Value Analysis of Complex Systems and Industrial Application to

Ind. Eng. Chem. Res. 2003, 42, 5165-5181

5165

Value Analysis of Complex Systems and Industrial Application to Refineries Jhuma Sadhukhan,† Nan Zhang,* and X. X. Zhu‡ Department of Process Integration, UMIST, P.O. Box 88, Manchester M60 1QD, U.K.

A generalized strategy for the modeling and integration of an overall system is developed for the purpose of detailed economic analysis of industrial systems. The work uses the basics of value analysis method (Sadhukhan, J. Ph.D. Dissertation, UMIST, Manchester, U.K., 2002) to identify major material streams and their elements of production and processing. These major material streams are evaluated for economics, and these economics are used to predict the economics of elements of production and processing expressed as profit functions of process units. However, in a complex network system, there exist a variety of streams forming a number of processing networks in addition to the core system of major material streams and utilities. To consider the effects of overall network interactions in the economics of major material streams and elements, these processing networks are modeled interchangeably as material or utility networks and integrated with the core system of major material streams and utilities. Further, these economics of streams and elements are used to establish the overall system economics and thereby capturing the effects of overall network interactions in the overall system economics. The insights developed to build economic models at various stages are illustrated with several examples and an industrial case study from a refinery. In addition to the economic analysis of an overall refining system, the refinery crude switch problem is used to demonstrate the application of system economic analysis to optimum feedstock selection. 1. Introduction The process/manufacturing industries are facing severe challenges that lie in improving economic competitiveness, while achieving a variety of the highestquality, lowest-cost, and environmentally most benign products from a limited supply of low-quality feedstocks. In such a constrained situation, a simple and smart methodology for a detailed and differential economic analysis of an industrial system under any market and environmental conditions can be very useful for achieving the optimal operations. This paper considers the practical applications of the value analysis method1 for such an economic analysis of complex systems having a number of processing networks. Economic analysis of a system establishes the economic performances of individual streams and processes with respect to the current system operation, network configuration, and market situation. Such differential economic analysis of streams and processes can also provide the design basis for deriving the optimum network layout that achieves the maximum economic margin for the overall system. The weaker parts (problematic areas) of a system and the stronger parts that can process the shifted load from the weaker parts can be identified, and integration among them can be accomplished. In addition, the optimum market integration with a process network can be achieved to exploit the best market opportunities available. Consequently, an analytical optimization procedure for systems can be conceived on the basis of the economic analysis of existing systems.1 * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: 44-161-200 4384. Fax: 44-161236 7439. † E-mail: [email protected]. ‡ E-mail: [email protected].

Currently, LP optimization provides the economic value structure of systems in terms of the marginal value analysis2 of streams. However, marginal values are only relevant to those streams for which any change in variables affects the current optimality. Such an analysis is based on fixed operating conditions, and therefore, it requires continuous updating of mathematical models and use of an optimizer to evaluate the current most marginal values. The main drawback of LP lies in the restriction on the use of any nonlinear correlation while dealing with the mixing, splitting, and blending of streams and highly nonlinear process operations. On the other hand, marginal values obtained from NLP and MINLP formulations3-5 do not provide the transparency in the optimization procedure to arrive at these values. Then, the process of interpreting the marginal values obtained and finding physical explanations becomes difficult. Consequently, users do not feel confident applying the marginal values in practice. Furthermore, the reliability of marginal value analysis depends on whether the optimization model can provide a global solution. For local optimal solutions from nonconvex NLP and MINLP formulations, the marginal values can be misleading. The above discussions show the need for a more fundamental approach to the economic analysis of industrial systems. This paper aims to establish a complete economic analysis of such systems without the use of optimization. It starts with the determination of the economics of small components in a system, after which the complex overall system is addressed to represent its economics as the contributions of the economics of the small components. Because the problem is large and complex, it can benefit most from the application of graph theory,6 according to which the underlying mechanism of a network is

10.1021/ie020968z CCC: $25.00 © 2003 American Chemical Society Published on Web 09/18/2003

5166 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003

described at the base level as a combination of paths and trees (elements) consisting of streams and processes. 2. Overview of Economic Analysis of a System The objective is to generate more precise economic models for basic streams, their production and processing elements, and the overall system in various stages. For this reason, an overall integration strategy is developed so as to capture the impacts of real plant operations (no fixed operating conditions) and the effects of network interactions in the detailed economic analysis of complex systems. The various network integration issues such as the incorporation of multiple feeds and multiple products of processes and recycle streams, the use of rigorous simulation/nonlinear process models, and the consideration of environmental regulations and market constraints are undertaken to generate a complete value structure for any complex system. Broadly, there are four major stages to a thorough analysis of the economics of a system. The first stage is to develop the models for determining economic margins of individual streams that are integrated with the process-level models. The stream economic models primarily convert the qualitative information on streams obtained from process yield models into quantitative measures for streams. The purpose of integration with the process-level models is to estimate operating costs and product yields of processes and coordinate them with the stream economic models to capture the impact of real plant operations on a stream’s economic margin. In the second stage, the economic margins of basic elements (paths and trees) of the production and processing of streams are expressed as the profit functions (marginal contributions) of process units and integrated with the stream economic models. Thus, the marginal correlations of elements also make use of the process-level models. In the third stage, the problem is addressed at a higher level of complexity by integrating all of the processing networks in addition to the major material and utility networks in a system, and the effect of overall integration is captured in the economic analysis of streams and elements. These individual economic margins of streams and elements are finally correlated with the overall system economic margin in the centralized integrated system model that represents a system operation in totality. The various economic analysis stages that are highlighted in the paper are as follows: (1) economic modeling of streams, (2) process modeling aspects for integration with stream economic models, (3) strategies for overall integration of various processing networks, and (4) centralized modeling of the integrated system. In addition, the key issues for detailed economic analysis of complex process networks are further illustrated through simple examples. Industrial case studies on refining are used for practical demonstrations at every stage of application of the methodology. 3. Economic Modeling of Streams The stream economic model is used to predict the economic margin of a stream using the value and cost of the stream. The value of a stream is its value on processing (VOP) in producing end products. This is calculated from the prices of the end products less the operating costs of the units processing the stream using

Figure 1. Process network.

Figure 2. Basic elements (paths and trees) of the process network.

a backward calculation procedure (BCP). The cost of a stream is its cost of production (COP), which is calculated from the prices of the feedstocks added to the operating costs of the units producing the stream applying a forward calculation procedure (FCP). The difference between the two (VOP minus COP) provides the specific economic margin achieved by the stream. In this section, the models for predicting the VOP and COP of streams are further illustrated to highlight the key issues for integration with the process-level models. The generalized equations of the economic models of the streams are derived using the process network example in Figure 1.1 This process network consists of four basic elements (two paths and two trees), as indicated in Figure 2. 3.1. COP of a Stream. To evaluate the COP of a product from a process, the unit operating cost of the process is added to the COP of the feed to the process. Refer to element 1 that is path 1-2-3 in Figure 2 for developing the following equations to evaluate the COP of streams in the path.

(F1-2)COP ) F1 + oˆ 1(F1,F1-2)

(1)

(F1-2-3)COP ) (F1-2)COP + oˆ 2(F1-2,F1-2-3) (2) (P1-2-3)COP ) (F1-2-3)COP + oˆ 3(F1-2-3,P1-2-3) (3) The above equations use the process-level models to estimate the operating cost of a process unit per unit flow rate of feed as a function of the feed and products of the unit (e.g., oˆ 2 for process unit 2 is estimated from the feed, F1-2, and the product, F1-2-3). The operating costs of units wherever used in the paper are presented as functions of incoming feeds and outgoing products of the units. For differential economic analysis of streams, the basic component streams rather than the total streams are evaluated for the COP. An example is that the basic component streams F1-2, F14-2, and F1-5-2 of the total feed stream F2 to unit 2 are evaluated for the COP. The operating costs in such a case also correspond to the processing of a single-

Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5167

component feed. Following the above equations, the generalized correlation in eq 4 is developed for predicting the COP of intermediate and end products, Fe-ie′ and Pe-i(p), respectively, from a unit i. The unit operating cost of a process is a function of the feed as well as all of the coproducts of the process.

(Fe-i-e′)COP ) (Pe-i(p))COP ) (Fe-i)COP + oˆ i[Fe-i,Fe-i-e′,Pe-i(p)] ∀i ∈ UNIT, e ∈ EU(i), e′ ∈ ED(i), p ∈ NP(i) (4) Equation 5 below indicates how to determine the COP of the total or overall feed stream to unit i.

∑

F (Fe-i)COP × me-i ]/

e∈EU(i)

∑

F me-i

∀i ∈ UNIT

e∈EU(i)

(5)

For a more precise prediction of the COP of an overall feed, we can track the network flowsheet upstream to identify the point at which the components of the feed from various paths of production first meet and use the operating costs corresponding to the overall feed from that point onward.

COP of overall feed stream ) (Fi-j)COP )[

∑

F (Fe-i)COP × me-i /

e∈EU(i)

∑

p∈NP(i)

[Pe-i(p),p∈NP(i)]} ×

∑

F me-i ]/

e∈EU(i)

∑

F me-i

e∈EU(i)

∀i ∈ UNIT, e ∈ EU(i) (11) The VOP of the overall feed to a unit i is a function of the VOPs of its component feed streams to the unit and the operating cost of the unit corresponding to the processing of the overall feed as given by

VOP of overall feed stream ) (Fi)VOP

COP of overall feed stream ) (Fi)COP )[

∑

∑

F (Fe-i-e′)VOP × me-i-e′ + e′∈ED(i) P Pe-i(p) × me-i(p) - oˆ i{Fe-i,[Fe-i-e′,e′∈ED(i)];

(Fe-i)VOP ) [

F me-i ] + oˆ i(Fi,Fi-j)

e∈EU(i)

∀i, j ∈ UNIT (6) The unit operating cost is the variable through which the economic model for predicting the COP of streams is integrated with the process-level model. 3.2. VOP of a Stream. The VOP of a stream depends on the VOPs of its multiple products and operating costs of downstream processes. The VOP of stream F1 in Figure 1 is evaluated from the VOPs of its product streams F1-2, F1-4, and F1-5 as follows F + (F1)VOP ) [(F1-2)VOP × m1-2 F F + (F1-5)VOP × m1-5 (F1-4)VOP × m1-4

oˆ 1(F1,F1-2,F1-4,F1-5) × mF1 ]/mF1 (7) Similarly, the VOP of stream F1-4 is a function of the VOPs of its product streams from unit 4 belonging to path 1-4-2-3 and tree 1-4-6-3. F + (F1-4)VOP ) [(F1-4-2)VOP × m1-4-2 F (F1-4-6)VOP × m1-4-6 F F ]/m1-4 (8) oˆ 4(F1-4,F1-4-2,F1-4-6) × m1-4

The following correlations show how the VOPs of streams (in path 1) with a single product stream generating from them are evaluated using BCP starting from the end of the network and then proceeding backward.

(F1-2-3)VOP ) P1-2-3 - oˆ 3(F1-2-3,P1-2-3) (9) (F1-2)VOP ) (F1-2-3)VOP - oˆ 2(F1-2,F1-2-3)

(10)

The generalized economic model for predicting the VOP of a feed stream Fe-i to a unit i is given by eq 11.

)[

∑

F (Fi-e′)VOP × mi-e′ +

e′∈ED(i)

∑

P Pi(p) × mi(p) -

p∈NP(i)

oˆ i{Fi,[Fi-e′,e′∈ED(i)],[Pi(p),p∈NP(i)]} ×

∑

e∈EU(i)

F me-i ]/

∑

F me-i

∀i ∈ UNIT (12)

e∈EU(i)

A numerical illustration of eqs 4-6, 11, and 12 is provided in the case study on the refinery. As in the evaluation of the COP, the economic model for evaluating the VOP of a feed stream to a unit is integrated with the process-level model through the flow distribution of products from the unit and the operating cost of the unit. 4. Process Modeling Aspects for Integration with Stream Economic Models The process-level models are required to develop the correlations for the operating costs and yields, properties of the products of the processes in terms of flow rate, and properties of the feed as used by the stream economic models. The product properties are also needed to verify whether they satisfy the property specifications (process and market constraints). All of these constraints must be satisfied, and therefore, stream economic models indirectly make use of the product property set calculated from the process models. For each process, two types of models are developed, typical lumped models based on the bulk properties and flows of the overall feed and models based on the individual feed components. The former type of model is required to represent the actual operation (taken into account in the centralized system model), whereas the latter is needed to differentiate among the economic contributions from the individual stream components. To predict the unit operating cost, the type of correlations and the choices of variables will depend on the purpose for which the operating costs are to be used. For planning purposes, the operating cost is assumed to be linearly proportional to the feed flow. For application to day-to-day decision-making purposes, the operating costs of processes should be determined more accurately and rigorously to represent the actual utility consumption by the processes in reality. As the economic models of the streams (eqs 1-12) use simple correlations with summation/subtraction of the predicted operating costs, the simplistic process models are not mandatory, and accuracy in prediction can be the sole objective of process modeling. Process models based on rigorous process simulation can therefore be used for value analysis. To derive simplified correlations of the operating cost, precautions should be taken so that values and


Figure 3. Total operating cost of unit i vs flow rate of feed Fe-i to unit i.

Figure 4. Total operating cost of unit j vs flow rate of feed Fei-j to unit j.

costs predicted for streams are on the conservative side. For this reason, the predicted VOP should never exceed the actual VOP (eq 13), and the predicted COP should never be lower than the actual cost (eq 14). In both cases, a tolerance limit can be defined as a very small number to restrict the maximum difference between the actual and predicted values (eqs 15 and 16). The purpose of the conservative approach for process modeling is to avoid predicting an economic margin that is unachievable in reality (eq 17).

(Fe-i)VOP e (Fe-i)act VOP

∀i ∈ UNIT, e ∈ EU(i) (13)

(Fe-i)COP g (Fe-i)act COP

∀i ∈ UNIT, e ∈ EU(i) (14)

(Fe-i)act VOP - (Fe-i)VOP ) ξVOP g 0 ∀i ∈ UNIT, e ∈ EU(i) (15) (Fe-i)COP - (Fe-i)act COP ) ξCOP g 0 ∀i ∈ UNIT, e ∈ EU(i) (16) act (Fe-i)act VOP - (Fe-i)COP g (Fe-i)VOP - (Fe-i)COP ∀i ∈ UNIT, e ∈ EU(i) (17)

Instead of defining individual tolerance limits for VOP and COP, alternatively, the overall tolerance limit, ξ, for each stream can be specified as the difference between the actual margin and the predicted margin per unit flow. act (Fe-i)act VOP - (Fe-i)COP - [(Fe-i)VOP - (Fe-i)COP] ) (ξe-i)COP + (ξe-i)VOP ) ξe-i g 0 ∀i ∈ UNIT, e ∈ EU(i) (18)

Figures 3 and 4 present an example of the linearization of operating costs following the conservative approach. The plots represent the total operating costs of process units i and j as functions of the flow rates of feeds Fe-i and Fe-i-j, respectively. The operating cost per unit flow rate is given by the slope of the curve. The actual correlation of the operating cost is presented by the dotted line and the linearization is presented by the solid line (Figures 5 and 6). To evaluate the COP and

Figure 5. Linearization of total operating cost of unit i vs flow rate of feed Fe-i to unit i.

VOP of stream Fe-i-j, the operating costs of units i and j have to be taken into account. During the calculation of the COP of the stream, the linearization presented in Figure 5 yields a calculated COP value that is higher than the actual value. Similarly, for predicting the VOP of the stream, the operating cost of unit j is overestimated to satisfy the conservative approach given by eqs 13 and 15. Equations 19a and 19b are for integrating the stream economic models/process-level models with the economic models of network elements. The economic margin that can be achieved from a stream (given by the difference between its VOP and COP multiplied by the flow rate) is presented for stream Fe-i-j from unit i to unit j (right-hand side of the equation). This is equal to the marginal contributions of the process units in the element to which the stream belongs. All of the process units that are somehow connected to the stream, i.e., participating in the stream’s production and processing, contribute to the economic margin of the stream. The marginal contribution of a process unit to the margin of a stream cannot be full unless the unit processes no streams other than that particular stream, in which case the profit of the unit is presented without the stream’s function (eq 19a). In the case of partial contributions of processes (eq 19b), the marginal contributions of the processes to the margin of a stream are represented as the stream’s function. This convention has been followed throughout the paper by representing any partial marginal contributions of process units as functions of the corresponding stream names to differentiate them from the full marginal contributions of process units that are not associated with stream names.

∑ ∆u + ∆i + ∆j + ∑ ∆d )

u∈U(i)

d∈D(i)

F [(Fe-i-j)VOP - (Fe-i-j)COP] × me-i-j ∀i, j ∈ UNIT, e ∈ EU(i) (19a)

∑ ∆u(Fe-i-j) + ∆i(Fe-i-j) + ∆j(Fe-i-j) +

u∈U(i)

∑ ∆d(Fe-i-j) )

d∈D(i)

F [(Fe-i-j)VOP - (Fe-i-j)COP] × me-i-j ∀i, j ∈ UNIT, e ∈ EU(i) (19b)

The above equations are for computing the total economic margin from the production and processing of streams. It is also possible to differentiate between the two individual margins from the production and processing of streams by the use of their market prices, as shown later.


Figure 6. Linearization of total operating cost of unit j vs flow rate of feed Fe-i-j to unit j.

Figure 8. Hydrogen network with the major material processing network of the refinery.

Figure 7. Balanced refinery flowsheet with names and existing flow rates (kilotons per day) of major material streams.

5. Strategies for the Overall Integration of Various Processing Networks A large process network system has a number of streams other than major material streams forming various processing networks. For example, in a refining system, there are a number of streams other than liquid hydrocarbons. To establish an effective economic analysis of a system, the overall integration of the system should be considered by taking into account the complex interactions among all networks. This section discusses some important issues for the overall integration of networks for value analysis. At the end of this section, a refinery case study is used for demonstration. To simplify the nomenclature for the streams, the numbers 1-11 are used instead of unit names such as CDU, ISO, NHT, KHT, GHT, VDU, VBU, BIT, REF, VGOHDS, and FCC in Figure 7. The flow rates of major material streams in kilotons per day are also provided in the figure. A brief description of the process units (including full names) and streams and the data for the case study are provided in Appendix A. A common problem that can arise in dealing with recycle streams because of the sequential nature of the calculation procedure of the value analysis method is presented. The nature of calculations of the value analysis method is such that the FCP and the BCP can each be performed in only one direction, forward and backward, respectively, to evaluate the COP and VOP, respectively. An example is presented in Figure 8, where REF (unit 9) is downstream of NHT (unit 3) in terms of processing of the major material stream. These two units are also linked through the hydrogen stream, and with respect to hydrogen, REF is upstream of NHT. To evaluate the COP of HT naphtha from NHT to REF, we need to know the COPs of all of the feed streams, including that of hydrogen from REF to NHT. In turn, the COP of the product hydrogen from REF to NHT depends on the COP of the feed HT naphtha that is its

original source. Here, we propose the tearing6 of such streams and present a systematic procedure to include the economics of such streams in the detailed economic analysis of systems. The second consideration for overall integration is the categorization of streams into material and utility streams. To apply the value analysis method, certain streams are identified as material streams so that they can be evaluated from the costs of other streams, which are considered as utilities. The existence of a number of processing networks in one system indicates that there needs to be a deliberate consideration to categorize the streams into material streams and utilities. Identifying the major material streams containing liquid hydrocarbons in a refinery is straightforward. The most common utilities are solid fuels, HP and LP steam, boiler feedwater (BFW), cooling water, power, and chemicals. However, in addition to the major material streams and utilities, there are networks of hydrogen, hydrogen sulfide, and light gas products, among others, in the existing refining site. For an effective value analysis, the refiner has to make a decision about these streams as to whether to specify them as material streams or as utilities. It has been realized that the value analysis method provides full flexibility to the process industries to alternate in the categorization of a stream as a material stream or as a utility depending on the problem requirements, as detailed in a later section. The hydrogen, hydrogen sulfide, and light gases networks are presented separately with the material network in Figures 8-10, respectively. 5.1. Resolution of the Problems That Arise Because of the Sequential Nature of the Calculation cProcedure of the Value Analysis Method. A simpler network, shown in Figure 11, is used as an example. The COPs of streams F1-2-3 and P4 are evidently dependent on the COPs of inlet streams F′3-2 and F′3-4, respectively. At the same time, without knowing the COP of stream F1-2-3, it is not possible to evaluate COP of streams F′3-2 and F′3-4. Streams F′3-2 and F′3-4 are internal streams for which the market value might not be readily available. To resolve the consequent problem due to the sequential calculation procedure of the value analysis method, recycle streams F′3-2 and F′3-4 are handled in the following manner. Process unit 3 accounts for the production of these two streams separately from units 2 and 4, which deal with the processing of these two streams. Now, internal streams F′3-2 and F′3-4 are treated as the utilities, and reasonable values for them are considered


Figure 12. Elements of the network example used to illustrate how to perform the sequential calculation procedure of the value analysis method.

Figure 9. Hydrogen sulfide network with the major material processing network of the refinery.

processing of streams are equated with the economic margins of the streams incurred from their production and processing, respectively. The economic margins from the production of streams are calculated from the difference between the market price and the COP multiplied by the flow rates of the streams (FCP), whereas that from the processing of streams is given by the difference between the VOP and the market price multiplied by the flow rates of the streams (BCP). The following equations represent the marginal correlations for producing the streams in paths 1-2-3 and 1-4, respectively.

Path 1-2-3 F ∆1(F1-2) ) [F1-2 - (F1-2)COP] × m1-2

(20)

∆1(F1-2-3) + ∆2 ) F (21) [F1-2-3 - (F1-2-3)COP] × m1-2-3

∆1(P3) + ∆2 + ∆3 ) [P3 - (P3)COP] × mP3

(22)

Path 1-4 Figure 10. Light gases network with the major material processing network of the refinery.

F ∆1(F1-4) ) [F1-4 - (F1-4)COP] × m1-4

(23)

∆1(P4) + ∆4 ) [P4 - (P4)COP] × mP4

(24)

The COPs of streams F1-2, F1-2-3, P3, F1-4, and P4 are evaluated using the following economic models based on the preceding discussions.

(F1-2)COP ) F1 + oˆ 1(F1,F1-2,F1-4) Figure 11. Network example used to illustrate how to solve the problem resulting from the sequential calculation procedure of the value analysis method.

so that the rest of the material streams can be evaluated. By treating the internal streams as utilities in the marginal formulation, their individual impact on the evaluation of the material streams is greatly reduced. Finally, during the calculation of the overall network margin from the economic contributions of the streams, these assumed values for the internal streams cancel, ultimately resulting in zero error. The two elements generated are 1-2-3 and 1-4, as shown in Figure 12. In the actual case, these two elements are the trees involving the processing paths of streams F′3-2 and F′3-4. However, in the current problem, they are treated as paths because the streams are utilities. To develop the marginal correlations between the streams and elements, the profit contributions of the process units in the elements of the production and

(25)

F F ) (F1-2)COP × m1-2 + (F1-2-3)COP × m1-2-3 F (26) oˆ 2(F1-2,F1-2-3) × m1-2 F + (P3)COP × mP3 ) (F1-2-3)COP × m1-2-3 F (27) oˆ 3(F1-2-3,P3) × m1-2-3

(F1-4)COP ) (F1)COP + oˆ 1(F1,F1-2,F1-4)

(28)

F + (P4)COP × mP4 ) (F1-4)COP × m1-4 F (29) oˆ 4(F1-4,P4) × m1-4

The operating cost formulations for units 2, 3, and 4 account for the costs of streams F′3-2 and F′3-4 as indicated by eqs 30-32, respectively. This is how the streams are considered as utilities for value analysis.


oˆ 2(F1-2,F1-2-3) )

[P4 - (P4)COP] × mP4

[O2(F1-2,F1-2-3) + F′3-2 ×

F′ F m3-2 ]/m1-2

(30)

oˆ 3(F1-2-3,P3) ) [O3(F1-2-3,P3) - F′3-2 ×

F′ ] F′3-4 × m3-4

F′ F′ F - F′3-4 × m3-4 ]/m1-2-3 (31) m3-2 F′ F ]/m1-4 oˆ 4(F1-4,P4) ) [O4(F1-4,P4) + F′3-4 × m3-4 (32)

The marginal correlations using BCP for the processing of streams in paths 1-2-3 and 1-4 are as follows

Path 1-2-3 F ∆3 ) [(F1-2-3)VOP - F1-2-3] × m1-2-3

(33)

F ∆2 + ∆3 ) [(F1-2)VOP - F1-2] × m1-2

(34)

∆1(P3) + ∆2 + ∆3 ) [(F1)VOP - F1] × mF1

(35)

Path 1-4 F ∆4 ) [(F1-4)VOP - F1-4] × m1-4

F ) P4 × mP4 - [(F1-4)COP × m1-4 + O4(F1-4,P4) +

(36)

The VOPs of the above streams are determined using the economic models of eqs 37-40. F (F1-2-3)VOP × m1-2-3 ) F (37) P3 × mP3 - oˆ 3(F1-2-3,P3) × m1-2-3 F F ) (F1-2-3)VOP × m1-2-3 (F1-2)VOP × m1-2 F (38) oˆ 2(F1-2,F1-2-3) × m1-2

F + (F1-4)VOP × (F1)VOP × mF1 ) (F1-2)VOP × m1-2 F - oˆ 1(F1,F1-2,F1-4) × mF1 (39) m1-4 F (F1-4)VOP × m1-4 ) F (40) P4 × mP3 - oˆ 4(F1-4,P4) × m1-4

To compute the overall network economic margin from the economic contributions of the streams, a boundary,1 as shown in Figure 13, is considered to identify the material streams F1-2-3 and P4 across the boundary. The summation of their economic margins is equal to the margin of the overall network.1 Expansions of the differences between the VOP and COPs of the identified streams using eqs 37, 31, 26, 30 and 29, 28, 32, respectively, are performed as follows. F [(F1-2-3)VOP - (F1-2-3)COP] × m1-2-3

) P3 × mP3 - [O3(F1-2-3,P3) - F′3-2 ×

F - oˆ 1(F1,F1-2,F1-4) × ) P4 × mP4 - F1 × m1-4 F F′ - O4(F1-4,P4) - F′3-4 × m3-4 (42) m1-4

Upon summation of eqs 41 and 42, the prices assumed for streams F′3-2 and F′3-4 cancel each other without affecting the overall margin of the network. In the refinery example, the recycle hydrogen stream can be treated in the same way. The total hydrogen stream generating from REF can be cut down at the inlets of the various consuming units NHT, DHT, GHT, ISO, and VGOHDS (as guided by Figure 12). The cuts can then be treated separately in the individual elements. A reasonable market value of hydrogen can be assumed to proceed with the stream value analysis while treating hydrogen as a utility stream. If the market price of hydrogen is available, it can also be conveniently treated as a second feed to the units discussed in the following section. The tearing of the hydrogen stream from the sources to the consumers as directed in Figure 12 is still retained to resolve sequential problems of the value analysis method while it is considered as a material stream. 5.2. Important Modeling Aspect: Interconvertibility between Material Streams and Utilities in the Calculation Procedure. In this section, we consider processes with multiple feeds as an example to illustrate the material stream/utility interconvertibility aspect. Two situations can arise in such multiple-feed processing. In the first situation, a unit cannot be run on one feed at a time. In such a case, the primary feeds are considered as material streams, whereas the secondary feeds can be treated as utilities. In the second situation, the feeds can be processed separately through a unit. The value analysis method allows for the flexibility of treating such feeds either as utilities or as material streams according to user needs, as discussed below. Secondary Feeds Treated as Utilities. The network in Figure 14 has one main feed F1 to unit 1 and a secondary feed F′3 to unit 3. The main feed to unit 3 is the product stream from unit 1 and is denoted as F1-

Figure 13. Boundary for margin calculation of the network example used to illustrate how to perform the sequential calculation procedure of the value analysis method.

F′ F′ F - F′3-4 × m3-4 ] - (F1-2)COP × m1-2 m3-2 F′ ] [O2(F1-2,F1-2-3) + F′3-2 × m3-2 F′ ) P3 × mP3 - O3(F1-2-3,P3) + F′3-4 × m3-4 F F - oˆ 1(F1,F1-2,F1-4) × m1-2 F1 × m1-2 O2(F1-2,F1-2-3) (41)

Figure 14. Network example used to illustrate interconvertibility aspect between material streams and utilities.


3. The basic elements identified in the network are path 1-2 and tree 1-3-2, as shown in Figure 15. A separate element does not result from the processing of feed F′3, as this feed is treated as a utility. By applying FCP to various production elements, the following marginal correlations (eqs 43-45) between the profit contributions of process units and the COPs, the market prices of the streams, are developed.

Element 1: Path 1-2 F ∆1(F1-2) ) [F1-2 - (F1-2)COP] × m1-2

(43)

Element 2: Tree 1-3-2 ∆1(F1-3) ) [F1-3 - (F1-3)COP] ×

F m1-3

(44)

F ∆1(F1- 3) + ∆3 ) [F1-3-2 - (F1-3-2)COP] × m1-3-2 +

[P3 - (P3)COP] × mP3 (45) The economic models for calculating the COPs of streams F1-2, F1-3, F1-3-2, and P3 are given by eqs 46-48.

(F1-2)COP ) F1 + oˆ 1(F1,F1-2,F1-3)

(46)

(F1-3)COP ) F1 + oˆ 1(F1,F1-2,F1-3)

(47)

F + (P3)COP × mP3 ) (F1-3)COP × (F1-3-2)COP × m1-3-2 F F + oˆ 3(F1-3,F1-3-2,P3) × m1-3 (48) m1-3

The economic effect of stream F′3 is taken into account through the operating cost formulation of unit 3.

oˆ 3(F1-3,F1-3-2,P3) ) F [O3(F1-3,F1-3-2,P3) + (F′3)COP × mF′ 3 ]/m1-3 (49)

Figure 15. Elements of the network example used to illustrate interconvertibility aspect between material streams and utilities (F′3 is a utility).

To evaluate the overall network economic margin from the economic margins of the streams, a boundary is considered (Figure 16). The streams that cross the boundary are F1-2 and F1-3. The selection of the boundary ignores the material contribution of stream F′3, as this stream has been considered as a utility (eq 49). As in the previous example, the differences between the VOPs and COPs are expanded using eqs 53, 46 and 55, 54, 49, 47 for streams F1-2 and F1-3, respectively. F [(F1-2)VOP - (F1-2)COP] × m1-2 F ) [P1-2 - oˆ 2(F1-2,P1-2)] × m1-2 F (56) [F1 + oˆ 1(F1,F1-2,F1-3)] × m1-2 F [(F1-3)VOP - (F1-3)COP] × m1-3 F ) [P1-3-2 - oˆ 2(F1-3-2,P1-3-2)] × m1-3-2 + P3 × F mP3 - oˆ 3(F1-3,F1-3-2,P3) × m1-3 F [ F1 + oˆ 1(F1,F1-2,F1-3)] × m1-3 F ) [P1-3-2 - oˆ 2(F1-3-2,P1-3-2)] × m1-3-2 + P3 ×

mP3 - [O3(F1-3,F1-3-2,P3) + F′3 × mF′ 3] F (57) [ F1 + oˆ 1(F1,F1-2,F1-3)] × m1-3

Using BCP, the following marginal correlations are obtained for the various processing elements in terms of the profit contributions of the process units and the VOPs, the market prices of the streams.

Summing eqs 56 and 57 and using the material balance, one can verify that the final equation below provides the overall economic margin of the network that already includes the cost of stream F′3.

Element 1: Path 1-2

F + P3 × [P1-3-2 - oˆ 2(F1-3-2,P1-3-2)] × m1-3-2

∆2(F1-2) ) [(F1-2)VOP - F1-2] ×

F m1-2

(50)

F + [P1-2 [ F1 + oˆ 1(F1,F1-2,F1-3)] × m1-3

Element 2: Tree 1-3-2 F (51) ∆2(F1-3-2) ) [(F1-3-2)VOP - F1-3-2] × m1-3-2 F (52) ∆3 + ∆2(F1-3-2) ) [(F1-3)VOP - F1-3] × m1-3

The economic models for calculating the VOPs of the streams using the operating costs of the units processing the streams and the VOPs of the products are given by eqs 53-55.

(F1-2)VOP ) P1-2 - oˆ 2(F1-2,P1-2)

mP3 - [O3(F1-3,F1-3-2,P3) + F′3 × mF′ 3] -

(53)

F oˆ 2(F1-2,P1-2)] × m1-2 F [F1 + oˆ 1(F1,F1-2,F1-3)] × m1-2 P P ) (P1-3-2 × m1-3-2 + P1-2 × m1-2 ) + P3 × mP3 F F + m1-2 ) - F′3 × mF′ F1 × (m1-3 3 F + oˆ 2(F1-2,P1-2) × [oˆ 2(F1-3-2,P1-3-2) × m1-3-2 F F ] - [oˆ 1(F1,F1-2,F1-3) × m1-3 + m1-2 F ] - O3(F1-3,F1-3-2,P3) oˆ 1(F1,F1-2,F1-3) × m1-2

(54)

) P2 × mP2 + P3 × mP3 - F1 × mF1 - F′3 × mF′ 3 (O1 + O2 + O3) (58)

F (55) mP3 - oˆ 3(F1-3,F1-3-2,P3) × m1-3

The application is in the process networks where the costs of some of the material streams are to be treated

(F1-3-2)VOP ) P1-3-2 - oˆ 2(F1-3-2,P1-3-2) F F ) (F1-3-2)VOP × m1-3-2 + P3 × (F1-3)VOP × m1-3


Figure 16. Boundary for margin calculation of the network example used to illustrate interconvertibility aspect between material streams and utilities (F′3 is a utility).

(F1-3-2)COP ) (F1-3)COP + oˆ 3(F1-3,F1-3-2)

(61)

(P1-3)COP ) (F1-3)COP + oˆ 3(F1-3,P1-3)

(62)

(F′3-2)COP ) F′3 + oˆ 3(F′3,F′3-2)

(63)

(P′3)COP ) F′3 + oˆ 3(F′3,P′3)

(64)

In the above equations, the unit operating costs of process unit 3 in processing feed streams F1-3 and F′3 are distinguished from each other as indicated below.

oˆ 3(F1-3,F1-3-2) ) oˆ 3(F1-3,P1-3) ) F (65) O3(F1-3,F1-3-2,P1-3)/m1-3

oˆ 3(F′3,F′3-2) ) oˆ 3(F′3,P′3) ) O3(F′3,F′3-2,P′3)/mF′ 3 (66) Equations 67-69 are generated in terms of the profit contributions of the process units and the VOPs, the market prices of the streams, in elements 2 and 3, as indicated.

Element 2: Tree 1-3-2 Figure 17. Elements of the network example used to illustrate interconvertibility aspect between material streams and utilities (F′3 is a material stream).

∆3 (F1-3) + ∆2(F1-3-2) )

as the utility costs even though the streams participate in the material balance of the network. An appropriate example from refineries is the use of methyl tertiary butyl acetate (MTBE) as an additive to the refinery fuels for octane improvement. Refineries might want to account for the cost of MTBE in the costs of the utilities to evaluate the main material streams. Secondary Feeds Retained as Material Streams. An alternative situation is considered where stream F′3 is retained as a material stream. An additional tree (third element) processing feed stream F′3 is generated in Figure 17. From the new set of elements, end product P2 is reconstituted as a combination of components P1-2 (from element 1), P1-3-2 (from element 2), and P′3-2 (from element 3). Similarly, end product P3 is a combination of components P1-3 and P′3 from elements 2 and 3, respectively. The marginal expressions for tree 1-3-2 now change because the operating cost of unit 3 no longer includes the cost of stream F′3. The modified marginal equations for tree 1-3-2 and the additional marginal equations for tree 3-2 are given below. The FCP is performed to correlate the profit contributions of process units producing streams with the COPs and market prices of the streams (eqs 59 and 60).

Element 3: Tree 3-2

Element 2: Tree 1-3-2 ∆1(F1-3) + ∆3(F1-3) ) [F1-3-2 - (F1-3-2)COP] × F P + [P1-3 - (P1-3)COP] × m1-3 (59) m1-3-2

Element 3: Tree 3-2 F′ + ∆3 (F′3) ) [F′3-2 - (F′3-2)COP] × m3-2

[P′3 - (P′3)COP] × mP′ 3 (60) The COPs of streams F1-3-2, P1-3, F′3-2, and P′3 are calculated as follows

F (67) [(F1-3)VOP - F1-3] × m1-3

F′ ∆2(F′3-2) ) [(F′3-2)VOP - F′3-2] × m3-2

∆3 (F′3) + ∆2(F′3-2) ) [(F′3)VOP - F′3] × mF′ 3

(68) (69)

The VOPs of the above streams are evaluated from the end productions of the streams, and the associated operating costs as given by eqs 70-72. F F ) (F1-3-2)VOP × m1-3-2 + P1-3 × (F1-3)VOP × m1-3 P F - oˆ 3(F1-3,F1-3-2,P1-3) × m1-3 (70) m1-3

(F′3-2)VOP ) P′3-2 - oˆ 2(F′3-2,P′3-2)

(71)

F′ P′ (F′3)VOP × mF′ 3 ) (F′3-2)VOP × m3-2 + P′3 × m3 -

oˆ 3(F′3,F′3-2,P′3) × mF′ 3 (72) The boundary in this case needs to be modified to account for the material flow of feed F′3 through the network. The new boundary, as shown in Figure 18, has the outlet streams F1-2, F1-3-2, and F′3-2 (components of feed F2 to unit 2) and P1-3 and P′3 (components of end product P3 from unit 3). The marginal contributions of the process units as functions of the VOPs and COPs of the identified streams are given by eqs 50, 51, 68 and 43, 59, 60, respectively. It can be noted that the VOPs of the end products are their market prices. Summing these marginal contributions of the process units provides the total margin of the network. A useful application is in case of the selection of the optimum feedstock for a system, which is illustrated with a refinery crude switch problem in a later section. 5.3. Application of the Overall Integration Strategies to the Refining Network. The strategies developed for integrating various processing networks are


Figure 18. Boundary for margin calculation of the network example used to illustrate interconvertibility aspect between material streams and utilities (F′3 is a material stream).

applied to the refinery case study in Figures 7-10 for economic analysis of the overall system. As indicated earlier, the various networks that are to be considered for the overall integration are the hydrogen, hydrogen sulfide, and light gases networks, in addition to the material and utility networks. The SRU, although has a very small intake of hydrogen sulfide, can be treated as an additional processing unit (unit 12) of the refinery, and its profit contribution can be included in the marginal correlations. Thus, hydrogen sulfide is treated as a material stream. Hydrogen is treated as a utility

considering its internal usage as the refinery fuel gas (with the same market price). Because the light gases in the existing system are derived as refining products, they are treated as the material streams. The major material streams and their individual elements of production and processing are identified, and the appropriate marginal contributions of the process units for producing/processing such streams are indicated in Table 1. An illustration of developing the marginal contributions of the process units is presented for the processing of stream F1-6. Stream F1-6-5 is a product of stream F1-6 from unit 6 and is one of the feeds to unit 5. Therefore, a marginal contribution from unit 5 for the processing of stream F1-6-5 is present in the marginal correlation of the element of the processing of stream F1-6. Similarly, stream F1-610 is another product of stream F1-6 consumed in units 10 and 11 through streams F1-6-10 and F1-6-1011, respectively. The remaining route of consumption of stream F1-6 is through product stream F1-6-7 to

Table 1. Marginal Contributions of Processes in the Elements of the Production and Processing of the Major Material Streams profit function of processes in element of stream

productiona

identification

F1 F1-2 F1-3 F3-9

feed to CDU C5 + naphtha feed from CDU to ISO naphtha feed from CDU to NHT HT naphtha feed from NHT to REF

F1-4 F1-5 F1-6

kero feed from CDU to KHT LGO feed from CDU to GHT A residue feed from CDU to VDU

market ∆1(F1-2) ∆1(F1-3) ∆1(F3-9) + ∆6(F1-6-7-3-9) + ∆7(F1-6-7-3-9) + ∆3(F3-9) ∆1(F1-4) ∆1(F1-5) ∆1(F1-6)

F1-6-5 F1-6-10

LGO feed from VDU to GHT VGO feed from VDU to VGOHDS

∆1(F1-6-5) + ∆6(F1-6-5) ∆1(F1-6-10) + ∆6(F1-6-10)

F1-6-7

V residue feed from VDU to VBU

∆1(F1-6-7) + ∆6(F1-6-7)

F1-7

A residue feed from CDU to VBU

∆1(F1-7)

F1-8

A residue feed from CDU to BIT

∆1(F1-8)

F1-8-10

VGO feed from BIT to VGOHDS

∆1(F1-8-10) + ∆8(F1-8-10)

F10-11

HT gasoil feed from VGOHDS to FCC A residue product from CDU isomerate product from ISO kero product from KHT naphtha product from GHT distillate product from GHT naphtha product from GHT LGO product from BIT bitumen product from BIT reformate product from REF

∆1(F10-11) + ∆6(F1-6-10-11) + ∆8(F1-8-10-11) + ∆10(F10-11) ∆1(P1) ∆1(P2) + ∆2(P2) ∆1(P4) + ∆4(P4) ∆1(P5(1)] + ∆6(P5(1)] + ∆5(P5(1)] ∆1(P5(2)] + ∆6(P5(2)] + ∆5(P5(2)] ∆1(P7) + ∆6(P7) + ∆7(P7) ∆1[P8(1)] + ∆8[P8(1)] ∆1[P8(2)] + ∆8[P8(2)] ∆1(P9) + ∆6(P9) + ∆7(P9) + ∆3(P9) + ∆9(P9) ∆1(P10) + ∆6(P10) + ∆8(P10) + ∆10(P10) ∆1[P11(1)] + ∆6[P11(1)] + ∆8[P11(1)] + ∆10[P11(1)] + ∆11[P11(1)] ∆1[P11(2)] + ∆6[P11(2)] + ∆8[P11(2)] + ∆10[P11(2)] + ∆11[P11(2)] ∆1[P11(3)] + ∆6[P11(3)] + ∆8[P11(3)] + ∆10[P11(3)] + ∆11[P11(3)] ∆1[P11(4)] + ∆6[P11(4)] + ∆8[P11(4)] + ∆10[P11(4)] + ∆11[P11(4)]

P1 P2 P4 P5(1) P5(2) P7 P8(1) P8(2) P9 P10 P11(1)

naphtha and distillate product from VGOHDS naphtha product from FCC

P11(2)

HCO product from FCC

P11(3)

LCO product from FCC

P11(4)

slurry product from FCC

a

processingb ∆1 + ∆2 + ...+ ∆12 ∆2 ∆3(F1-3) + ∆9(F1-3-9) + ∆12(F1-3-12) ∆9 ∆4 + ∆12(F1-4-12) ∆5(F1-5) + ∆12(F1-5-12) ∆6 + ∆5(F1-6-5) + ∆10(F1-6-10) + ∆11(F1-6-10-11) + ∆7(F1-6-7) + ∆3(F1-6-7-3) + ∆9(F1-6-7-3-9) + ∆12(F1-6-5-12) + ∆12(F1-6-10-12) + ∆12(F1-6-10-11-12) + ∆12(F1-6-7-12) + ∆12(F1-6-7-3-12) ∆5(F1-6-5) + ∆12(F1-6-5-12) ∆10(F1-6-10) + ∆11(F1-6-10-11) + ∆12(F1-6-10-12) + ∆12(F1-6-10-11-12) ∆7(F1-6-7) + ∆3(F1-6-7-3) + ∆9(F1-6-7-3-9) + ∆12(F1-6-7-12) + ∆12(F1-6-7-3-12) ∆7(F1-7) + ∆3(F1-7-3) + ∆9(F1-7-3-9) + ∆12(F1-7-12) + ∆12(F1-7-3-12) ∆8 + ∆10(F1-8-10) + ∆11(F1-8-10-11) + ∆12(F1-8-10-12) + ∆12(F1-8-10-11-12) ∆10(F1-8-10) + ∆11(F1-8-10-11) + ∆12(F1-8-10-12) + ∆12(F1-8-10-11-12) ∆11 + ∆12(F1-6-10-11-12) + ∆12(F1-8-10-11-12) market market market market market market market market market market market market market market

Profit function ) (market price - COP) × flow rate of stream. b Profit function ) (VOP - market price) × flow rate of stream.

Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5175 Table 2. VOPs, COPs, and Economic Margins of Major Material Streams stream

VOP ($/t)

COP ($/t)

economic margin from streama ($1,000/day)

F1 F1-2 F1-3 F3-9 F1-4 F1-5 F1-6 F1-6-5 F1-6-10 F1-6-7 F1-7 F1-8 F1-8-10 F10-11 P1 P2 P4 P5(1) P5(2) P7 P8(1) P8(2) P9 P10 P11(1) P11(2) P11(3) P11(4) P12 LG

125.18 160.88 155.60 157.64 144.94 150.23 102.57 150.21 112.66 73.79 73.79 104.44 112.66 118.74 89 170 149 170 155.26 65.50 65.50 104 170 163.82 169.16 82.50 65.50 65.50 15 82.74

111.53 113.01 113.01 114.81 113.01 113.01 113.01 114.33 114.33 114.33 113.01 113.01 114.33 122.34 113.01 120.43 116.20 115.61 115.61 113.71 114.33 114.33 118.50 122.34 125.65 125.65 125.65 125.65 125.48 123.64

576.36 53.91 302.41 313.29 115.09 384.78 -112.30 13.03 -12.71 -112.62 0 -33.49 -2.31 -28.43 -113.06 54.76 117.43 9.89 407.65 -119.10 -6.43 -24.76 335.48 39.19 166.61 -48.88 -37.56 -31.16 -39.18 -94.85

Figure 19. Tree 1-4-12 in the refinery case study with flow distributions (kilotons per day) of the major material streams.

total operating cost consists of two terms. The first term represents the utility cost, and the second term corresponds to hydrogen consumption (hydrogen intake to unit 4 ) 0.02 kt/day, price ) 82.74 $/t). The FCP for predicting the COPs is as follows.

(F1)COP ) F1 ) 111.53 (F1-4)COP ) (111.53 × 42.23 + 62.34)/42.23 ) 113.01 (P4)COP ) (F1-4-12)COP ) (LG4)COP ) (113.01 × 3.60 + 12.05 + 0.02 × 82.74)/ (3.60 + 0.02) ) 116.20 The BCP generates the VOPs of the streams as follows.

(P4)VOP ) P4 ) 149

Economic margin ) (VOP - COP) × flow rate of stream.

(LG4)VOP ) LG4 ) 82.74

unit 7. The process units consuming this stream are 7, 3, and 9 through streams F1-6-7, F1-6-7-3, and F16-7-3-9, respectively. To include the marginal contributions of unit 12 in the processing of stream F1-6, the integrated flowsheet in Figure 9 is considered to identify the routes/elements connecting units 6 and 12. The elements identified are 1-6-5-12, 1-6-10-12, 1-6-10-11-12, 1-6-7-12, and 1-6-7-3-12. The respective streams consumed by these elements are streams F1-6-5-12, F1-6-10-12, F1-6-10-11-12, F1-6-7-12, and F1-6-7-3-12. Thus, unit 12 contributes to the margin of the element of the processing of stream F1-6 by consuming these streams, which are generated from paths 1-6-5, 1-6-10, 1-6-10-11, 1-6-7, and 1-6-7-3, respectively. Through the generation of such marginal contributions of the process units producing and processing the streams, the effects of the overall network interactions are captured in the marginal correlations between the elements and streams. The the VOPs, COPs, and economic margins of the streams are provided in Table 2. The COPs and VOPs of the component streams are determined using generalized eqs 4 and 11, respectively. The COPs and VOPs of the feeds to units 9 and 10 are provided for the overall feeds (F3-9 and F10-11, respectively) using eqs 5, 6, and 12, respectively. The calculation of the VOPs and COPs of the streams in tree 1-4-12 (Figure 19) is presented below. The process units present in this tree are 1, 4, and 12, and the streams are F1, F1-4, P4, F14-12, and LG4. The process models7 are used for calculating8,9 the process yields and utility consumption. The total operating costs of process units 1, 4, and 12 corresponding to their current throughputs and product distributions are $62,340/day, $(12,050 + 0.02 × 82,740)/day, and $2,300/day62.34 k$/d 12.05 0.02 x 82.74 k$/d and 2.30 k$/d, respectively. For unit 4, the

(F1-4-12)VOP ) (F12)VOP ) (15 × 0.35 - 2.30)/0.38 ) 7.82

a

(F1-4)VOP ) [(149 × 3.58 + 82.74 × 0.02 + 7.82 × 0.38) (12.05 + 0.02 × 82.74)]/3.6 ) 144.94 The overall economic margin ($576,360/day576.36 k$/ d) of the refinery can be computed by calculating the difference between the VOP and the market price (COP) multiplied by the flow rate of the crude or by using the VOPs and COPs of other material streams across the various boundaries in Figure 20. Two boundaries are indicated: one is around the crude unit, and the other addresses the end products. Various other boundaries can be considered to address the rest of the intermediate streams. Figures 21 and 22 are the network economic profiles (NEPs1) representing the overall refinery economic margin as the contributions of the margins of individual streams across boundaries 1 and 2, respectively. The positive areas above the COP between the VOP and COP of the profitable streams are the added, and negative areas below the COP between the COP and VOP of the nonprofitable streams are subtracted to evaluate the overall system economic margin. Therefore, the net positive area bounded between the VOP and COP of the streams in an NEP diagram provides the economic margin of the overall system. From the NEP diagram in Figure 21, the profitable streams are streams F1-2, F1-3, F1-4, and F1-5, and the nonprofitable streams are streams F1-6, F1-7, F1-8, the atmospheric residue, and the light gases product. Similarly, in Figure 22, of the streams identified across boundary 2, streams P2, P4, P5(1), P5(2), P9, P10, and P11(1) are the profitable steams, and streams P1; P7;


Figure 23. Variation of VOP and COP with flow rates in the SEP diagram of crudes to refinery. Table 3. Market Constraints on Maximum and Minimum Availabilities and Market Prices of the Three Crudes in the Refinery Crude Switch Problem

Figure 20. Boundaries for the overall refinery.

crude

minimum (kt/day)

maximum (kt/day)

market price ($/t)

1 2 3

0 30 0

50 50 30

110 105 115

Table 4. Range of Processing Capacities of Individual Crudes in the Refinery Crude Switch Problem

Figure 21. NEP diagram across boundary 1 in Figure 20.

Figure 22. NEP diagram across boundary 2 in Figure 20.

P8(1); P8(2); P11(2); P11(3); P11(4); P12; and all of the light gases from units 1-5, 7, and 9-11 (light gases from units 3 and 7 are not shown in the figure) are the nonprofitable streams. 5.4. Modeling and Optimization for Selecting the Feedstock for an Overall System (Refinery Crude Switch Problem). Planning for a multiperiod plant such as a refinery, where prices and demands of streams change with time period, might not always provide the appropriate solutions for day-to-day plant operations. Use of mathematical programming techniques to achieve optimal plant performance on a day-to-day basis can give rise to such a complex problem that a solution is practically impossible to achieve. The work in this paper presents a simple tool that can incorporate rigorous process models in the generation of a complete economic analysis for a process network system at any stage

crude

processing capacity (kt/day)

1 2 3

0-30 30-50 0-30

according to which real-time plant solutions can be achieved. The problem of the day-to-day selection of the optimum feedstock for a process network is addressed using the example of the problem of switching the crude at a refinery. First, individual economic margins achieved from processing of each feedstock through a plant at a given time are determined, and then, these results are used to select the optimum feedstock distribution for the network at that time. To determine the overall margin from the individual crudes, a refiner needs to predict the VOP of each crude. Refiners can develop rigorous in-house process models to predict the process operating costs and flowsheet distributions, and hence the VOP (eqs 11 and 12), of each crude. The COPs of the crudes are already known, i.e., their market prices. The difference between the two values provides the specific economic margin achieved from a crude. In the following example, the refiner has to make a selection among three crudes. Table 3 shows the three crudes and their maximum and minimum availabilities, which are based on the market constraints. Taking into account the market constraints and the maximum refinery capacity constraint of 60 kt/ day, the range of processing capacities with respect to the above three crudes were calculated as reported in Table 4. The minimum and the maximum processing capacities of crudes 2 and 3 are constrained by the market availabilities. When the total capacities of crudes 2 and 3 are equal to the minimum, which is 30 kt/day, the balance of the existing capacity, which is 30 kt/day, is to be filled by crude 1. In this way, the maximum processing capacity of crude 1 is constrained, even though its market availability is greater. The next task is to determine the VOPs of each crude for different flow rates within the range specified (Table 4). The VOPs of the individual crudes are plotted against the flow rate in the stream economic profiles (SEPs1) of Figure 23.

Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5177 Table 5. Overall Refinery Economic Margins and Unit Feedstock Costs for the Various Crude Distributions crude distribution mF,crude1 1 (kt/day)

mF,crude2 1 (kt/day)

mF,crude3 1 (kt/day)

unit feedstock cost ($/t)

ERoverall ($1,000/day)

30 0 10 0

30 30 50 50

0 30 0 10

107.5 110.0 105.8 106.7

669 870 817 910

The correlations for the VOPs of the crudes as a function of flow rate are provided in eqs 73-75. The VOP vs flow rate correlation for crude 3 is linear, whereas the best fits for the other two crudes are captured by the binomial variations with the flow rate.

Crude 1: (Fcrude1 )VOP ) 114.7 + 0.19 × mF,crude1 + 0.001 × 1 1 )2 (mF,crude1 1

(73)

Crude 2: (Fcrude2 )VOP ) 125.0 - 0.6 × mF,crude2 + 0.01 × 1 1

centralized model coordinates with the economic models of streams to estimate the economic margin for the overall system. The integrated system model also predicts the bulk properties of the overall streams and therefore considers lump models of the overall streams. The overall system margin is given by the sum of economic margins of the streams across a boundary.1 Boundary 1 for the refinery in Figure 20 is taken into consideration to identify streams F1-2, F1-3, F1-4, F1-5, F1-6, F1-7, F1-8, P1 (A residues), and LG1 (light gases from CDU) across the boundary. The overall refinery economic margin is given by eq 79. This expression inherently captures all of the cost and benefit effects from the networks of material, utility, hydrogen, hydrogen sulfide, and fuel gases through the consideration of overall network interactions. F [(F1-2)VOP - (F1-2)COP] × m1-2 + [(F1-3)VOP F F + [(F1-4)VOP - (F1-4)COP] × m1-4 + (F1-3)COP] × m1-3 F + [(F1-6)VOP [(F1-5)VOP - (F1-5)COP] × m1-5 F F + [(F1-7)VOP - (F1-7)COP] × m1-7 + (F1-6)COP] × m1-6 F + [(P1)VOP [(F1-8)VOP - (F1-8)COP] × m1-8

)2 (74) (mF,crude2 1 Crude 3:

(Fcrude3 )VOP 1

) 130.0 - 0.1 ×

mF,crude3 1

(75)

The atmospheric distillation unit is numbered 1, and thus, the values and the flow rates of the crudes in the above equations refer to process unit 1. Thereafter, the , mF,crude2 , optimum distribution of the crudes (mF,crude1 1 1 F,crude3 ) is determined that corresponds to the and m1 maximum economic margin of the refinery. The economic margin (ER) of the overall refinery (eq 76) is the sum of the economic margins of the individual crudes (eq 77).

ERoverall ($1,000/dayk$/d) )

∑ ERc

∀c ∈ NC

(79) (P1)COP] × mP1 + [(LG1)VOP - (LG1)COP] × mLG 1 In addition to the overall system economic margin, the bulk property set of the overall streams at the inlet and outlet of every process and the blending correlations are formulated.7 The process constraints are imposed on the stream property set.7 The blended finished products are subject to the market constraints imposed on the property set.7 In addition, there are market constraints on the minimum and maximum production of the products and the availability of the feeds.7 Similarly, for utilities, there are constraints on purchasing and selling.7 This centralized integrated system model can also be used for conventional optimization using NLP.1

c∈NC

(76) ERc ($1,000/day) )

[(Fcrudec )VOP 1

-

Fcrudec ] 1

mF,crudec 1

× ∀c ∈ NC (77)

Equation 76 is obviously the objective function. With constraints on the total refining capacity and the individual crudes flow rates, the various crude distributions and the corresponding overall economic margin are as reported in Table 5. The unit feedstock cost is calculated with the equation

unit feedstock cost ($/t) ) Fcrudec × mF,crudec / 1 1

∑ c∈NC

mF,crudec ∑ 1 c∈NC

(78)

The best feedstock distribution results inan optimum overall economic margin of $910,000/day, k$/d for which crudes 2 and 3 have flow rates of 50 and 10 kt/day, respectively. The lowest cost of the feedstock is provided by the distribution of 10 and 50 kt/day of crudes 1 and 2, respectively. 6. Centralized Integrated System Model The objective of developing a centralized system model is to represent a system in its totality. The

7. Conclusions This approach to the economic analysis of a system is simple and provides a transparent and complete set of economic values for all basic components and correlates these values with the overall system economic margin. The approach considers all possible effects of interactions among streams and processes and retains the overall integrity in the economic analysis. At the same time, rigorous process models can be used to capture the effects of real plant operations in the economic analysis. Even for complex systems such as refineries with many processing networks interacting in complicated ways, such an economic analysis can be conveniently carried out by integrating the overall system while retaining the quality of the models at the process level. In contrast, with the current mathematical-programming-based optimization techniques, all of these aspects are difficult to achieve. Nomenclature Sets NC ) {c: crudes to refinery} UNIT ) {i, j, k, l: process units} D ) {d (i ∈ UNIT): downstream process units of process unit i}

5178

Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003

U ) {u (i ∈ UNIT): upstream process units of process unit i} ED ) {e (i ∈ UNIT): downstream elements of process unit i} EU ) {e (i ∈ UNIT): upstream elements to process unit i} NP ) {p (i ∈ UNIT): end products from process unit i} Economic Margins of Process Units ∆1 ) economic margin of process unit 1 ∆2 ) economic margin of process unit 2 ∆3 ) economic margin of process unit 3 ∆4 ) economic margin of process unit 4 ∆5 ) economic margin of process unit 5 ∆6 ) economic margin of process unit 6 ∆7 ) economic margin of process unit 7 ∆8 ) economic margin of process unit 8 ∆9 ) economic margin of process unit 9 ∆10 ) economic margin of process unit 10 ∆11 ) economic margin of process unit 11 ∆12 ) economic margin of process unit 12 ∆i ) economic margin of process unit i ∆d ) economic margin of downstream process unit d ∈ D(i) of unit i ∆u ) economic margin of upstream process unit u ∈ U(i) of unit i ∆j ) economic margin of process unit j Allowable Errors in Predictions of VOPs, COPs, and Overall Values ξVOP ) error in prediction of VOP ξCOP ) error in prediction of COP (ξe-i)VOP ) error in prediction of VOP of feed stream to unit i from upstream element e ∈ EU(i) (ξe-i)COP ) error in prediction of COP of feed stream to unit i from upstream element e ∈ EU(i) ξe-i ) total error in prediction of margin from feed stream to unit i from upstream element e ∈ EU(i) Market Prices of Feeds F ) market price of feed F F1 ) market price of feed F1 to unit 1 F1-2 ) market price of feed F1-2 to unit 2 from unit 1 F1-2-3 ) market price of feed F1-2-3 to unit 3 from path 1-2 F1-3 ) market price of feed F1-3 to unit 3 from unit 1 F1-3-2 ) market price of feed F1-3-2 to unit 2 from path 1-3 F1-4 ) market price of feed F1-4 to unit 4 from unit 1 F′3 ) market price/value of second feed F′3 to unit 3 F′3-2 ) market price/value of second feed F′3-2 to unit 2 from unit 3 F′3-4 ) market price/value of second feed F′3-4 to unit 4 from unit 3 Values on Processing of Feeds (F1)VOP ) value on processing of feed F1 to unit 1 (Fcrude1 )VOP ) value on processing of crude 1 to unit 1 1 )VOP ) value on processing of crude 2 to unit 1 (Fcrude2 1 (Fcrude3 )VOP ) value on processing of crude 3 to unit 1 1 (Fcrudec ) VOP ) value on processing of crude c to unit 1 1 (F12)VOP ) value on processing of overall feed F12 to unit 12 (F1-2)VOP ) value on processing of feed F1-2 to unit 2 from unit 1 (F1-2-3)VOP ) value on processing of feed F1-2-3 to unit 3 from path 1-2 (F1-2-4)VOP ) value on processing of feed F1-2-4 to unit 4 from path 1-2 (F1-3-2)VOP ) value on processing of feed F1-3-2 to unit 2 from path 1-3

(F1-4)VOP ) value on processing of feed F1-4 to unit 4 from unit 1 (F1-4-2)VOP ) value on processing of feed F1-4-2 to unit 2 from path 1-4 (F1-4-6)VOP ) value on processing of feed F1-4-6 to unit 6 from path 1-4 (F1-4-12)VOP ) value on processing of feed F1-4-12 to unit 12 from path 1-4 (F1-5)VOP ) value on processing of feed F1-5 to unit 5 from unit 1 (F1-6)VOP ) value on processing of feed F1-6 to unit 6 from unit 1 (F1-7)VOP ) value on processing of feed F1-7 to unit 7 from unit 1 (F1-8)VOP ) value on processing of feed F1-8 to unit 8 from unit 1 (F′3)VOP ) value on processing of second feed F′3 to unit 3 (F′3-2)VOP ) value on processing of second feed F′3-2 to unit 2 from unit 3 (Fe-i)VOP ) value on processing of feed Fe-i to unit i from upstream element e ∈ EU(i) (Fe-i)act VOP ) actual value on processing of feed Fe-i to unit i from upstream element e ∈ EU(i) (Fe-i-e′)VOP ) value on processing of feed Fe-i-e′ to downstream element e′ ∈ ED(i) from unit i/element e-i (Fe-i-j)VOP ) value on processing of feed Fe-i-j to unit j from unit i/element e-i (Fe-i-j-e′)VOP ) value on processing of feed Fe-i-j-e′ to downstream element e′ ∈ ED(i) from unit j/element e-i-j (Fe-j)VOP ) value on processing of feed Fe-j to unit j from upstream element e ∈ EU(j) (Fi)VOP ) value on processing of overall feed Fi to unit i (Fi-e)VOP ) value on processing of feed Fi-e to downstream element e ∈ ED(i) from unit i (Fi-e′)VOP ) value on processing of feed Fi-e′ to downstream element e′ ∈ ED(i) from unit i (Fi-j-k)VOP ) value on processing of feed Fi-j-k to unit k from unit j/element ...-i-j (Fi-j-k-l)VOP ) value on processing of feed Fi-j-k-l to unit l from unit k/element ...-i-j-k Costs of Production of Feeds (F1)COP ) cost of production of feed F1 to unit 1 (F1-2)COP ) cost of production of feed F1-2 to unit 2 from unit 1 (F1-2-3)COP ) cost of production of feed F1-2-3 to unit 3 from path 1-2 (F1-2-4)COP ) cost of production of feed F1-2-4 to unit 4 from path 1-2 (F1-3-2)COP ) cost of production of feed F1-3-2 to unit 2 from path 1-3 (F1-4)COP ) cost of production of feed F1-4 to unit 4 from unit 1 (F1-4-2)COP ) cost of production of feed F1-4-2 to unit 2 from path 1-4 (F1-4-6)COP ) cost of production of feed F1-4-6 to unit 6 from path 1-4 (F1-4-12)COP ) cost of production of feed F1-4-12 to unit 12 from path 1-4 (F1-5)COP ) cost of production of feed F1-5 to unit 5 from unit 1 (F1-6)COP ) cost of production of feed F1-6 to unit 6 from unit 1 (F1-7)COP ) cost of production of feed F1-7 to unit 7 from unit 1 (F1-8)COP ) cost of production of feed F1-8 to unit 8 from unit 1 (F′3)COP ) cost of production of second feed F′3 to unit 3 (F′3-2)COP ) cost of production of second feed F′3-2 to unit 2 from unit 3

Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5179 (Fe-i)COP ) cost of production of feed Fe-i to unit i from upstream element e ∈ EU(i) (Fe-i)act COP ) actual cost of production of feed Fe-i to unit i from upstream element e ∈ EU(i) (Fe-i-e′)COP ) cost of production of feed Fe-i-e′ to downstream element e′ ∈ ED(i) from unit i/element e-i (Fe-i-j)COP ) cost of production of feed Fe-i-j to unit j from unit i/element e-i (Fe-i-j-e′)COP ) cost of production of feed Fe-i-j-e′ to downstream element e′ ∈ ED(i) from unit j/element e-i-j (Fe-j)COP ) cost of production of feed Fe-j to unit j from upstream element e ∈ EU(i) (Fi)COP ) cost of production of overall feed Fi to unit i (Fi-e)COP ) cost of production of feed Fi-e to downstream element e ∈ ED(i) from unit i (Fi-e′)COP ) cost of production of feed Fi-e′ to downstream element e′ ∈ ED(i) from unit i (Fi-j)COP ) cost of production of feed Fi-j to unit j from unit i (Fi-j-k)COP ) cost of production of feed Fi-j-k to unit k from unit j/element ...-i-j (Fi-j-k-l)COP ) cost of production of feed Fi-j-k-l to unit l from unit k/element ...-i-j-k Flow Rate of Feeds mF1 ) flow rate of feed F1 to unit 1 mF,crude1 ) flow rate of crude 1 to unit 1 1 ) flow rate of crude 2 to unit 1 mF,crude2 1 mF,crude3 ) flow rate of crude 3 to unit 1 1 ) flow rate of crude c to unit 1 mF,crudec 1 F m1-2 ) flow rate of feed F1-2 to unit 2 produced from unit 1 F ) flow rate of feed F1-2-3 to unit 3 produced m1-2-3 from path 1-2 F ) flow rate of feed F1-2-4 to unit 4 from unit 1-2 m1-2-4 F m1-3-2 ) flow rate of feed F1-3-2 to unit 2 from path 1-3 F ) flow rate of feed F1-4 to unit 4 produced from m1-4 unit 1 F m1-4-2 ) flow rate of feed F1-4-2 to unit 2 produced from path 1-4 F ) flow rate of feed F1-4-6 to unit 6 produced m1-4-6 from path 1-4 F m1-5 ) flow rate of feed F1-5 to unit 2 produced from unit 1 F ) flow rate of feed F1-6 to unit 6 from unit 1 m1-6 F m1-7 ) flow rate of feed F1-7 to unit 7 from unit 1 F ) flow rate of feed F1-8 to unit 8 from unit 1 m1-8 mF′ 3 ) flow rate of second feed F′3 to unit 3 F′ ) flow rate of second feed F′3-2 to unit 2 from unit m3-2 3 F ) flow rate of feed Fe-i to unit i from upstream me-i element e ∈ EU(i) F me-i-e′ ) flow rate of feed Fe-i-e′ to downstream element e′ ∈ ED(i) from unit i/element e-i F me-i-j ) flow rate of feed Fe-i-j to unit j from unit i/element e-i F me-i-j-e′ ) flow rate of feed Fe-i-j-e′ to downstream element e′ ∈ ED(i) from unit j/ element e-i-j F me-j ) flow rate of feed Fe-j to unit j from upstream element e ∈ EU(j) mFi ) flow rate of overall feed Fi to unit i F ) flow rate of feed Fi-e to downstream element e ∈ mi-e ED(i) from unit i

F ) flow rate of feed Fi-e′ to downstream element e′ ∈ mi-e′ ED(i) from unit i F ) flow rate of feed Fi-j-k to unit k from unit mi-j-k j/element ...-i-j F ) flow rate of feed Fi-j-k-l to unit l from unit mi-j-k k/element ...-i-j-k flow rate of end products mLG 1 ) flow rate of light gases from unit 1 mP1 ) flow rate of end product P from unit 1 P ) flow rate of end product P1-2 from path 1-2 m1-2 P m1-2-3 ) flow rate of end product P1-2-3 from path 1-2-3 P m1-3 ) flow rate of end product P1-3 from path 1-3 P m1-3-2 ) flow rate of end product P1-3-2 from path 1-3-2 mP2 ) flow rate of end product P2 from unit 2 mP3 ) flow rate of end product P3 from unit 3 mP′ 3 ) flow rate of end product P′3 from second feed F′3 of unit 3 P′ m3-2 ) flow rate of end product P′3-2 from second feed F′3-2 of unit 2/element 3-2 mP4 ) flow rate of end product P4 from unit 4 P ) flow rate of end product Pe-i(p) from element me-i(p) e-i mPi ) flow rate of end product Pi from unit i P ) flow rate of end product Pi-j-k from element mi-j-k i-j-k P mi(p) ) flow rate of end product Pi(p) from unit i

Unit Operating Costs oˆ 1 ) operating cost feed oˆ 2 ) operating cost feed oˆ 3 ) operating cost feed oˆ 4 ) operating cost feed oˆ i ) operating cost feed oˆ j ) operating cost feed oˆ k ) operating cost feed

of process unit 1 per unit flow rate of of process unit 2 per unit flow rate of of process unit 3 per unit flow rate of of process unit 4 per unit flow rate of of process unit i per unit flow rate of of process unit j per unit flow rate of of process unit k per unit flow rate of

Total Operating Costs O1 ) total operating cost of process unit 1 O2 ) total operating cost of process unit 2 O3 ) total operating cost of process unit 3 O4 ) total operating cost of process unit 4 Oi ) total operating cost of process unit i Oj ) total operating cost of process unit j Ok ) total operating cost of process unit k Market Prices of End Products LG4 ) market price of light gases from unit 4 P1 ) market price of end product P1 from unit 1 P1-2 ) market price of end product P1-2 from path 1-2 P1-2-3 ) market price of end product P1-2-3 from path 1-2-3 P1-3 ) market price of end product P1-3 from path 1-3 P1-3-2 ) market price of end product P1-3-2 from path 1-3-2 P2 ) market price of end product P2 from unit 2 P3 ) market price of end product P3 from unit 3 P′3 ) market price of end product P′3 from second feed F′3 of unit 3

5180 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 P′3-2 ) market price of end product P′3-2 from second feed F′3-2 of unit 2/element 3-2 P4 ) market price of end product P4 from unit 4 Pe-i(p) ) market price of end product Pe-i(p) from element e-i Pi(p) ) market price of end product Pi(p) from unit i

Market Constraints on Property Sets

Values on Processing (Market Prices) of End Products

Appendix A: Data for the Refinery Case Study

(LG1)VOP ) value on processing of light gases from unit 1 (LG4)VOP ) value on processing of light gases from unit 4 (P1)VOP ) value on processing of end product P from unit 1 (P1-2)VOP ) value on processing of end product P1-2 from path 1-2 (P1-2-3)VOP ) value on processing of end product P1-2-3 from path 1-2-3 (P1-3)VOP ) value on processing of end product P1-3 from path 1-3 (P1-3-2)VOP ) value on processing of end product P1-3-2 from path 1-3-2 (P2)VOP ) value on processing of end product P2 from unit 2 (P3)VOP ) value on processing of end product P3 from unit 3 (P′3)VOP ) value on processing of end product P′3 from second feed F′3 of unit 3 (P′3-2)VOP ) value on processing of end product P′3-2 from second feed F′3-2 of unit 2/element 3-2 (P4)VOP ) value on processing of end product P4 from unit 4 (Pe-i(p))VOP ) value on processing of end product Pe-i(p) from element e-i (Pi)VOP ) value on processing of end product Pi from unit i (Pi-j-k)VOP ) value on processing of end product Pi-j-k from element i-j-k (Pi(p))VOP ) value on processing of end product Pi(p) from unit i Costs of Production of End Products (LG1)COP ) cost of production of light gases from unit 1 (LG4)COP ) cost of production of light gases from unit 4 (P1)COP ) cost of production of end product P from unit 1 (P1-2)COP ) cost of production of end product P1-2 from path 1-2 (P1-2-3)COP ) cost of production of end product P1-2-3 from path 1-2-3 (P1-3)COP ) cost of production of end product P1-3 from path 1-3 (P1-3-2)COP ) cost of production of end product P1-3-2 from path 1-3-2 (P2)COP ) cost of production of end product P2 from unit 2 (P3)COP ) cost of production of end product P3 from unit 3 (P′3)COP ) cost of production of end product P′3 from second feed F′3 of unit 3 (P′3-2)COP ) cost of production of end product P′3-2 from second feed F′3-2 of unit 2/element 3-2 (P4)COP ) cost of production of end product P4 from unit 4 (Pe-i(p))COP ) cost of production of end product Pe-i(p) from element e-i (Pi)COP ) cost of production of end product Pi from unit i (Pi-j-k)COP ) cost of production of end product Pi-j-k from element i-j-k (Pi(p))COP ) cost of production of end product Pi(p) from unit i Property Sets Pr Fi ) property set of overall feed Fi to unit i F Pr e-i ) property set of feed Fe-i to unit i

minPr Fi ) minimum property set of overall feed Fi to unit i maxPr Fi ) maximum property set of overall feed Fi to unit i

The hydroskimming section of the refinery includes topping [atmospheric and vacuum distillation units (CDU and VDU, respectively)], reforming (REF), isomerization (ISO), hydrodesulfurization (VGOHDS), and various hydrotreaters: naphtha (NHT), kero (KHT), and light gasoil (GHT). The conversion section includes catalytic cracking (FCC) of vacuum gas oil (VGO), visbreaking (VBU) of vacuum residues (V residue), and bitumen treating (BIT). A brief description on the refinery system is as follows. The refinery processes Mediterranean crude Urals. The main products produced are two grades of gasoline with motor octane numbers 80 and 95 (MOG80 and MOG95, respectively), jet fuel, two types of diesel (EUDSL and DSL), hydrotreated oil (HTO), light fuel oil (LFO), bunker, bitumen, etc. To yield gasoline of grade MOG80, the good-quality cracker naphtha with high octane number in the range of 92 is blended with poor-quality naphtha with octane number in the range of 65 from the VGOHDS unit. In addition to the octane number, the Reid vapor pressure (RVP) of MOG80 is also improved Table A1. Purchase Costs of Feeds and Utilities cost ($1000) Urals (kt) fuel (gcal) HP steam (kt) LP steam (kt)

cost ($1000) BFW (m3/1000) cooling water (m3/1000) power (MW‚h) chemicals (kt)

111.53 6.89 2.50 2.10

0.30 0.03 0.05 10.00

Table A2. Sales Prices of Products and Utilities price ($/t) mixed C3 MOG80 MOG95 kero EUDSL DSL

price ($/t)

149 161 170 149 165 155

HTO LFO INFO bunker bitumen sulfur

82.5 65.5 97 89 104 15

Table A3. Property Constraints on Final Products min RON MOG80 MOG95 kero EUDSL

max sulfur (ppm)

80 95

max RVP (psia)

max specific gravity

min cetane no.

0.840 0.845

51

10.15 8.40 300 250

Table A4. Properties of Crude specific gravity

sulfur (wt %)

0.8622

1.63

Urals

Table A5. Hardware Constraints unit

max capacity (kt/day)

CDU ISO NHT KHT GHT VDU

46.67 1.24 10.00 6.00 10.70 13.33

unit

max capacity (kt/day)

VBU BIT REF VGOHDS FCC

5.00 5.00 10.00 11.50 10.00


by blending with cracker naphtha. The balance of cracker naphtha is blended with reformate, isomerate, and naphtha from the gasoil hydrotreater to yield the high-grade gasoline MOG95. For good-quality diesel (EUDSL), the distillate from VGOHDS is blended with the distillate from GHT. LFO is produced by blending light gasoil (LGO) from BIT, heavy cycle oil (HCO) and slurry from FCC, and distillate and tar from VBU (together called VB product). The light cycle oil (LCO) from FCC produces HTO. Bunker consists of atmospheric residues (A residue). The market constraints (sale/purchase cost information for products, feeds, and utilities; property constraints for end products and properties of crudes), and the hardware constraints (process capacities) are as reported in Tables A1-A5.

(3) Grossmann, I. E. Mixed-Integer Programming Approach for the Synthesis of Integrated Process Flowsheets. Comput. Chem. Eng. 1985, 9, 463. (4) Kravanja, Z.; Grossmann, I. E. Multilevel-Hierarchical MINLP Synthesis of Process Flowsheets. Comput. Chem. Eng. 1997, 21(Suppl), S421. (5) Kallrath, J. Mixed Integer Optimisation in the Chemical Process Industry: Experience, Potential and Future. Trans. Inst. Chem. Eng. A 2000, 78, 80. (6) Mah, R. S. H. Application of Graph Theory to Process Design and Analysis. Comput. Chem. Eng. 1983, 7, 239. (7) Sadhukhan, J.; Zhu, X. X. Integration Strategy of Gasification Technology: A Gateway to the Future Refining. Ind. Eng. Chem. Res. 2002, 41 (6), 1528. (8) Baird, C. Petroleum Refining Process Correlations; HPI Consultants Inc.: Houston, TX, 1987. (9) Gary, H. J.; Handwerk, E. G. Petroleum Refining: Technology and Economics, 3rd ed.; Marcel Dekker Inc.: New York, 1994.

Literature Cited (1) Sadhukhan, J. A Novel Value Analysis Method for Process Network Optimisation. Ph.D. Dissertation, UMIST, Manchester, U.K., 2002. (2) Hartmann, J. C. M. Interpreting LP Outputs. Hydrocarbon Process. 1999, February, 64.

Received for review December 3, 2002 Revised manuscript received July 19, 2003 Accepted August 6, 2003 IE020968Z

Value Analysis of Complex Systems and Industrial Application to

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