Gas Pressure 474.3 kPa

8 psi 0.2 hp lb/hr 54,576 54,598 Op

100 97 68.8 p s i

0 kPa 3 kW kg/hr 24,755 24,753 °C 37.8 37.8 474.3 kPa

0 psi 4 hp lb/hr 54,576 54,572 OF 100 100 68.8 p s i

p r e s s i n g and the choices appear t o be evenly matched, it might be hard t o j u s t i f y t a k i n g the time t o work through the extent o f a n a l y s i s t h a t a f i r s t law study ( n e c e s s a r i l y , o f the whole sys tem) would r e q u i r e ; s i n c e the c a p i t a l cost is s u b s t a n t i a l l y lower, system A would probably be chosen. In c o n t r a s t , it is hard to j u s t i f y not u s i n g an a v a i l a b l e energy a n a l y s i s in t h i s case, since the l o g i c and c a l c u l a t i o n s , being s t r a i g h t f o r w a r d , take so little time and e f f o r t . An a v a i l a b l e energy a n a l y s i s o f t h i s problem c o n s i s t s o f f i r s t e v a l u a t i n g the r a t e s o f a v a i l a b l e energy d e s t r u c t i o n f o r the two systems. Using the n o t a t i o n o f Figure 1, the same a v a i l a b l e energy balance can be w r i t t e n f o r both A and B: = A v a i l a b l e Energy D e s t r u c t i o n = (Â - JL ) + Â + i = ΔΑ + Â + k I Ε ρ M gas ρ M T

Since the makeup water is e s s e n t i a l l y " f r e e " from the e n v i ronment it t r a n s p o r t s no a v a i l a b l e energy: Â

M

= 0 f o r both vendors A and B.

The a v a i l a b l e energy input to the spray pump is merely the pump s h a f t power requirement : Â

ρ

= W . f o r both vendors A and B. shaft

A v a i l a b l e energy t r a n s p o r t e d with the gas will be evaluated as three independent c o n t r i b u t i o n s : thermal, p r e s s u r e , and chemi cal. The change in t o t a l a v a i l a b l e energy content o f the gas may be expressed


11.

Venturi

PETIT

ΔΑ

gas

= k

191

Scrubber

a

I

- À = m (a4, -+a -r + i_ _) Έ I therm,! press,! chem,I T

therm,E

press,E

chem,E)

Note from the information in Table I that the change in mass (and presumably the change in composition) of the gas as it flows through either scrubber is very small. If we assume that in both cases m = m-j-, then the above expression for AAg reduces to: E

as


ΔΑ

gas

= πι (Aa + Aa + Aa , ) I therm press chem iL

If the composition remains essentially unchanged throughout either scrubber, then Aa

0 for both vendors A and B.

chem

The change in thermal available energy per unit mass will be approximated using c = 1 kJ/(kg K) = .24 Btu/(lb °F), assumed constant for such a small change in temperature : p

Aa

Τ f = 'Τ

therm

C

Aa Aa

Τ (l--°)dt ρ τ

P(TE " V

"

o

T

c

p

l n

(

V V

0 for vendor B, since Τ = Τ . Ε Χ

therm therm

c

= -.09 kJAg = -.04 Btu/lb gas for vendor A.

The drop in available energy content of the gas stream due to pressure reduction can be quickly evaluated: Aa press For vendor B, Aa press

RT

Q

in ( p / ) E

Pl

0 since P„ = P„ Ε I

But for vendor A, = 0.0083178(kJ/gmole Aa press

°K)(23g/gmole)(298.15°K)X

kJ In (419.2/474.3) = - 13.32 — = -5.73 Btu/lb

The change in total available energy content of the gas stream may now be evaluated by substituting the above values into


192


the expression for AÂg . A summary of the destructions of available energy in the system is presented in Table II. An available energy consumption analysis lends i t s e l f to this method of presenting results since comparison of corresponding consumptions may be done at a glance. ag

TABLE II.


SUMMARY OF AVAILABLE ENERGY CONSUMPTIONS FOR VENTURI SCRUBBER/CYCLONE COMPARISON Location of Consumption of Available Enerqy

kw

hp

kw

Pump Power, A

0.15

0.2

3

4

0

0

0

0

Vendor Β

Vendor A

ρ Makeup Water, A M Gas Losses, A gas : thermal chemical pressure

0.7 0 91.6

0.9 0 122.9

0 0 0

0 0 0

Total Consumption

92.45

124.0

3

4

Conclusions Presuming that the information quoted by the vendors is ac curate, then scrubber system A is effectively consuming over 30 times the "power" that system Β consumes to do the same jobl The results, presented in Table I I , show clearly that the 55.1 kPa (8 psi) pressure drop reduces all other consumptions of available energy to insignificance. If additional compressor capacity must be purchased to cover this power drain, the added capital cost would be roughly $ = — η

($50/hp) = $9276

ιι

where = 0.68 represents a typical second law efficiency for a compressor. (Compressor costs are usually scaled on input power, which may be estimated here using as assumed value of n j j . The value of n j j used here neglects any thermal available energy which the compressor might impart to the gas. This was done so that an accurate estimate of additional compressor input power might be obtained from the pressure available energy r i s e alone.) This raises the effective capital cost of choosing ven dor A to $17,276.


11.

PETIT

Venturi

Scrubber

193

Furthermore, assuming 300 hrs/yr operation and a compressor with η-j-j 0.68, the cost of power to operate system A would be =

$/yr = (.15 + 91.6/0.68) kW ($0.025AW-hr) (3000 hrs/yr) = $10,114/yr compared to system Β operating costs of


$/yr = 3 kW ($0.025AW-hr)(3000 hrs/yr) = $225/yr Under such circumstances, the scrubber/cyclone of vendor Β is clearly the better choice. Since no additional compressor capacity would be required, the actual capital costs associated with vendor Β are nearly 50% lower than for vendor A. Further more, vendor B's operating costs due to power consumption are a l most negligible compared with vendor A's—lower by a factor of 45, when a typical compressor efficiency (njj) is taken into account. (With such evidence in hand, one might want to give vendor A a change to modify his operating s p e c i f i c a t i o n s — o r his price!) (In this example, a subtle advantage of second law analysis has come to light. Any available energy flow or consumption can properly be expressed directly in kW (hp), which often tends to improve one s "feel" for what is actually happening. In contrast, it is usually inappropriate to express certain kinds of energy flows or losses in dimensional units normally reserved for work or electricity.) 1

Closure For the venturi scrubber/cyclone comparison, evaluation of available energy consumptions revealed that the 55.1 kPa (8 psi) pressure drop of system A implied additional operating and capital costs which by far exceed its apparent cost savings over system B. This dramatic revelation proceeded from only a very few straight forward calculations. The available energy consumption represented by the pressure drop was 92 kW (123 hp). These results not only illuminated the impact of the pressure drop on power consumption but also enabled the associated capital and operating cost implications to be quickly and straightforwardly evaluated. L i s t of Symbols A a Cp h m ρ

= = = = = =

available energy per unit time specific available energy heat capacity at constant pressure specific enthalpy mass flow rate pressure


194 *0 s τ w

X


= universal gas constant = specific entropy = temperature = power; work rate = mole fraction = f i r s t law efficiency = second law efficiency; true efficiency


Subscripts and Superscripts δ Ε I M Ρ 0

= = = = = =

destruction exit inlet makeup water shaft power reference ("dead") state

Literature Cited 1. 2. 3.

4. 5. 6. 7.

Gaggioli, R.; Petit, P. Chemtech, 1977, 7, 496. Rodriguez, L.; Petit, P. "Calculation of Available Energy Quantities," this volume. Wepfer, W.; Gaggioli, R.; Obert, E. "Proper Evaluation of Available Energy for HVAC," ASHRAE Paper No. 2524 (to appear in ASHRAE Transactions, 1979). Tribus, M.; Evans, R. "Thermoeconomics," UCLA Report No. 52-63, 1962. Obert, E.; Gaggioli, R. "Thermodynamics," 2nd ed., New York: McGraw-Hill Book Co., 1963. Reistad, G.; Gaggioli, R. "Available Energy Costing," this volume. Wepfer, W. "Applications of Availability Accounting," this volume.

RECEIVED

October 26, 1979.


Thermodynamics: Second Law Analysis - American Chemical Society

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