Use of the dimensional relation approach in a computerized model for the simulation of a batch production plant

998 I n d . E n g . Chem. Res. 1989, 28, 998-1003

Murtagh, B. A.; Saunders, M. A. Minos 5.0 User’s Guide. Technical Report Sol 83-20, Dec 1983; Stanford University.

Rich, S. H.; Prokopakis, G. J. Scheduling and Sequencing of Batch Operations in a Multipurpose Plant. Ind. Eng. Chem. Process Des. Deu. 1986, 25, 979-988.

Sparrow, R. E.; Forder, G. J.; Rippin, D. W. T. The Choice of Equipment Sizes for Multiproduct Batch Plants. Heuristic vs Branch and Bound. Ind. Eng. Chem. Process Des. Dev. 1975,14, 197-203.

Suhami, I.; Mah, R. S. H. Optimal Design of Multipurpose Batch Plants. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 94-100.

Vaselenak, J. A.; Grossmann, I. E.; Westerberg, A. W. Optimal Re- trofit Design of Multiproduct Batch Plants. Ind. Eng. Chem. Res.

Receiued for review September 1, 1988 Revised manuscript received February 21, 1989

Accepted March 9, 1989

1987, 26, 718-726.

Use of the Dimensional Relation Approach in a Computerized Model for the Simulation of a Batch Production Plant

Beno Zaidman Casali Ins t i tu te of Applied Chemistry, School of Applied Science a n d Technology, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel

In order to facilitate an early evaluation of R & D projects, a computerized model which simulates a multistage batch process in the chemical industry has been produced. The costing of feedstocks and the sizing of stage reactors is done from input stoichiometric data. Dimensional relations between the stage reactors and the auxiliary equipment items are used in order to size the equipment. The costing of equipment items is based on established cost-dimension relations, and the investment estimate is made by the factorial method. Labor costs are calculated analytically. Other cost components are determined by built-in relations. The model uses a limited number of inputs tha t can be obtained even at the very beginning of a research operation, and i t generates as output the technical and economic information needed to evaluate the proposed process. Thus, with an acceptable reliability (*25%), the model yields an assessment of the economics of the proposed process and can perform an analysis of the respective influence of various parameters.

The growing use of specialty chemicals with complex molecular structure, obtainable by multistage synthesis, has increased the interest in batch manufacturing processes. Literature on the planning and optimization of industrial batch processes is relatively abundant, especially in the area of multipurpose plants (Vaselenak 1987a,b; Kuriyan 1987), but no general simulation model has been proposed, a t least as far as we know.

A model for the simulation of an industrial multistage batch process has been built. The aim of this simulation is to provide technoeconomic data for the evaluation of R & D projects a t their early stage of implementation. As such, the model uses the limited input information that can be obtained even at the very beginning of the research. (A complete list of the input information to be furnished by the user appears in the supplementary material.) This basic constraint of the model imposes the use of adequate, simple formulas in order to perform the calculation of the layouts of an industrial batch process, which are needed for the estimation of the potential profitability of the research projects.

The use of such shortcut formulas is especially required when the estimation of the investment value-therefore sizing and costing of equipment items-is sought. The empirically determined shortcut formula used for the estimation of the investment in a continuous process (Zev- nick and Buchanan, 1963; Allen, 1975) cannot be applied with good results to batch operations. It has been decided to tackle this problem by adopting an analytical approach that deals separately with each stage of operation. This approach has been named the dimensional relation approach, and it is based on the following assumptions:

A batch process for the manufacture of a chemical product is composed of a number of consecutive production stages. In each stage, an intermediate product is obtained which is used as a raw material in the following stage.

0888-5885/89/2628-0998$01.50/0

In each production stage, the operation is performed in a batch stirred tank reactor with auxiliary standard equipment items.

The dimensions of the reactors in each stage can be established according to stoichiometric and operational data obtained from input information or compiled in a previous stage.

Quantitative relations can be established between one of the physical dimensions of the stage reactor and a functional dimension of the auxiliary equipment item.

The delivered cost of the equipment items can be expressed as a relation connected to the functional dimensions.

The application of the dimensional relation approach imposes the use of different algorithms and numerical factors, established in an empirical way. In the computerized simulation model, those relations that in our opinion, represent the state of the art, at the present time, have been introduced. Those relations can be updated, remaining in the frame of the general approach.

Determination of Quantities and Cost of Feedstocks

A subroutine calculates the quantities and cost of the feedstocks needed for the manufacture of the desired product. The method is similar to one published (Silver and Bacher, 1969) and uses the following concepts:

An intermediate is the product of a step of the manufacturing process and is related to the final product by a stoichiometric ratio SI and by a yield YT.

A reactant is a feedstock related to an intermediate by a stoichiometric ratio SR and by a yield YI.

An auxiliary is a feedstock related to an intermediate by a weight ratio AR.

The quantity RM(1,NS) of a reactant (I) needed for the manufacture of the intermediate (NS) is evaluated with the relation

0 1989 American Chemical Society

Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989 999

DECREASE NS BY 1

RM(1,NS) = (SR(1,NS) - MC(I,NS))YRR(I,NS) X RMW(I,NS)IMW(NS)-lYI(NS)-l (1)

A similar calculation is made for the quantity CA(J,NS) of auxiliary material J needed for 1 ton of intermediate NS:

CA(J,NS) = AR(J,NS)(l - YRA(J,NS)) (2)

The prices of reactants (PR) and auxiliary materials (PA) being given inputs, the calculation of the feedstock cost per tone of intermediate, COST(NS), is

COST(NS) = ?RM(I,NS)PR(I) + ?CA(J,NS)PA(J) 1 1

(3)

-

Estimation of Fixed Capital Requirements Determination of Reactor Size and Cost. As the

model simulates a single-purpose batch plant, the minimum reactor size required for the production of the desired quantity of product, Q, is sought. The minimum batch size is determined by the following parameters: total annual working hours of the equipment, TEWH; total annual volume to be processed in the stage, YVSTEP(NS), in order to produce a quantity, Q, of product; time needed to perform a full batch cycle, TBT.

The TEWH value is compiled from the inputs: working days per year and number of shifts per day.

In order to establish the value of YVSTEP(NS), the quantity of intermediate corresponding to annual production, Q, is determined:

QS(NS) = QSI(QS)IMW(NS)PMW-lYT(NS)-' (4)

The specific gravity of reactants (VR) and auxiliary materials (VA) being given inputs, the total yearly volume to be processed in a stage is YVSTEP(NS) =

QS(NS)~RM(I,NS)VR(I) + ~CA(J ,NS)VA(J ) (5) 1 1

In order to facilitate the evaluation of the batch cycle period, the total batch time is segmented into the time of reactor filling (TF), the time of heat transfer (TH), the time of reaction (TR), and the time of evacuation (TE):

TBT = (2TH) + TF + TR + T E (6)

The time span for filling, TF, is a built-in value, connected with the volumetric capacity of a filling pump provided as an auxiliary equipment item.

The reaction time is an input usually obtained from laboratory or literature data. The heating (and subse- quently cooling) time is a function of the operational temperature of the reactor (TREACT). Based on exper- imental data from a 100-L reactor, the following heating gradient has been adopted:

T H = O.OOG(TREACT - 30) ( 7 )

When the size of the reactor increases, the ratio of volume to heat-transfer surface changes, and the value of T H must be increased. A convenient correction of the heating time, for an incremental increase in reactor volume VREACT, has been calculated:

THi+l = THi + (VREACTi+l - VREACTi)-o.66 (8)

The time for evacuating the reaction mixture a t the end of the batch cycle (TE) varies as a function of the reaction mixture composition. When the reaction mixture is a liquid, the evacuation time is taken as equal to the filling

START z CALC. REACTANTS a AUXILIAR

QUANTITIES a COSTS

I -

1 CALC. YEARLY VOLUME

FOR STAGE(NS1

1 CALC.TOT.EFFECT.WORK.H 1

CALC. TIME OF HEATING FOR (MRV in, MR a VINC)

c I CALC. TOT. BATCH TIME I

CALC. NR. OF BATCHES

S MRV SUFFICIENT? -L; NO I

NO

t Figure 1. Determination of minimum reactor size.

time. If a filtration operation is necessary, a qualitative assessment of the filtration must be provided as input, and the time of evacuation is determined by built-in rates of filtration. When the filtration is assessed as difficult, an intermediate storage vessel is considered by the model, and the evacuation time is equal to the time of filling.

The total annual equipment working hours (TEWH), the annual volume to be processed in the stage (YVSTEP), and the time period of a batch (TBT) being known, the determination of the minimum reactor volume (MRV) goes through the following algorithm (Figure 1): (a) YNB = TEWH/TBT (9)

YNB is the annual number of batches possible. A correction is introduced if a weekly work interruption is planned or if the number of working hours per day is smaller than 24.

An initial value of 100 L is taken for the minimum reactor volume MRV, and the following condition is verified: (b) YVSTEP I 0.75(YNB)(MRV) (10)

An incremental increase in the reactor volume and in the time of heating (as previously described) is made by a built-in loop until condition 10 is fulfilled. The final figure obtained for the volume of the reactor is checked against a built-in value for a maximum acceptable size. If necessary, a solution comprising a number of smaller, equal sized reactors is adopted.

The cost of the stage reactors is determined from data published by Peters and Timmerhaus (1980a). The following relation has been established by us for the cost

1000 Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989

Table I . Dimensional Relations of Auxiliary Equipment auxiliary equipment selection criterion operational connection dimensional relation

1. feeding pump feedstock liquid pump flow = f (reactor volume) PSIZE = 4(0.8MRV) 2. heating furnace TREACT = 140 "C thermal load = f (reactor volume) FHL = 1.66IMRV(TREACT - 30)l 3. heat exchanger

4. distillation module (still, column, condenser, receiver)

5. filtration module (filter receiver, pump, optional stirred tank)

6. drying module (dryer, fan, vacuum pump, condenser, receiver)

7. sizing unit

TREACT = 70 "C and P = 1 atm or exogenous input

thermal load = ) (thermal load reactor)

exogenous input (0, 1, 2) still size = f (reactor volume) or still size = f (quantity of intermediate); condenser, receiver = f (still size)

rate of filtration) exogenous input (0, 1, 2, 3) filter surface = f (reactor volume,

exogenous input (0, 1, 2) drying surface = f (quantity of product, type of solvent)

exogenous input (0, 1) grinding capacity = f (quantity of product)

Table 11. Costing Relations for Auxiliary Equipment

CSIZE = l.g7DR2(150 - TREACT)(TREACT - 375)-' where DR = (MRV/1000)0.33

1.25 (1000QB) DP SIZE = 0.75MRV or

FSIZE = (MRV)RF-'TF"

DSIZE = 1000QBCl[(TB)(RT)]DR

GSIZE = 1000(QB)(WH)-'

auxiliary technical source of data equipment characteristics range costing relation*,' correlationd

1. pump centrifugal cast iron; PSIZE > 40 L/min; PCOST = 735.6 + (10.29PSIZE)MS1 or Peters and dyn head 40 psi 4 < PSIZE 5 40 1042.9 + (2.92PSIZE)MSI Timmerhaus (1980~)

2. heating furnace with Dow Them.; fired; 1.105-3.106 kcal/h

3. heat exchanger fixed tube; carbon 10 m2 5 CSIZE 5 250 m2 carbon steel; 30 bar

steel/carbon steel; 150 psi

4. distillation" carbon steel; 5 bar module

5. filtrationn vertical; pressure leaf; 1.8 m2 5 FSIZE 5 65 m2 carbon steel

6. drying module vacuum; shelf 2 m2 5 DSIZE 5 95 m2

7 . sizing unit jaw crusher 250 5 SIZE 5 4500

0.997, 0.979 FHCOST = 0.29FHLo.Bs6MS, Guthrie (1974)

0.9978 CCOST = 1164CSIZEo.525MS1 Peters and

Timmerhaus (1980b) 0.9945


Timmerhaus (1980~) 0.9975


Timmerhaus (1980~) 0.9977

DPCOST = 128.5DPSIZEo.64MS1 Peters and

FCOST = 8797eFS'ZE(002&)MS1 Peters and

DCOST = 4430DSIZEo.538MS1 Peters and

GCOST = 189GSIZEo.552MS1 Peters and

Composition of module as in Table I. bThe term MS1 has the signification of current value of M & S index/M & S index for 1980. 'A material Correlation between the algorithm presented and the graphical presentation of cost data, as correction factor is introduced in corrosive conditions.

in the quoted source.

(RCOST) of a stirred, jacketed reactor, carbon steel, a t a working pressure of 5 atm:

RCOST = 183.55(MRV)0,54MS 1 (11)

A correlation of 0.991 has been found for this relation for a capacity range between 100 and 25000 L.

When the stage reactors are operating under conditions of pressure and corrosion, the value of RCOST previously obtained must be multiplied by a pressure factor and by a material factor. The calculation of the pressure factor is based on data presented by Guthrie (1974) and has been translated by us into the following relations: for 5 I PRES I 50

RPF = 0.813 + 0.0527PRES (12)

RPF = 1.778 + 0.318PRES (13) in which PRES is the working pressure in atmospheres-a given input.

The material factor is built-in and determined by an input that is a qualitative appreciation of the corrosive conditions. Five values are available for RMF.

Determination of the Size and Cost of Auxiliary Equipment

A t each process stage, the simulation model considers the standard auxiliary equipment needed for the per- formance of the operation and computes the size and the

for 50 I PRES I 375

cost of the equipment items. The algorithm used (see Figure 2) is the following: The necessity to use a specific equipment item is

checked according to a built-in selection criterion. The size of a standard auxiliary equipment item is de-

termined by built-in, dimensional relations between the size of the reactor and a functional characteristic of the considered equipment item. The above dimensional relations have been established in the course of this work, and they express the operational connection between the two items. The auxiliary items are standard equipment items, operating under average conditions. The list of standard equipment items, selection criteria, relevant operational correlations, and dimensional relations is presented in Table I.

The cost of the auxiliary equipment item is determined by using built-in correlations between the size of the item and its cost. The costing correlations have been established from published data and are presented in Table 11.

To illustrate the application of this algorithm, we will present the selection, dimensioning, and costing of a heat exchanger. The selection criterion is a reaction temperature greater than 70 O C and a working pressure equal to or smaller than atmospheric or an exogenous input. The standard equipment is a heat exchanger, fixed tube sheet, with a pressure rating of 10 atm, carbon steel/carbon steel construction.

The following average operating conditions have been adopted: ratio heightldiameter for a standard reactor, 1.5;

Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989 1001

t YES 1 I CALC. DiMENSlON OF EQUIP. ITEM 1

CALC. STANDARD COST

CALC. SPECIAL

P W E ?

YES I I

1

Figure 2. Determination of type and size of auxiliary equipment.

heating agent (reactor), condensing steam a t 5 atm; cooling agent (condenser), water 20 "C entrance, 40 OC exit; heat-transfer coefficients k , for reactor, 1500 kcall"- C/m2/h, for condenser, 750 kcal/"C/m2/h.

The dimensional relation expresses the operational connection: the heat load of the heat exchanger must equal the heat load of the reactor:

KrSrTr = KcScTc (14)

The surface of the heat exchanger (CSIZE) with the same heat load as the reactor will be

KrTr Sc = Sr-

KcTc

(15) 150 - TREACT TREACT - 37.5

Sc = CSIZE (m2) = 1.57DR2

in which DR is the diameter of the stage reactor and has the value

DR = (MRV/1000)0,33 (16) The dimension-to-cost relation for the heat exchanger was derived from Peters and Timmerhaus (1980b) and is the following:

CCOST ($) = 1164.2CSIZE0~525(MFC)(MS1) (17)

A correlation of 0.99 has been found for expression 17 in the range 10-50 m2 heat-transfer surface.

Five built-in values for the condenser material factor, MFC, which correspond to qualitative assessments of corrosion, are provided.

Estimation of Fixed Capital The investment estimate is made by the factorial me-

thod as described by Holland et al. (1974) in which the different expenses connected with the construction of an industrial plant are compiled by the factorial multiplication of the total delivered equipment cost (TEQCOST). The different cost factors adopted and their built-in numerical

Table 111. Cost Factors for Fixed Investment Evaluation description notation value adopted

equipment installation f l

process piping f 2

instrumentation f 3 buildings f 4

facilities f 5

engineering f 7 contingency f 8

outside lines f 6

1.4OCSF 1.25 1.10 1.45CSF" 1.25CSF" 1.1OCSF" 1.20 1.35

Reduced if a "battery limits" type investment is considered.

values are presented in Table 111. For more experienced users, the possibility of choosing values of cost factors, more adequate to specific situations, is offered. The following intermediate values are estimated: total installed equipment cost

TIEQC = TEQCOSTf,CSF (18) total physical cost

total plant cost

TPLC = TPHCf7f8 (20)

A smoothing factor (CSF) has been introduced in order to avoid an unrealistic estimate of the total investment due to the high cost of equipment imposed by corrosion con- siderations. This factor is generated by a built-in relation, as a function of the corrosion coefficients of the process stages.

Estimation of Labor Costs The estimation of direct labor costs involved in the

manufacturing of the product is based on previously determined times of equipment operation. The algorithm used is the following: (a) evaluation of labor load per batch (BLL, h/batch)

BLL = (TF)(FLF) + 2(TH)(HLF) + (TR)(RLF) + (TE)(ELF) (21)

where HLF, FLF, RLF, and ELF are factors reflecting the ratio between the time of equipment occupancy and the real time of the operators. The built-in values adopted by us for these factors are FLF = 0.5, HLF = 0.3, RLF = 0.1, and ELF = 0.8. (b) determination of the unitary labor load per ton

of intermediate (ULL(NS), h/ton of intermediate)

ULL(NS) = BLL(NS)/QB(NS) (22)

(c) determination of the total labor load of the product

TLL = ~ULL(NS)QS(NS)/Q (23)

(TLL, h/ton of product)

1

(d) determination of the unitary cost of labor (UCL, $/ton

UCL = (TLL)(LC) (24)

of product)

LC ($/h.labor cost) is a given input.

Estimation of Utility Costs The subroutine that performs the estimation of the cost

of utilities (CU) is based on a relation that connects the

1002 Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989

INPUT DATA

DIRECT LABOR I

' I

I L-- ~~- ____

[ PROFIT AND LOSS ACCOUNT- MATURE YEAR I

CASH FLOW L IST FOR PLANT L IFE

[FCOYOMIC PARAMETERS 1 Figure 3. General flow sheet of the BATCHOP simulation model.

Table IV. Built-In Cost Components indirect labor maintenance

40% of direct labor 5% of fixed capital investment

for an FCI 5 $1 X lo6, 3% for FCI > $1 X lo6

supplies 15% of maintenance packaging %50/ton sales expense 10% gross sales depreciation straight line method general and administrative costs 3.5% of gross sales factor administrative costs 40% of direct labor local taxes and insurances 2% of fixed capital investment R & D 4% of sales value working capital receivable accounts (price/ton

X production/day X 30) + raw materials inventory (raw materials cost/ton of product production day X 30) + finished goods inventory X direct cost/ton of production/day X 30

cost of utilities in a process with the number of process stages, the capital intensiveness, and the cost of fuel (01): CU ($/ton) = 0.1 1201(NS0.774)(TPLC /Q)o.75110-Fa (25)

This relation has been established by Bridgewater (1976) and updated by Cevidalli and Zaidman (1980). For in- stallations with a production capacity smaller than 5000 tons/year, a multiplying correction factor (VCF) must be used. We have found that a suitable expression for this factor is

VCF = 6.03 x 10-3~0.6 (26) The supplementary layouts of the industrial enterprise

simulated by the model are established as functions of the cost components previously determined. The built-in relations express ratios between cost components, which are averages for the specific segment of the chemical industry in which batch processes can play a significant role and are presented in Table IV.

The general flow sheet of the model is presented in Figure 3.

Generated Output Information The model generates the following output: raw material

economics for each of the production stages; a list of the necessary equipment items (type, number, and cost); total fixed investment evaluation; profit and loss account for

a mature year; economic indicators of the process such as maximum cash exposure, return on investment, pay-back time, yearly cash flow (along the life of the project), net present value (for a given interest rate), and internal rate of return.

A built-in procedure allows for performing the sensitivity analysis for some of the input parameters. The influences of variations in the sale price, sale volume, fixed capital value, and raw material cost, on the economic parameters of the project, can be calculated. (Examples of the output files are given in the supplementary material.)

Computer programs for the simulation model have been written in FORTRAN IV for a main-frame computer (CDC-) and in BASIC for IBM PC. In the BASIC version, the input collection is interactive.

Discussion and Conclusions After the presentation of the simulation model, we must

deal with the question of how accurate is the information provided and especially the economic indicators which permit us to assess the potential profitability of a R & D project. The accuracy of the determination of some cost components is, in our opinion, decisive for the reliability of the model, and we will discuss them.

The raw material subprogram used, being based on stoichiometry, is not a source of error. The output obtained is as good as the input (yields, degrees of conversion, recovery, and costs).

In the determination of the fixed investment value, three possible sources of error are present: the determination of the cost of the equipment items from tables and graphs as expressed by our equations; the determination of the investment value from the total cost of the equipment cost by the multifactorial method; the built-in determination of the size of the equipment items, based on the dimensional relationships specific to our model.

Cran (1981) published a statistical analysis of the first two points and arrieved a t some interesting conclusions, relevant also to our model:

When the number of equipment items, whose cost is to be determined, is greater than 12-15 (which signifies a process with at least 3 stages for our model) and standard equipment is considered, the deviation of the sum of costs will be approximately one-third of the deviation of the individual items. This brings a deviation (our estimation) not larger than f10-15%.

Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 1003

RMF = material factor RMWi,, = molecular weight of reactant RPF, = pressure factor SI, = stoichiometric ratio between an intermediate and the

SR,,, = stoichiometric ratio between a reactant and an in-

TBT, = total batch cycle time, h TE, = time of evacuation of reactor, h TEWH = total annual working hours, h/year TF, = time of filling, h TH, = heat-transfer time, h TR, = time of reaction, h TREACT, = maximum temperature in a stage, “C VA,,, = specific gravity of auxiliary material VR,,, = specific gravity of reactants YIi,n = yield of conversion, reactantlintermediate, % YNB = annual number of batches YRAi,n = yield of recovery of an auxiliary material, % YRRi,, = yield of recovery of a reactant, % YT, = yield of conversion, intermediatelproduct, % YVSTEP, = annual volume processed in a stage, L

Subscripts i = ordinal number of a reactant in a stage j = ordinal number of an auxiliary in a stage n = ordinal number of the stage

final product

termediate

Supplementary Material Available: Required input information and an example of the output files (6 pages). Ordering information is given on any current masthead page.

Li te ra ture Cited Allen, D. H. Revised technique for Predesign Cost Estimating.

Chem. Eng. 1975, March 3, 142. Bridgewater, A. V. The Functional Unit Approach to Rapid Cost

Estimation. Am. Assoc. Cost Eng. Bull. 1976, Oct, 153. Cevidalli, G.; Zaidman, B. Evaluate Research Projects Rapidly.

Chem. Eng. 1980, July 14, 1945. Cran, J. Improved Factored method Gives Better Preliminary Cost

Estimates. Chem. Eng. 1981, April 6, 65. Guthrie, K. M. Process Plant Estimating Evaluation and Control;

Craftman Book Co. of America: CA, 1974; Chapter 5, pp 119-181. Holland, F. A.; Watson, F. A.; Wilkinson, J. K. Introduction to

Process Economics; Wiley: London, 1974; Chapter 5, pp 117-134. Kuriyan, K.; Reklaitis, G. V.; Joglekar, G. Multiproduct Plant

Scheduling Studies Using BOSS. Znd. Eng. Chem. Res. 1987,

By use of direct cost factors (as in our model) instead of a bulk factor, a deviation of f2090 can be attained. In general, “battery limits” estimation have smaller deviations than “grass roots”.

The third aspect is the estimation of the size of the equipment. The determination of the minimum reactor size is based on a previously determined mass balance, and good accuracy should be expected. The dimensional relations between the reactor and the supplementary equipment items are based on simple engineering relations, and their simplicity, paradoxically as it can appear, assure, in our opinion, their reliability. Again, the greater the number of items to be estimated, the greater the total accuracy. The evaluation of the fixed investment value generated by the simulation model is between the error limits of &25%. On two occasions, we had the opportunity to compare the values obtained for fixed investment by the application of the simulation model to those obtained by a computation made according to standard engineering methods. The values generated by the model have been greater by about 10% than those obtained by the engineering companies.

The labor cost determination as a function of the operator’s real work time is more accurate than the method of assigning one operator to each operation, which is usually applied during the early stage of a project evaluation.

The utilities cost evaluation, as it has been detailed, has a lower accuracy, and the error can be *30%. The abso- lute influence of this error on the total reliability of the model is reduced by the fact that, for a specialty chemical, the utilities cost usually represent a small fraction of the total costs.

The other cost components being a function of those previously discussed, or average fixed values, does not change the reliability of the model output.

We can conclude, by attributing to the economic parameters generated by our model, an accuracy of &25%, which is considered satisfactory for the evaluation of an R & D project at an early stage.

Nomenclature AR,,, = weight ratio between an auxiliary and an intermediate CA,,, = quantity of auxiliary material for the manufacture of

COST = cost of feedstocks, $/ton of intermediate CSF = corrosion smoothing factor IMW, = molecular weight of intermediate MC,,, = number of nonconverted moles of reactant MRV, = minimum volume of reactor MS = Marshal and Swift cost index Q = annual quantity of final product, tonslyear QS, = annual quantity of intermediate, tonslyear PA],, = price of auxiliary material, $/ton PMW = molecular weight of final product PR,,, = price of reactant, $/ton PRES, = maximum pressure in a stage, atm RCOST, = cost of reactor, $ RM,,, = quantity of reactant for the manufacture of an in-

an intermediate, tons of auxiliaryfton

termediate, tons of reactantlton of intermediate

m a ) , 2551. Peters. M. S.: Timmerhaus. K. D. Plant Desim and Economics for

Chemical Engineers; McGraw-Hill: New york, 1980; (a) Chapter 15, pp 711-809; (b) Chapter 14, pp 632-710; (c) Chapter 13, pp

Silver, L.; Bacher, S. Computer Estimation in Batch Processes. Chem. Eng. Prog. 1969, 65(6), 56.

Vaselenak, J. A.; Grossman, J. E.; Werterberg, A. W. Ind . Eng. Chem. Res.: (a) An Embedding Formulation for the Optimal Scheduling and Design of Multipurpose Batch Plants, 1987,26(1), 139; (b) Optimal Retrofit Design of Multiproduct Batch Plants, 1987, 26(4), 718.

Zevnick, F. C.; Buchanan, R. L. Generalized Correlation of Process Industries. Chem. Eng. Prog. 1963, 59(2), 70.

508-631.

Received for review June 9, 1988 Revised manuscript received April 7, 1989

Accepted April 26, 1989

Documents

Use of the dimensional relation approach in a computerized model for the simulation of a batch production plant