Platform for Techno-economic Analysis of Fouling Mitigation Options

Energy & Fuels 2009, 23, 1323–1337

1323

Platform for Techno-economic Analysis of Fouling Mitigation Options in Refinery Preheat Trains† E. M. Ishiyama, W. R. Paterson, and D. I. Wilson* Department of Chemical Engineering, UniVersity of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA, United Kingdom ReceiVed July 15, 2008. ReVised Manuscript ReceiVed September 12, 2008

The rise in energy prices has increased interest in improving the efficiency of heat-transfer systems, particularly for the heat exchangers in crude oil preheat trains. Fouling in heat exchangers can result in reduced throughput, extra fuel consumption, or the imposition of limits on the operation of distillation columns. There are several mitigation options available, ranging from chemical (e.g., use of anti-fouling chemicals) to capital (new units, inserts, or configurations). Selecting the best option requires a techno-economic analysis of the performance of the preheat train before and after modification. This requires simulation to quantify the impact of molecular processes on unit performance and plant economics. We present examples of the use of a new simulation tool, incorporating the impact of fouling on the heat transfer in and throughput of preheat trains. We examine dynamic phenomena, such as pump performance, flow splits across parallel sets of heat exchangers, and fouling rates dependent upon temperature and flow. The versatility of the tool is demonstrated by calculating optimal cleaning operations for a representative preheat train subject to fouling under (a) different energy and crude costs and (b) impact of different fouling rates (e.g., simulating the use of chemical mitigation). We shall also demonstrate application of the tool to assess the consequences of column revamps.

1. Introduction The preheat trains (PHTs) on crude distillation units (CDUs) are networks of heat exchangers that recover heat from column product and pumparound streams and transfer it to the crude oil feedstock, to reduce the load on the furnace. The performance of the PHT can have a strong impact on the profitability of the CDU. Fouling has been a long-standing problem in PHT operations (ESDU1) because it reduces the heat-transfer efficiency and throughput capacity of the system, both of which incur significant costs. The increasing cost of crude oil and the associated cost of furnace energy, as well as the need to reduce CO2 emissions, have prompted a revisit of the fouling problem (ESDU1). While molecular studies have for some time sought to elucidate the mechanisms of fouling (Watkinson and Wilson2), quantitative studies of the effect of fouling on PHT operation and dynamics are a relatively recent development. Several quantitative models for calculating (or estimating) crude oil fouling rates have appeared, following the introduction of the “fouling threshold” concept by Ebert and Panchal.3 This semiempirical approach, originally introduced to evaluate the rate of crude oil tube-side fouling at a local condition (point † Presented at the 9th International Conference on Petroleum Phase Behavior and Fouling. * To whom correspondence should be addressed. Fax: +44-(0)1223334796. E-mail: [email protected]. (1) ESDU. Heat exchanger fouling in the pre-heat train of a crude oil distillation unit. Data Item 00016, IHS ESDU International plc., London, U.K, 2000. (2) Watkinson, A. P.; Wilson, D. I. Chemical reaction fouling: A review. Exp. Therm. Fluid Sci. 1997, 14, 361–374. (3) Ebert, W.; Panchal, C. B. Analysis of Exxon crude-oil slip stream coking data. In Fouling Mitigation of Industrial Heat Exchange Equipment; Panchal, C. B., Bott, T. R., Somerscales, E. F. C., Toyama, S., Eds.; Begell House: New York, 1997; pp 451-460.

condition), describes the fouling rate as the combination of a deposition term and a fouling suppression term. The rate exhibits two primary dependencies: it (i) increases with increasing surface (and film) temperature and (ii) decreases with increasing flow velocity. The concept has become an accepted basis for the development of many heat exchanger (HEX) design and control strategies, as reviewed by Wilson et al.4 Popular fouling mitigation and control techniques include the use of anti-foulant chemicals, manipulation of operating parameters, use of tube inserts, and network revamps. Complete mitigation of PHT fouling has rarely been achieved, partly because of the variability in nature of crude feedstock fed to the unit over time. Cleaning fouled HEXs, both while the CDU is operating and during shutdowns, is a responsive mitigation approach and is widely practiced. The associated scheduling problem, i.e., determining when to clean which HEX, combines continuous temporal variables, including temperature and pressure drop, with integer variables representing the HEX cleaning decisions. Decaying efficiency gives rise to a nonconvex mixed integer nonlinear programming (MINLP) problem. Since the initial work by Smaïli and co-workers (Smaïli et al.5), the PHT cleaning problem has attracted the attention of the numerical optimization community, e.g., Georgiadis et al.,6 (4) Wilson, D. I.; Polley, G. T.; Pugh, S. J. Ten years of Ebert, Panchal and the ‘threshold fouling’ concept. In Conference Proceedings of Heat Exchanger Fouling and Cleaning: Challenges and Opportunities, Kloster Irsee, Germany, 2005; http://services.bepress.com/eci/heatexchanger2005/ 6/. (5) Smaïli, F.; Angadi, D.; Hatch, C. M.; Herbert, O.; Vassiliadis, V. S.; Wilson, D. I. Optimisation of scheduling of cleaning in heat exchanger networks subject to fouling: Sugar industry case study. Food and Bioprod. Process. 1999, 77, 159–164. (6) Georgiadis, M. C.; Papageorgiou, L. G.; Macchietto, S. Optimal cleaning policies in heat exchanger networks under rapid fouling. Ind. Eng. Chem. Res. 2000, 39, 441–454.

10.1021/ef8005614 CCC: $40.75  2009 American Chemical Society Published on Web 11/12/2008

1324 Energy & Fuels, Vol. 23, 2009

Figure 1. Distribution of solutions generated by a refinery scheduling study for a 3 year operating horizon reported by Smaïli et al.8 The dashed line and square represents the cost-based objective resulting from the “greedy algorithm”. Circles show minima generated by their MINLP method. The dotted line presents an example for the different schedules having similar cost-based objectives. Obj is the objective function, here in £. NC is the number of cleaning actions. Constant flow rate scenario.

Georgiadis and Papageorgiou,7 Smaïli et al.,8 Wilson et al.,9 Lavaja and Bagajewicz,10-12 Markovski and Urbaniec,13 and Sanaya and Niroomand.14 These MILP and MINLP approaches are not widely used at present. One reason is that, even when plant data are used to estimate fouling rates, the problems are still idealized and are not readily amenable to including control strategies used in practice. Another challenge is that the scheduling problem has multiple solutions, with several local optima and consequent difficulty in identifying a globally optimal solution when the accuracy of the fouling models is poor. This is illustrated by Figure 1, reported by Smaïli et al.:8 they consequently suggested that simpler optimization techniques, such as the “greedy” algorithm applied with a timediscretization approach, are adequate for the task, because they permit the inclusion of features that would cause stability problems in a large-scale MILP/MINLP problem, including variable throughput and changing of splitter ratios to minimize the impact of fouling when a HEX is removed for cleaning. (7) Georgiadis, M. C.; Papageorgiou, L. G. Optimal energy and cleaning management in heat exchanger networks under fouling. Chem. Eng. Res. Des. 2000, 78 (2), 168–179. (8) Smaïli, F.; Vassiliadis, V. S.; Wilson, D. I. Mitigation of fouling in refinery heat exchanger networks by optimal management of cleaning. Energy Fuels 2001, 15, 1038–1056. (9) Wilson, D. I.; Vassiliadis, V. S.; Smaïli, F. Mitigating fouling at the plant scale by strategic cleaning: Potential, pitfalls, and needs. In Heat Exchanger Fouling: Fundamental Approaches and Technical Solutions; Mu¨ller-Steinhagen, H., Eds.; Publ. Publico Publications: Germany, 2001; pp 325-332. (10) Lavaja, J. H.; Bagajewicz, M. J. On a new MILP model for the planning of heat exchanger network cleaning. Ind. Eng. Chem. Res. 2004, 43, 3924–3938. (11) Lavaja, J. H.; Bagajewicz, M. J. On a new MILP model for the planning of heat exchanger network cleaning. Part II: Throughput considerations. Ind. Eng. Chem. Res. 2005, 44, 8046–8056. (12) Lavaja, J. H.; Bagajewicz, M. J. On a new MILP model for the planning of heat exchanger network cleaning. Part III: Multiperiod cleaning under uncertainty with financial risk management. Ind. Eng. Chem. Res. 2005, 44, 8136–8146. (13) Markovski, M.; Urbaniec, K. Optimal cleaning schedule for heat exchangers in a heat exchanger network. Appl. Therm. Eng. 2005, 25, 1019– 1032. (14) Sanaya, S.; Niroomand, B. Simulation of heat exchanger network (HEN) and planning the optimum cleaning schedule. Energy ConserV. Des. 2007, 48, 1450–1461.

Ishiyama et al.

Few PHT scheduling studies have incorporated the effect of local operating conditions on fouling behavior and its mitigation. An important exception is the work of Rodriguez and Smith,15 who used a fouling threshold model to calculate local rates and thereby optimized network performance and cleaning schedules for a time-discretized problem using simulated annealing. They did not consider the variable throughput case, whereas several refineries experience severe throughput limitations arising from the hydraulic impact of fouling and pump limitation. We present a PHT simulator implemented in readily available software tools (MATLAB and Excel), which incorporates a comprehensive set of network and fouling dynamics (both thermal and hydraulic performance). The simulator was tested in a series of case studies chosen to include practical refinery situations. Fouling rates are calculated using a fouling threshold model, but any functional form could be used. The simulator is combined with a modified version of the time-discretization/ greedy algorithm approach reported by Smaïli et al.8 to evaluate optimal cleaning schedules, incorporating realistic control actions. We demonstrate how the network simulation code is able to incorporate day-to-day plant operational features, such as use of anti-foulants, planning for cleaning HEXs during a plant shutdown, and simple column revamps. 2. Model Formulation 2.1. HEX Network. 2.1.1. Heat Transfer. The majority of the HEXs used in PHTs are shell-and-tube devices. The performance of individual HEXs are evaluated here using lumped parameter models, as in most network simulation studies, in effect assuming uniform thermal properties, heattransfer coefficients, and single-phase flow. The NTU-effectiveness (ε) method is used to calculate the duty and outlet temperatures for each HEX using standard equations (e.g., Hewitt et al.16). This method lends itself to simulating the thermal performance of the PHT network, because the inlet and outlet temperatures from each HEX appear in simultaneous linear equations, which can be written in matrix form and solved rapidly (see Smaïli et al.8). 2.1.2. Fouling. Fouling is assumed to occur only on the tube side, partly because reliable models for shell-side fouling of noncrude streams are not currently available. The fouling rate, R˙f, is calculated here using one of the “fouling threshold” models presented by Polley et al.17 R˙f ) max{0, aRe-0.66Pr-0.33 exp(-E/RTfilm) - bτw}

(1)

where a and b are dimensional constants, which establish the time scale of the process, τw is the wall shear stress on the inner tube/foulant surface, Tfilm the tube-side film temperature, and E and R are the activation energy and gas constant, respectively. The Reynolds number, Re, is calculated via Re )

um(di - 2δ) υ

(2)

where um is the corrected axial mean velocity in the heat exchanger tube with the new reduced cross-sectional area, di is (15) Rodriguez, C.; Smith, R. Optimization of operating conditions for mitigating fouling in heat exchanger networks. Chem. Eng. Res. Des. 2007, 85, 839–851. (16) Hewitt, G. F.; Shires, G. L.; Bott, T. R. Process Heat Transfer; CRC Press, Inc.: Boca Raton, FL, 1994; pp 183-184. (17) Polley, G. T.; Wilson, D. I.; Yeap, B. L.; Pugh, S. J. Evaluation of laboratory crude oil threshold fouling data for application to refinery preheat trains. Appl. Therm. Eng. 2002, 22, 777–788.

Fouling Mitigation Options in Refinery PHTs

Energy & Fuels, Vol. 23, 2009 1325

the tube internal diameter, δ is the deposit thickness, and υ is the kinematic viscosity. All of the thermo-physical properties of the crude oil associated with a particular HEX are calculated at the arithmetic mean temperature of the crude oil at the HEX inlet and outlet. Likewise, the Prandtl number, Pr, for the crude is defined via Pr )

C pµ λc

(3)

where Cp is the crude specific heat capacity, µ is the crude dynamic viscosity, and λc is the crude thermal conductivity. In eq 1, τw is not likely to vary markedly across a HEX but Tfilm is, and therefore, the average fouling rate in the unit is evaluated using the exponential integral approach presented by Ishiyama et al.18 At any instant, the overall heat-transfer coefficient, U, in a HEX is calculated using Rf Rw 1 1 1 ) + + + UAi,cl Ai,fhi Aoho Ai,cl Ao

(4)

where Ai,cl is the internal (clean) surface area, Ai,f is the internal surface area after fouling, Ao is the external surface area of the tube, Rf is the fouling resistance, Rw is the tube-wall resistance, and hi and ho are the internal and external film heat-transfer coefficients, respectively. When there is variation in throughput, the effect of the flow rate on the film heat-transfer coefficients hi and ho has to be included, and this is performed using standard correlations. hi is a function of the tube-side Fanning friction factor, Cf, which is in turn dependent upon surface roughness, e, and flow velocity, as described by the Colebrook-White equation. An explicit form of this given by Sousa et al.19 is used 1

√Cf

) -4 log10

(

(

5.16 e e log 3.7(di - 2δ) Re 3.7(di - 2δ)

The relationship developed by

hi )

(

λc di - 2δ

)

Gnielinski20

()

Cf (Re - 1000)Pr 2

1 + 12.7

))

5.09 (5) Re0.87 for hi is used

(6)

It is assumed that there is no fouling occurring on the shell side. Initial values for the external heat-transfer coefficient were calculated using standard methods (Bell-Deraware method): variation in the shell-side heat-transfer coefficient caused by a change in the shell-side flow rate is calculated via ho,1 M1 ) ho,2 M2

δ ≈ Rfλf

(8)

where λf is the thermal conductivity of the deposit. Deposit aging and temporal changes in λf are not considered here. Fouling can (i) change the roughness of the surfaces, (ii) reduce the cross-sectional area available for flow, and (iii) potentially block tubes, causing flow maldistribution. Ignoring (i) and (iii), the pressure drop across a HEX, ∆P, is given by ∆P ) ∆Pends + ∆Ptubes ≈ a′m2 + b′m1.75-2(di - 2δ)-(4.75-5) (9) where m is the crude oil mass flow rate, di is the clean tube inner diameter, a′ and b′ are dimensional constants, ∆Pends is the pressure drop at tube bends, and ∆Ptubes is the pressure drop across tubes. ∆P is therefore roughly proportional to m2 and very sensitive to changes in duct size (a δ/di value of 0.06 will double ∆Ptubes). Incorporating the head loss for fluid contraction, expansion, and flow reversal, the tube-side pressure drop is given by Fum Fum L + 2.5Npass (di - 2δ) 2 2 2

∆P ) 4NpassCf

2

n

(7)

Here, ho,i is the shell-side heat-transfer coefficient for shellside mass flow rate Mi, and n is a constant with value 0.5 (Coulson and Richardson21). (18) Ishiyama, E. M.; Paterson, W. R.; Wilson, D. I. Thermo-hydraulic channelling in parallel heat exchangers subject to fouling. Chem. Eng. Sci. 2008, 63, 3400–3410. (19) Sousa, J.; da Conceic¸a˜o, M.; Marques, A. Sa´. An explicit solution to the Colebrook-White equation through simulated annealing. In Water Industry Systems: Modelling and Optimization Applications; Research Studies Press Ltd.: Baldock, Hertfordshire, U.K., 1999; Vol. 2, pp 347355.

(10)

where L is the tube length, Npass is the number of tube passes, F is the crude density, and um is the mean tube-side velocity. The energy supplied by the network pump(s) is also dissipated across HEXs, piping run lengths, fittings, and control valves, so that ∆P ) ∆Ppiping + ∆PHEX

Cf 0.67 (Pr - 1) 2

( )( )

We acknowledge that the dynamics of fouling behavior in the network would become more complicated if effects such as deposit aging were incorporated. 2.1.3. Pressure Drop and Network Hydraulics. Rf is a thermal parameter, but estimation of the hydraulic impact of fouling requires knowledge of the thickness of the foulant layer and its surface roughness. Changes in surface roughness are not considered here. For tube-side fouling, Yeap et al.22 have shown that, for typical crude oil systems, the deposit layer thickness, δ, may be related reasonably well to Rf by the “thin-slab” approximation as

(11)

where ∆Ppiping is the pressure drop expended across pipes, valves, and other fittings and ∆PHEX is the pressure drop across the HEXs in the network. By assumption, fouling does not affect the resistance to flow across fittings, valves, etc., whereas throughput does, with ∆Ppiping ∝ m2. We therefore introduce a pressure distribution factor, R, to quantify this distribution based on clean operation at the design throughput R)

∆Ppiping ∆PHEX,cl

(12)

where ∆PHEX,cl is that corresponding to operation under clean conditions at the design throughput. The piping component at any time can then be estimated via

( )

∆Ppiping ) R∆PHEX,cl

m mcl

2

(13)

(20) Gnielinski, V. New equations for heat and mass-transfer in turbulent pipe and channel flow. Int. Chem. Eng. 1976, 16 (2), 359–368. (21) Coulson, J. M.; Richardson, J. F. Chemical Engineering: Design; Pergamon Press: Oxford, U.K., 1986; Vol. 6, pp 511-621. (22) Yeap, B. L.; Wilson, D. I.; Polley, G. T.; Pugh, S. J. Mitigation of crude oil refinery heat exchanger fouling through retrofits based on thermohydraulic fouling models. Chem. Eng. Res. Des. 2004, 82 (A1), 53–71.


Ishiyama et al.

NTU-ε expressions are updated, and the network temperature field is updated. Application of the simple Euler method dRf ∆t (16) dt t-∆t can generate problems if the time period, ∆t, is too coarse: the fouling rate will often slow down dramatically as deposits accumulate (for instance, as a result of changes in Tfilm); however, this would not be captured, and the effect of fouling would be overestimated. Very short time steps are computationally undesirable, but identifying the optimal value of ∆t is complicated by the fact that HEXs foul at different rates and the rank order of rates may change over the time span of the problem. An adaptive step-size algorithm for determining ∆t to maintain accuracy while minimizing effort was therefore developed on the basis of that described by Press et al.24 for solving sets of ordinary differential equations. Let Rf(t + ∆t) denote the fouling resistance in a HEX at time t + ∆t and Rf,1(t + ∆t) and Rf,2(t + ∆t) denote the estimates of Rf(t + ∆t) calculated using one step of length ∆t and two steps each of ∆t/2, respectively. The error involved in using the single step is Rf,t ) Rf,t-∆t +

Figure 2. Construction of the combined characteristic curve. Solid line, pump characteristic; dashed lines, PHT characteristic, with fouling increasing from 1 to 3; bold solid line, combined characteristic curve. At position 3, the control valve is fully open or “saturated”.

The pumps providing the hydraulic driving force are normally centrifugal devices operating at constant rotational speed, so that the flow rate depends upon the operating head, H, and therefore the pressure drop across the network. The pressureflow characteristic curve is approximated here by H ) p1 - p2m

2

(14)

where {pi} are dimensional constants: p1 is related to the pump shut-off head, Hs, which is determined by the pump design via (Kay and Nedderman23) p1 ) Hs ) (rω)2/2g

(15)

err ) Rf,1(t + ∆t) - Rf,2(t + ∆t)

(17)

Now, if the calculated error, err, is greater than the acceptable error, err*, the current time step, ∆tcurrent, should be shortened. Likewise, if err > err*, it is desirable to increase the time step. Integration with fourth-order Runge-Kutta shows that

| |

err* 0.2 (18) err In this work, an initial ∆t value of 1 day and err* ) 1 × 10-6 m2 K W-1 are used. 2.2. Scheduling of Cleaning. HEXs may be isolated from service for cleaning, incurring an initial penalty in terms of heat transfer and network operability, in return for a longer term gain in heat duty and reduction in pressure drop. Scheduling cleaning in a PHT commonly employs cost-based objective functions extending over the operating time span; that reported by Smaïli et al.8 is ∆tacceptable ) ∆tcurrent

where r is the impeller radius and ω is the rotational speed. The pump characteristic is not usually the sole determinant of the flow rate, because the flow is also subject to control valve action. This is illustrated in Figure 2, which shows the characteristic of a pump that has been overdesigned (OD) (design throughput, mdesign) for the combination of target throughput, mtarget, and clean pressure drop. Initially, under clean conditions, the control valve will partly close to maintain the flow at the set point, mtarget. As the pressure drop across fouled HEXs increases, the control valve will open to compensate, until it is fully open. Thereafter, the flow rate will decrease as fouling proceeds. The hydraulic effect of fouling is therefore masked by the operation of the control valve: a period of constant throughput is followed by a decline in throughput determined by the pump characteristic curve. This combined characteristic curve is represented in Figure 2. Changes in the crude feed rate are matched by proportional changes to the hot stream flow rates, because most of the hot streams are column products and their flow is proportional to the feed rate. It should be noted that the variation in crude feed rate creates problems for linear programming approaches. 2.1.4. Simulation. The dynamics of the network are evaluated by piece-wise integration in time. At any instant, t, the fouling resistance in each HEX is evaluated, the coefficients in the

where CE denotes the unit cost of energy, tf is the operating time span (often the interval between shutdowns), Qfurnace is the furnace heat duty, CM is the maintenance cost, Clo is the lost opportunity cost (the profit forgone as a result of reducing throughput below mtarget), and Nc,i and Cc,i are the number and cost of cleaning actions for HEX i. Most scheduling studies to date have not considered throughput changes, although Lavaja and Bagajewicz10-12 did incorporate changes in throughput imposed by furnace firing limits (i.e., a thermal limit) rather than hydraulic impacts. Constraints, such as furnace firing limits, can be included in the above objective function by adding penalty functions based on the approach to the furnace firing limit. The scheduling approach employed here is based on discretization of the operating time span into Np regular periods, which are divided into subperiods for cleaning, of length ∆tcleaning, and

(23) Kay, J. M.; Nedderman, R. M. Fluid Mechanics and Transfer Processes; Cambridge University Press: Cambridge, U.K., 1990; pp 263294.

(24) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes: The Art of Scientific Computing; Cambridge University Press: Cambridge, U.K., 1989; pp 554-560.

Obj )

∫

tf

0

{CEQfurnace(t) + CM(t) + Clo(t)(mtarget - m)}dt + all HEX

∑

Cc,iNc,i (19)

i)1



where Q(t) is the heat duty of the network at time t and subscripts “no clean” and “clean i in period j” refer to no cleaning action and the cleaning of HEX i at period j, respectively. The sliding time horizon is truncated when it exceeds tf, i.e., when tj + Ns > tf, then tj + Ns ) tf. A benefit threshold is set, viz. Gi|j > ∆G

Figure 3. Time discretization in formulating the scheduling algorithm.

Figure 4. Schematic of temporal formulation of the scheduling approaches on a typical profile of CIT versus time. The solid bold line represents operation without cleaning, and the dotted line represents the idealized effect of cleaning a HEX in period j (after Smaïli et al.8).

(22)

where ∆G is the “greedy threshold” value and, in practice, will be some multiple of the cost of cleaning the exchanger. The HEX with the highest G value satisfying eq 22 is selected for cleaning in period j, and the algorithm then moves on to period j + 1. One could select more than one HEX for cleaning in a subperiod, either simultaneously or in sequence. This requires a straightforward adaptation of the algorithm (see Wilson et al.25). The total network fouling penalty function, Γ, is calculated after the final period using eq 23 for comparison of different scenarios, such as the benefit of performing cleaning compared to taking no cleaning action. Γ)

∫

tf

0

{CEQfurnace,additional(t) + Clo(mtarget - m(t))}dt + all HEX

operation, ∆toperation, as indicated in Figure 3 The optimization approach uses a simple and robust “greedy” algorithm (GrA), which considers the cleaning actions allowed in the current period (say, tj) and the impact of this action over a “sliding” horizon, ∆ts, consisting of Ns periods in the future. For a typical profile of coil inlet temperature, CIT, against time, a schematic of the temporal formulation of the scheduling approach is presented in Figure 4. Evaluating Obj requires simulating the network over several time periods, and we employ a shortcut “merit list” algorithm to identify favorable candidates to be compared in a full simulation. At the start of each time period, the performance of the network at its current, fouled, condition is evaluated. The improvement obtained from cleaning each HEX at that point is calculated, and the difference between the two is used to generate an estimated benefit γi|j ) {Clo(mcl,i,j - mf,j) + CE(εi,cl - εi,f)QHEX i,cl}∆tw (20) Here, γ is the estimated benefit from cleaning HEX i at period j, carrying the benefit forward over a time window of length ∆tw, and ignoring losses incurred during cleaning, Clo is the lost opportunity cost per unit mass, mf,j is the current mass flow rate at period j, mcl,i,j is the mass flow rate when HEX i is cleaned at period j, εi,cl is the effectiveness of HEX i when clean, εi,f is the current, (possibly) fouled effectiveness, and QHEX i,cl is the heat duty of HEX i in the clean state. Transients in throughput and heat transfer during the cleaning period are not considered at this stage; eq 20 simply considers the benefit in the refurbished state. The cleaning actions are used to generate a “merit list” of most attractive actions. Detailed simulations are then performed for the three highest ranked HEXs, over the sliding time window. The GrA decision parameter, Gi|j, is calculated for each of the selected units from Gi|j )

∫ ∫

tj+Ns

tj tj+Ns

tj

CE{Q(t)|no cleaning - Q(t)|clean i in period j}dt + Clo{m(t)|clean i in period j - m(t)|no cleaning}dt - Cc,i (21)

∑

Cc,iNc,i (23)

i)1

Here, Nc,i is the number of cleaning actions performed for HEX i and Qfurnace,additional is the additional heat duty of the furnace because of fouling. 3. Demonstration on a Preheat Train 3.1. Example Network. Figure 5 shows a PHT network consisting of 14 HEXs, resembling that presented by Smaïli et al.8 The PHT includes a desalter and a flash tower, which are common features of modern refineries. The design details of the HEXs and the temperatures and flow rates affected by the desalter and flash tower are detailed in Table 1. The crude is split into two parallel streams downstream of the flash tower. The split fraction and those of the hot streams serving HEXs 9-14 add additional control variables to the simulation. In the standard case, the PHT starts in a clean condition with equal flow splits and operates continuously until a shutdown 3 years later. The thermo-physical properties of the crude oil are summarized in Table 2. Upstream of the desalter, the deposition mechanism is dominated by crystallization and particulate fouling and is not described by eq 1. Hence, fouling is represented by constant fouling rates in HEXs 1-5, i.e., linear fouling. The fouling rates of HEXs downstream of the desalter are described by eq 1. Table 3 summarizes the fouling model parameters, which are used in the simulations unless otherwise specified. Evaluation of eq 1 for the network in the clean condition indicates that initially HEXs 8-14 are operated above the fouling threshold. The highest fouling rates are found in units at the hot end, particularly 10, 11, 13, and 14. To evaluate the time duration taken for the simulation, all simulations were performed on an AMD Athlon 64 Processor 2.41 GHz PC with 2 GB RAM. 3.2. Comparison of Network Performance under the Absence of Cleaning: Thermal and Hydraulic Limits. Here, we look at network simulations when no cleaning actions are performed. The simulation is able to compare the effect of pressure drop limits because of fouling, under different pumping


Ishiyama et al.

Figure 5. Case study heat exchanger network. Solid line, cold stream; dotted line, hot stream. Stream temperatures indicate network performance under clean condition. Table 1. Summary of Heat Exchanger Details: Clean Operation heat exchangers number Ao (m2) tube passes total number of tubes crude flow rate (kg/s) crude velocity (m/s) Re Pr product flow rate (kg/s) U (W m-2 K-1) initial fouling rate (m2 K J-1) Q (MW)

1 323.2 2 900

2 323.2 2 900

3 323.2 2 900

4 323.2 2 900

5 323.2 2 900

6 323.2 2 900

7 323.2 2 900

8 323.2 2 900

9, 12 179.54 2 500

10, 13 179.54 2 500

11, 14 179.54 2 500

190

190

190

190

190

190

190

190

91.96

91.96

91.96

2.31

2.36

2.40

2.44

2.48

2.51

2.56

2.60

2.30

2.36

2.42

7400 64 40

10500 48 20

13200 40 20

16500 33 20

21600 27 20

24600 32900 40900 24 19 16 40 20 40

42900 13 20

60700 10 20

83100 8 20

300 500 650 500 500 500 1 × 10-11 1 × 10-11 1 × 10-11 1 × 10-11 1 × 10-11 0

400 0

600 600 650 600 9.83 × 10-12 9.36 × 10-11 1.41 × 10-10 1.89 × 10-10

10.2

9.3

4.4

7.3

4.9

7.5

8.0

Table 2. Crude Oil Thermo-physical Propertiesa parameter

value

specific heat capacity (J kg-1 K-1) density (kg m-3) dynamic viscosity (mPa s) thermal conductivity (W m-1 K-1)

Cp ) 1787.5 + 5.0433(T) F ) 877.02 - 0.8379(T) µ ) 7.270744 exp(-0.015028T) λc ) 0.1367 - 0.00009(T)

a

T is the crude bulk temperature in °C.

Table 3. Fouling Model Parameters and Foulant Thermal Conductivity Used in the Reference Case Study a E b λf

4100 m2K kW-1h-1 28 kJ mol-1 2.63 × 10-5 m2K kW-1h-1 Pa-1 0.5 W m-1 K-1

capacities. When the throughput is limited by pressure drop across the HEXs, it is also important to have an idea on how much the pressure is distributed along the rest of the network, namely, the piping and the fittings. To approach the pressure distribution problem, we considered a set of R values (described by eq 12) to define the network hydraulics at the clean design state. The simulation results for the heat duty, throughput, and

8. 6

6.1

5.2

5.5

coil inlet temperature (CIT) are summarized in Figure 6. The pumps are assumed to be designed for 5% overcapacity, and R ) ∞ indicates the constant throughput scenario. As R is increased from 1 to 2, the hydraulic performance becomes less sensitive to the effect of fouling and throughput is throttled later and at a more gradual rate (Figure 6a). The averaged throughput values in Table 4 show that the loss in throughput is relatively small for this scenario (2 kg/s for R ) 1, i.e., ∼1% over the whole period), but Figure 6b shows that there is a noticeable drop in network heat duty (from 93 to 82 MW for R ) 1).This is not reflected in the CIT profile (Figure 6c). The illustration emphasizes that CIT alone is not a good indicator for monitoring network performance. The hydraulic impact of fouling indicates that higher R values could mitigate adverse effects. In practice, however, higher R values are normally achieved by reducing the pressure drop across the HEXs, by operating at lower tube-side velocities, and this increases the rate of fouling predicted by eq 1, both through the flow terms (Re and τw) and by an associated increase in Tfilm. We acknowledge here the sensitivity of these calculations to the value of λf (here, 0.5 W m-1 K-1, related through


Energy & Fuels, Vol. 23, 2009 1329 Table 5. Total Fouling Penalty (in Million U.S.$) for Different Energy and Throughput Cost Structures: Figure 6 Network, r )1 CE (U.S.$ kW-1 day-1) scenario

Clo (U.S.$

constant throughput variable throughput (R ) 1)

kg-1)

0 0.01 0.05

0.1

0.5

1

2

0.82 2.31 8.66

4.08 5.20 11.55

8.16 8.81 15.16

16.31 16.03 22.39

Table 6. Cleaning Cost Parameters cleaning cost (U.S.$/clean) greedy threshold value (U.S.$) cleaning period (weeks) initial ∆ts (weeks)

20000 10000 1 48

eq 8), which has been discussed at length elsewhere (Ishiyama et al.26) but which remains a rarely reported or investigated parameter. The economic performance can be driven by the increase in furnace firing because of reduced heat transfer, the decrease in

throughput caused by the hydraulic effect of fouling, or both. The costs associated with each penalty determine the driving factor. Here, we consider the influence of different energy and lost opportunity costs on the economic performance of the network in Figure 5. Two Clo values, 0.01 and 0.05 U.S.$ kg-1, and four CE values, 0.1, 0.5, 1, and 2 U.S.$ kW-1 day-1, were considered. The results are summarized in Table 5. At the lower Clo value, the total cost of fouling increases with CE. The penalty is roughly proportional to CE for the constant throughput case but not for the variable throughput case: the former incurs a lower penalty initially; however, the difference decreases as CE increases, and the order changes at the highest CE value. In the last case, the penalty is dominated by energy prices and a network with reduced throughput may be allowable. The converse is true at the higher Clo value, where the constant throughput case is always more attractive and the network operation should focus on maximizing throughput. 3.3. Cleaning for Constant Throughput Operation. We first consider cleaning actions under the constant throughput scenario to illustrate the thermal impact of fouling on the network performance. One HEX was allowed to be cleaned in each cleaning subperiod. Practical rules, such as cleaning identical HEXs in series or avoiding cleaning on particular HEXs to maintain temperature targets, could be included here without the loss of generality in the approach. The cleaning cost factors and other parameters used in the GrA approach are summarized in Table 6. In some refineries, pumps are overdesigned (OD) and will not encounter throughput limits based on pressure drop relationships. Different CE values still influence whether or not it is economical to clean HEXs often. Here, we explore the influence of the energy cost on scheduling and the associated fouling penalty. Given the cost for cleaning and a minimum expected return (greedy threshold value), it will be less profitable to take HEXs offline for cleaning if the energy cost is very low. As the energy cost increases, the scheduling algorithm identifies HEXs that are more likely to yield energy benefit if cleaned, thus increasing the number of cleaning actions. The changes in the number of cleaning actions with increasing energy cost are shown in Figure 7. For the lowest energy cost considered (scenario i, CE ) 0.1 U.S.$ kW-1 day-1), there is only one cleaning action, occurring only after 2 years of operation. Scenario i in Figure 7b shows that HEX 11, one of the units with the highest surface temperature, is cleaned. The fact that only one cleaning action proves economical is due to the fact that taking units offline at

(25) Wilson, D. I.; Smaïli, F.; Vassiliadis, V. S. Mitigating of fouling in refinery pre-heat trains by optimal management of cleaning and antifoulant treatment. In Proceedings of the 2nd International Conference on Petroleum Phase Behaviour and Fouling, Copenhagen, Denmark, 2000.

(26) Ishiyama, E. M.; Paterson, W. R. P.; Wilson, D. I. Simulating operation of refinery preheat trains for assessing fouling mitigation strategies. In Conference Proceedings of Heat Exchanger Fouling and Cleaning-VII, Tomar, Portugal, 2007.

Figure 6. Network performance, constant (R ) ∞) versus variable throughput scenarios: (a) throughput, (b) heat duty, and (c) CIT. Performance summarized in Table 4. Table 4. Summary of PHT Performance (Averaged over a 3 Year Period) under Constant Throughput (No Pumping Limit) and Variable Throughput (Pump 5% Overdesigned) (No cleaning scheduled; Figure 6) constant throughput average throughput (kg/s) average network heat duty (MW) average CIT (°C) CPU time (s)

variable throughput

R)∞

R)1

R)2

190

188

189

86

85

86

200 44

200 68

200 65


Ishiyama et al.

Figure 7. Effect of different energy costs. Constant throughput scenario: (a) CIT variation over time and (b) schedule, for different energy costs CE ) (i) 0.1, (ii) 0.5, (iii) 1, and (iv) 2 U.S.$ kW-1 day-1. Performance summarized in Table 7.

any point causes a drop in network heat duty (Figure 7a). Cleaning also incurs a cleaning cost and a minimum expected

return: frequent cleaning is therefore uneconomical when the energy cost is very low.



Table 7. Network Performance Summary for Cleaning under Constant Throughput (Figure 7) energy cost, CE (U.S.$ kW-1 day-1) 0.1 average CIT (°C) average network heat duty (MW) fouling penalty cost (million U.S.$) number of cleaning actions CPU time (s)

0.5

1

2

200 86.2 0.82

202 87.3 3.63

203 87.7 6.67

203 87.7 13.12

1 1970

11 1983

16 2012

17 1998

Table 8. Network Performance Summary: Cleaning with “Fixed” Flow Split (Clo ) 0.01 U.S.$/kg) (Figure 8) energy cost, CE (U.S.$ kW-1 day-1) 0.1 average CIT (°C) average throughput (kg/s) average network heat duty (MW) fouling penalty cost (million U.S.$) number of cleaning actions CPU time (s)

0.5

1

2

200 188 85.7 1.99

201 189 86.4 4.46

203 189 87.2 7.10

202 189 86.7 14.08

2 2560

9 3162

14 3211

12 3058

The other cases presented in Figure 7 show that the number of cleaning actions increases as CE increases and the period before the first cleaning operation shortens. The number of cleaning actions stops increasing at high CE values, owing to the incremental gain from cleaning a further exchanger being offset by the energy penalty upon taking a unit off-line (compare cases iii and iv). It is noticeable that only the units in the parallel trains are cleaned, even though others are also subject to fouling. These units experience high fouling rates and also affect CIT directly: loss in heat transfer in upstream units can be countered by higher temperature driving forces downstream. If the average CIT is considered (first row of Table 7) the differences because of CE values appear small but the number

of cleaning actions has increased dramatically (increasing with CE from 0.1 to 1 U.S.$ kW-1 day-1) as the system tries to achieve higher network duty. The benefit of operating a structured cleaning regime can be obtained by comparing the fouling penalty costs in Table 7 to the analogous results for the no cleaning scenario (first row of Table 5). At the lowest CE value, there is no difference but they soon separate, by about 2 million U.S.$ over 3 years, in the highest CE case. The frequency of cleaning required (17 times over 3 years, scenario iv in Figure 7a) is acknowledged as being unlikely to be attractive in practice: the tool gives an indication of how often the plant needs to consider cleaning to optimize the mitigation option. It would be noted that the schedules are also sensitive to the GrA parameters (e.g., Cci and ∆G), and these can be tuned to give more “acceptable” patterns. This has not been presented here because practices vary between refineries and operators. 3.4. Cleaning with Variable Throughput. We now consider a more realistic PHT scenario, which is scheduling under variable throughput operation. Here, both CE and Clo affect the network performance (as discussed in section 3.2). Another factor to include is that, when a HEX on a parallel train is taken off-line for cleaning, the resistances to flow in the two limbs are unbalanced. Hence, we have compared simulations where (i) the flow splits are forced to be the same throughout and (ii) the flow splits are optimized to minimize pressure drop and maximize throughput. First consider scheduling when the flow splits are not changed. Simulations were run with the four energy cost structures presented in section 3.3 for a pump that was overdesigned by 5%. The CIT-time profiles are shown in Figure 8, and network performance is summarized in Table 8. As CE increases, the number of cleaning actions first start to increase (2, 9, and 14) and then decrease (to 12) as energy penalties

Figure 8. CIT profiles for variable throughput, fixed flow split case, pump OD 5%. CE ) (i) 0.1, (ii) 0.5, (iii) 1, and (iv) 2 U.S.$ kW-1 day-1. Performance summarized in Table 8.


Ishiyama et al.

Figure 9. (a) CIT profiles and (b) schedules for operation with variable throughput and flow split optimization, pump OD 5%. CE ) (i) 0.1, (ii) 0.5, (iii) 1, and (iv) 2 U.S.$ kW-1 day-1. Performance summarized in Table 9.

upon cleaning become important. The fixed flow split therefore affects the network performance directly, particularly when opportunity cost dominates (scenarios i-iii in Figure 8). The average heat duty and CIT results in Table 8 indicate that, at CE g 1 U.S.$ kW-1 day-1, the network performance has reached an optimum.

Now, we will illustrate how flow split optimization can improve scheduling. While the HEX is out of service, the drop in heat-transfer duty can be large, and flow split optimization can reduce this decrease. Likewise, throughput can temporarily increase, owing to the absence of the fouled HEX. These dynamics are considered here. For this illustration, the algorithm



Table 9. Network Performance Summary: Cleaning with Flow Split Optimization (Clo ) 0.01 U.S.$/kg) (Figure 9) energy cost, CE (U.S.$ kW-1 day-1) 0.1

0.5

1

2

average CIT (°C) 204 204 204 203 average throughput (kg/s) 190 190 190 190 average network heat duty (MW) 88.1 88.1 87.8 87.6 fouling penalty cost (million 1.02 3.85 6.38 12.70 U.S.$) number of cleaning actions 20 20 18 17 CPU time (s) 4123 4062 4415 3795

initially seeks to minimize the crude stream pressure drop across the two parallel trains by manipulating the flow split. An upper limit for the tube-side flow velocity of 3 m s-1 is assigned, to incorporate realistic operational interests, such as avoidance of erosion and vibration. The hot streamflow fractions to the HEXs 9/12 (HEX 9/12 is used as shorthand for pairs of units in parallel, i.e., HEX 9 and HEX 12), 10/13, and 11/14 are then changed to match the crude stream, to maximize heat recovery. The CIT-time profiles and schedules in Figure 9 show that cleaning is performed more often than in the fixed split scenario and across a larger fraction of the campaign. The regular cleaning schedule maintains CIT at 203-204 °C, irrespective of CE (Table 9), and the number of cleaning actions is large, at ∼20, reducing only slightly as CE increases. HEXs 11 and 14 are cleaned most often, because these are the units with the highest surface temperature and thus (a) influence CIT directly and (b) experience the highest fouling rates. Comparison of Tables 8 and 9 shows that the benefit of flow split optimization is primarily through the increased heat duty: the throughput is similar. This more than offsets the cost associated with cleaning, even at low CE values. The increased annual saving from split optimum is roughly 1 million U.S.$ over the 3 year campaign, irrespective of CE. These scenarios demonstrate that when throughput is reduced because of a pumping limit, a larger number of cleaning actions needs to be performed to maintain economic operation. One response is to install greater pumping capacity. This is illustrated by considering the Figure 5 network with a pump overdesigned by 7.5%. The larger pump will extend the initial constant throughput period; cleaning actions scheduled in this period will be aimed at reducing furnace duty rather than maximizing throughput. The results in Figure 10 show a marked reduction in cleaning actions at CE ) 0.1 U.S.$ kW-1 day-1; from 20 to 5. Priority in cleaning is again given to the hottest units, HEXs 11/14. With this CE value, opportunity costs dominate and HEXs are taken off-line to maximize throughput. At the higher CE value, more cleaning is performed and more energy is recovered. Comparing the network performance summary in Table 10 to the smaller pump (OD 5%, Table 9) shows annual gains of ∼200 000 U.S.$, as well as a less demanding cleaning schedule. These scenarios illustrate how the ability of predicting longterm performance can be used to assess the viability of structural or operational changes. 4. Additional Features of Plant Operation We have demonstrated how thermal and hydraulic fouling considerations can be incorporated into a PHT scheduling algorithm. The results are highly sensitive to the energy, opportunity, and cleaning costs. It is also important to consider operational strategies and decisions. Here, we apply the simulation code to consider the influence of a plant shutdown and the use of anti-foulants and assess the changes resulting from a simple column revamp.

4.1. Plant Shutdowns. Equation 23 implies that scheduling will result in a region without cleaning near the end of the campaign because there is insufficient time to offset the energy lost when a unit is taken off-line for cleaning. This artifact works well, if only the period up to tf is concerned. Most plant operations are, however, associated with a turn-around or shutdown and a period of operation thereafter. Incorporating the shutdown or long-term viability in a cleaning scheduling calculation was discussed by Wilson et al.,9 who suggested four different approaches: (i) setting tf to infinity, (ii) adding a period of time following tf, wherein the network is simulated (and costed) but cleaning is not allowed, (iii) adding a cost penalty for a dirty HEX at time tf proportional to the fouling resistance at that time, and (iv) setting a reflection or periodic boundary condition (as reported in ref 7). Here, we explore three different constructions by which our simulation tool can handle these “end zones”. The sliding time horizon approach is used, as illustrated by Figure 11. Construction I: Horizon extending to the end of the operating period, so that ∆ts varies for each period (Figure 11a). Construction II: Sliding time horizon of fixed length (Figure 11b). Construction III: Sliding time horizon, truncated as it reaches the end period (Figure 11c). The work presented above in section 3 is equivalent to III, where the sliding time horizon was truncated as tf is approached. The different approaches are compared for the variable throughput, flow split optimized case with lowest CE, 0.1 U.S.$ kW-1 day-1. With the longer sliding time horizon (construction I, scenario i in Figure 12) the delay before cleaning starts is reduced, because there is now a longer time available in which to generate an economic return. Simulation with a fixed time horizon extending beyond tf (construction II) results in the “end zone” disappearing (scenario ii in Figure 12). It is noteworthy that the schedule in scenario ii in Figure 12b shows, for the first time, units other than those in the parallel trains being cleaned. The pattern is otherwise similar to before. Both points illustrate a strong feature of the greedy algorithm; i.e., only the benefit of cleaning a HEX at its current state is considered, and at this stage, cleaning actions at future states are not considered: the longer time horizon results in more frequent cleaning. Comparing the network performance (Table 11) to the standard approach confirms the increase in the number of cleaning actions, with very little difference in average CIT and duty, and a 10-20% increase in the fouling penalty cost. Construction II offers improved operability of the PHT after the shutdown, because HEXs are cleaned later, whereas construction I offers little improvement in subsequent performance (and the highest fouling penalty cost). 4.2. Cleaning at Shutdown. Another approach used in practice is to delay cleaning of fouled exchangers until the plant shutdown and to clean units at this point when there is no energy or lost opportunity penalty. Deciding which units to clean at the shutdown is now determined using the simulator, for consecutive 36 month campaigns. At the end of the first campaign (tf ) 3 years), eq 23 is evaluated for each HEX in the PHT, representing the benefit to be realized upon restoring the plant. This benefit is denoted θ and does not include the cost of cleaning. The results for the low energy cost scenario are summarized in Table 12; the benefit is calculated for three values of cleaning cost, namely, 0, Cc, and 2Cc, to represent different margins or differences in effecting cleaning. In the former case, all units show a benefit on cleaning but introducing a cleaning cost of Cc reduces the list to units 2, 4, and


Ishiyama et al.

Figure 10. Effect of pump overdesign for comparison to scenarios i and ii in Figure 9. Variable throughput (pump OD 7.5%), flow split optimization: (a) CIT variation over time and (b) schedule, for CE ) (i) 0.1 and (ii) 0.5 U.S.$ kW-1 day-1. Performance summarized in Table 10. Table 10. Network Performance Summary: Larger Pump (OD 7.5%) Cleaning with Flow Split Optimization (Clo ) 0.01 U.S.$/kg) (Figure 10) CE (U.S.$ kW-1 day-1) average CIT (°C) average throughput (kg/s) average network heat duty (MW) fouling penalty cost (million U.S.$) number of cleaning actions CPU time (s)

0.1

0.5

201 190 86.8 0.84 5 3325

202 190 87.3 3.60 12 4032

9-14 and increasing it to 2Cc reduces it further to 9-14. All three scenarios were simulated over a further 3 year campaign. When all units are cleaned (scenario I), the performance will be identical to the first campaign (scenario i in Figure 9). The new CIT network performance is compared in Table 13, alongside the option where no cleaning is performed during the shutdown. This shows that the latter is the least attractive strategy, requiring most cleaning actions and the lowest thermal performance during the subsequent campaign. Cleaning all of the exchangers proves to be excessive because fouling mainly affects those on the parallel trains. Both scenarios II and III, with selected cleaning, offer better performance with the former numerically superior, but the difference of 50 000 U.S.$ over 3 years is probably at the limit of reliability of the input data. The key point of cleaning selected units is nevertheless clearly made. The simulator can be used to identify those units. 4.3. Anti-foulants. A popular method of fouling mitigation is the use of anti-foulant chemicals. Predicting the effect of antifoulants on fouling rates is not currently possible; therefore, we consider here a spread of possible scenarios. The fouling rate is set to a fraction of the untreated value by multiplying the parameter

Figure 11. Methods of incorporating shutdowns in cleaning scheduling: Np is the number of time periods. (a) Horizon extending to shutdown, tf, (b) fixed horizon (here, 1 year), extending past the shutdown, and (c) 1 year horizon, truncated as shutdown is approached.

“a” in eq 1 by a fixed value, ranging from 0.5 to 1.5. The latter represents an unsuitable additive, which accelerates fouling.



Figure 12. Effect of different sliding time horizon treatments: (a) CIT variation over time and (b) schedule. Variable throughput (pump OD 5%), flow split optimization. CE ) 0.1 U.S.$ kW-1 day-1. (i) Construction I, horizon extending to plant shutdown. (ii) Construction II, fixed 1 year window. Performance summarized in Table 11. Table 11. Network Performance Summary: Effect of Sliding Time Window (Figure 12) Variable Throughput, Flow Split Optimization (Clo ) 0.01 U.S.$/kg, CE ) 0.1 U.S.$ kW-1 day-1)

Table 12. Network Performance Summary: Cleaning during Shutdown, Benefit on Start-up (Scenario: Clo ) 0.01 U.S.$/kg, CE ) 0.1 U.S.$ kW-1 day-1, pump OD 5%)

construction

average CIT (°C) average network heat duty (MW) fouling penalty cost (million U.S.$) number of cleaning actions

scenario

I extended until plant shutdown

II fixed, ∆ts ) 1 year

III truncated (from Table 9

204 88.3

204 88.1

204 88.1

1.2 30

1.12 27

I

II

III

HEX number

cleaning benefit for the year following start-up θ (in 1000 U.S.$)

θ - Cc (in 1000 U.S.$)

θ - 2Cc (in 1000 U.S.$)

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

22a 37.8a 24.2a 39.2a 19.2a 2.9a 3.9a 13.9a 53.3a 69.6a 71.2a 63.5a 62.3a 64.0a

-3.0 7.8a -5.8 9.2a -10.7 -27.1 -26.1 -16.1 23.3a 39.6a 41.2a 33.5a 32.3a 34.0a

-18.0 -2.2 -15.8 -0.8 -20.7 -37.1 -36.1 -26.1 13.3a 29.6a 31.2a 23.5a 22.3a 24.0a

1.02 20

Figure 13 shows the effect of the different fouling rate parameter on the heat recovered in the PHT, without any cleaning. The benefit of reducing the fouling rate is evident. This plot also serves to illustrate the uncertainty involved in these methods, because the accuracy to which fouling rates can be predicted is poor. The advantage of a simple algorithm is speed, which allows schedules to be compared, for different scenarios, in reasonable time. The network performance costs in Table 14 reflect the trends in Figure 13. The fouling costs include an anti-foulant cost of 0.1 million U.S.$/year, where appropriate. An alternative approach is to use the simulator to calculate the benefit from using anti-foulants and, hence, the scope to pay for the treatment. Cleaning in combination with anti-foulants is simulated for the cases of fouling rate reduction by (i) 10%, (ii) 20%, and (iii) 50%. The summaries in Table 15 show the expected improvement in performance over Table 15 (but little in terms of duty) and fewer cleaning actions, with 50% rate reduction

a

Units cleaned before the second campaign.

obviating the need to clean any exchangers. Cleaning makes a significant improvement only in the 10% rate reduction case: the benefit in the 20% case of 50 000 U.S.$ is unlikely to be significant given the uncertainty in the simulation parameters. These calculations illustrate how the algorithm is sensitive to the fouling model parameters. 4.4. Effect of Column Revamp. Crude distillation units are often revamped or retrofitted to increase capacity or enhance


Ishiyama et al.

Table 13. Network Performance Summary for a Second 3 Year Campaign (Operation after Shutdown), Cleaning with Flow Split Optimization (Clo ) 0.01 U.S.$/kg, CE ) 0.1 U.S.$ kW-1 day-1), OD 5% (Figure 13) HEXs cleaned during plant shutdown scenario

I

average CIT (°C) average network heat duty (MW) fouling penalty cost (million U.S.$) number of cleanings penalty cost + cleaning cost during shutdown (million U.S.$)

II

III

none

204 88.1

203 87.8

202 86.7

201 86.6

1.02

1.00

1.10

1.60

20 21 24 28 1.02 + 14 × 1.01 + 10 × 1.10 + 6 × 1.60 0.02 ) 1.30 0.02 ) 1.20 0.02 ) 1.22

Figure 13. Effect of anti-foulants on network performance: total network heat duty versus time. Performance summarized in Table 14. Table 14. Simulating Anti-foulant Action: Network Performance Summary, No Cleaning (Clo ) 0.01 U.S.$/kg) (Figure 13) fouling rate parameter, a (m2 K kWh-1) 4100 (base case, 3690 3280 2050 6150 no anti-foulant) (-10%) (-20%) (-50%) (+50%) average CIT (°C) average network heat duty (MW) fouling penalty cost (million U.S.$) CPU time (s)

200 85 2.31 68

202 86.7

204 88.0

1.61

211 91.7

0.98

65

68

0.51 61

191 77.7 9.39 72

Table 15. Simulating Anti-foulant Action: Network Performance Summary, Cleaning with Flow Split Optimization (Clo ) 0.01 U.S.$/kg) fouling rate reduction by average CIT (°C) average network heat duty (MW) fouling penalty cost (million U.S.$) number of cleaning actions CPU time (s)

10%

20%

50%

204 88.3 1.11 12 3951

205 88.5 0.92 5 3685

211 91.7 0.51 0 3421

performance. Calculation of the benefits of a column revamp should include PHT fouling considerations, because this can influence its operation markedly. Column revamps have mostly been considered simultaneously with heat integration (Liebmann et al.27) and retrofit (Barletta et al.28) Here, we demonstrate how the simulator is used to quantify changes in network operation caused by a simple column revamp. Barletta et al.28 reported a case study in which the flows of diesel

Figure 14. Effect of column revamp on scheduling: (a) CIT variation over time and (b) schedule, for different energy costs CE ) 0.1 U.S.$ kW-1 day-1. Variable throughput (pump OD 5%), flow split optimization. Performance summarized in Table 16. Table 16. Simple Column Revamp Study (Clo ) 0.01 U.S.$/kg) (Figure 14) average CIT (°C) average network heat duty (MW) fouling penalty cost (million U.S.$) number of cleaning actions CPU time (s)

before revamp

after revamp

204 88.1 1.02 20 4123

205 88.4 1.07 23 4265

(gas oil) and atmospheric residue were changed. Their revamp is represented here by increasing the hot stream (diesel) flow rate to HEX 10/13 by 15% and reducing the flow to HEX 11/14 by the same amount. The increase in flow rates in 10/13 increases the surface temperatures in these units and consequently the fouling rate. The revamp scenario was simulated, and the results are presented in Figure 14 and Table 16. The increase in fouling rate in HEX 10/13 requires more frequent cleaning in these units, offsetting the other benefits of the revamp. Figure 14b shows that the HEXs 10-13 perform worse after the column revamp (compare to scenario i in Figure 9 and the first column in Table 16). The simulation can thus be used to identify which HEXs require reconfiguration following a column revamp, where fouling plays a significant part in the economics of PHT performance. 5. Conclusions The scheduling of heat exchanger cleaning in crude distillation unit preheat trains on the basis of techno-economic analyses (27) Liebmann, K; Dhole, V. R.; Jobson, M. Integrated design of a conventional crude oil distillation tower using pinch analysis. Trans. Inst. Chem. Eng., Part A 1998, 76, 335–347. (28) Barletta, T.; Smith, M.; Macfarlane, C. Crude unit revamp increases diesel yield. Pet. Technol. Q. 2004, Spring, 45–51.


incorporating both thermal and hydraulic performance has been investigated. A network simulator tool has been constructed, incorporating both thermal and hydraulic features, as well as the dynamics in the fouling rate. Cleaning action scheduling employed a “greedy” optimization algorithm modified from that proposed by Smaïli et al.8 The tool was tested by applying it in a series of case studies corresponding to practical refinery situations. The impact of fouling on hydraulics can have significant effects when a preheat train has parallel streams and the pressure drop across the heat exchangers is large. The simulation tool was able to incorporate these aspects, as well as the use of more powerful pumps. Scheduling is an optimization problem, and the results are determined by the formulation of the objective function. The relative costs of energy and lost production (reduced throughput) on scheduling have been demonstrated: some of the results are unlikely to be attractive in practice, but this should be addressed in the formulation of the objective function and the constraint set adopted. The particular issue of scheduling near a plant shutdown has been considered in depth, and a number of approaches have been tested. Again, the most attractive result will be determined by the practice and preference of the operator. Fouling mitigation strategies including the use of anti-foulants and simple column revamps were investigated. Management decision-making requires quantitative operability indicators of the improvement in performance offered by such measures, and thus, the tool has been used to generate these data. The method of simulating anti-fouling, by adjusting the fouling rates, demonstrates the sensitivity of the results to the fouling model used. This work on revamps introduces interaction between the preheat train and the crude tower. The ultimate aim in refinery applications will be to optimize the combined distillation/heattransfer system, with additional degrees of freedom being exploited in the tower (i.e., draw rates) and using the available heat duty optimally. The first step on this path must be to demonstrate that the preheat train subsystem can be solved reliably and at the correct level of detail. We would suggest that this paper demonstrates this to be the case, so that the more complex task can now be addressed. Acknowledgment. Funding from EPSRC project EP/D50306X and financial support for EMI from the Cambridge Overseas Trust is gratefully acknowledged, as well as helpful discussions with Dr. Graham Polley and Simon Pugh of IHS-ESDU.

Nomenclature a′ ) constant, A ) heat-transfer area, m2 a ) constant in fouling model, m2K kW-1h-1 b′ ) constant, m3.75-4 kg-(0.75-1) s-(0-0.25) b ) constant in fouling model, m2K kW-1h-1 Pa-1 Cc ) cleaning cost, U.S.$/clean CE ) energy cost, U.S.$/MJ Cf ) Fanning friction factor (calculated via eq 5) Clo ) lost opportunity cost, U.S.$/kg CM ) maintenance cost, U.S.$/day Cp ) specific heat capacity, J kg-1 K-1 d ) tube diameter, m e ) surface roughness, m err ) error involved in the fouling resistance estimation, m2 K W-1 E ) activation energy, kJ/mol g ) gravitational acceleration, m/s2 G ) greedy objective function, U.S.$ h ) film heat-transfer coefficient, W m-2 K-1 H, Hs ) head developed by the pump, shut off value, m L ) tube length, m M ) shell-side mass flow rate, kg/s Kg-1

M-1

Energy & Fuels, Vol. 23, 2009 1337 m ) crude oil mass flow rate, kg/s n ) constant Nc ) number of cleaning actions Np ) number of time periods Npass ) number of tube-side passes Ns ) number of sliding time periods NTU ) number of transfer units Obj ) objective function value, U.S.$ p1 ) constant in pump equation, m p2 ) constant in pump equation, m s2 kg-2 Pr ) Prandlt number, defined by eq 3 Qfurnace ) furnace heat duty, MW QHex ) heat exchanger duty, MW Q ) network heat duty, MW r ) impeller radius, m R ) gas constant, kJ mol-1 K-1 Rf ) fouling resistance, m2 K W-1 R˙f ) fouling rate, m2 K J-1 RW ) wall resistance, m2 K W-1 Re ) Reynolds number, defined by eq 2 t ) time, day tf ) time at plant shutdown, day T ) temperature, K um ) mean flow velocity, m/s U ) overall heat-transfer coefficient, W m-2 K-1 Subscripts acceptable ) acceptable value cl ) clean cleaning ) period when a HEX can be taken off line for cleaning current ) current value design ) design condition ends ) tube bends f ) fouled state film ) film HEX ) heat exchanger i ) internal/ith period j ) jth period o ) external/outer operation ) period where all of the HEXs are in operation piping ) across pipes, valves, and other fittings t ) at a time instance, t ∆t ) at a time interval, ∆t target ) target value tubes ) across tubes/pipes Superscripts * ) reference state Greek Letters R ) pressure drop distribution ratio γ ) estimated benefit, U.S.$ δ ) thickness of the foulant layer, m ε ) effectiveness λc ) thermal conductivity of the crude, W m-1 K-1 λf ) thermal conductivity of the foulant material, W m-1 K-1 µ ) dynamic viscosity, kg m-1 s-1 F ) density, kg/m3 τw ) wall shear stress, Pa υ ) kinematic viscosity, m2/s ω ) rotational speed, rad/s Γ ) total network fouling penalty, U.S.$ ∆G ) greedy decision threshold parameter, U.S.$ ∆P ) pressure drop, Pa ∆t ) time gap, days ∆tw ) time window, days Θ ) cleaning benefit for the year following startup, US$ EF8005614

Platform for Techno-economic Analysis of Fouling Mitigation Options

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