On-Line Optimization of a Crude Distillation Unit ... - ACS Publications

Ind. Eng. Chem. Res. 2002, 41, 1557-1568

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On-Line Optimization of a Crude Distillation Unit with Constraints on Product Properties Kaushik Basak,† K. S. Abhilash, Saibal Ganguly,‡ and D. N. Saraf* Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India

The optimization of chemical processes has gained immense importance in the present day. This work is aimed at the on-line optimization of an industrial crude distillation unit (CDU). A nonlinear, steady-state CDU model has been developed in-house for this purpose. Model tuning parameters in the form of vaporization efficiencies were incorporated to minimize the discrepancy between the measured and simulated column parameters on-line. The crude feed composition, represented by the true boiling point (TBP) curve, is known to vary with time. A procedure was developed to back-calculate the TBP curve using on-line plant data. Finally, the objective function was formulated to simultaneously maximize the net achievable profit and set the product properties within a user-specified range. The entire scheme was tested using real plant data off-line, but the problem formulation is suitable for supervisory-level on-line optimization without further modifications. It is shown that substantial increases in profitability can be achieved using supervisory on-line optimization. Introduction Optimization is a primary quantitative tool in the process of decision making. Because of increased energy costs, raw material scarcity, stringent environmental regulations, and a host of other reasons, the major objective of industry has become improving the efficiency in existing plants rather than undertaking large-scale plant expansion. The key has been maximum utilization of the available resources for maximum profitability, and on-line optimization can play a crucial role in this regard. The crude distillation unit (CDU) is one of the most complex units in the field of separation processes. The presence of side strippers, pump-around flows, and a large number of equilibrium stages, coupled with unknown feed properties, make the modeling of CDUs a complex exercise. Although the actual composition of a crude oil is seldom known, one measure of it is the true boiling point (TBP) as a function of the percent volume distilled, which, along with the density (or density as a function of the percent volume distilled), is used to completely characterize the feed. The crude oil, which is a complex mixture of a very large number of hydrocarbons, is assumed to be represented by a finite number of pseudocomponents. Each pseudocomponent is assigned an average boiling point and density, which are then used to find the critical and other thermodynamic properties. Once the feed is characterized in this fashion, the crude distillation unit can be modeled in a way similar to any multicomponent, multistage distillation column.1-4 The modeling exercise recently completed in this laboratory4 provided the requisite steady-state model equations for the present optimiza* Corresponding author: Prof. D. N. Saraf, Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India. Phone: 91-512-597827. Fax: 91-0512-590104. E-mail: [email protected]. † Presently at Indian Oil Corporation, R&D Center, Faridabad, India. ‡ Presently Assoc. Professor, Department of Chemical Engineering, I.I.T. Kharagpur, India.

tion study. These equations consist of component material balance, energy balance, and summation equations around each equilibrium stage, as well as thermodynamic relations (refer to Appendix 1 for the model equations). No reasonable method is available for estimating the actual behavior of each stage in terms of its deviation from equilibrium. An approximate ideal analogue that behaves more or less like the real column is, therefore, developed by trial and error. Fine-tuning of the model is accomplished by assigning efficiencies to each of the ideal stages of the analogue so as to match the analogue output with the actual column output. Another uncertainty in the model arises from the lack of knowledge of the exact TBP curve of the feed being processed at any time. Crude TBP analysis in the laboratory can take several days, and therefore, it is not possible to find the exact TBP of the crude being processed by analysis. However, for every crude, a TBP curve is available from its assay report. This TBP curve must be modified for minor changes that might have crept into its composition over a period of time. Once the feed TBP curve is reconciled with the present operations, one is ready to proceed to optimization. Of the various goals of optimization, the objective of economic optimization has always been of utmost importance to industry as long as the products are within specifications and the plant operating conditions are within allowable limits. Although the latter are constantly monitored and recorded in most modern refineries, there is no direct means of determining whether the products are meeting the desired specifications. Several products are obtained from a CDU, such as distillate, heavy naphtha (HN), superior kerosene/aviation turbine fuel (SK/ATF), light gas oil (LGO), heavy gas oil (HGO), and the residual crude oil (RCO), which are obtained through the top condensor or side strippers or the bottom. Each of these products are characterized by one or more properties such as Reid vapor pressure (RVP) for the distillate and HN; flash point for the HN, SK/ ATF, and LGO; end point for the SK/ATF; and recovery

10.1021/ie010059u CCC: $22.00 © 2002 American Chemical Society Published on Web 02/26/2002

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Ind. Eng. Chem. Res., Vol. 41, No. 6, 2002

Table 1. Some Industrial Applications of CLRTO no.

authors al.17

1

Hardin et

2

Pedersen et al.18

3

Yoon et al.19

4

Georgiou et al.20

5

Besl et al.21

6

Georgiou et al.22

7a

Geddes and Kubera23

unit/refinery Conoco’s Lake Charles, LA, Refinery 20 000 bpdb hydrocracker complex at Sunoco Inc., Sarinia Refinery (Canada) Hyundai Petrochemicals Complex at Daesan, Korea, with 350 000 tons of ethylene and 175 000 tons of propylene per annum Steady-state implementation of CLRTO at Mobil Chemical’s Beaumont, TX, ethylene plant Penex process for light naphtha isomerization at RVI’s Ingolstadt Refinery, Germany CLRTO of FCC and alkylation complex in Mobil’s Joliet Refinery CLRTO in olefin production

contributions Aspen Tech’s RT-Opt was used for modeling and optimization, and the results were implemented through Set Point’s Idcom Controller, yielding an additional $ 0.03/bbl.c Commercial equation solving and optimization packages used, along with interface software to solve flowsheeting problems. Applied with advanced DMC controllers, resulting in huge incremental profit. Equation-based model with 60 000 equations. SQP used for optimization; 2.45% reduction in energy and feedstock consumption reported.

Accurate furnace models having material balance closure checks developed for optimization of the unit. The system was also used for off-line planning and performance monitoring. Aspen Tech’s RT-OPT open-form equation-based optimization software used. Library model from AspenTech used for optimization, implemented through DMC Plus type controller for maximum profitability. Production scheduling LP model coupled with CLRTO to improve overall olefin plant operations significantly

a Other references on on-line optimization of olefins plants include Georgiou et al.,24 Nath et al.,25 Hess et al.,26 Nath and Alzein,27 and Cervantes et al.28 b Barrels per day. c Barrel.

at 366 °C for the HGO and RCO. However, on-line sensors either are not available for the measurement of these properties or are very expensive and difficult to maintain and hence seldom used. Moreover, no equations relating measured operating variables and enabling easy calculations of the product properties exist that could be used as constraint equations in the optimization. Because of these limitations, productproperty constraints are normally not used in the optimization of petroleum processing units. Optimization is a mature discipline studied and researched by applied mathematicians and operations research scientists, and the open literature is full of texts, monographs, and research papers, which we do not wish to review here. Although very little information is available in the published literature on the optimization of crude distillation units, several studies have been reported on the optimization of simple distillation columns and other process units, and we present a brief review of these here, with an emphasis on the recent literature. The objective of the industrial application of optimization is obviously profit, as outlined by Cutler and Perry.5 Kim et al.6 used the golden section search method for a similar profit-maximization exercise for binary distillation systems. Al-Haj-Ali and Holland7,8 used the box complex method to optimize economic objective functions for distillation columns of varying degrees of complexity. Shyamsundar and Rangaiah9 reported one of the latest works on steady-state optimization of multiphase distillation columns, in which they applied the NLP technique for the linear objective function and nonlinear constraints. Optimizations of secondary processing units such as catalytic cracking and hydrocracking units have been much-researched areas because of the importance of these processes in the oil refining industry. Lee and Tayyabkhan10 used dynamic programing to determine the operating conditions in a catalytic cracker that maximized a profit function. Fiero and Kelly11 solved a two-variable unconstrained optimization problem to increase revenue in a fluid catalytic cracking unit using the sequential simplex method. Much progress has since been made

in the optimization of catalytic cracking, for example, with Lid and Strand12 using 40 equations involving 20 variables. Ellis et al.13 used Model IV fluid catalytic cracking for on-line optimization of an economic objective function using a sequential quadratic programming algorithm, and Jakhete et al.14 applied LP techniques for FCC optimization. Bailey et al.15 reported optimization of a profit function of a hydrocracker fractionation plant using a generalized reduced gradient algorithm (MINOS). Clifford et al.16 illustrated the industrial application of closed-loop real-time optimization (CLRTO) for the optimization of the hydrocracker unit at Sunoco Group’s Sarnia Refinery. Additional industrial applications of CLRTO are summarized in Table 1. Recently, several workers have been researching unconventional optimization techniques such as artificial neural networks (ANNs) for refinery fractionators,29 genetic algorithms and their modifications for distillation column systems,30,31 and object-oriented language packages.32 An industrial application of an ANN for the optimization of Mobil’s Beaumont Refinery, Beaumont, TX, was also discussed by Riddle et al.33 The concept of overall refinery optimization using novel decomposition strategies was outlined by Zhang and Zhu,34 wherein site-level (master) and process-level (sub-) models were used. The former determined the common issues among the processes such as raw materials and utilities, whereas the latter optimized the individual processes. The technique, when applied to a 100 000 bpd refinery, had the potential to achieve incremental benefits on the order of 30 million dollars. The latest research in the field involves solving an on-line optimization problem in off-line mode, as discussed by Pistikopoulos et al.,35 where a parametric technique was applied, and the optimization solver was not called on-line, but the dynamic problem could be solved. However, none of these workers used product-property constraints explicitly either in design or in operation, which is discussed in this paper. The on-line optimization of a crude distillation unit poses a complex problem of needing a very complicated nonlinear analytical model and a robust and efficient

Ind. Eng. Chem. Res., Vol. 41, No. 6, 2002 1559

Figure 1. Schematic diagram of CDU analogue.

algorithm to solve it repeatedly in a reasonable amount of time. Perhaps this is one of the reasons for the lack of published literature on the optimization of crude distillation units. There is yet another practical problem, however. No satisfactory quantitative measures of product quality is available that could be used as constraints in the optimization problem. In the present study, attempts have been made to overcome this problem. Constraints on product properties such as the flash points of heavy naphtha (HN), kerosene (SK), and light gas oil (LGO); the end point of aviation turbine fuel (ATF); and the recoveries at 366 °C of heavy gas oil (HGO) and residual crude oil (RCO) have been included in the objective function. The optimal solution

is ensured to honor all of the constraints on the product properties while maximizing a profit function. Although only off-line optimization has been attempted in the present study, the methodology developed in this study is suitable for on-line optimization without any modification. Figure 1 shows the typical crude distillation unit used in this study, which consists of four side strippers and three pump-around flows. The actual column consisted of 82 trays, but the number of ideal equilibrium stages that could achieve the same fractionation would be much smaller as the stage efficiency rarely exceeds 0.5 in these columns. In the absence of availability of any procedure for realiably estimating these efficiencies, it

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is customary to develop an analogue of the actual column in terms of ideal equilibrium stages. In the present case, the analogue consists of 42 stages (34 in the main column and 2 each for the four side strippers). Selection of the analogue is a trial-and-error procedure in which the number of ideal stages between the various product streams are chosen so as to match the actual column behavior. However, such an analogue is only approximate, and further tuning is usually required to model the column exactly. The model equations for the steady-state model are provided in Appendix 1. Mathematical Formulation Parameter Estimation. On-line optimization requires model identification36 as a first step. For a distillation column, the model parameters are the stage efficiencies, which must be determined using data measured on-line. Because the model used in this study is a steady-state model, one must ensure that the unit is operating at steady state37 before parameter estimation can be carried out using on-line data. Whereas the feed composition is usually precisely known for a normal multistage, multicomponent distillation, for the crude distillation unit, it is approximated through a finite number (25 in the present study) of pseudocomponents, obtained by discretizing the TBP curve. It is well-known that, because of stratification in the storage tanks, small variations in the composition of the crude being processed occur as a function of time. Also, as crude is a natural product, it can be expected that small variations in the crude composition can occur depending on the part of the oil field from which it is being obtained. Moreover, as a refinery switches from processing one crude to another, some mixing of the crudes occurs. It is therefore necessary that the feed TBP also be suitably modified as part of model tuning. Feed TBP Reconciliation. The feed TBP determines not only the relative amounts of the products that can be obtained but also their compositions and, hence, properties. Therefore, the ability of a model to accurately predict the plant performance greatly depends on the accuracy of the TBP curve used. Horn38 stated that quality control of the outputs from a crude tower could be accomplished by product TBP cut-point control. Unfortunately, product TBP data are seldom measured in the laboratory. However, ASTM distillation data for the products are routinely collected and can be converted into a TBP curve using the semiempirical correlation given by Edmister39 or Riazi and Daubert.40 The CDU model provides the calculated product TBP data, and hence, the problem can be formulated as an optimization problem where the manipulated variable is the feed TBP curve. The objective function is formulated as a least-squares minimization problem where the difference between the product TBP obtained from the plant and that found from the CDU simulator is to be minimized subject to the conditions that the model equations (available in Appendix 1) be honored. Because the TBP curve is monotonically increasing, an additional constraint is added to ensure that the optimized curve does not violate this requirement. Mathematically, this results in

I) min[

∑i (product TBPmeasured - product TBPcalculated)i2]

(1)

where the feed TBP is subject to the model equations and the condition that the nth TBP temperature be less than the (n + 1)st TBP temperature. The product TBPs included in the objective function are those for HN, SK, LGO, HGO, and RCO. A total of 23 points were used for minimization. The manipulated variables were 1820 discrete points on the feed TBP curve. A sequential quadratic programming algorithm (NPSOL) was used for the minimization.41 The crude TBP available from the crude assay could be used as the initial guess as it was not far from the TBP of the crude being processed. Feed TBP Back-Calculation. The reconciliation process discussed above can be considered reliable because it makes extensive use of laboratory-determined ASTM temperatures. However, this approach is not feasible for on-line applications, and a simpler method is required that utilizes measurements that are made on-line and not in the laboratory. The method used in the present study is an extension of the work of Friedman,42 who estimated two points on the TBP curve and approximated the curve between them by a straight line. In the present study,43 six points are estimated, which allows for a more accurate representation of the feed TBP. Five of the six temperatures measured in the column correspond to locations/trays from which various distillate products are withdrawn (the top tray and the four side-stream withdrawal trays), and the sixth location is the flash zone. These locations are chosen because the amounts of distillate product withdrawn from these stages are known (measured) and can be used to provide the x coordinates (or the volume percents distilled) of the crude TBP curve. The measured temperatures at these trays can be taken to represent the equilibrium flash vaporization (EFV) temperatures, except that the partial pressure of hydrocarbons at each of the trays is different. These partial pressures are calculated by a procedure given by Watkins,44 and then, using the Clausius-Claperon equation, the measured temperatures are adjusted to a uniform pressure of 1 atm. These are the EFV temperatures. The EFV temperatures are then related to the TBP temperatures through empirical correlations.42 The procedure involves enthalpy balance around the rectifying section of the column, which relies on the model-calculated stream enthalpies. An initial crude TBP is, therefore, required before the new TBP can be back-calculated. It has been found that use of a reconciled TBP curve (as described above) for the enthalpy balance greatly improves the accuracy of the back-calculation procedure. Efficiency Calculation. The lack of phase equilibrium on each ideal stage is not the only reason for the mismatch between the model predictions and plant data once the feed TBP has been back-calculated. Imperfect modeling and thermodynamic relations further add to model deviations. Hence, certain efficiency factors are associated with the equilibrium stages to enable the simulator results to match the available measured plant data. It should be noted here that the efficiencies that are taken into consideration are not Murphree tray efficiencies. Instead, they are actually tuning parameters incorporated into the model in the style of vaporization efficiencies used to match the column parameters with the model predictions45

yi,j ) Ki,j ηi,j xi,j

(2)


where Ki,j is the equilibrium constant, ηi,j is the vaporization efficiency, yi,j is the vapor mole fraction, and xi,j is the liquid mole fraction. Index i refers to the stage number, whereas j refers to the component number. In the present work, it has been assumed that the efficiency remains constant for all components and all points on a particular tray. This allows the second subscript to be dropped from the variables ηi,j, making them akin to stage efficiencies, with one for each stage of the analogue. The mathematical formulation of the least-squares problem takes the form minimize Fmod )

∑(column parameters

measured

- column parameterscalc)i2

i

with the efficiencies subject to the model equations and the condition

effmin e eff e effmax

(3)

The bounds on the efficiency terms have to be provided because the simulator will not converge for any arbitrary set of efficiencies. After developing some experience in this exercise, a set of lower and upper bounds was found for the efficiencies for which the simulator converges. The simulation (analogue) model comprising 42 equilibrium stages requires a total of 42 efficiencies, one for each stage. This, in turn, requires at least 42 measurements to be available, and if we wish to determine these tuning factors (or stage efficiencies) in the least-squares sense, then the number of measurements ought to be much greater than 42. So many measurements are almost never available, however, because of cost considerations. The actual number of temperature measurements made on-line seldom exceeds 12-15, and this drastically restricts the total number of efficiencies that can be estimated. This means that either a group of 4-5 trays must be assigned the same efficiency or the efficiencies of intermediate trays must be found by interpolation. The latter procedure was found to result in a smoother temperature profile along the column height and was therefore adopted. A total of 9 efficiencies were calculated for the trays at which on-line temperature measurements were available. For the present case, only 11 parameters were available through on-line measurements (10 temperatures and 1 flow). Estimation of Product Properties. The product properties required to be controlled during on-line optimization were estimated, on-line, using model-based software sensors (also called virtual analyzers). These sensors were also developed in-house using semianalytical models and the CDU simulator.46 The models were tuned against extensive laboratory data. CDU Optimization Once the feed TBP has been back-calculated and the efficiencies tuned, the model results match the plant measurements well both on-line and in the laboratory when the plant is operating under steady-state conditions. We now proceed with the formulation of the economic objective function and constraints and the solution procedure for the maximization of profit per unit time with constraints on product properties.47,48

Problem Formulation. The following points were kept in mind during development of the economic optimizer: (1) The mathematical statement of the problem should be as simple as possible. (2) The variables to be selected for manipulation should have significant effects on the objective function. These variables also constitute the control variables for the process. (3) Because the success of the optimization method depends on the accuracy of the gradients, it is important that the perturbations on the variables be selected after a proper sensitivity study. (4) The optimization results should be obtained in the least possible time. This requires that the number of constraints and independent variables be kept to a minimum without losing the goal. (5) Proper scaling should be done so that all terms in the objective function are of the same order of magnitude. To achieve this result, the weights associated with the different terms should be properly adjusted. This point is discussed in greater detail later. Selection of Decision Variables. After due attention had been paid to the effects of each of the variables on the results, the requirements of industry, and the ease with which the variables can be changed in the plant, the following parameters were taken as the manipulated variables for the optimization problem: (1) the side-stripper draw rates for heavy naphtha, kerosene/ aviation turbine fuel, light gas oil, and heavy gas oil; (2) the pump-around (PA) flow rates for heavy naphtha PA, kerosene PA, and LGO PA; (3) the reflux flow rate (to control the distillate flow and composition); and (4) the feed temperature, which is also called the coil outlet temperature (COT). A total of nine variables were used for manipulation, as detailed above. Objective Function. The objective function in its final form can be expressed mathematically as

maximize

φ ) P1 - P2 - P3 + P4

minimize

φ ) -(P1 - P2 - P3 + P4)

or

(4)

with respect to the above-listed nine manipulated variables where φ is the profit-based objective function, P1 is the selling price of the products, P2 is the price of the raw materials, P3 is the operating costs, and P4 is the part of the objective function related to productproperty optimization. In the present study, minimization was chosen to suit the requirements of the optimization package used. The various terms in eq 4 are detailed below.

P1 )

∑i (prodi × pricei × wti × flag)

(5)

where i ) 1, ..., 7 for HN, kero/ATF, LGO, HGO, RCO, LPG, and SRN, respectively; prodi is the draw-down rate of product i (kg/h); pricei is the price of a unit quantity of product i expressed in units of rupees per kilogram; wti is the weighting on the ith term of the objective function; and flag is the flag whose value depends on the product properties.

P2 )

∑(F × pricef × wtf)

(6)

where F is the feed flow rate (kg/h), pricef is the cost of the feed expressed in units of rupees per kilogram, and

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wtf is the weighting on the term related to the cost of raw materials. In the present study, the crude feed was taken as the only raw material. The cost of other materials, if any, can be taken into account similarly. P3 )

∑(RF × RC × wt + PA × PC × wt r

p

+ U × UC × wtu) (7)

where RF is the reflux flow rate (m3/h); RC is the cost of pumping the reflux (Rs/m3); PA is the pump-around flow rate (combined flow rates of all three pumparounds) (m3/h); PC is the cost of the pump-around (Rs/ m3); U is the utility, e.g., total steam, rate (m3/h); UC is the cost of the utility (Rs/m3); wt is the weighting associated with the particular cases; and the subscripts r, p, and u stand for reflux flow, pump-around flow, and utilities, respectively. In the present study, only the pumping and steam costs have been taken into account under the heading of “operating costs” for simplicity. P4 )

∑[(prop k

u l des - propmod)k(propmod - propdes )k × flag × wtk}

(8)

where k ) 1, ..., 6 for the five products (from HN to RCO, in that order) and the ASTM end point of ATF; propudes is the desirable or permissible upper limit on the product property; propldes is the desirable or permissible lower limit on the product property; propmod is the property value obtained by the model; and wtk is the weighting associated with the kth product property. The lower and upper bounds on the product properties were specified by the operating refinery on the basis of quality-control requirements. Whereas most of the terms in the objective function are self-evident, two terms (weight factor and flag) require elaboration. Weight Factors (wt). The reason for using weight factors is to ensure that all terms constituting the objective function are scaled so that all constituents are given due importance during calculation of the optimum. Bossen et al.49 applied the technique of scaling and explained its necessity during optimization of ammonia synthesis operations. In the present study, the weights are adjusted by trial and error to ensure that the variables that are more important from the industrial point of view are multiplied by larger weight factors. The use of greater weighting factors does not allow the bounds on the variables in the objective function to be violated easily. However, the application of a very large weighting factor to any particular term can result in the undue emphasis of that term and must be avoided. Obviously, the weights must be chosen very carefully and should be changed as required by the user. Flag. The purpose of this term is to ensure that the properties remain within the acceptable bounds. A lower value is given to the flag when a property of a product crosses either the lower or upper bound. If the property is within the specified range, then the flag assumes a higher value. This ensures that the bounds on the product properties are not violated. In the present study, the flags were set to 0.65 and 1.00 for violating the bounds and not doing so, respectively, for all of the properties except for HN. For HN, the corresponding flag values were 0.35 and 1.00. The difference between the flag values can be increased if it is required to

provide greater emphasis on product properties. The introduction of the flag goes a long way toward maintaining product properties within the desirable range. Properties. In optimization problems, it is customary to include bounds on parameters as constraints. Hence, the standard approach would have been to incorporate the bounds on the product properties as constraints. In contrast, the properties have been included within the objective function here. There are two reasons for this. First, the properties do not have any direct functionality in terms of the system variables, and hence, it is mathematically very difficult to include the former as explicit constraints. Second, even if the properties could have been included as constraints, the output of the simulator would have had to be manipulated to bring the properties into the required ranges, which is physically impossiblesone cannot decide a priori the output of the CDU simulator for better property values and set the input parameters accordingly. Of the various properties that could have been included, the following were selected on the basis of their importance in product salability, downstream processing, ease of measurement in the plant, and sensitivity to the changes in the input conditions: (1) heavy naphtha flash point, (2) kerosene flash point, (3) light gas oil flash point, (4) heavy gas oil percent recovery at 366 °C, (5) residual crude oil percent recovery at 366 °C, and (6) ATF ASTM end point. It can be seen that no bound was imposed on the properties of the top products, as it has been observed that these properties remain within the allowable range as long as the properties and flow rates of the other products remain within the acceptable bounds. Moreover, the top-product properties are not regularly measured in the refinery, thus making it difficult to acquire any data for model tuning. Constraints. The constraints on the objective function are the model equations, which are given in Appendix 1, and the upper and lower bounds that are imposed on the side-stripper, reflux, and pump-around flow rates and on the feed temperature (also referred to as the coil outlet temperature, COT).

e SSi e SSmax SSmin i i for i ) 1, ..., 4 (four side-stripper flows) RFmin e RF e RFmax

for the reflux flow

PAimin e PAi e PAimax for i ) 1, ..., 3 (three pump-around flows) COTmin e COT e COTmax

(9)

One additional constraint, called the total distillate (distillate plus four side-stripper flows) constraint, is used in the optimizer to make it more realistic. This constraint limits the increase in total distillates to be within certain bounds, say 5-10%, during a single step, as sudden large changes in the vapor-liquid traffic in the column might destabilize the system.

Ftot (optimized) e IFtot (operating)

(10)

where 1.0 e I e 1.1 and Ftot is the total distillate flow. In the present work, I ) 1.07 was used, which limited the total distillate increase to be within 7% during a single optimization cycle.


Figure 2. Flow diagram for the CDU optimization algorithm.

Solution Procedure. The objective function in eq 4 is to be minimized subject to the model equations given in Appendix 1 as the equality constraints and the upper and lower bounds given by eqs 9 and 10. The algorithm for the solution is described in Figure 2. Gradients of the objective function with respect to the manipulated variables were calculated numerically using the backward-difference method. The choice of the magnitude of the perturbation is important, and for the present case, 0.1% of the value of the variable was found to be adequate. All calculations were performed in the doubleprecision level. Termination Criterion. The termination criterion used for this problem is

φn+1 - φn e

(11)

where φ denotes the value of the objective function and the subscript indicates the iteration number. represents the absolute difference in magnitude of the objective function in two successive iterations. It has been found that an value on the order of 0.1-0.2% of the initial value of the objective function yields an accuracy that is sufficient for the present work. Implementation of the Scheme On-Line A step-by-step procedure for on-line implementation of the present optimization package is as follows: (1) Check for steady state. (2) Check on-line data for gross errors. (3) Back-calculate the TBP and tune the efficiencies. (4) Validate the model. (5) Perform system optimization. (6) Review the optimization results and, if acceptable, implement them on the plant. The first two steps are prerequisite to the use of the optimizer because the model used for optimization is valid only for steady state and any gross error will adversely affect the outcome. A crude TBP back-calculation using on-line data must be carried out using reasonable values of stage efficiencies such as those

from previous cycle. If such data are not available, then the TBP back-calculation and efficiency tuning must be repeated in succession a couple times to ensure that the model results match the plant observations reasonably. This is the validation step, where the operator can determine on-screen whether some key calculated results are in agreement with on-line and/or laboratory measurements. After the completion of the entire set of computations, the operator reviews the optimization results, and if the values are found to be acceptable, then the results are transferred to the advanced or regulatory control layer as the new set points; otherwise, a fresh optimization cycle begins. The average CPU time required for overall convergence of the optimization problem is on the order of 10-20 min, but it can be larger for some of crudes or for a more stringent convergence criterion. Normally, the cycle time for on-line optimization is 1-2 h, i.e., reoptimization after every 1-2 h, is considered to be adequate. All of the programs were written using Microsoft Fortran (Visual Workbench) on the MS Windows 95 operating system and were compiled and run on a Pentium PC platform. The optimizer has been developed in the form of a user-friendly interactive package where all of the inputs are read from files and error messages generated if the given values are grossly in error. Results and Discussion In the present study, three different crudes and two blends were considered, the details of which are provided in Table 2. Also included in this table are the TBP data for the three crudes. The plant operating data are given in Table 3. Computed results for only two cases (crude 2 and blend 1) are included here to conserve space. The results for the remaining cases were very similar and only confirm the ones presented here. Feed TBP Back-Calculation and Model Tuning. The results of the feed TBP back-calculation are shown

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Figure 3. Comparison of back-calculated feed TBP curve and reconciled feed TBP curve for crude 2.

Figure 4. Comparison of back-calculated feed TBP curve and reconciled feed TBP curve for blend 1.

Table 2. Types of Crudes Investigated and Their TBP Data

Table 3. Plant Operating Data for Different Crudes

crude

source

crude 1 crude 2 crude 3 blend 1 blend 2

Persian Gulf India Saudia Arabia 80% crude 1 + 20% crude 3 20% crude 1 + 80% crude 3

vol % distilled

crude 1

TBP (K) crude 2

crude 3

0.73 1.73 3.00 4.55 6.36 8.45 10.82 13.45 16.36 19.55 23.00 26.73 30.73 35.00 39.55 44.36 49.45 54.82 60.45 66.36 72.55 79.00 85.73 92.73 100.00

279.67 289.53 298.71 314.37 327.35 340.93 353.46 370.04 385.67 405.07 425.66 445.25 467.90 490.11 515.95 540.05 565.66 590.53 618.17 648.05 679.70 713.64 759.70 809.59 890.78

281.56 288.80 293.71 306.00 314.33 322.73 337.24 350.24 362.24 379.59 393.21 413.89 435.72 459.90 480.35 502.06 525.04 549.28 574.78 601.55 629.70 663.64 709.70 769.59 844.78

279.67 289.53 298.71 314.37 323.47 338.30 350.52 363.01 380.24 396.00 413.35 427.67 446.93 467.23 490.08 510.11 530.04 554.28 577.78 604.55 632.70 664.64 664.64 769.59 844.78

in Figures 3 and 4. Also included in these figures are reconciled TBP curves for comparison. For reconciliation, laboratory-measured ASTM temperatures were used, as detailed earlier, corresponding to the same operating data for which the TBP curves were backcalculated. A good match between the two shows the efficacy of the back-calculation procedure. Recall that only six points are back-calculated, which result in approximately one-half of the total range being spanned. The first calculated point corresponds to the top of the column (or distillate product), and the last point corresponds to the flash zone (total distillate). To obtain the complete TBP curve, the back-calculated curve is extrapolated assuming that initial and final boiling points are the same as in the reconciled curves. After back-calculation of the feed TBP, the model parameters (stage efficiencies) are tuned using a minimization procedure. As discussed earlier, only nine efficiencies are found using this algorithm, and the

input parameters

crude 2

crude 3

blend 1

blend 2

feed (m3/h) reflux (m3/h) distillate (m3/h) HN (m3/h) kero (m3/h) LGO (m3/h) HGO (m3/h) HN SS steam (tpha) kero SS steam (tpha) LGO SS steam (tpha) HGO SS steam (tpha) HN PA (m3/h) kero PA (m3/h) LGO PA (m3/h) bottom steam (tpha)

flows 1191.7 1204.9 225.0 296.0 225.0 280.0 71.2 62.8 143.9 221.1 182.5 186.9 31.9 80.4 1.57 1.32 2.91 2.84 0.67 0.67 0.78 0.78 438.4 749.8 444.5 350.6 420.6 421.3 9.95 8.52

1199.0 253.0 250.0 75.7 220.7 220.0 50.2 1.59 2.89 0.67 0.78 746.2 445.5 430.0 9.96

1225.9 229.0 230.0 64.1 126.3 180.2 59.9 1.63 2.81 0.67 0.78 490.0 420.6 422.8 8.48

1229.8 262.0 270.0 72.9 230.5 180.1 40.2 1.6 2.48 0.67 0.78 719.7 420.3 425.9 9.95

coil outlet (°C) condenser (°C) reflux return (°C) top tray (°C) HN return PA (°C) kero return PA (°C) LGO return PA (°C) HN SS draw (°C) HN PA draw (°C) kero SS draw (°C) kero PA draw (°C) LGO SS draw (°C) HGO SS draw (°C) bottom tray (°C)

temperatures 352.7 330.8 90.0 85.0 34.5 46.6 119.9 126.2 112.1 126.2 128.9 114.7 167.1 169.3 150.6 155.8 161.5 165.5 200.9 198.6 219.7 221.0 283.4 280.2 343.9 322.0 335.0 312.7

333.5 87.5 38.3 123.4 126.8 129.3 165.9 152.1 161.3 200.1 225.1 283.1 323.3 312.1

348.5 90.0 36.5 116.6 121.6 123.8 161.7 148.4 158.9 190.9 212.6 276.7 331.6 329.9

334.1 85.0 38.3 126.8 127.2 118.2 163.6 157.9 166.9 204.3 225.5 283.4 323.4 312.9

column top (kg/cm2) flash zone (kg/cm2)

pressures 2.76 2.71 3.0 3.0

2.67 3.0

2.69 3.0

2.62 3.0

a

crude 1

Tons per hour.

efficiencies for the rest of the stages are obtained by interpolation. Tables 4 and 5 show the results of feed TBP back-calculation and model tuning for crude 2 and blend 1. Column 2 shows measured plant operating data and product properties. Columns 3-5 show simulation results before TBP back-calculation, after TBP backcalculation, and after model tuning, respectively. Whereas straightforward simulation results exhibit significant deviations, the results from the tuned model match the measured plant values and laboratory results quite well for almost all of the cases investigated. In actual practice, all of the product properties are not measured at a given instant, and for such products, average values of the properties are included in the plant data column of these tables. The properties of the distillate (density and RVP), which includes LPG and light naphtha, are

Ind. Eng. Chem. Res., Vol. 41, No. 6, 2002 1565 Table 4. Comparison of Calculated Column Parameters and Product Properties with Measured Plant Values for Crude 2 CDU simulator results column parameters and product properties

plant data

simulator

after back-calculation

after back-calc and tuning

after optimization

top temperature (°C) HN pump-around temperature (°C) HN column draw temperature (°C) kero pump-around temperature (°C) kero column draw temperature (°C) LGO pump-around temperature (°C) LGO column draw temperature (°C) HGO column draw temperature (°C) bottom plate temperature (°C) RCO flow rate (m3/h) top distillate density (g/cm3) top distillate RVP (atm) HN density (g/cm3) HN RVP (atm) HN flash point (°C) kero density (g/cm3) kero flash point (°C) kero/ATF end point (°C) LGO density (g/cm3) LGO flash point (°C) LGO pour point (°C) HGO density (g/cm3) HGO flash point (°C) HGO recovery at 366 °C (%) RCO density (g/cm3) RCO recovery at 366 °C (%)

126.2 165.5 155.8 221.0 198.6 280.2 280.2 322.0 312.7 NRa 0.710b 0.420b 0.750 0.042c 10.8 0.790 45.0 259.0 0.840c 78.0c NRa 0.865 105.9c 80.0 0.925 23.0

108.30 155.53 146.99 224.65 192.34 283.23 283.23 321.70 219.61 444.21 0.6977 0.6643 0.7384 0.1049 -2.63 0.7742 25.45 251.01 0.8239 61.97 -8.72 0.8528 75.29 84.61 0.9224 23.59

111.60 159.60 150.63 226.68 195.76 283.49 283.49 310.06 320.68 424.91 0.6996 0.6498 0.7411 0.0932 -0.76 0.7755 30.28 251.85 0.8231 62.09 -6.08 0.8493 73.97 85.45 0.9199 23.68

124.90 166.17 152.27 221.46 197.44 280.13 280.13 317.45 285.77 378.44 0.7057 0.5818 0.7523 0.0437 10.48 0.7862 40.68 260.88 0.8325 78.00 -7.75 0.8575 83.46 80.93 0.9254 23.39

123.80 166.39 151.87 225.30 199.11 285.21 285.21 319.51 281.35 352.76 0.7051 0.5877 0.7523 0.0449 10.04 0.7884 41.50 265.50 0.8365 80.49 -7.26 0.8635 94.96 79.26 0.9277 23.35

a

NR ) not reported in experimental set of values. b Properties pertaining to SRN. c Represents an average value.

Table 5. Comparison of Calculated Column Parameters and Product Properties with Measured Plant Values for Blend 1 CDU simulator results column parameters and product properties

plant data

simulator

after back-calculation

after back-calc and tuning

after optimization

top temperature (°C) HN pump-around temperature (°C) HN column draw temperature (°C) kero pump-around temperature (°C) kero column draw temperature (°C) LGO pump-around temperature (°C) LGO column draw temperature (°C) HGO column draw temperature (°C) bottom plate temperature (°C) top distillate flow rate (m3/h) RCO flow rate (m3/h) top distillate density (g/cm3) top distillate RVP (atm) HN density (g/cm3) HN RVP (atm) HN flash point (°C) kero density (g/cm3) kero flash point (°C) kero/ATF end point (°C) LGO density (g/cm3) LGO flash point (°C) LGO pour point (°C) HGO density (g/cm3) HGO flash point (°C) HGO recovery at 366 °C (%) RCO density (g/cm3) RCO recovery at 366 °C (%)

116.6 158.9 148.4 212.6 190.9 276.7 276.7 331.6 329.9 230.0 NRa 0.743b 0.440b 0.789 0.040c 13.5c 0.815 43.0 254.0 0.860c 74.0c NRa 0.883 95.4 87.0c 0.989 18.0c

119.5 168.6 158.6 217.9 197.5 274.4 274.4 309.9 337.8 199.04 579.27 0.739 0.557 0.782 0.068 5.86 0.809 33.62 242.73 0.854 58.66 -21.46 0.885 69.56 81.25 0.9823 18.78

117.9 166.1 156.4 215.7 195.6 271.9 271.9 307.6 338.0 179.28 599.07 0.729 0.566 0.774 0.068 4.53 0.802 30.01 241.1 0.845 55.51 -27.67 0.876 68.17 82.22 0.967 19.07

118.1 161.6 148.9 215.7 192.2 279.0 279.0 331.6 338.5 228.06 550.46 0.748 0.485 0.797 0.035 15.83 0.823 43.12 258.24 0.867 62.69 -21.22 0.899 75.89 75.75 0.987 18.87

112.3 159.9 146.49 220.2 194.2 285.1 285.1 340.6 336.7 209.63 523.97 0.745 0.514 0.794 0.039 13.32 0.825 43.68 260.62 0.873 72.69 -18.46 0.916 83.42 71.25 0.988 18.87

a

NR ) not reported in experimental set of values. b Properties pertaining to SRN. c Represents an average value.

compared with those of the corresponding straight-run naphtha and hence cannot be expected to match. The calculated flash point of HGO deviated significantly for almost all cases. However, this is not an important property from an industrial viewpoint, and it is seldom used to characterize the product. Figures 5 and 6 provide a comparison of the column temperature profiles before and after tuning with the measured plant data. Again, an excellent match is obtained between the measured and simulated profiles after tuning.

On-Line CDU Optimization. In this section, the results of the on-line optimization of the CDU are presented. On-line optimization was carried out using a tuned model and a back-calculated feed TBP. This ensures that any additional profit arising from this exercise should be realizable in practice. The results of the on-line optimization are reported in Tables 6 and 7. The third column consists of the nine manipulated variables and six properties after back-calculation and tuning, i.e., just before the optimization is started. The

1566

Ind. Eng. Chem. Res., Vol. 41, No. 6, 2002 Table 7. Results of On-Line Economic Optimization for Blend 1a

Figure 5. Comparison of calculated temperature profile before and after tuning and after optimization with measured values for crude 2.

Figure 6. Comparison of calculated temperature profile before and after tuning and after optimization with measured values for blend 1. Table 6. Results of On-Line Economic Optimization for Crude 2a no.

variable or property value (units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

HN flow rate (m3/h) kero flow rate (m3/h) LGO flow rate (m3/h) HGO flow rate (m3/h) reflux flow rate (m3/h) HN PA flow rate (m3/h) kero PA flow rate (m3/h) LGO PA flow rate (m3/h) COT (°C) HN flash point (°C) kero/ATF flash point (°C) LGO flash point (°C) HGO recovery (%) RCO recovery (%) kero/ATF end point (°C)

base case lower value bound 62.77 221.07 186.92 53.41 280.00 749.79 350.60 421.30 330.8 10.48 40.68 78.00 80.93 23.39 260.88

50.00 200.00 170.00 40.00 240.00 600.00 330.00 330.00 329.0 9.00 39.00 55.00 60.00 15.00 240.00

upper optimum bound value 80.00 250.00 220.00 80.00 320.00 900.00 550.00 550.00 333.0 15.00 45.00 85.00 90.00 25.00 250.00

70.78 233.71 192.07 57.88 281.35 748.41 349.13 419.86 332.8 10.04 41.50 80.49 79.26 23.35 265.50

a Initial objective function ) -12 126.547, final objective function ) -12 818.767, no. of iterations ) 14, initial value of profit function ) 6 062 898.81, final value of profit function ) 6 117 677.41, net increase in profit (Rs/h) ) 54 778.60, CPU time ) 255 s.

fourth and fifth columns give lower and upper bounds for manipulated variables and properties. The sixth column consists of the values of the manipulated variables and properties at the optimal point. The optimum conditions, if implemented, can yield substantially increased profits without compromising the quality of the products, as almost all of the properties are

no.

variable or property value (units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

HN flow rate (m3/h) kero flow rate (m3/h) LGO flow rate (m3/h) HGO flow rate (m3/h) distillate flow rate (m3/h) HN PA flow rate (m3/h) kero PA flow rate (m3/h) LGO PA flow rate (m3/h) COT (°C) HN flash point (°C) kero/ATF flash point (°C) LGO flash point (°C) HGO recovery (%) RCO recovery (%) kero/ATF end point (°C)

base case lower value bound 64.05 126.31 180.17 59.96 230.00 490.02 420.60 422.81 348.47 15.83 43.12 62.69 75.75 18.87 258.24

50.00 100.00 160.00 40.00 200.00 300.00 330.00 330.00 345.00 9.00 39.00 55.00 60.00 15.00 240.00

upper optimum bound value 90.00 150.00 200.00 80.00 250.00 550.00 550.00 550.00 351.00 15.00 45.00 85.00 90.00 25.00 250.00

78.14 146.51 191.86 66.30 209.63 454.41 382.76 385.07 350.32 13.32 43.68 72.69 71.25 18.87 260.62

a Initial objective function ) -9454.933, final objective function ) -13 131.739, no. of iterations ) 12, initial value of profit function ) 6 368 810.78, final value of profit function ) 6 434 638.87, net increase in profit (Rs/h) ) 65 828.09, CPU time ) 196 s.

within the prescribed bounds. However, the ASTM end point of ATF deteriorated and exceeded the upper bound in some cases. By increasing the weighting factor for the ASTM end point in the objective function, one can perhaps bring it within bounds. In the present investigation, a higher weighting was given to flash point, and the results were as expected. The increase in net profit as a result of improved operating conditions was on the order of 1% in all of the cases investigated. A comparison of column parameters and product properties after optimization is shown in Tables 4 and 5. These tables provide a comparison of the calculated column profile and product properties before backcalculation, after back-calculation, after tuning, and after optimization with plant measured data. The column temperature profiles using the optimum conditions of operation have been included in Figures 5 and 6. These figures also include temperature profiles before and after model tuning, as well as measured data. As seen in these figures, after optimization, the temperature profile is slightly above the base temperature profile (operating conditions) because of the increase in the feed temperature. Note that, in all of the above cases, the increase in profit obtained is on the order of several thousand rupees per hour, which can add up to a hefty sum per year, while the properties still remain within allowable limits. However, the use of actual economic parameters can slightly alter these values. Even if only a fraction of the predicted increase in profit is realized in the actual plant operation, however, the exercise of on-line optimization will be fully justified. The algorithm cannot ensure that all of the properties stay within the prescribed bounds and also that the profit objective function is improved without violating column hydrodynamics. If the simulator fails to converge in some cases, then it is to be understood that the bounds given on the variables and/or properties cannot be achieved and, hence, that some of those bounds must be changed accordingly. The optimized control parameters, including product draw rates, pump-around flow rates, reflux flow rate, and COT, can be passed on to appropriate controllers as set points. The exercise can be repeated every 1-2 h, which ensures that the unit is operating under optimal conditions most of the time.


Conclusions

Literature Cited

In this work, the primary goal of on-line optimization of a crude distillation unit (CDU) has been successfully achieved. The code developed in Microsoft Fortran for the maximization of profit with simultaneous maintenance of the product properties within prescribed bounds has been tested for a wide range of plant data with different kinds of crude oils, and it has been found to be effective in all cases. All of the cases that were investigated in this study showed potential increases in yearly profit of several million rupees from the CDU. Before application of on-line optimization, it is necessary to ensure that the model being used is completely in tune with the plant operation for only then can the computed profits be expected to be realized. This can be achieved by back-calculating the crude TBP and tuning the model parameters (stage efficiencies) on-line using measured temperatures and other column parameters. It is important that the objective function for optimization is carefully formulated to reflect the objectives of the refinery. The selection of weights and decision variables and their bounds must be made judiciously. The choice of step size for calculating the objective gradients is important for successful application of SQP for optimization.

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Acknowledgment Financial support from the Center for High Technology, New Delhi, India, is gratefully acknowledged. Appendix 1: Steady-State Model Equations for CDU For an equilibrium stage i, the equations are as follows:

mass balance equations (1 + SLi )Li xi,j + (1 + SVi )Vi Ki,j xi,j - Li-1xi-1,j + Vi+1,j Ki+1,j xi+1,j + Fi zi,j ) 0

[j ) 1, ..., C]

F ) or the vapor feed Fi zi,j can be the liquid feed (LFi x i,j F F (V i Ki,j x i,j) or a mixture of liquid and vapor. The liquid feed enters above the feed tray, whereas the vapors are introduced below it.

summation equations C

Li )

li,j ∑ j)1 C

Vi )

vi,j ∑ j)1

enthalpy balance equation C

C

(1 + SLi )Li xi,j hi,j + ∑(1 + SVi )Vi Ki,j xi,j Hi,j ∑ j)1 j)1 C

C

Li-1xi-1,j hi-1,j - ∑Vi+1Ki+1,j xi+1,j Hi+1,j + ∑ j)1 j)1 C

Fi zi,j HFi,j ( Q ) 0 ∑ j)1 For N stages (i ) 1, ..., N), there are a total of N(C + 3) nonlinear equations that must be solved simultaneously.

1568


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Received for review January 17, 2001 Revised manuscript received October 3, 2001 Accepted January 5, 2002 IE010059U

On-Line Optimization of a Crude Distillation Unit ... - ACS Publications

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