I
KENNETH M. WATSON Lake Zurich, 111.
Economics of Process Development
SMALL once collected must be used in conjunction with other techSCALE DATA
niques to achieve a good development program with maximum profit. Thus the question arises: How is a good program recognized and defined? Many indexes of attractiveness for proposed research projects are used ( 9 ) and others appear each year. Most of these involve three basic factorsestimated 'financial return, cost of research, and probability of success. Development Venture Worth
Indices of attractiveness may be based on the venture profit and present venture worth concepts introduced by Happel and Aries ( 2 , 3) for evaluating the desirability of initiating or modifying a commercial operation. Venture profit is defined as the annual incremental net return above that corresponding to the minimum acceptable return on the capital involved. Thus, for any year during the life of a project initiated a t time B and terminated a t time F
ZZ is the total capital invested during B
the life of the project, discounted to time B a t the minimum acceptable return rate, .2, Present venture worth W is the summation of the venture profit V for the life of the commercial project, discounted to a present worth basis a t the minimum acceptable return i,. T h e most attractive commercial projects are those having maximum present venture worths and maximum average rates of venture profit return on capital invested.
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Variation of venture profit during the life of a hypothetical proposed development project is shown by the solid lines in Figure 1. During the initial exploratory phase OA of development, wide ranges of conditions are investigated to determine over-all relationships between rates, product distributions, and process variables. During the second, confirmatory phase AB, these relationships are tested by detailed investigations in the indicated optimum region. If results are favorable, the decision to commercialize is a t time B when a period of design and construction, BC, is initiated. Large scale operations begin a t time C with a resulting venture profit which increases as the operation is perfected and markets are expanded. At time D expansion of operations occurs, followed by a period of relatively constant and high venture profits. At time E, because the process or product is obsolete, a decline in profit begins, and a t time F the profit falls below the minimum acceptable value. T h e differences between parts A and B of Figure 1 indicate the effect of B and C. In Figure 1.A, early development leads to advantages from superior patent protection. first commercial production, and capture of the initial market. I n Figure 1,B, these advantages are lost to competitors. When the decision to commercialize is made, past research and development costs are not considered because their magnitude has no bearing on the attractiveness of future expenditures. However, when a development program is initiated, future development costs are of primary importance-they are largely tax-deductible and may be considered as negative venture profits which continue during the development period, OB, a t variable annual rate, J k . Development costs may be combined with commercial venture urorth in a n expression for development worth, WD:
INDUSTRIAL A N D ENGINEERING CHEMISTRY
WD =
2
i;=R
W-
Jk(l
-
t ) (1
+
(2)
k=O
u', is the venture worth a t time 0 expressed as equivalent value a t time B. Thus, as development progresses, re-evaluating W D should give larger values because less development costs are included. If large capitalized costs such as a specialized pilot plant are involved, a someirhat more elaborate expression is required for development costs. T h e broken lines in Figure 1 represent the development costs and venture profits reduced to their equivalent values a t time B Compound interest a t rate i, is charged on development costs incurred between the time of evaluation 0 and time B. Venture profits are discounted to time B by dividing by the compound interest factor (1 ' " ) , z Thus, a t the time of evaluation 0. the development project has a net worth a t time E equal to the algebraic sum of the crosshatched areas.
+
Development Project Indexes
Unfortunately, development venture worth must be a n estimated forecast which may involve errors from a variety of sources, including technical development data, cost estimation, and market analysis. Before using it as an index of attractiveness, some factor must be introduced to reflect the probability that the venture will proceed as forecast. One method is to multiply by a probability factor between 0 and 1.0, based on experience and judgment. A procedure less dependent on intuition is to make two estimates of an index factor-one where in the range of uncertainty, major contributing factors are assumed to be a t the favorable extreme, and the other where such factors are assumed to be a t the unfavorable extreme. The arithmetic mean of the two estimates may be taken as the most prob-
t
!Io L L -
8 a W
TIME
F
lA I
U
3 !-
B
Z + W
>
F I
A
Figure 1. A.
B.
I
Development time has a marked effect on venture profit
Early development means superior patent protection, first commercial production, capture of initial market With extended development time the advantages are lost to competitors
able value, +av. The standard deviation s is one half of the difference between the two. If a standardized procedure is followed in preparing the two estimates, a confidence factor, 7, for comparing index factors of projects having different degrees of certainty may be arrived a i by assuming that 4, the estimated index factor, has a normal. distribution with standard deviation ws. Constant w, the conservatism weighting factor, has a value greater or less than 1.0 depending on the standardized procedure used in preparing the two estimates and on the weight which it is elected to assign to conservatism in the comparisons. Both procedures for calculating the estimates and the value of w must be constant in any series of comparisons. Then, if &m, ni is the minimum acceptable value of 4, (3) where the function f is the apparent noimal probability that a n estimated value of 4 will fall between c$~,,, and 24,“ 4min. This function is the area under the standard normal probability curve #,,,i,)/ws and ( b i n between (iV +,,)/ws. Thus, if (daV- &ln)/wS = 2.0, the value of q is 0.954. Values of (1 - q ) are plotted against - &in)/ IUS in Figure 2. Two indexes of attractiveness for comparing development projects are obtained by combining Equations 2 and 3: Expected development worth, a is
For a, the ‘minimum acceptable value can be assumed zero and &,in = 0 used in calculating qa. Expected ratio of return of development cost, p is
For /3 the lowest acceptable value may be taken as 1.0 and &,in = 1.0 used in calculating vp. A third index is obtained by converting the development venture worth to a n average annual venture profit by the interest and amortization factor as proposed by Happel ( 2 ) . The index factor is the ratio of the probable annual venture profit to the total capital involved. Expected average venture return on capital is Y =
-
-
-
For y, the minimum acceptable value , = 0 used may be taken as zero and + in calculating q y . B(Z Iw) is the total capital requireB
+
ment of the commercial project discounted to time B when development is terminated. The venture worth and average venture return concepts are valuable as a basis for indexes of development at-
tractiveness because they focus attention on the incremental gain in profit rate which is expected from a development project. A convenient means is also afforded for combining and comparing total development costs with total expected benefits on a common basis. An alternative measure of profitability is the “discounted cash flow” or “interest rate of return” or “profitability index” recently discussed by Weaver and Reilly (70) and by Reul (8). This method in effect determines the rate of annual return which must be substituted in Equation 1 for venture worth to be zero. I t is determined by a graphical procedure where rate of return is plotted against either venture worth or ratio of capital to the total discounted cash flow as demonstrated by Reul ( 8 ) . The advantage of the interest rate of return is that it gives a single, easily understood measure of profitability which does not depend on establishing a n acceptable minimum rate of return. The fact that it requires a series of venture worth computations for its evaluation is of little significance because the effort required in the computation of such indexes is negligible compared to that involved in arriving a t the necessary data. I t may be desirable to consider both venture worth and interest rate of return in appraising a project. Indexes of attractiveness similar to y are obtained by applying a suitable confidence factor to either the interest rate of return or to the difference between the interest rate of return and the acceptable minimum rate. This difference will be larger than the average venture rate of return in Equation 6, but it will be subject to similar variations. Present venture worths for calculating indexes a! and /3 corresponding to any desired minimum rate of return are readily obtained from the interpolation curve used in establishing interest rate of return. Calculation of Confidence Factor
Preparing the two estimates on which q is based is usually not excessively more complicated than preparing a single best estimate. 7 is not used to establish absolute probabilities of deviation or confidence limits, but rather to compare different projects semiquantitatively on more or less arbitrarily standardized bases. A typical procedure may be illustrated by considering a process where a n organic material reacts in the vapor phase over a solid catalyst and forms carbonaceous catalyst deposits which must be removed by periodic regeneration. In a n economic analysis, the principal factors to be considered are process design, capital requirements, VOL. 50,
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raw material unit costs, and market volume and price. In an operation of this type, the process factors having the greatest economic influence are catalyst life, yield, conversion per pass, carbon formation, and mass of catalyst. Process variables fall into. two general classes-those which have been investigated on both sides of the best valve and those for which the best value is arrived a t by projection beyond the range of investigation. Catalyst life is generally in the latter classification. For a single estimate early in a project, the life is generally taken a t a value somewhat greater than that actually demonstrated. If two estimaies are prepared? the unfavorable value is taken as the demonstrated life while the favorable extreme is taken as the difference between twice the selected best value and the demonstrated life. Process variables yield, conversion per pass, carbon formation, and catalyst mass, are interrelated since yield, carbon formation and mass of catalyst are all primary functions of conversion per pass. These relationships are subject to secondary effects of such factors as temperature and pressure. I n preparing a single estimate, best curves relating yield, carbon formation, and mass of catalyst to conversion are generally found by averaging minimum and maximum expected values. If two estimates are prepared, the unfavorable case is based on the minimum yield curve and the minimum carbon and catalyst curves. The favorable case is based on the curves of the opposite extreme. In preparing a single estimate, a preliminary calculation is required to determine the optimum conversion per pass. The advantages of high yield with low carbon formation and low catalyst mass a t low conversions are weighed against the accompanying increase in separation and recycling costs to determine the conversion resulting in the highest venture profit. As a first approximation, the optimum con-
Figure 2.
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Confidence factor
version may be assumed independent of moderate changes in the process factor relationships, market volume and price. Then two estimates may be based on yield, carbon formation, and catalyst-mass values from the favorable and unfavorable curves a t the optimum conversion level. In preparing estimates of capital costs for process plants, it is customary to use estimating procedures of varying refinement depending on the stage of development. Each procedure should be characterized by estimated standard deviations from which confidence limits can be established. Also, such estimates are readily expressed as functions of plant capacity by assuming that cost is proportional to capacity, raised to an appropriate power by an exponent generally in the range of 0.5 to 0.8. Thus, two extreme curves can be established relating capacity to cost. The favorable curve is-based on the favorable process factors combined with the lower confidence limit of the estimating procedure. Because several factors are combined a t favorable and unfavorable levels, it is desirable to avoid large standard deviations in the final estimate by establishing limits of only moderate confidence-e.g., 68% in the contributing factors. Market analysis data are given in terms of estimated sales volume as a function of price and time. Again the accuracy of the analysis should be estimated ; thus, two sets of relationships can be established, corresponding to upper and lower confidence limits. If 68% confidence levels are used in the capital and raw materials estimates, it will be desirable to use the same level for the market analysis limits. From the foregoing sets of relationships, optimum price and corresponding market volume which will produce maximum venture profit can be calculated, using favorable values of the three independent process factors-capital requirement, raw material unit costs, and market estimates. Similarly, the unfavorable estimate of venture worth is calculated from the unfavorable values of the seven basic factors considered. Favorable and unfavorable estimates of development costs are arrived at by the same type of reasoning that leads to the best values used in single estimates. The only added problem is that of estimating the probable deviation to assign confidence limits to the estimate. Favorable values of each attractiveness index function are obtained by combining the favorable venture profit estimates with the favorable development cost estimates. For quantitative comparison of the indexes for alternative projects, all phases of the procedure should be as uniform as possible. I n the foregoing
INDUSTRIAL AND ENGINEERING CHEWS1'RY
illustration, seven independent factors were considered a t two levels in arriving a t the favorable and unfavorable estimates of venture profit. The number of factors so considered should be held constant where possible because, as the number of factors increases, the probability of them all being simultaneously favorable or unfavorable diminishes. The choice of a suitable weighting factor LL depends on the numbcr of factors considered at two levels in preparing the estimates as well as on the confidence levels used.
Significance of indexes
Each index cy, /3> and y, measures ihe attractiveness of a development venture in maximizing profit under certain restrictions. If both capital a t rate i, and development facilities are unlimited, a: is most significant. \Vith limited development capacity, /3 becomes important and with limited capital, y is of primary importance. Advantages of these indexes over other proposals are consideration of the time equivalence of money ; combination of development and commercial costs on a common basis; and use of a computed confidence factor rather than a n estimated probability. Indexes of the foregoing type are not in any sense a substitute for managerial judgment. However, they do resolve complex situations into a relatively few clearly defined and comparable alternative choices. Decisions as to which index is the most significant in a particular situation is a matter of management judgment. -4lthough they appear complex, little effort is involved in calculating these indexes, once the necessary relationships and estimates are established. Complete, formal evaluation of such indexes is not justified for many development projects. However, even if appraisal is based entirely on judgment rather than on computation, it is believed that there is merit in guessing a t the individual factors and then combining them as a refinement of over-all judgment. Such a procedure forces consideration of the relative importance of the factors involved and is a valuable guide in prosecuting the development. Re-evaluation a t intervals during the development period, particularly when starting any ne\v 'activity is desirable because only the future is considered. For establishing absolute levels of the indexes on which to base acceptance or rejection of a project, the standardized methods of calculation used must be applied to past projects whose histories are known. However, there is no substitute for the type of project which is so good that no method of evaluation can make it look bad.
SMALL SCALE ENGINEERING D A T A Time of Development
As previously shown, establishing optimum times of development B and commercialization C is important in determining worth of a venture. Frequently, relatively short periods of time are equivalent to large sums of money. A limited development effort can be used most profitably by distributing it among a n optimum number of projects to give maximum over-all values of expected development venture worth and the other indexes of attractiveness. Too many projects will reduce total venture worth by extending times of development. Too much effort on one project will reduce the attractiveness index p and eliminate other projects. Development time for a single project is determined by the intensity of effort which is measured by the cost rate J , and by the confidence factor 7 which is desired. Also involved is the effectiveness of development u, which is the number of development results of specified confidence obtained per unit of cost. B = f ’ [ ( l / ’ J ) ;(7); ( l / u ) l
(7)
Effectiveness should be maximized while both the cost rate and the confidence factor must be optimized for maximum over-all attractiveness of the entire program. The values of both J and 7, to produce optimum time of development, depend on effectiveness u. Development Effectiveness
Any change in a development procedure, which will simultaneously reduce costs and improve accuracy, will obviously improve effectiveness. However, in many instances improved accuracy is obtained only a t the price of increased cost. Then maximum effectiveness is obtained by a n optimum procedure which results in the combination of cost and accuracy producing maximum indexes of attractiveness. Understanding the economic objectives of the program and the interrelationships of the contributing factors is invaluable for reaching individual decisions. Obviously, it is foolish to strain for a standard deviation of 1% in establishing a technical result, when the market data have a standard deviation of 100yo ( 4 ) . One important factor determining effectiveness is the elapsed time efficiency, defined as 1.0 minus the fraction of elapsed time which is spent in waiting before new results are produced. An entire project may be a t a standstill for a prolonged period, waiting for an essential piece of equipment to be delivered. Because each new result may change future plans, a certain 1
amount of nonproductive waiting is inevitable even with the best of planning. However, it should be minimized in every way possible because such delays almost invariably reduce effectiveness and require greater total effort and costs in achieving a given development time. Two other important factors determining development effectiveness are patterning of experimental observations and scale of experimentation. Much has been written on optimum patterns of observation which may be arrived at by statistical or graphical analysis, making maximum use of theoretical principles. Use of such patterns increases effectiveness by ensuring maximum information from a minimum number of observations. Scale of experimentation influences effectiveness through its effects on the relationship between cost and accuracy of experimental observations and on the time efficiency. In many cases, a particular scale of experimentation will yield both maximum accuracy and minimum costs. In other cases, it is necessary to select the optimum scale which will give a combination of accuracy and cost rate resulting in maximum effectiveness. I t is in these cases that it becomes essential to consider the relative importance of accuracy and cost rate in the entire project. If equipment involves long delivery or fabrication periods, effectiveness may be increased by choosing some basically less attractive but more available scheme. Maximum time efficiency is achieved by using suitable equipment already on hand. This situation is most likely to exist for small scale experimentation. Micro Pilot Plants
T h e scale of experimentation in development work has been progressively diminished by new micro analytical techniques and improved theoretical methods for interpreting data. As a result, much development work is carried out in micro pilot plants. One early unit of this class, described by Dodd and Watson (7), included a 1inch diameter tube which with suitable cores served as a reactant mixer, preheater, catalytic reactor, and quench cooler. All piping normally connecting such a series of equipment items was eliminated, together with the attendant problems of heat losses and leaks. Standardized preheater-reactor units of this general type have been built which can operate a t temperatures up to 1200’ F. and pressures above 1000 p.s.i. I n conjunction with standardized heating and insulating elements, they can be operated either as pseudoisothermal or adiabatic reactors. Suitably standardized companion pumps,
Merits of Micro Pilot Plants Advantages Disadvantagee Versatility Precision of control Small reactant and catalyst needs Standardized components Low operating labor
Small product output Difficulties in separations for recycling Low mass velocities Abnormal edge and end effects Inability to simulate cumulative instability
micro compressors, separators, and control instruments permit quick assembly of a complete plant, for a variety of purposes, from stock-room items. Low operating labor results from simplicity of control and compactness which permit a n operator to handle a multiple group of several units in operations where large amounts of data are not required. Low mass-velocity may be serious, if streamline flow exists in the small unit. Generally turbulent flow can be ensured, giving results which can be extended to commercial ranges by existing relationships. The seriousness of edge and end effects is minimized by the differential reactor technique (5) which reduces both lateral and. longitudinal concentration gradients. Improvement in distillation and extraction methods that is continuing will minimize recycling difficulties. Transient instability effects are particularly difficult to detect or simulate in micro scale-e.g., the potential thermal instability of a heat-balanced adiabatic reactor for dehydrogenating butane. The heat of reaction is supplied by heat stored in the catalyst from oxidation of the deposits formed in the preceding cycle. Under certain conditions, a localized zone of high temperature causes more deposit formation which in turn further raises temperature in a cumulative effect which causes the localized temperature to go out of control. Other examples involving flow instabilities are described by Payne (7). Exploratory Period
In the exploratory phase of development, the micro pilot plant is most certain to represent the optimum scale. For exploration of wide ranges of conditions, the versatility of the micro pilot-plant can be most effectively used in combination with optimum patterns of observations and sound interpretive theory. Electronic computing facilities made theoretical analyses useful today which were hopelessly laborious a few years ago. Another objective of the exploratory phase is frequently exploration of the uses of the product. For this purpose VOL. 50,
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micro-scale experimentation is generally useless and a choice must be made between a dual purpose, large scale pilot plant and a dual-scale program in which a large plant is built solely for manufacturing experimental quantities of product with no attempt to gather design data. For some products, manufacturing pilot plants may employ different reactants under entirely different conditions than are contemplated for commercial operation. Batch operations may be employed even though the commercial plant wili be continuous. I t is believed that an optimum program is frequently achieved by such a segregation of objectives \vith a microscale plant for design data and another plant solely for making the product at minimum cost. Confirmatory Period
I n the confirmatory period of development, it is desirable to improve the confidence factors of the project to acceptable levels and test the conclusion reached in the exploratory phase. In many problems a microscale operation is again optimum. Catalyst lives can be effectively established and compared by small scale tests. If a differential reactor technique is used in exploratory work, confirmation of integrated results frequently can be obtained by integral operation of a microreactor, some times with t’ivo or more reactors in series to increase mass velocities. With improved continuous microseparation techniques, complete equilibrium recycling can frequently be done. However, where precise distillations are involved, it may be necessary to resort to larger scale or to simulate recycling by successive-pass operations, interpreted by mathematical extrapolation. Instability effects such as the butane dehydrogenation example previously discussed are difficult to evaluate, except in commercial scale experimentation. In some cases, the optimum development procedure is to evaluate all the basic rate and thermal relationships involved by microscale experimentation. Differential equations can then be established and integrated with respect to position and time to mathematically determined stability. Problems of flow instability (7) may be solved by experimentation on progressively increasing scale as a basis for extrapolation to commercial sizes.
mercial scale frequently should be considered. This is equivalent to shortening or eliminating the confirmatory development period and proceeding immediately with the best commercial design possible. Such a course will have high attractiveness indexes if the venture worth is very high; this offsets the danger of low confidence factors. Pilot plant experimentation is expensive, frequently costing over $1 000 per day and, even if continued indefinitely, it will leave some questions to be ansivered only on a commercial scale. However, loss of profits and competitive position resulting from delay may bc more serious. During the past 15 years. the author has personally participated in the process design of the first commercial units of six processes on which only fragmentary data ere available. Included was the world’s largest butadiene plant. In each case. major technological innovations were involved and commercialization was initiated far in advance of normal practice Justification was either high expected profits or wartime urgency. Some troubles were encountered in initial commercial operations which might have been minimized by more extensive development. However, in no case did the cost of commercial experimentation and changes equal more than a small fraction of the costs and loss of profits which would have accompanied a traditional development program. It is concluded that in many cases the optimum development time is shorter than is normally contemplated. Where indicated venture profits are high, there may be great economic attractiveness in development by microscale experimentation combined with sound theoretical interpretation and the acceptance of a limited amount of commercial-scale experimentation in lieu of conventional pilot-plant confirmation. The opposite conclusion is ably defended by Kapnicky (6) in considering projects of apparently marginal venture profit, Such differences emphasize the importance of arriving at an optimum procedure for each individual project. Acknowledgment
The helpful criticism and suggestions of B. W. Gamson are gratefully acknowledged. Nomenclature
Commercial Scale Experimentation
Although it is traditionally opposed by the management of operating divisions: experimentation on a full com-
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A, B C
INDUSTRIAL AND ENGINEERING CHEMISTRY
time of completion of exploratory and confirmatory development, respectively, yr., = time of completion of design and construction, yr.
D,E
time of expansion, and initial profit decline, respectively, yr. F = time of termination of venture profit, yr. I = capital invested in commercial equipment, $ I, = commercial working capital, $ J = development expenditure rate, 8 per yr. R = gross annual profit before depreciation and taxes, f per yr. Sa = commercial equipment salvage value, $ V = venture profit, $ per yr. TI’ = present venture worth of commercial project a t time B, S W D = venture worth of development project at time B d = depreciation rate for tax purposes, fraction per yr. ,i = minimum acceptable net rate of return on capital, fractionlyr. Sometimes current rate of return on invested capital; typically 10 to 1270 per year k = representative year during a project s = standard deviation = total income tax rate, fraction t per yr. ZL = conservatism weighting factor cy, C,y = indexes of development attractiveness 11 = confidence factor, between 0 and 1.0 u = development effectiveness = arithmetic mean value of index factor &in = minimum value of index function which can be tolerated =
literature Cited
(1) Dodd, R. H., Watson, K. M., Trans Am. Inst. Chem. Engrs. 42, 263-89 (1946). (2) Happel, J., Chem. Eng. Progr. 51,
533-9 (1955). (3) Happel, J., Aries, R. S., Ibid., 46, 115-20 (1950). (4) Hicks, J. S., Steffens, L. R., Zbzd., 52, 191-4 (1956). (5) Hougen, 0. A., Watson, K. M., ‘LChemicalProcess Principles,” Pt. 3, Wiley, New York, 1947. (6) Kapnicky, J. A., IND. ENC. CHEM. 48, NO. 8, 47 A-48 A (1956). (7) Payne, J. W., Petrol. Rejiner 35, 126-8 (June 1956). (8) Reul, R. I., Haroard Business Rev. 35, NO. 4, 116-32 (July-August 1957). (9) Rosen, B. H., Regnier, A. L., Chem. Engr. Progr. 52, 500-2 (1956). (IO) Weaver, J. B., Reilly, R. J., Zbid., 52, 405-12 (1956). RECEIVED for review September 6, 1957 ACCEPTED December 23, 1957
=
Division of Industrial and Engineering Chemistry, Symposium on Collection of Engineering Data on a Small Scale, 132nd Meeting, .4CS, September 1957.
