Optimiz. Ciclos Limpieza Intercamb

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lassically, process optimization evalu-ates the trade-off of capital expendi-ture against reduced operating ex-

penses. The standard approach in-volves an incremental analysis using

a discounted cash-flow technique, such as netpresent value (NPV) or discounted cash-flow

rate of return (DCFROR). However, thismethod is not applicable in all situations.

For example, when determining an opti-mum cleaning schedule for heat exchangers,one must factor in that a one-time expendi-ture can lead to both a reduction in expensesand a change in the life of the project. This isalso a good example of an optimization whereexpenses vary with time (unsteady state). Inthis case, incremental analysis is still re-quired, but the discounted cash flow analyseswill require the use of the equivalent uniformannual worth (EUAW) technique. This arti-

cle explains how to use the this technique todetermine the optimum heat exchanger clean-ing schedule.

The theoryConsider a single bank of process exchang-

ers, as shown in Figure 1. Assume that the tar-

get temperatures for both the hot and coldstreams are such that any degradation in ex-changer performance results in incrementalutility consumption on trim heaters and cool-ers elsewhere in the plant.

The equations associated with this system are:

QE100 = mcCpc(t2t1) (1)

QE100 = mhCph(T2T1) (2)

QE100 = UATlm (3)

C

Optimize

Heat ExchangerCleaning Schedules

Evaluate the trade-offs between a one-timeexpenditure and reduced operating expenses,

increased income, and/or longer operating life span.

Brendan R. ODonnell

and Bruce A. Barna,

Michigan Technological University

Chris D. Gosling,

UOP LLC

56 www.aiche.org/cep/ June 2001 CEP

Heat Transfer


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QE101 = mhCph(TfT2) (4)

QE102 = mcCpc(tft2) (5)

Note that any change in process duty due to fouling orcleaning results in a similar change in the duty for bothtrim exchangers. Thus:

QE-100 = QE-101 = QE-102 (6)

Economic parametersThe analysis requires an understanding of the loss in

performance vs. time for the process exchanger due to

fouling and of the incremental utility rates for the plant.The overall heat-transfer coefficient, U, can be trackedvs. time to indicate the loss in process exchanger perfor-mance as the heat exchanger fouls. Given the change inU, Eqs. 15 can be solved to arrive at the new processand trim duties.

Although not required, it can be useful to model thedegradation in U with time. A first-order degradationequation works quite well for many fouling situations:

dU/dt= kU (7)

or the integrated form:

ln(U/U0) = k(tt0) (8)

or:

U= U0ekt (9)

By fitting a limited amount of operating data to thisequation, the required time vs. cost information can becalculated. This approach can also be used to integratethe performance over the year to more correctly deter-mine annual costs. In addition to heat-transfer informa-tion, the following cost data are also needed:

minimum acceptable return (MAR); marginal hot utility cost; marginal cold utility cost; and direct and indirect cost of cleaning process exchanger.

Finding an optimum scheduleUsing the decline of U over time, one can calculate

the duty of the process exchanger from the end of year 0to the end of years 1, 2, 3, and so on, by solving Eqs. 13simultaneously. Because energy not recovered in the pro-cess exchanger must be made up in the trim exchangers,incremental increases in utility costs that result for eachyear of the analysis can also be calculated.

Cleaning is a one-time expense, which is assumed toreturn U to its original (i.e., clean exchanger) value. Fig-ure 2 plots U vs. time for various cleaning schedules.

CEP June 2001 www.aiche.org/cep/ 57

020

30

40

50

60

70

80

90

100

1 2 3 4 5

Every 5 yr

Every 10 yr

Every 2 yr

Time, yr

U,

Btu/ft2hrF

6 7 8 9 10

s Figure 2. Uvs. time for various cleaning schedules.

Nomenclature

A =process exchanger area, ft2

Cpc =heat capacity of cold stream, Btu/lbF

Cph =heat capacity of hot stream, Btu/lbF

k =fouling rate constant for degradation ofU, yr1

mc =mass-flow rate of cold process stream, lb/h

mh =mass-flow rate of hot process stream, lb/h

Q =exchanger duty, Btu/h

t =time, yr (or mo)

t0 =initial time (year 0)

t1 =entering cold stream temperature, F

t2 =cold stream temperature exiting process exchanger, F

tf =target temperature of cold stream, F

T1 =entering hot stream temperature, F

T2 =hot stream temperature exiting process exchanger, F

Tf =target temperature of hot stream, F

Tlm =log mean temperature difference=[(T2t1) (T1t2)]/ln[(T2t1)/ (T1t2)], F

U =overall heat-transfer coefficient, Btu/ft2hF

Process Exchanger(E-100)

Trim Cooler(E-102)

Trim Heater(E-101)

T1

Tf

mh, Cph

tf

T2t1

t2mh, Cpc

s Figure 1. Model heat exchanger system.


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Cleaning changes the project life, oranalysis period, to the number ofyears between cleanings. A cashflow analysis is used to find incre-mental increases in operating ex-

penses until the year of cleaning.

Cleaning is treated as a year zerocost for a new analysis period. Dis-counted cash flow is used to calcu-late a net present value for thecleaning and subsequent incremen-tal operating costs. From the net

present value, an EUAW can be calculated based uponthe life of the project between cleanings.

Using EUAW allows a direct comparison of resultsbetween projects with varying life spans. Plotting EUAWvs. cleaning schedule reveals the maximum annual worthor optimum cleaning schedule.

Using the techniqueWe can illustrate the application of this technique bylooking at a model heat exchanger system. Table 1 summa-rizes the initial conditions and requirements for this system.

A sensitivity analysis was conducted to investigate theeffect of the fouling rate, represented by the degradationconstant (k), and the effect of the total cleaning cost overthe following ranges: k= 0.01, 0.05, 0.1, 0.2; total clean-ing costs = $5,000, $10,000, $15,000, $20,000.

The fouling rate constant is easily calculated from Uvs. time historical operating data (Figure 3). The first-order fouling model fits the data with a slope, which isthe value ofk, equal to 0.1 yr1.

Using this model, we can readily find discrete U val-ues at the end of each year. The degradation ofU is con-tinuous over time, and the first-order model could be in-tegrated to determine incremental trim duties and costsfor each year. However, the slow change in U in this ex-ample indicates that linearizing the curve over a one-year

period is reasonable and that the average value can be

used to represent each year. Table 2 presents the solutionof Eqs. 13 and the resulting required duties and energycosts for a degradation constant ofkequal to 0.1 yr1.

To evaluate different cleaning options, we assume thata cleaning occurs in year zero for all cases and starts anew project life for the analysis. For example, a two-yearcleaning schedule would have the following cash flows:

Year 0 expenses = 0 + cleaning cost. Year 1 expenses = hot utility + cold utility for aver-

age decrease in U from Year 0 to Year 1. Year 2 expenses = hot utility + cold utility for aver-

age decrease in U from Year 1 to Year 2.A cash flow table, incorporating the marginal tax rate,

Heat Transfer


0

10

1 2 3 4 5 6 7 8 9 10

Time, yr

U,Btu/ft2hrF

100

s Figure 3.The fouling

rate constantcan be calculated

from a Uvs.time plot.

Table 2. Incremental utility increase for k= 0.1 yr1.

Process Duty, Trim Duty, Incremental Incremental

QE100, QE101, QE102 Hot Utility, Cold Utility,

Year MM Btu/h MM Btu/h $/yr $/yr

0 10.00 0.00 0 0

1 9.93 0.07 3,269 327

2 9.76 0.24 10,415 1,042

3 9.59 0.41 18,156 1,816

4 9.40 0.60 26,489 2,649

5 9.19 0.81 35,408 3,541

6 8.97 1.03 44,902 4,490

7 8.75 1.25 54,951 5,4958 8.50 1.50 65,532 6,553

9 8.25 1.75 76,615 7,661

10 7.99 2.01 88,161 8,816

Table 1. Data for model heatexchanger system.

Hot Fluid:

mh = 50,000 lb/hCph= 0.5 Btu/lbFT1 = 600FT2(Clean) = 200F

Cold Fluid:mc= 40,000 lb/hCpc= 0.5 Btu/lbFt1 = 50Ft2(Clean) = 550F

Exchanger:UClean= 100 Btu/ft

2hFA = 1,098 ft2

Economics:

MAR = 20% DCFTax Rate = 34%Hot utility cost = $5.00/MMBtuCold utility cost = $0.50/MMBtuOperation time = 8,760 streamh/yr

(100% service factor)


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is developed for each cleaning case, and the NPV andEUAW are calculated. This is repeated for cleaning inter-vals of one to ten years and all combinations of the twosensitivity variables (total cleaning cost and degradationconstant). The results are presented in Figures 47. (The

EUAW results are all negative, as expected for a cashflow analysis that has only costs and taxes involved.)

The optimum occurs at the maximum EUAW (mini-mum cost). As we would anticipate, higher fouling rates(degradation constant) lead to shorter optimum cleaningcycles, and higher total cleaning costs (direct cost plusdowntime) lead to longer optimum cleaning cycles.

It is interesting that the optimum cleaning schedulesare all relatively short for the range of parameters used inthis model system. For example, only at the very low kvalues or high cleaning costs are the optimum cleaningcycles three or more years. This may suggest that current

practices deserve review.

The plots in Figures 47 can also be used to estimatethe incremental cost of using a nonoptimal cleaningcycle. This is done by comparing annual worth at the op-timum cleaning cycle to annual worth at the actual clean-ing cycle. For example, consider a process where the

degradation constant is k = 0.05 yr1

, incremental utilitycosts are similar to the model system, and total cost ofcleaning is $5,000 (the upper cleaning cost curve in Fig-ure 5). If the exchanger is cleaned every eight years, theincremental losses due to not cleaning at the optimumare approximately $5,000/yr.

Example

This example illustrates the application of this opti-mization technique to a commercial problem where thesolution lies outside the boundaries of the previousmodel system. The data (Table 3) are representative ofactual performance results for a combined feed exchang-

CEP June 2001 www.aiche.org/cep/ 59

0

0

-4

-8

-12

-16

1

$5,000

Total Cleaning Costs

$10,000

$15,000

$20,000

2 3 4 5 6 7 8 9 10

Cleaning Interval, yr

EUAW,

$1,0

00

s Figure 5. EUAW vs. cleaning interval for k= 0.05 yr1.

0

0

-5

-10

-25

-30

-20

-15

1

$5,000


$10,000

$15,000

$20,000

2 3 4 5 6 7 8 9 10


EUAW,$

1,000


0

0

-10

-20

-50

-60

-40

-30

1

$5,000Total Cleaning Costs

$10,000

$15,000

$20,000

2 3 4 5 6 7 8 9 10


EUAW,$

1,000


0

0

-4

-8

-12

-16

1

$5,000


$10,000

$15,000

$20,000

2 3 4 5 6 7 8 9 10


EUAW,$

1,000



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er in a gas-oil hydrotreater. The unit is a 12 million bbl/d

hydrotreater processing a 30 API gas-oil. As in themodel system, trim units must supply energy not recov-ered in the process exchanger. The heated reactor feed issent to a f ired charge heater and the cooled reactor efflu-ent is sent to a water-cooled condenser.

Results. Based on the overall heat-transfer coeffi-cient data, k= 0.35 yr1. Rapid fouling requires the anal-ysis to be performed on a monthly basis (rather than theyearly basis used previously), so the input parameters,operation time, MAR, and k are adjusted to reflect amonthly analysis.

Equations 13 are solved and cash flow tables gener-ated for cleaning intervals of 1 to 24 months. The results

are presented graphically in Figure 8. The optimumcleaning schedule is found to be 10 months.

As before, we can use the results to examine the im-pact of cleaning at a less-than-the optimum point. Stan-dard practice in this service is to clean in conjunctionwith normal turnarounds at 24 months. The incrementalcost for a 24-month cleaning interval over the 10-monthoptimum is (from Figure 8) approximately $15,000/yr.

No downtime has been built into the cleaning cost. Ifdowntime were a component, then the incremental costfor cleaning at a turnaround would have to be correctedto reflect the fact that downtime costs should not be as-signed to the cleaning operation at a normal turnaround.

Closing thoughtsThe optimization techniques illustrated here permit

prediction of the optimum cleaning schedule from thefouling rate data, incremental utility costs, and cleaningcosts for a given situation. The same optimization tech-niques could also be applied to a wide variety of opti-mization problems dealing with expense trade-offs, suchas those often found in optimization related to mainte-

nance and repairs.CEP

Heat Transfer


0

0

-4

-8

-12

-165

Month

EUMW,$

1,000

10 15 20

s Figure 8.EUAW vs.

cleaning intervalfor gas-oil

hydrotreaterexample (k= 0.35

yr1 and totalcleaning costs =

$22,000).

Table 3. Gas-oil hydrotreater combined

feed exchanger data.

Hot Fluid:

mh = 160,000 lb/hCph= 0.56 Btu/lbFT1 = 700FT2(Clean) = 312F

Cold Fluid:mc= 160,000 lb/hCpc= 0.53 Btu/lbFt1 = 250Ft2(Clean) = 660F

Exchanger:UClean= 45 Btu/ft

2hFU1 = 38 Btu/ft

2hF (6 mo)U2 = 32 Btu/ft

2hF (12 mo)U3 = 27 Btu/ft

2hF (18 mo)

U4 = 22 Btu/ft2hF (24 mo)A = 15,412 ft2 (4 shells)

Economics:MAR = 10%Hot utility cost = $4.25/MMBtuCold utility cost = $0.40/MMBtuCleaning costs = $22,000

(labor and materials)Operation time = 8,760 streamh/yr

(100% service factor)

B. R. ODONNELL is an MS candidate at Michigan Technological Univ.,

Houghton, MI in the field of process design and optimization. His

primary research focus is developing software to automate

opportunities for process improvement. He obtained a BS in chemical

engineering from Michigan Tech in 1999 and is a member of AIChE.

B. A. BARNAis a professor of chemical engineering at Michigan

Technological Univ., Houghton, MI (Phone: (906) 487-2569; Fax: (906)

487-3213; E-mail: [email protected]). He holds BS and MS degrees in

chemical engineering from Michigan Tech and a PhD in chemical

engineering from New Mexico State Univ. Prior to joining the faculty at

MTU, he worked as a process engineer for Reynolds Metals and Exxon,

and as a plant engineer and plant manager for Kalsec, Inc. He is aregistered professional engineer in Michigan. He is a member of AIChE.

C. D. GOSLING is the alkylation, oxygenates, and treating technologies

manager in UOPs FCC, Alkylation, Oxygenates, and Treating Business

Group, Des Plains, IL (Phone: (847) 375-7759; Fax: (847) 391-2253;

E-mail: [email protected]). He joined UOP after graduating from

Michigan Technological Univ. in 1980 with a BS and MS in chemical

engineering. He has had assignments in UOPs technical service and

R&D departments, involving development and commercialization of a

number of new technologies and products. Since 1996, he has been

responsible for new alkylation technology developments. He is a

registered professional engineer in Michigan.

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Optimiz. Ciclos Limpieza Intercamb