A Simultaneous Optimization Strategy for Overall Integration in

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Ind. Eng. Chem. Res. 2001, 40, 2640-2653

A Simultaneous Optimization Strategy for Overall Integration in Refinery Planning J. Zhang,† X. X. Zhu,* and G. P. Towler‡ Department of Process Integration, UMIST, Post Office Box 88, Manchester M60 1QD, U.K.

The refining industry is under immense pressure to produce cleaner products but faces low economic margins because of stricter environmental regulations and depressed market demand. In this situation, refinery planning becomes very important as it can exploit all potential opportunities to push the economic margin to the maximum limit. This paper presents a method for overall refinery optimization through integration of the hydrogen network and the utility system with the material processing system. The problem of optimizing each of these three systems is very complex in its own right. To make the problem of overall optimization solvable, the current practice adopts a decomposition approach, in which material processing is optimized first using linear programming (LP) techniques to maximize the overall profit. Then, supporting systems, including the hydrogen network and the utility system, are optimized to reduce operating costs for the fixed process conditions determined from the LP optimization. Essentially these three systems are dealt with separately, which usually leads to nonoptimal solutions for refinery operations. A new optimization method is proposed that is developed on the basis of a sound understanding of interactions between the three systems and the proper use of mathematical modeling. This method considers the optimization of refinery liquid flows, hydrogen flows, and steam and power flows simultaneously. As a result, this method furnishes new insights into the problem of refinery optimization and can provide significant benefits to the refining industry in exploiting the true potential of the processes and obtaining truly optimal operation. 1. Introduction A refinery consists of many processes that convert crude oils into valuable products such as gasoline, jet fuel, and diesel by consuming energy (fuel, steam, and power), hydrogen, etc. The energy and hydrogen required in some processes can be supplied from some other processes, which are producers of energy and hydrogen. Thus, processes are interlinked by energy and hydrogen flows, which form a complex energy system and a hydrogen network. The net energy and hydrogen deficits are satisfied from the fired boilers and hydrogen plants, respectively, or from external suppliers, whereas any surplus can be exported to the market. To make the problem of refinery optimization mathematically solvable and computationally efficient, linear programming (LP) has played an essential role in refinery planning and optimization since the 1950s.1 In the past, people have applied LP methods aiming to maximize the profit and attempting to deal with the following issues: (a) selection of crude oils and optimization of crude blending ratios; (b) determination of the most valuable product slates; (c) optimization of product blending ratios; and (d) selection of the most economic processing schemes, operations, etc. However, linear programming requires that the objective function and that all constraints be linear. To satisfy this requirement, current refinery LP methods adopt a two-stage optimization strategy. In the first * To whom all correspondence should be addressed: F.Zhu@ umist.ac.uk. † Current Address: AspenTech Ltd., Birkdale House, Warrington WA3 7RB, U.K. ‡ Current address: Engineering Sciences Skill Centre, UOP, 25 E. Algonquin Ave., Des Plaines, IL.

stage, oil liquid flows are taken into account and formulated as a LP model with simplistic consideration of the allocation of utilities (e.g., energy and hydrogen). The objective of this model is to maximize the economic margin (sale of products - crude oil costs - simplistic operating costs) by determining the optimal crude oil slates, products, and throughputs of all processes. In the second stage, based on the fixed process conditions and throughputs determined from the first-stage LP optimization, the hydrogen network and energy system are optimized individually to determine the actual operating costs. In this stage, the scope and size of the problems are much smaller than that of the first stage. Finally, overall refinery profit is determined by combining operating cost savings with LP margins. Essentially, the processing system is dealt with separately from the energy system and hydrogen network in the LP approach. However, it has been found that there are strong network interactions among these three systems and these interactions can have a significant influence on refinery economics. Separate consideration of these three systems could miss opportunities for improving the economic margin. To be more specific, in a traditional planning model, the hydrogen network is typically modeled in such a way that the purity of the hydrogen makeup to the process (e.g., hydrocracker, hydrotreater, etc.) is fixed, and its flow rate is modeled as a function of only the process feed flow and properties (e.g., sulfur content, aromatic content, etc.). In reality, apart from the above variables, the hydrogen makeup flow into the process is strongly dependent on its purity, i.e., the makeup flow is inversely proportional to the hydrogen makeup purity. Thus the hydrogen purity is an important degree of freedom for optimization. Optimization neglecting this parameter can lead to a nonoptimal solution.

10.1021/ie000367c CCC: $20.00 © 2001 American Chemical Society Published on Web 05/08/2001

Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001 2641

Figure 1. Typical fuel refinery flow chart.

Similarly, the configuration and details of utility systems are not addressed in a conventional LP planning model, which also misses significant degrees of freedom in optimization. Based on these insights, a new optimization strategy is proposed that tackles the problem of refinery optimization by considering proper integration of the different systems. To consider actual hydrogen consumption, a model addressing the hydrogen makeup rate and hydrogen purity is developed that links hydrogen consumers with liquid processing. In contrast, in the hydrogen consumer model used in the conventional LP approach, only the consumption of hydrogen with a fixed purity is explicitly considered, so the actual hydrogen consumption cannot be considered. A Base-Delta formulation2,3 is then used to integrate the hydrogen model into the overall optimization model. For the utility system, the steam and power flows are modeled as functions of process liquid throughputs based on the energy balance. In this work, we adopt linear programming to comply with the current optimization practice in refineries, aiming for wide application of the proposed method for refinery planning. Therefore, we apply proper linearization and successive linear programming (SLP) techniques4,5 to deal with the original nonlinear problem. Comparing the new simultaneous optimization strategy with the conventional approach, the new approach can provide solutions with improved profit by exploiting synergistic interactions between processes. This can help refineries to become more competitive in a time of low refining margins. It should be noted that simplified process models are used in this work because commercial models are not available in the open literature. However, this does not affect our intention of developing a methodology for integrating both hydrogen and utility systems into overall refinery optimization without introducing much mathematical and computational difficulties. Users can readily apply this proposed approach in implementing their in-house models in the framework for generating realistic solutions. 2. Problem Definition Refinery optimization involves many aspects ranging

from economic analysis to selection of crude oils and products, from arrangement of processing schemes to decidsions on process operation modes, and so on. To focus on network integration and associated modeling issues, the refinery optimization problem is defined as follows. For the specified refinery feedstocks including crude oils, other liquids, and gases and for selected products with their prices, the overall objective is to maximize the overall refinery profit (or margin), which is defined as the total revenue minus the total operating costs for a given refinery system. The total operating costs refer to the purchase costs of all kinds of utilities such as hydrogen, fuel, power, catalysts, etc. The hydrogen network is given as a set of hydrogen sinks, defined as those processes consuming hydrogen, and a set of hydrogen sources, defined as those processes producing hydrogen, together with the interconnections between them. The objective of hydrogen integration is to optimize hydrogen use and generation in terms of purity and flow rate among all of the hydrogen sinks and sources. The steam and power network in the refinery is given by the steam header conditions, the steam network configuration, and the hardware capacities for boilers, turbines, etc. The objective of energy integration is to optimize power generation and steam distribution among all refinery processes. These two integration problems are considered simultaneously with the overall objective defined above. In other words, these two integration problems are used to enhance the economic performance of the refinery under the given market situations and capacity constraints of existing processes and equipment. 3. Understanding the Three Major Systems Oil Liquid Flow System. A typical fuel refinery flow sheet (Figure 1) is used for illustration. In this refinery, crude oil is sent to the crude distillation unit first to conduct the preliminary separation. Light fractions such as naphtha and distillates are further upgraded in the downstream units (e.g., catalytic reformer, hydrotreater, etc.) to produce products that meet the required quality specifications. Heavy fractions such as gas oils and residue are upgraded into light fractions in either the catalytic conversion or the thermal conversion units

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Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001

Figure 2. Typical hydrogen distribution system in refinery.

(e.g., catalytic cracker, delayed coker, etc.). The products from all of the upgrading processes are then blended to form the final refinery products (e.g., gasoline, kerosene, diesel, fuel oil, etc.). In addition, some solid products such as coke, sulfur, and black carbons are also produced as byproducts. In refinery operation, the selection of crude oils is one of the most important aspects. This is especially true for refineries that process different crude oil mixtures to satisfy the downstream process loads. In this case, the optimal crude oil mixing ratios are important variables in optimization that significantly affect plant profit. In the crude oil, cut points determine the portions of fractions and can vary within certain ranges. This variation affects the yields and properties of the column products. Hence, the cut points of crude distillation are major optimization variables as well. In addition to feedstock selections, process conditions such as distillation cut points and reaction severity also affect the refinery operating margins. Another important degree of freedom to be exploited is product blending, which is optimized subject to the product specifications and market conditions. The above aspects, together with other related issues, are taken into account in optimization of the oil liquid flows. The aim of this optimization is to select the type of crude oil, the final refinery products, and the process operating conditions. The major modeling aspects focus on information about the oil liquid such as product yields, product qualities, product blending ratios, etc. Hydrogen System. A simplified hydrogen distribution system for a fuel refinery is shown in Figure 2. This system consists of hydrogen producers [e.g., hydrogen generation unit (HGU), catalytic reformer (CCR)], consumers [e.g., hydrocracking unit (HCU), diesel hydrotreater (DHT), etc.], and recovery units [e.g., pressure swing adsorption (PSA) unit, etc.]. One of the two hydrogen producers is the hydrogen generation unit (HGU), where high-purity hydrogen is produced. The other producer is the catalytic reformer (CCR), where hydrogen is generated as a byproduct. Hydrogen consumers include the hydrocracking unit (HCU), diesel hydrotreater (DHT), cracked naphtha hydrotreater (CNHT), and naphtha hydrotreater (NHT). They require hydrogen at different purities and pressures. To use hydrogen more efficiently, the purge gas from some consumers can be reused as the makeup of other hydrogen consumers. For example, the high-pressure purge from the HCU normally contains a large amount of hydrogen and can be used as part of the hydrogen makeup to the DHT. To use hydrogen efficiently, some

purge gases with low-purity hydrogen can be purified in hydrogen recovery processes such as pressure swing adsorption (PSA). The purified hydrogen can then be sent to other hydroprocessing units as hydrogen makeup. The rest of the purge gases with small amounts of hydrogen that are not worth recovering are delivered to the refinery fuel plant. The makeup gas rates of most hydrogen consumers (e.g., hydrotreaters and hydrocrackers) depend heavily on the hydrogen purity in the gas makeup. In other words, the purer the hydrogen contained in the makeup gas, the lowere the gas flow rate, and thus, the less compression work required for the same liquid throughput. However, to increase the hydrogen purity, lowpurity hydrogen needs to be purified, which results in hydrogen loss and extra operating costs. Therefore, there is tradeoff between the hydrogen purity, the gas flow rate, and the cost penalties. In addition, the feed conditions of the purification process are another important issue in hydrogen network optimization, as the purification process can take purge gases from different processes at different purity and pressures as feed. Overall, the objective of optimizing the hydrogen network is to minimize the hydrogen operating costs, including the feedstock cost for the hydrogen generation unit and the total compression cost. Steam and Power System. A simplified utility system in a refinery is shown in Figure 3. In such a system, steam at different pressure levels is generated in either the fuel-fired boilers or the waste-heat boilers of processes. Generally, steam is used for heating, processing, and driving steam turbines. Returned saturated condensate from steam heating and condensing turbines is combined with makeup water, and recycled to the boilers. The steam turbines, including backpressure, extraction, and condensing turbines, are used to drive pumps, fans, and compressors or to generate electricity. For the utility system, power generation and fuel consumption in the boilers are the major concerns. There is a tradeoff between these two aspects. In other words, power is generated by expanding high-pressure steam through steam turbines, which occurs at the cost of fuel consumption in boilers. In addition, product slates and process operating conditions frequently vary with the type of crude oil used. This variation results in changes in steam demands and steam generation from processes, which, in turn, affect steam and power generation from the utility system. The major degrees of freedom in optimizing the utility system include the steam and power distribution, the selection of process drivers (e.g., turbines vs motors), the freshwater makeup rate, etc. The overall objective of utility system optimization is to minimize the operating costs, including costs associated with fuel consumption in the boilers, power import, cooling duties in the condensing turbine, and water makeup. 4. Current Practice of Refinery Optimization The current refinery optimization methods follow a sequential procedure, which is summarized in Figure 4. In the first stage, LP optimization determines the selection of crude oils, products, yields, and throughputs for each process, the blending schemes, and the simplistic allocation of energy, hydrogen, and other utilities. However, in this optimization, the hydrogen makeup rate is modeled with a fixed hydrogen purity. The hydrogen production rate in the overall LP model


Figure 3. Typical steam and power network in refinery.

Figure 4. Sequential procedure in refinery optimization.

represents the deficit of the hydrogen balance. This hydrogen production rate can be reduced by optimizing the purity of the hydrogen makeup in each hydrogen consumer. Hence, in the second stage of hydrogen network optimization, after process conditions are determined from the LP optimization, actual hydrogen streams with gas contamination are considered, and the hydrogen distribution in the network is optimized. At this stage, the interactions between the purity and flow rate of the hydrogen are exploited to minimize total hydrogen consumption. Similarly, only simple steam and power balances are modeled in the LP optimization. Steam turbines and the steam network configuration are not explicitly modeled, and connections between steam levels are addressed only through letdowns. For the power demand, a linear equation is used to estimate the power generated through the steam turbines (e.g., kWh of power and ton/h of steam). Therefore, the actual energy cost cannot be addressed properly. Following the LP optimization

and in parallel with the hydrogen optimization, the existing utility system is optimized by considering the existing configuration and the capacity limits. The optimization then determines the tradeoff between fuel consumption and power import for the existing utility system to minimize the operating costs. Sometimes network optimization cannot reach a feasible solution using the existing process and network conditions; therefore, modifications of either the processes or the networks have to be made, and the associated capital investments also need to be taken into account. It should be noted that optimization of the hydrogen network and the utility system is based on the fixed throughput and operating conditions determined from the liquid flow optimization. This sequential procedure cannot fully exploit the interactions between the processes and the hydrogen and energy networks. Hence, it cannot obtain the true optimal solution for overall refinery operation. For the hydrogen network, optimization aims only to reduce the hydrogen output from the hydrogen plant to save hydrogen costs based on the fixed refinery throughputs. Similarly, the steam distribution through the extracting turbines is optimized to save fuel costs based on the fixed steam and power demands of the processes. Therefore, the sequential optimization strategy features cost savings to improve economic margins. In contrast, if we can exploit the synergistic effects of interactions among these three systems in a systematic way, we might be able to use saved energy and hydrogen to produce more valuable products by processing more feedstock, which can bring much more profit. 5. New Insights on Network Interactions Hydrogen Flows vs Oil Liquid Flows. Consider part of a refining plant for producing gasoline (Figure 5). After fractionation in the crude distillation unit, crude oil is separated into several fractions. Of the fractions, heavy naphtha (HN) is sent to the naphtha

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Figure 5. Gasoline production routes without hydrogen flows.

Figure 7. Oil liquid flows vs steam flows. Figure 6. Gasoline production routes with hydrogen flows.

hydrotreater (NHT) and then to the catalytic reformer (CCR). Vacuum gas oil (VGO) goes to the fluid catalytic cracker (FCC), and then cracked naphtha (CCN) is sent to the cracked naphtha hydrotreater (CNHT), which produces gasoline blendstocks. Unsaturated gas such as propylene and buteylene from the FCC are the feedstocks to the alkylation unit (ALKY) to produce highquality alkylate. The outlets from the FCC, ALKY, and CNHT are then blended in the gasoline pool. Judging only from the liquid flows shown in the figure, it seems that there is no direct link between the CCR and the FCC. However, if we want to meet new gasoline specifications (e.g., aromatic content, benzene content, etc.), then the CCR severity has to be reduced. This will reduce the hydrogen production from the CCR, which is the hydrogen supply to CNHT (Figure 6). One might consider increasing the FCC throughput for extra CCN and alkylate production to offset the loss in the CCR, if the FCC has spare capacity. However, this option might not be possible because now the CNHT is short of hydrogen because of the reduced hydrogen supply from the CCR. In this way, the hydrogen flow links the CCR and FCC units, and changes in the CCR operation might affect the FCC operation. This is a typical example of how hydrogen flows affect liquid flows and vice versa. Similar observations can be made for other parts of a refinery. Energy Flows vs Oil Liquid Flows. Let us use Figure 7 to examine the interaction between the liquid flows and the energy flows. For the same reason as mentioned above, the CCR throughput has to be reduced. Then, one might increase the FCC throughput to offset the gasoline loss in the CCR. In this case, the CNHT requires extra steam because of the increased CCN flows. However, it might not be practical in this case because the steam generation and turbine expansion rates decrease with the reduced CCR throughput. Although the FCC can produce extra steam, it might be limited by the capacity of the letdown if it already reaches its maximum limit. Hence, in this way, the FCC and CCR interact with each other through the steam and power flows.

Figure 8. Interactions between the hydrogen network and the utility system.

H2 Flows vs Energy Flows. Apart from the interactions between the liquid flows and the hydrogen and energy flows, there are also interactions between the hydrogen network and the utility system (Figure 8). Although mainly producing hydrogen, the HGU also generates high-pressure steam as a byproduct. With regard to energy management, the steam system expects to import as much steam as possible from the HGU to minimize fuel consumption in the boilers. On the other hand, from the viewpoint of hydrogen management, the hydrogen production needs to be minimized in the HGU, which will result in less steam export. In this way, the two systems interact with each other through the steam exported from the HGU. In addition, the hydrogen network affects the utility system through compressors. For instance, to reduce hydrogen production from the HGU, hydrogen purges from the hydrotreating and hydrocracking units have to be used more efficiently. One way of achieving this is to increase the hydrogen purge purity. This requires the purge to be purified and then compressed in order to be used as hydrogen makeup. This, however, might increase the shaft work demand in the compressors, which are driven by steam turbines. Consequently, more high-pressure steam needs to be generated in the utility system to satisfy the extra power demand.


pure hydrogen consumption R () RR + Rs), and net inert gas production β () βR - βs). According to this model, the hydrogen makeup rate is inversely proportional to the hydrogen makeup purity, which indicates the tradeoff between the hydrogen makeup purity and the makeup flow rate. Note that these two equations are formulated on a molar basis.

M)

R(1 - yp) + βyp ym - yp

P)M-R+β Figure 9. Overall interactions.

By investigating the relationships among the hydrogen network, the utility system, and the refinery processes, strong interactions are found in the overall refinery operation, which manifests a three-way tradeoff among these systems (Figure 9). These interactions provide opportunities for achieving a greater economic potential by exploiting the degrees of freedom these interactions provide. 6. Modeling Hydrogen and Utility Systems To consider the integration of both the hydrogen and utility systems into the refinery optimization, we need to model these two systems properly and link them with process conditions and process yields. Modeling the Hydrogen Network. Hydrogen Consumer. A simplified flow sheet of a hydrogen consumer (e.g., hydrotreater or hydrocracker) is used to illustrate model development (Figure 10). The preheated liquid feed and hydrogen-rich gas are charged into the reactor, in which an amount of pure hydrogen (RR) is consumed and inert gas (βR) is generated. After being cooled, the reactor effluent containing gas and liquid is separated in the flash drum. A purge stream is removed to prevent inert gas accumulation in the system. The liquid-phase product containing dissolved hydrogen (Rs) and light gases (βs) is pumped to the downstream separation units,where the gas and liquid products are finally separated. For this typical hydrogen consumer, Alves and Towler6 proposed a simple mass balance model, which is expressed in eqs 1 and 2. In this model, the hydrogen makeup rate (M) is expressed as a function of the hydrogen makeup purity (ym), the purge purity (yp), the

Figure 10. Simplified hydrogen consumer flow sheet.

(1) (2)

This model assumes that the hydrogen consumption (R), net inert gas production (β), and hydrogen purge purity (yp) are constant. This assumes fixed process conditions (feeds, products, and operating conditions), which results in a fixed hydrogen partial pressure in the reactor. However, in real plant operation, process conditions vary frequently, which causes changes in R and β as well. Therefore, these parameters should be treated as variables and linked with process conditions through yield models. In this way, the hydrogen information can be optimized together with material processing. The existing linear yield model of a hydroprocessing unit assumes a fixed hydrogen makeup purity (ymf). As a result, the hydrogen makeup and purge and light gas yield are represented as linear functions of the liquid throughput, feed properties, and operating conditions (eqs 3 and 4). To consider the variations of R and β with process conditions, let us first examine the connection between the light gas yield and βR.

M|ymf ) aF +

∑g Fg|y

f

m

)

∑p bpPFp + ∑j cjPRj

∑g (agF + ∑p bp,gPFp + ∑j cj,gPRj)

(3) (4)

When gas with a fixed hydrogen purity of ymf is used as the makeup, the gas generation (βR) and the gas in the makeup [M|ymf(1 - ymf)] are the only sources for the total gas yield from the process (Figure 11). Thus, a material balance must hold between them (eq 5). When a makeup gas with variable hydrogen purity is used, the gas generation βR does not change as long as the reaction kinetics does not change. The only difference

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recovery yield Y, it is possible to balance these parameters in the recovery process to achieve the best economic performance.

Y P ) Fz y

Figure 11. Predicting the inert gas generation rate in the reactor.

is that the inert gas contained in the makeup changes from M|ymf(1 - ymf) to M(1 - ym); thus, the corresponding total light gas yield (∑gFg) can be estimated using eq 6. In addition to βR, Rs and βs can be represented as a linear functions of the throughput for certain flash and liquid conditions, respectively.

βR + M|ymf(1 - ymf) )

∑g Fg|y

f

m

∑g Fg ) βR + M(1 - ym)

(5) (6)

After substituting eqs 3-5 into eqs 1 and 2, eqs 7 and 8 are obtained, where b and c are constants. Now, the hydrogen makeup rate and purge flow rate are all defined as variables, which relate to throughput (F), feed properties (PF), and operating conditions (PR). At the same time, the light gas yield can be estimated using eq 6. In this way, the extended hydrogen model (eqs 6-8) is integrated with the process yield model.

cF + M) P ) bF +

∑p cpPFp + ∑j cjPRj ym - yp

∑p bpPFp + ∑j bjPRj

(7) (8)

Note that this extended model is on a weight basis because most process yield models are formulated on a weight basis. It should be pointed out that the purge in the new process model is not a pure component but contains hydrogen and light gases. For simplicity, we assume that only methane appears in the high-pressure purge and that the rest of the light gases (from ethane to n-butane) are totally dissolved in the liquid phase. Hydrogen Producer and Hydrogen Recovery Process. Hydrogen producers are mainly the hydrogen generation unit (e.g., steam reforming plant) and the units that generate hydrogen as a byproduct (e.g., catalytic reformers, dehydrogenation units). For the latter producers, the hydrogen flow rate can be modeled as a linear function of the process throughput, and the hydrogen purity can be treated as a constant. The hydrogen production in a hydrogen generation unit can be expressed as a function of the feed flow. The feeds, which could be either gas or liquid, are included in the corresponding material balance. For the hydrogen recovery processes, hydrogen product flow (P) can be represented by eq 9. In general, hydrogen recovery yield (Y) is inversely proportional to the hydrogen product purity (y), that is, the higher the purity required, the lower the recovery yield. Therefore, given the relationship between product purity y and

(9)

Compressor. The compressor work is modeled as a function of the gas flow G (eq 10).7 In this equation, compressor inlet pressure (P1), outlet pressure (P2), and temperature (T1) are assumed to be fixed. In modeling a hydrogen consumer, it is assumed that the gas contains only hydrogen and methane; thus, the gas average specific heat capacity ratio (r) can be calculated from the specific heat capacities of these two components and the hydrogen purity (yc). As a result, this equation turns out to be nonlinear because of the unknown hydrogen purity. With the proper linearization, eq 10 can be converted to the linear form (eq 11), where a and b are constants.

W)

[( )

rRT1 P2 r - 1 P1

(r-1)/r

]

-1 G

W ) aG + byc

(10) (11)

Modeling the Utility System. Steam Boilers. A boiler for steam generation can be modeled as follows

FB )

QB (H - Hl)ηb v

(12)

It is assumed that the steam enthalpy (Hv), water feed enthalpy (Hl), and boiler efficiency ηb are constant. Thus, the steam generation (FB) is a linear function of the fuel consumption (QB). The fuel used in the boilers can be supplied from the residual fuel oil or fuel gas from other processes; hence, the fuel consumption in the boilers is part of the overall fuel balance in the refinery optimization model. Turbines. Two types of turbines are considered in the utility system model, back-pressure turbines and extraction turbines. For a back-pressure turbine, the passout steam flow (FS) can be modeled as follows

FS )

W ∆Htηis

(13)

It is assumed that a turbine operates within a narrow range. Hence, the turbine isentropic efficiency (ηis) can be roughly treated as a constant. For fixed isentropic enthalpy changes (∆Ht), the turbine shaft work (W) is linearly related to the steam flow (FS). Following the work of Marecki,8 an extraction turbine is modeled using eqs 14 and 15. The first equation is the steam balance on a turbine with two extractions, which implies that the total steam inlet (FSin) must be equal to the steam pass out (FSpas) plus the steam exhaust (FSexh). The second equation represents the energy balance on the turbine. Coefficients a and b are functions of the conditions of the steam inlet, steam outlet, and turbine efficiency, which are assumed to be constant; thus, the turbine model becomes linear.

FSin ) FSpas + FSexh

(14)

FSin ) aW + bFSpas

(15)


flow and shaft work of the turbines, the condensate balance on the deaerator, etc., are explicitly considered in the model for the utility system.

Figure 12. Steam generation in the process.

In some cases, process power demands vary significantly so that the turbine efficiency cannot be considered as a constant value. To accurately model the turbine performance, binary variables zi are introduced so that a nonlinear turbine efficiency curve is linearized with several linear segments (eq 16). A segment becomes active if the optimized turbine load falls within the region of this segment (eq 17). In this case, the corresponding value is zi ) 1. All other segments are assigned a zero value for their binary variables because they are inactive (eq 18).

ηis )

∑i (ciWi + dizi)

max zi Wmin i zi e Wi e Wi

∑i zi ) 1

zi ∈ {0,1}

(16) (17) (18)

Steam Production, Consumption, and Turbine Shaft Work. Steam use/generation and power demand by processes vary with the process liquid throughput and operating conditions. By conducting process simulations, steam and power demands (FS and W) can be linked to the process throughput (F), feed properties (PFp), and operating parameters (PRj).

FS(W) ) aF +


(19)

For steam generation, as shown in Figure 12, some hot streams from processes might be able to generate HP, MP, or LP steam. Once the steam conditions are known, the quantity of steam generated (FSh) from a process can be calculated from the energy balance (eq 20). Steam is usually generated by cooling a reaction effluent at high temperature, and the heat load (Q) of the effluent is related to the process throughput and reaction conditions (eq 21). By using eqs 19-21, the steam use/generation and power demand from individual processes are considered in the context of the overall refinery.

Q) Q ) aF +

∑h chFSh


(20) (21)

In addition, a steam desuperheator is modeled by applying the method proposed by Townsend and Linnhoff.9 Other constraints such as limits on the steam

7. Overall Integration Model for Refinery Planning Using the above models for both the hydrogen network and the utility system, an overall integration model for refinery planning can be formulated. The indices, parameters, and variables defined in the model are listed in the Notation section. The Objective Function. The objective function is the total refinery gross margin, which includes the revenues from all products and possible utility sales, as well as the total purchase costs of feedstock and operating costs. For certain economic conditions (e.g., given crude oil prices, product prices, and utility costs), the objective function is a linear function of material flows and utility flows.

Maximize RGM ) VjSj CiFi -

∑j

∑i

∑u CuUPu + ∑u VuUSu

(22)

Mass Balances on Processes. To allow the streamflows and properties to vary in a column (e.g., crude oil distillation, FCC main fractionation column, etc.), a swing cut is adopted to model the distillation process as in eq 23. The product yield for each process is modeled as a linear function of the feed flows, properties, and operating parameters (eq 24).

Fk -

∑s (Fs,k + SWs,k- + SWs-1,k+) ) 0

Fs,k ) as,kFk +

∑p bp,s,kPFp,k + ∑r cr,s,kPRr,k

(23) (24)

Mass Balances on Oil Liquid Streams. The mass balance on each oil stream is modeled in eqs 25-28. The first equation represents the feed balance on each process. In this equation, because of the fixed refinery configuration, the feed stream component l from process n to process k (n * k) is specified. The second equation is the mass balance on each process stream, which implies that the total flow of stream l to the process m (m * k) must be the same as the flow of stream l produced in process k. Equation 27 represents the feedstock balance, which indicates that the total feedstock i sent to the process k must equal the total purchase of feedstock i. Finally, eq 28 is the swing cut balance.

∑i Fi,k + ∑n ∑l Fl,n,k - Fk ) 0

(25)

n*k

Fl,m,k - Fl,k ) 0 ∑ m

(26)

m*k

∑k Fi,k - Fi ) 0

(27)

s+1 + wts,k Fk - SWs,k + SWs,k )0

(28)

Property Balance on Oil Liquid Streams. In addition to the flow rate calculation, properties of oil streams (eqs 29 and 30) should be modeled as well. When different streams are mixed together to form a

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process feed stream, the feed stream properties can be calculated on the basis of weight or volumetric summation of the corresponding properties of the mixed streams (eq 29). The product properties of the process can be predicted from the feed stream properties using eq 30, in which c and e are constants.

∑i Fk,iPFp,i + ∑n ∑l Fl,n,kPFp,l,n - FkPFp,k ) 0 PFp,s,k ) cp,s,kPFp,k + ep,s,k

(30)

∑d ∑t Ft,d,j - PSj ) 0

(31)

∑j Ft,d,j - Ft,d ) 0

(32)

∑d ∑t Ft,d,jPPq,t,d - PSjUBq,j e 0

(33)

∑d ∑t Ft,d,jPPq,t,d - PSjLBq,j g 0

(34)

Market Constraints. Market constraints are also taken into account (eqs 35 and 36). It must be emphasized that the upper and lower bounds for the feedstock purchase and product sales are determined from market investigation. These numbers usually vary dramatically with the market situation, and thus the market impact on the refinery operation and margins should be investigated thoroughly.

UBj e PSj e LBj

(35)

UBi e Fi e LBi

(36)

Process Capacity Constraints. The process capacity limit is taken into account by constraining the process throughput.

(37)

Hydrogen Network Model. In addition to the individual unit models (eqs 6-9), the hydrogen network must also be modeled in terms of the connections between the hydrogen consumers, producers, and recovery processes. The makeup gas (Fhc) to the hydrogen consumer (hc) consists of purge gases (Fhc,hg) from other hydrogen consumers and hydrogen gases (Fhc,hp) (eq 38). The purge gases that are sent to other consumers (Fhc,hg) must be made equal to the total purge flow (Fhg) (eq 39). The hydrogen makeup purity (ym,hc) for the consumer is calculated by eq 40. Finally, the hydrogen (Fhp) from the hydrogen producers must be made equal to the total hydrogen demand from all consumers (eq 41).

Fhc -

Fhc,hg + ∑Fhc,hp ) 0 ∑ hg hp

Fhcym,hc -

(29)

Blending Constraints. Blending constraints include the mass balance and the quality constraints (eqs 3134). Because the blending components for each product are specified, the blendstock t from process d for product j is pre-selected by the user. Some qualities (e.g., pour point, cetane number, etc.) used in the blending constraints (eqs 33 and 34) are replaced by corresponding quality indices to make the model linear.

LBk e Fk e UBk

Fhg -

(38)

Fhc,hg ) 0 ∑ hc

(39)

Fhc,hgyp,hg - ∑Fhc,hpyhp ) 0 ∑ hg hp

(40)

Fhc,hp - Fhp ) 0 ∑ hc

(41)

Steam and Power Network Model. In addition to eqs 12-21, the mass balance in the steam and power system is modeled as follows.

Fh - ∑Fh ) 0 ∑ in out

(42)

Additional Utility Balance. For other utilities (e.g., fuel, water, catalyst, etc.), the mass balance can be represented using eq 43. In this equation, the utility deficit is satisfied from the purchase UPu, and the surplus USu is sold to the market. The utility consumption in a process can be modeled as a linear function of the feed flow, properties, and operating conditions (eq 44).

∑k Fu,k + UPu - USu ) 0 Fu,k ) γu,kFk +

∑p λp,u,kPFp,k + ∑r Fr,u,kPRr,k

(43) (44)

Dealing with Nonlinear Terms. It can be noted that several nonlinear terms appear in both the process models and the network constraints. In eq 7, the nonlinearity in the hydrogen makeup purity can be handled with a proper linearization technique (e.g., the Base-Delta approach). The calculation of process feed properties (eq 29) results in bilinear terms in the form of (property) × (flow rate). In the network constraints, the calculation of the hydrogen makeup purity through the hydrogen balance (eq 40) also contains a bilinear term in the form of Fhcym,hc. After introducing the linearized turbine efficiency model, the turbine model incurs bilinear terms in the form of (steam flow rate) × (shaft work). These nonlinear terms are linearized using different methods as follows. For the bilinear terms associated with the turbine and hydrogen models, separable programming and piecewise linearization are applied. First, the bilinear terms are separated by introducing new variables and constraints. For the general bilinear term xy, two new variables are introduced to make it separable in the form of w12 w22, where w1 ) (x + y)/2 and w2 ) (x - y)/2. Then according to the boundary of x and y, w12 and w22 can be linearized in a piecewise manner using binary variables. Because a relatively small number of bilinear terms exists in the turbine and hydrogen models, this approach introduces a manageable number of binary variables. For the bilinear constraints in the process models, because there is a large number of processes and connections between processes, using the piecewise linearization method with binary variables for each bilinear constraint could require a prohibitive number of binary variables, which could make the problem suffer combinatorial explosion. Instead, a nonlinear recursion algorithm10 is used in this case. The concept of the recursion method can be explained by the idea of


Figure 13. Simplified refinery flow chart.

the SLP algorithm although the formulation is slightly different. In most cases, the effectiveness of the recursion is justified in successfully solving large-scale planning models. Through the use of linear approximations in the process and network models, errors can occur, and thus, the results should be tested via simulation. If the errors are large than a specified tolerance, the linear approximation should be updated using newly generated results, and the optimization should be repeated until the errors satisfy the specified tolerance. Remarks. Equations 6-44 form a complete model for overall refinery optimization. The number of optimization variables can vary significantly depending on the optimization techniques employed. If piecewise linearization techniques are used and binary variables are also introduced to incorporate the piecewise linear equations, the number of variables can be dramatically increased. However, if the technique of successive linear programming (SLP) is applied, the number of variables can be reduced significantly. For a typical refinery, the number of optimization variables could range from several hundred up to 10 000, depending on the level of detail involved in the process models. By using commercial optimization packages (e.g., Aspen PIMS), the model can be solved in the range of 100-1000 CPU seconds. The essential contribution of this work lies in connecting the process models to the utility network models to obtain a full mathematical description of the interactions between these systems. This requires modeling the hydrogen system, including the relation between the hydrogen consumption and the feed properties, process conditions, and hydrogen purity, and also connecting the steam and power system with the processes. The improved model is achieved through a newly developed understanding of the interactions between the different systems. With such integration, this overall model can determine the selection of feeds and products, the optimal process operating conditions, and the sensible use of utilities including hydrogen, steam and power, catalysts, etc. Simultaneous optimization can exploit all of the available degrees of freedom to achieve the true

potential of refinery operation. Unlike the conventional sequential strategy, the advantage of this simultaneous optimization is that it maximizes profit in a single step, rather than first maximizing profit for the processes and then saving operating costs in the utility networks. 8. Case Study A simplified oil refinery flow chart (Figure 13) is used to illustrate this method. In this refinery, Arabian Heavy (ARH), Arabian Light (ARL), and Tia Juana Light (TJL) crude oils are used as refinery feedstocks. After being separated in the CDU and VDU, the crude oils are separated into several straight-run fractions such as naphtha, jet fuel, diesel, gas oil, and residues. After being hydrotreated in the NHT, straight-run naphtha blended with DLC naphtha is sent to the CCR to produce gasoline. The straight-run middle distillates are combined with similar products from other processes and are hydrotreated and then blended as jet fuel and diesel. Gas oils and residues are sent to the secondary processes including FCC, DLC, and HC to increase the gasoline and distillate yields. The final products consist of two grades of gasoline (UPG and URG), jet fuel (JET), diesel (DSL), and residual fuel oil (HSF). In the existing hydrogen network (Figure 14), hydrogen demand in the refinery is mainly satisfied from the steam reformer (SMR) and CCR, in which the hydrogen purities are 92% and 85%, respectively. The hydrogen product purity and recovery yield of the PSA process are fixed at 99.9% and 86%, respectively. The pressure information of the processes (Table 1) is used to calculate the compression work. In the utility system (Figure 15), the power demands in the refinery are satisfied partly by the turbogenerator and partly by purchased power. Steam turbines are used as process drivers for the FCC air blower, hydrogen compressors, etc. Steam demands are met with steam boilers and process waste heat boilers. The steam conditions (pressures and temperatures) of each header are listed in Table 2. The overall objective of this case study is to maximize the refinery profit. First, the sequential optimization approach is applied to solve this problem and benefits are obtained. Then,

2650


Figure 14. Hydrogen flows before and after network optimization in the sequential approach. Table 1. Hydrogen Delivery and Desired Pressure in Processes process HGU CCR PSA HC DHT JHT CNHT NHT IS4 fuel plant

delivery pressure, psia

desired pressure, psia

300 300 350 2050 200 170 170 120 300

350 2500 600 500 500 350 400 400

the simultaneous approach with overall integration is used to solve the same problem. A comparison between these two approaches is also made.

Figure 15. Utility plant in the case study.

Table 2. Steam Conditions in the Utility Plant pressure, psia temperature, °F

VHP

HP

MP

LP

condensate

580 842

290 572

174 392

58 212

1.1 100

Sequential Approach to Refinery Planning. Following the conventional approach, a two-stage optimization is conducted; that is, oil liquid flows are optimized first, and then utility and hydrogen systems are optimized separately. For the oil liquid optimization, the refinery model is formulated using the commercial process industry modeling system (PIMS) software licensed by AspenTech. As explained previously, considerations of the hydrogen and energy costs are taken into account through simple mass balances. The purities of hydrogen makeup to the consumers are considered

Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001 2651 Table 3. Oil Liquid Optimization Results

Table 5. Utility System Optimization Results

overall margins, k$/D

574 utility system

crude oil flows, kBPD ARH ARL TJL

56.7 38.0 5.3

major products, kBPD URG UPG JET DSL

39.6 23.1 12.3 16.9

process throughput and capacity limit process

throughput, kBPD

capacity, kBPD

CDU CCR FCC DLC HC DHT CNHT NHT HGU, MMSCFD boilers, MMBTU/D

100 31 35.6 21.4 18.5 2.5 21.3 27.5 49 20 500

100 35 40 23 20 5 25 30 49 20 500

Table 4. H2 Network Optimization H2 network HGU, MMSCF/D natural gas consumption, Ton/D total compression work, MWh/D total costs, k$/D

before optimization 49 644

after optimization 43 565

95.3

103.3

67.4

60.5

hydrogen makeup purity, mol/mol HC 0.92 0.94 DHT 0.92 0.94 CNHT 0.92 0.94 NHT 0.85 0.75 JHT 0.8 0.76 final savings from network optimization ) 7.0 k$/d

to be fixed, as shown in Table 4. The SLP algorithm is employed to solve the model taking account of nonlinear constraints. The results of this optimization are given in Table 3, which shows the crude oil flows, major product flows, and process throughputs. In the second stage, network optimization is conducted to reduce the hydrogen and utility costs. Using the first-stage optimization results, the optimization model for the hydrogen network is set up in a spreadsheet environment. In this model, the hydrogen consumption, inert gas production, and hydrogen purge purity are kept constant in the hydrogen consumers because of the fixed liquid feed and process conditions. After optimization, the HGU production is reduced by a large amount, and the results shown in Table 4 and Figure 14 indicate the major difference between the hydrogen flows before and after network optimization. From these results, it is found that the hydrogen makeup purity is optimized to reduce the total hydrogen consumption in the processes. The power consumption is increased because more gases (mainly the gas makeup to the JHT and NHT) with low-purity hydrogen need to be compressed and recovered as hydrogen makeup. The results indicate that hydrogen network optimization can reduce the total hydrogen consumption through better use of the existing hydrogen sources based on the same liquid throughput. The final tradeoff shows that 7 k$/day savings can be achieved from hydrogen network optimization.

before optimization

after optimization

fuel consumption in boilers, 20 500 18 715 MMBTU/D total operating cost, 30.8 28.1 k$/d final savings from network optimization ) 2.7 k$/d

A utility system model is also built into the spreadsheet environment. In the model, steam use and power demands from the processes are constants, having been predetermined in the oil liquid optimization. Because all turbine efficiencies and steam conditions are constant, the utility system can be modeled as linear. Table 5 shows the results from the utility plant optimization. In the oil liquid optimization, because no turbine hardware is considered, only a simple energy balance is used to estimate the steam consumption during power generation. However, in the utility plant optimization model, the steam turbines are explicitly modeled, and the steam distribution through the steam turbines is optimized to reduce the fuel consumption in the boilers. As a result, the total operating cost is reduced by 2.7 k$/day via utility system optimization. By combining the margins achieved in the oil liquid optimization with the hydrogen and utility cost savings obtained from the network optimization, the overall profit is 583.7 k$/day, which is 9.7 k$/day higher than that obtained by optimizing the oil liquid flows alone. The benefits mainly result from cost reductions in the hydrogen system. In this case, it is interesting to note that, although the crude oil throughput reaches the maximum capacity of the crude distillation column, the heavy oil upgrading units such as the HC, DLC, and FCC still have spare capacity. This is largely because the hydrogen generation unit (HGU) and steam boilers reach their maximum capacities and, thus, there is not enough hydrogen and energy in the refinery to process more of the cheaper heavy crude oil. Note that optimization of both the hydrogen and utility systems following oil liquid optimization gives technically feasible solutions in the first iteration. Thus, according to the sequential procedure in Figure 4, the procedure terminates without the need for further iterations. Simultaneous Optimization Approach. By employing the proposed method, oil liquid flows, hydrogen flows, and energy flows are optimized simultaneously. The main optimization results are listed in Table 6 for feedstocks, products, and capacity utilization. Comparing Table 3 with Table 6, it can be seen that, although the total crude oil throughput remains unchanged, the throughputs of most processes reach or approach their capacity boundaries. This is partly due to the cut point changes in the crude distillation column where more distillates other than the naphtha cuts are produced (the NHT throughput is reduced, whereas th JHT and DHT feed flow rates are increased). In addition, because of the heavier crude oil slates, the heavy-end upgraded processes such as DLC, FCC, and HC are utilized fully to exploit the price difference between the light sweet TJL and the heavy sour ARH. Instead of saving hydrogen and energy resources, the refinery is driven to its maximum capacity limit to increase its revenues. As a result, the overall refinery profit is 590 k$/day compared with 583.7 k$/day from the sequential approach, which

2652


Table 6. Simultaneous Optimization Results for Liquid Flows overall margins, k$/D

590

crude oil flows, kBPD ARH ARL TJL

60.0 37.4 2.6

major products, kBPD URG UPG JET DSL

38.5 23.4 13.5 16.8

Instead, they should be treated as parts of the overall system and optimized simultaneously with other processes. Acknowledgment The financial support of the Process Integration Research Consortium at UMIST in conducting this research is gratefully acknowledged. Notation for Network Models Sets and Indices

process throughput and capacity limit process

throughput, kBPD

capacity, kBPD

CDU CCR FCC DLC HC DHT CNHT NHT HGU, MMSCFD boilers, MMBTU/D

100 32.3 38.1 25.0 20.0 3.8 25.0 25.0 49.0 20 500

100 35 40 25 20 5 25 35 49 20 500

results in about 1.9 m$/year more profit. It should also be emphasized that the simultaneous approach does not attempt to reduce hydrogen and energy consumption for the sake of reducing operating costs. Instead, the utilities are fully exploited to process more oil liquids. This is the fundamental difference between the sequential procedure and the simultaneous approach. The entire simultaneous optimization model contains 500 constraints and 482 variables. Because the SLP approach is applied and turbine efficiencies are fixed, there are no discrete variables in this case study. However, this could vary dramatically with the details of the process models and the accuracy of the solution required. 9. Conclusions Using a newly developed understanding of network interactions in refineries, a new refinery optimization approach is proposed, which can obtain better refinery margins. This improvement is achieved by introducing new degrees of freedom from the hydrogen network and the utility system into the refinery optimization. To exploit the network interactions, the hydrogen network and the utility system are modeled together with the process liquid flows. As a result, these two systems are seamlessly integrated with processes, which provides a solid foundation for building an overall refinery optimization model. Although the original model is MINLP, linearization techniques are applied to covert the MINLP problem to a MILP problem. This reduction is performed to broaden the scope of application of this method, as there are no robust MINLP solvers available commercially. From the case study for a refinery with 100 kBPD capacity, 1.9m$/year extra profit (1.0% improvement) can be achieved using the simultaneous approach compared with the sequential approach. This is because, in the new approach, the existing resources of energy and hydrogen are fully exploited to help produce more valuable products and process more feedstock. The results indicate that hydrogen and energy management should not be treated on a standalone basis as has been done in the sequential approach.

I ) {i | i is a segment in the turbine efficiency curve, NI} J ) {j | j is an operating parameter that affects process yields, NJ} H ) {h | h is a steam header, NH} P ) {p | p is a feed property that affects process yields, NP} G ) {g | g is an inert gas in the hydrogen consumer, NG} Parameters RR ) hydrogen chemical consumption Rs ) hydrogen loss in the liquid βR ) inert gas generated in reaction βs ) light gas dissolved in liquid product ∆Htk ) steam enthalpy change without entropic loss from steam header k max Wmin ) lower and upper bounds, respectively, on i , Wi turbine shaft work at the segment i ymf ) hydrogen makeup purity in the original hydrogen consumer model yp ) hydrogen purge purity Variables RR ) hydrogen chemical consumption βR ) inert gas generation ηie ) turbine isentropic efficiency F ) flow rate of process feed Fg ) inert gas flow rate M|ymf ) hydrogen makeup rate at purity ymf M ) hydrogen makeup rate P ) purge flow rate Q ) heat loads of process stream thatwhich can generate steam r ) specific heat capacity ratio W ) shaft work Wi ) shaft work in the segment i zi ) binary variable with regard to segment i FB ) steam rate from boilers FC ) gas rate in the compressor FS ) steam flow rate at condition of steam header s FSin ) steam flow rate at turbine inlet from steam header k FSpas ) steam flow rate at turbine extraction to steam header m FSexh ) steam flow rate at turbine exhaust cto steam header l PFp ) feed property p PRr ) operation parameter r QB ) fuel consumption in boilers yc ) hydrogen purity in the gas ym ) hydrogen makeup purity

Notation for Simultaneous Model Sets and Indices D ) {d | d is a process thatwho produces a blendstock t for product j, ND(j), D ⊂ K} H ) {h | h is a steam header}

Ind. Eng. Chem. Res., Vol. 40, No. 12, 2001 2653 I ) {i | i is a feedstock, NI} J ) {j | j is a final refinery product, NJ} K ) {k | k is a process, NK} L ) {l | l is a product stream from process n to process k as feed, NL(k), L ⊂ S} M ){m | m is a process that receives stream l from process k, NM(k), M ⊂ K} N ) {n | n is a process whose product is feedstock of process k, NN(k), N ⊂ K} P ) {p | p is a feed property that affects process yields, NP(k)} Q ) {q | q is a quality specification on final product j, NQ(j)} R ) {r | r is an operating parameter that affects process yields, NR(k)} S ) {s | s is a stream, NK} T ) {t | t is a blendstock of product j, NT(j), T ⊂ S} U ) {u | u is a utility stream, NU} HC ) {hc | hc is a hydrogen consumer, NHC, HC ⊂ K} HG ) {hg | hg is a hydrogen purge, NHG, HHG ⊂ S} HP ) {hp | hp is a hydrogen producer, NHP, HP ⊂ K} Parameters γu,k ) utility balance coefficients of utility u in process k λp,u,k )coefficient of feed property p on the rate of utility u in process k Fr,u,k ) coefficient of operation parameter r on the rate of utility u in process k as,k ) material balance coefficient of streams s in process k bp,s,k ) coefficient of feed property p of stream s in process k cr,s,k ) coefficient of operation parameters r of stream s in process k cq,s,k, eq,s,k ) linear model coefficients of quality q for stream s in process k wts,k ) weight percentage of stream s in the feed of process k S wts,k ) weight percentage of swing cut s/(s + 1) in the feed of process k Ci ) cost of feedstock i ($/unit purchased) Cu ) cost of utility u ($/unit purchased) Vj ) the sale price of product j ($/unit sold) Vu ) sale price of utility u ($/unit sold) UBk, LBk ) upper and lower bounds, respectively, on feed flow in process k UBj, LBj ) upper and lower bounds, respectively, on the sale of product j UBi, LBi ) upper and lower bounds, respectively, on the purchase of feedstock i UBq,j, LBq,j ) upper and lower bounds, respectively, on property q in product j yp,hg ) hydrogen purity of purge hg Variables Fi,k ) flow rate of purchased feedstock i to process k Fs,k ) flow rate of stream s from process k Fi ) amount of feedstock i purchased Fk ) feed flow rate of process k Fu,k ) amount of utility u for process k Fhc ) hydrogen makeup rate of hydrogen consumer hc Fhg ) flow rate of hydrogen purge hg Fhc,hg ) flow rate of hydrogen purge hg to hydrogen consumer hc

Fhc,hp ) flow rate of hydrogen gas from hydrogen producer hp to hydrogen consumer hc PFp,k ) feed property p of process k PRr,k ) operation parameters r of process k PPq,s,k ) quality q of stream s in process k PSj ) amount of product j sold RGM ) refinery gross margin SW+ s ) flow rate of the swing cut s/(s + 1) in fraction s + 1 SWs ) flow rate of the swing cut s/(s + 1) in fraction s USu ) amount of utility u sold UPu ) amount of utility u purchased ym,hc ) hydrogen makeup purity of hydrogen consumer hc

Notation for Figures and Tables ALK ) alkylation unit CDU ) crude distillation unit CCR ) catalytic reformer CNHT ) cracked naphtha hydrotreater DLC ) delay coker DHT ) diesel hydrotreater FCC ) fluid catalytic cracker HC ) distillate hydrocracker HGU ) hydrogen generation unit JHT ) jet fuel hydrotreater NHT ) naphtha hydrotreater IS4 ) butane isomer PSA ) pressure swing adsorption unit VDU ) vacuum distillation unit

Literature Cited (1) Simon, J. D.; Azma, H. M. Exxon experience with large scale linear and nonlinear programming applications. Comput. Chem. Eng. 1983, 7 (5), 605-614. (2) Bartholomew, K. D.; Soudek, A. LP Accuracy is improved by incorporating FCC simulation data. Oil Gas J. 1989, 87 (44), 57-62. (3) Hu, M. C.; Powell, R. T.; Kidd, N. F. Develop LP models using a steady-state simulator. Hydrocarbon Process. 1997, June, 81-86. (4) Lasdon, L. S.; Warren, A. D.; Sarkar, S.; Palacios-Gomez, F. E. Solving the Pooling Problem Using Generalized Reduced Gradient and Successive Linear Programming Algorithms. SIGMAP Bull. 1979, 77, 9-15. (5) Reklaitis, G.; Ravindran, A. Engineering Optimizations Methods and Applications; John Wiley & Sons: New York, 1983. (6) Alves, J.; Towler, G. P. Analysis of refinery hydrogen networks. Presentation at Process Integration Research Consortium Hydrogen Meeting, UMIST, Manchester, U.K., May, 1997. (7) Branan, C. R. Rules of Thumb for Chemical Engineers; Gulf Publishing Company: Houston, TX, 1994. (8) Marecki, J. Combined Heat & Power Generating Systems; Peregrinus: London, 1988. (9) Townsend, D. W.; Linnhoff, B. Part II: Design procedure for equipment selection and process matching. AIChE J. 1983, 29 (5), 748-771. (10) PIMS System Reference, version 11.0; Aspen Technology, Inc.: Cambridge, MA, 1999.

Received for review March 30, 2000 Accepted March 25, 2001 IE000367C

A Simultaneous Optimization Strategy for Overall Integration in

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