Control System Design for Furnaces with Multiple Parallel Passes

Article pubs.acs.org/IECR

Control System Design for Furnaces with Multiple Parallel Passes Ojasvi, Aryan Kumar, and Nitin Kaistha* Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208106, India S Supporting Information *

ABSTRACT: Systematic control system design for process furnaces with multiple parallel tube-passes is addressed. The control objectives are to regulate furnace outlet temperature while holding the temperature rise across the individual tubes to be the same (tube-pass heat load balancing). With respect to furnace throughput (Ftot), two operating scenarios are considered: (1) Ftot is held constant, and (2) short-term transient variability in Ftot is acceptable. Alternative control structures, CS1 for scenario 1 and CS2−CS3 for scenario 2, are synthesized and quantitatively evaluated for their closed-loop dynamic performance to expected load/servo changes. The scenario 1 heat load balancing problem is shown to exhibit strong multivariable dynamic interaction, and the control benefit of dynamic matrix control is quantified. On the basis of the results, the suitability of the alternative control systems in industrial settings is discussed.

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INTRODUCTION Furnaces are used in the process industry to heat process fluids to high temperatures. Industrial scale process furnace designs often employ multiple burners and parallel tube-passes to handle the high throughputs. Efficient and safe furnace operation requires appropriate distribution of the flows through the parallel passes such that the temperature rise across all the tubes is the same. This is referred to as balancing the heat loads of the parallel passes. It is essential as large imbalances can cause overheating induced pipe buckling with possible catastrophic failure in extreme cases. There also exists economic incentive for tight heat load balancing as it promotes more uniform fouling of the parallel tube-passes, prolonging its continuous operation period until the next cleanup. It also benefits smooth and economic operation of the downstream units. Notwithstanding the relevance of furnace parallel-pass heat load balancing to both safe and economic process operation, the open literature on it is very scarce. The only two open literature articles are by Wang and co-workers.1,2 In their heat load balancing control implementation, appropriate temperature differences are controlled to zero. The changes in the tube-pass flows are made such that the total flow remains constant. This is a highly multivariable interactive control problem as any change in the flow of a pass necessarily disturbs the heat load to one or more other passes for constant total flow rate (throughput). Even as the multivariable control problem is an ideal candidate for advanced model-based control, only traditional decentralized PID control has been studied. The benefit of advanced modelbased multivariable control for furnace heat load balancing thus remains largely untested. This is quite surprising as refinery personnel as well as DCS vendor booklets usually claim the furnace parallel pass load balancing control problem to be ideal for reaping advanced control benefits. © XXXX American Chemical Society

The apparent lack of open literature on furnace parallel pass heat load balancing, including the benefit of advanced control, motivated us to look at the control problem afresh. In this work, we systematically analyze the problem to develop effective control systems for multiple tube-pass furnaces with particular emphasis on quantifying the control benefit of advanced model predictive control (MPC). We consider two typical industrial

Figure 1. Furnace with multiple parallel tube-passes. Received: January 20, 2016 Revised: April 4, 2016 Accepted: April 7, 2016

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DOI: 10.1021/acs.iecr.6b00272 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research scenarios for furnace operation. In scenario 1, the throughput is tightly controlled at the desired value and therefore is not a

control degree of freedom (dof). In scenario 2, short-term variability in the throughput around its desired value is considered acceptable so that it may be allowed to vary for, e.g., tighter temperature control. In the following, we first briefly describe the furnace control problem, including qualitative operational requirements, and the consequent prioritization of the control objectives for the two industrial operating scenarios. Alternative control structures are then developed for regulating the prioritized control objectives for the two scenarios, including MPC for heat load balancing. The closed-loop performance of the control systems is then evaluated and compared for a three parallel tube-pass gas fired furnace for expected load/servo changes. We conclude with a summary of the main findings.

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CONTROL PROBLEM DESCRIPTION Consider a furnace with K parallel tube-passes as in Figure 1. We then have K + 1 manipulated variables (MVs), namely, the K tube oil flows, F = [F1 ... Fk ... FK], and the furnace firing rate, Q.

Figure 2. Temperature difference of adjacent tubes for heat load balancing.

Figure 3. Control structure 1 (CS1). B


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Industrial & Engineering Chemistry Research These K + 1 control dofs can be used to hold K + 1 controlled variables (CVs) at set point. In general, the furnace operational requirements are the following: (1) The total oil flow rate (Ftot = ∑Fk), or throughput, must be regulated to the desired value. (2) The oil outlet temperature (T) post mixing of the tubepasses must be tightly controlled. (3) The temperature rise across all tube-passes should be the same. These operational requirements correspond to throughput, furnace outlet temperature, and parallel tube-pass heat load balancing as the control objectives. Available measurements include the flow through each of the tubes (Fk), the tube outlet temperatures (Tk), and the furnace outlet temperature post tubepass mixing (T). For throughput control, typically there are two scenarios. In the more common scenario 1, the tightest possible throughput control at the desired value is required. The total flow through the furnace is then fixed and is not a control dof. In the less common scenario 2, loose regulation of throughput around the desired value is acceptable so that the throughput may be allowed to vary for, e.g., tighter furnace temperature control or heat load balancing. Scenario 1: Control System Design. Scenario 1, where the total process fluid flow through the furnace is constant, ensures negligible flow variability to the downstream unit, aiding its stable, smooth, and economic operation. Typically the unit immediately downstream of the furnace is crucial in the plantwide context as any flow variability to the unit gets propagated to the connected downstream units and onward to the associated material/energy recycle loops. “Local” flow transients then end up disturbing the entire plant or, in integrated industrial complexes, large sections of the entire complex. Examples of such crucial units that are usually operated at constant throughput include a refinery crude distillation unit/fluid catalytic cracker or a highly exothermic hot reactor in a chemical plant. Control Structure 1 (CS1). A fixed furnace throughput, Ftot, takes away one control dof, and we are left with K dofs for parallel-pass heat load balancing and furnace outlet temperature control. For heat load balancing at a fixed Ftot, a straightforward option is to drive the temperature difference between adjacent tube-passes to zero. In other words, the heat loads on the tubes are balanced if the adjacent tube temperature difference ΔTk = Tk - Tk+1 is zero for all k = 1 to K − 1 (see Figure 2). This implies that all the tube outlet temperatures are equal, i.e., T1 = T2 = ... = Tk = ... = TK. Even as the value of all the Tk’s is the same, the value itself can change. Consider a nonzero positive ΔTk, implying Tk > Tk+1. To drive ΔTk to zero, Tk must be reduced, and Tk+1 must be increased implying that Fk must be increased and Fk+1 must be decreased. Thus, Fk and Fk+1 must be changed in opposite directions to force Tk and Tk+1 toward each other. Forcing the requested change in Fk and Fk+1 to be of the same magnitude but opposite signs ensures both a constant Ftot and a vanishing difference between Tk and Tk+1. Thus, for a heat load balancer that demanded change ΔFkHBC in Fk, a simultaneous change of −ΔFkHBC is implemented in Fk+1. Since Tk affects ΔTk = Tk − Tk+1 and ΔTk−1 = Tk−1 − Tk, the total implemented change in the kth tube flow for heat load balancing control is given by

Figure 4. Control structure 2 (CS2).

is zero for a constant Ftot. To effect an Ftot change of magnitude ΔFtot, all tube flows are changed proportionately so that we have ΔFk = ΔFk* + rk ΔFtot

with the instantaneous flow ratio, rk = Fk/Ftot. The set point FtotSP is used to effect a throughput change. This leaves the furnace duty set point (QSP) as an available control dof. It is manipulated to hold the furnace outlet temperature T. The obtained control structure, CS1, is shown in Figure 3. In CS1, since the heat load balancing controller (HBC) is designed to make changes in the tube flows such that the total change in flow is zero, multivariable interaction exists between the ΔTk CVs. Specifically, if the HBC demands a change in Fk, an equal and opposite change to Fk+1 is also made. Both Tk and Tk+1 then change, which in turn causes ΔTk−1 and ΔTk+1 to change. If SISO ΔTk controllers are used, their combined action then ends up propagating local heat load balance disturbance on a particular tube to all the other tubes. In view of the multivariable interaction, there exists incentive to apply model-based advanced multivariable control for improved heat load balancing. Thus, in addition to a decentralized PID control, we also explore a (K − 1) by (K − 1) dynamic matrix controller (DMC) for HBC. The label, CS1DMC, is used to clearly identify the resulting control system. Scenario 2: Control System Design. Scenario 2 is usually applicable to older plants with significant surge capacity. The surge capacity helps filter out flow transients, attenuating the propagation of flow variability to downstream units. The furnace throughput may then be controlled somewhat loosely, with short-term deviations away from FtotSP being acceptable. In terms of furnace control objective prioritization, we want the tightest possible heat load balance control of all the tube-passes followed by as tight control as possible of the furnace outlet temperature and, last, the throughput. The number of available control dofs here is K + 1, including throughput. Control Structure 2. In view of the control objective prioritization above, we first pair loops for the tightest possible heat load balancing on each of the tube-passes, followed by furnace

ΔFk* = ΔFk HBC − ΔFk − 1HBC

where the second term is the correction necessary for maintaining constant throughput due to the heat load balancer demanded change in Fk−1. The total change in flow, ∑ΔFk*, then C


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Industrial & Engineering Chemistry Research outlet temperature control and finally throughput control. For the tightest possible heat load balancing, we simply maintain the outlet temperature Tk of each of the k = 1 to K tube-passes by manipulating their respective tube-pass flows, Fk. The throughput, Ftot = ∑Fk, then floats as per the demanded control action for Tk control. Note that, at a given furnace duty, Q, changing Fk affects only Tk so that there is little multivariable interaction between the Tk’s. Decentralized PID control with Tk − Fk pairings is then acceptable with very little incentive for model-based control. We choose the same set point value TkSP = TtubeSP for all k = 1 to K, so that the temperature rise across each of the tubes is the same. This set point value, TtubeSP, and the

furnace duty set point, QSP, are then the two available control dofs for controlling furnace outlet temperature (T) and the throughput Ftot to its set point. If T has higher prioritization than Ftot, we configure the dynamically fastest pairing for T control. The remaining unpaired dof then gets used for loose Ftot control. Between TtubeSP and QSP, we expect a change in TtubeSP to affect T more quickly than a change in QSP. This is because, when QSP is changed, first the combustion gas would heat up followed by the tubes heating up which in turn would cause the tube process fluid to heat up. On the other hand, as TtubeSP is altered, the individual aggressive tube outlet temperature controllers pull in more or less process fluid causing an immediate change in the furnace outlet temperature. These simple arguments then suggest T − TtubeSP and Ftot − QSP as the appropriate pairings for the prioritized control objectives. The obtained control structure, CS2, is shown in Figure 4. Control Structure 3. An alternative control structure, CS3, is obtained if the pairings for T and Ftot regulation are swapped. In CS3, T is controlled using QSP, and Ftot is controlled using TtubeSP. CS3, originally suggested by Shinskey,3 is shown in Figure 5. It has some justification when Ftot has higher prioritization over T. However, in such a case, CS1, that ensures constant Ftot, is more appropriate. Even so, we include CS3 in our study for comparison purposes. Case Study. A comprehensive quantitative dynamic evaluation of the control systems for furnace operation in scenario 1 (CS1) and scenario 2 (CS2 and CS3) is now undertaken on an example furnace. The specific example is of a three parallel tubepass gas-fired furnace. The base-case design and operating conditions are shown in Figure 6 and have been adapted from Roffell and Rijnsdorp.4 We also use their first-principles modeling approach to simulate the furnace. For ready reference, the modeling details are provided in Supporting Information. The furnace heats 270 kg/h of the process stream from 18 to 181 °C with each of the three identical parallel passes receiving 1/3 of the process fluid. The furnace heat duty is 600 kW.

Figure 5. Control structure 3 (CS3).

Figure 6. Case-study furnace base-case conditions. D


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Figure 7. Open-loop step responses for heat load balancer: (a) CS1, (b) CS2 and CS3.

The first step in designing the overall furnace control system is configuring the heat load balancer. Figure 7 shows the relevant open-loop step responses for the CS1−CS3 heat load balancer. In CS1, ΔT1 = T1 − T2 and ΔT2 = T2 − T3 are regulated by manipulating ΔF1HBC and ΔF2HBC, respectively. Note that for

maintaining constant Ftot, the control system changes F2 and F3 by −ΔF1HBC and −ΔF2HBC, respectively (see Figure 3). The corresponding open-loop step responses in Figure 7a clearly show symmetric multivariable interaction between the CVs. In CS2 and CS3, the pass outlet temperatures, T1, T2, and T3, are E


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Industrial & Engineering Chemistry Research regulated using F1, F2, and F3, respectively. The corresponding open-loop step response in Figure 7b shows that Fk only affects Tk with no effect on Tj≠k so that the heat balancer has negligible multivariable interaction. All Tk − Fk control loops in CS2 and CS3 are therefore decentralized and tuned individually. The control systems CS1−CS3 are systematically tuned using the sequential tuning approach. First, the heat load balancer is tightly tuned with all other loops open. The next prioritized control loop is then tuned with the heat load balancer on automatic. This corresponds to tuning the T − QSP, T − TtubeSP, and Ftot − TtubeSP in CS1/CS1DMC, CS2, and CS3, respectively. In CS1/CS1DMC, no further loops remain to be tuned. In CS2 and CS3, the last remaining loop, namely, Ftot − QSP and T − QSP, respectively, are tuned with all other loops on automatic. The specific tuning of the various loops in the control structures is now described. In CS1, the two PID ΔT control loops use the same tuning since all the tube-passes are similar. With both loops under P only control, the identical controller gain is increased until there are sustained oscillations. The controller gain, reset time, and derivative time for both controllers is then set to its Zeigler− Nichols (ZN) settings. For 2 × 2 DMC5−7 control of ΔT1 and ΔT2 in CS1DMC, the step response coefficient-based control calculation cum move implementation is executed every 1 s. At every execution step, the set point reference trajectory is generated as

Table 1. Detailed Controller Specifications CS1 CS2

CS3

CS1DMC

MV

Kp

Ti (Sec)

Td (Sec)

Fk Q Fk Q TkSP Fk Q TkSP P 400

2.1 (kg h−1) °C−1 39 KW °C−1 4.68 (kg h−1) °C−1 1.50 KW (kg h−1)−1 8.28 °C °C−1 4.68 (kg h−1) °C−1 33 KW °C−1 0.60 °C (kg h−1)−1 αk 0.50

50 70 45 60 110 45 80 90 γk 2

12.5 17.5 15 17.25 27.5 15 20 22.5 sample time 1s

Table 2. Time Normalized IAE and Maximum Deviation (MD) for CVs #CS CS1 CS1DMC CS2 CS3

ΔTk , i ref = ak ΔTk , i − 1 + (1 − ak )ΔTk SP

CS1

where ΔTk,0 is the current measured ΔTk, ΔTkSP is the set point (ΔTkSP = 0 always), and the prediction horizon index i = 1, 2, ..., P. The DMC calculates the future control moves ΔFk,j for j = 0 to M (M, control horizon; M < P) to minimize

CS1DMC CS2

J = ∑∑(ΔTk , i − ΔTk , i ref )2 + ∑∑ λk ΔFk , j 2

CS3

subject to the constraints CS1

−20 kg/h/s ≤ ΔFk , i ≤ 20 kg/h/s 0≤

CV ΔTk T Tk Ftot T Tk T Ftot M 100

CS1DMC

∑j ΔFk ,j ≤ 180 kg/h

CS2

Of the calculated optimal ΔF* move, the current move ΔF0 = [ΔF1,0 ΔF2,0 ... ΔFk,0 ... ΔFK,0] is implemented. The whole cycle is repeated at the next execution instant. For the reference trajectories, we use α1 = α2 = 0.5. Similarly, the move suppression factors λ1 and λ2 for ΔT1 and ΔT2 are kept the same, since all tubes are similar at the base-case design, and adjusted for a slightly oscillatory servo response. In CS2 and CS3, the heat load balancing tube temperature PID control loops are tuned to their individual ZN settings. Since all the tubes are similar, the three tube temperature control loops use the same tuning. In CS1/CS1DMC and CS2, the PID T−QSP loop for furnace outlet temperature control is tuned next to its ZN setting with the HBC on automatic (Ftot loop on manual). Similarly, in CS3, the Ftot−TtubeSP loop is next tuned to its ZN setting (heat load balancer on automatic; T loop on manual) since Ftot has higher prioritization over T in CS3. Finally, the Ftot−QSP and T−TtubeSP loops in CS2 and CS3, respectively, are tuned to their respective ZN settings with all other loops on automatic. The salient controller parameters obtained as discussed above are reported in Table 1. The control systems are now evaluated for their closed-loop load change and servo responses.

CS3

CS1 CS1DMC CS2 CS3

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metric

ΔT1

ΔT2

T

+10% Throughput Change IAE 0 0 4.615 MD 0 0 5.08 IAE 0 0 4.7006 MD 0 0 5.04 IAE 0 0 0.657 MD 0 0 0.88 IAE 0 0 5.168 MD 0 0 6.68 +5 °C Temperature Set Point Change IAE 0 0 4.819 MD 0 0 3.1 IAE 0 0 4.922 MD 0 0 3.1 IAE 0 0 1.34 MD 0 0 0.8 IAE 0 0 5.304 MD 0 0 3.2 30% Step Change in Heat Uniformity IAE 2.266 1.516 0.052 MD 2.1 1.6 −0.04 IAE 0.534 1.017 0.0454 MD 0.25 0.5 −0.025 IAE 3.061 0.7762 0.008 MD 1.75 0.45 0.013 IAE 1.3431 0.340 0.059 MD 1.6 0.4 −0.03 Extreme Fouling in a Particular Tube IAE 0.929 1.8552 0.0341 MD 1.1 1.65 −0.02 IAE 0.374 1.102 0.0307 MD −0.2 0.5 −0.015 IAE 0 2.822 0.0056 MD 0 1.6 0.005 IAE 0 2.827 0.048 MD 0 2.2 −0.03

Ftot 0 0 0 0 19.47 7.6 5.596 10.5 0 0 0 0 9.731 −19.68 1.6496 1.5 0 0 0 0 0.238 −0.2 0.0156 0.01 0 0 0 0 0.1627 −0.12 0.0172 0.01

CLOSED-LOOP RESULTS The closed-loop performance of the different control systems is tested for the following principal load/servo changes: (1) a 27 kg/h (10%) step increase in the desired throughput (FtotSP), (2) a 5 °C furnace outlet temperature set point (TSP) step increase, (3) a 30% step nonuniformity in heat distribution to the tubes, and (4) extreme fouling step change for a particular tube. F


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Figure 8. Closed-loop response for +10% throughput step change.

respectively (disturbance 3 above). To simulate extreme fouling of a particular tube (disturbance 4), the f value of that tube is reduced below 1. Here, we consider a step reduction in f 3 to 0.60 (tube 3 fouled 40%). It is highlighted that the factor f k = 1 refers to the nominal heat flux to the kth tube. It is therefore possible that f k > 1. For example internal “localized” eddies (internal flow nonuniformity) give extra convective heat flux to a particular tube. It is also possible that the radiation view factor for a certain tube is higher so that its radiation heat flux is more than nominal. Also, if the tubes are cleaned, then the tube heat transfer resistance goes to zero. If the nominal tube heat transfer coefficient corresponds to a

Nonuniform heat distribution and extreme fouling of a particular tube are simulated as follows. In the furnace model, the actual heat transfer rate to the kth tube is obtained as qk actual2tube = fk . qk tube

where the term qktube is obtained using radiation and convection heat transfer theory (see Supporting Information for modeling details). For nonuniformity in tube heating, the premultiplier, f k (default base-case value = 1), is changed appropriately. For example, altering the f k values to 1.3, 0.9, and 0.8 for tubes 1, 2, and 3, respectively, simulates 30% extra heating rate of tube 1 with 10% and 20% lower heating rate of tubes 2 and 3, G


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Figure 9. Closed-loop response for +5 °C TSP step change.

where yf is the final steady state value at which the CV settles. The normalization of the numerator (conventional IAE) by the time duration over which integration is performed (τ, which is 1500 s here) makes IAEt independent of the time units used. The data in the table clearly shows that CS1/CS1DMC achieves furnace operation at the desired constant throughput (scenario 1), as reflected in the zero Ftot IAE values for the 4 load/servo changes above. For FtotSP and TSP changes, the T IAE values of CS1 and CS1DMC are very similar implying no difference in decentralized PID or DMC heat load balancing. This is because all Tk’s move in tandem due to the identical nature of the tubes, when Ftot is changed and when QSP is changed by the T−QSP controller.

somewhat fouled tube, which is what an average tube would be, then a clean tube would have f k > 1. The closed-loop response of CS1/CS1DMC, CS2, and CS3 is obtained for the above load/servo changes. A concise quantitative comparison of CS1/CS1DMC, CS2, and CS3 control performance is provided in Table 2, which reports the time normalized IAEt and maximum deviation of ΔT1, ΔT2, T, and Ftot for the various load/ servo changes. The time normalized IAE of a CV, y, is calculated as τ

IAEt =

∫0 |y − yf | dt τ H


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Figure 10. Closed-loop response for nonuniform heat distribution to tubes.

Thus, ΔT1 and ΔT2 are essentially zero during the transients, which is evident in their near zero IAE values. With no error developing in ΔT1 and ΔT2 for the FtotSP and TSP changes, the heat load balancing control algorithm (2 × 2 decentralized PID or DMC) makes no control moves, and the CS1 and CS1DMC responses are essentially the same. For nonuniform heating and extreme tube fouling, the tube characteristics become different. Error then does develop in ΔT1 and ΔT2, and the heat load balancing control algorithm makes a noticeable difference to the variability in the tube outlet and furnace outlet temperatures. The response metrics in Table 2 suggest that parallel pass heat load balancing is far superior for CS1DMC compared to CS1. The same may be attributed to DMC effectively compensating for the strong multivariable interaction between ΔT1 and ΔT2. With ΔT1 and ΔT2 controlled tightly close to zero, the deviation

in T is smaller so that its transient maximum deviation is also lower. For furnace operation in scenario 2 (transient variability in throughput is acceptable), both CS2 and CS3 take the process to the desired FtotSP and TSP in 10−15 min. The Table 2 IAE and maximum CV deviation values suggest that, in comparison to CS3 and CS1/CS1DMC, CS2 provides noticeably tighter furnace outlet temperature control. This however comes at the cost of higher transient variability in throughput. This is expected as in CS2, the dynamically fastest MV (TtubeSP) is paired for controlling the T. In CS1/CS1DMC and CS3, on the other hand, the dynamically slower T−QSP pairing is used, resulting in loose T control. For completeness, the dynamic response of CS1, CS1DMC, CS2, and CS3 to the four principal load/servo changes is shown in Figures 8 −11. The throughput change and TSP change I


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Figure 11. Closed-loop response for extreme fouling of tube 3.

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DISCUSSION The closed-loop results clearly suggest that, for scenario 1 furnace operation (constant Ftot), CS1DMC should be the preferred control structure. Model-based controllers are however notorious for their fragility to increasing levels of plant-model mismatch. In the present case, the furnace would slowly drift over prolonged operation due to fouling, coking, etc. This drift implies increasing mismatch between the identified and actual DMC step response coefficients. To test the robustness of the tightly tuned DMC heat load balancer, we tested its performance for nonuniform heating/extreme fouling disturbances with the

responses complete within 600 s (10 min) for all the control structures. The heating nonuniformity and extreme tube fouling disturbance responses take longer (∼15 min) to complete. The plots also show that Ftot is (near) perfectly controlled in CS1 and CS1DMC with no variability. Also, tightest furnace outlet temperature control is achieved by CS2 in all cases with noticeably larger variability in Ftot. Lastly, the best heat load balancing, as reflected in lower variability in ΔT1 and ΔT2, is achieved in CS1DMC demonstrating the benefit of model-based compensation of multivariable interaction for tighter heat load balancing. J


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Industrial & Engineering Chemistry Research steady throughput changed by ±30% over its base-case throughput. For the DMC tuning reported in Table 1, even as larger ΔT1 and ΔT2 deviations occur, these deviations remain comparable to retuned SISO PID ΔT controllers at the altered throughputs. We also found that CS1DMC works well for ±10% throughput step change as well as ±5 °C TSP change with one or all tubes significantly fouled. The DMC tuning is thus deemed robust. For scenario 2 operation, CS2 is recommended as it is a simple decentralized control system that achieves tight furnace outlet temperature control with loose throughput regulation. Note that if the Ftot−QSP loop is put on manual, then QSP acts as the throughput manipulator in CS2. In cases where maximum throughput operation is desired with maximum furnace duty (QMAX) as the bottleneck constraint limiting throughput, we simply set QSP at QMAX, and the furnace automatically processes the maximum throughput possible. In CS1 and CS3, on the other hand, since QSP is manipulated to regulate T, QSP hitting QMAX implies loss of furnace outlet temperature control, which is not acceptable. One then needs an appropriate override to cut the process feed to ensure T remains regulated. This override, in effect, reconfigures CS1 and CS3 to CS2. CS2 is then the most natural control structure for operating the furnace at maximum throughput while ensuring tight heat load balancing and furnace outlet temperature control. In the literature, it has also been recommended that, instead of controlling the temperature difference between adjacent tubes for heat load balancing, the difference between the tube outlet temperature and overall furnace outlet temperature (Tk − T) be controlled by manipulating the respective tube flows, Fk.2 We explored this idea in some detail and found it to be inherently flawed. The basic problem is overcontrol that is inconsistent with the process degrees of freedom. Consider the (Tk − T) − Fk pairing-based heat load balancer in Figure 12. Assume that QSP is

To appreciate the potentially severe consequences of the above, consider a negative bias in the first tube outlet temperature measurement (T1) of our example three pass furnace, initially at the base-case steady state. With the bias, the sensed T1 becomes less than T, and to push it back to T, the corresponding (T1 − T) controller decreases F1. This causes T to increase since Ftot has reduced slightly (Q is held constant). With T slightly reduced, T2 and T3 are above T, and the corresponding controllers cause F2 and F3 to decrease. Thus, at constant Q, a small negative (positive) bias in T1 causes an unmitigated reduction (increase) in the flow through all the tubes (throughput) via the action of the flawed heat load balancer. The unmitigated throughput reduction translates to an unmitigated increase in T. If Q is manipulated to hold T, Q would reduce to hold T constant. This however does not have any effect on the unmitigated reduction in throughput via the action of the (Tk − T) controllers so that eventually the furnace shuts down with either the tube flow valves or the furnace duty valve fully closed. Thus, if any of the Tk measurements is biased, the flawed heat load balancer ends up integrating the bias causing a large drift in the furnace throughput. The overcontrol induced integration of the sensor bias is shown in Figure 13 for a −0.2 °C bias in T1 for the example furnace.

Figure 13. Illustration of sensor bias integration with (Tk − T) as CVs for example furnace.

As a way around this overcontrol problem, one can suggest that no control loop be implemented to regulate (TK − T) and it be allowed to float. Then, noticeably larger transients occur in (TK − T) compared to the other controlled (Tk − T), k ≠ K CVs (data not shown). The Kth tube then suffers greater heat load imbalance compared to the other tubes and is likely to foul more quickly. This defeats the heat load balancing objective of more uniform tube fouling across all the tubes. The illustration highlights the potential pitfalls in the proper design of consistent and robust furnace control system with proper heat load balancing across all tubes.

Figure 12. Control system with heat load balancing by driving (Tk − T) to zero.

fixed. The overcontrol problem arises as when the (Tk − T) CVs are zero for k = 1 to K − 1, the last remaining CV, (TK − T) must also necessarily equal zero. In other words if the first K − 1 tube outlet temperatures equal the furnace outlet temperature, T, then TK must necessarily equal T. By also forcing (TK − T) to zero using a control loop, we end up overcontrolling the process. K


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CONCLUSION In this work, we have considered control system design for furnaces with parallel tube-passes with two operating scenarios, namely, constant throughput (scenario 1) and operation with transient variability in throughput (scenario 2). For scenario 1, controlling the adjacent tube temperature differences to zero by appropriately manipulating tube-pass flows provides a simple means of furnace parallel pass heat load balancing. The furnace duty (Q) then gets used for furnace outlet temperature (T) control (CS1). The use of DMC to compensate for multivariable interaction between the ΔTs (CS1DMC) significantly improves heat load balancing control. For scenario 2, the individual tubepass flows are manipulated for holding the tube outlet temperature with each of the tubes at the same set point (TtubeSP). Using the T−TtubeSP and Ftot−QSP pairings (CS2), closed-loop results show that the tightest possible T control is achieved at the expense of relatively larger variability in Ftot.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b00272. First-principles furnace dynamic model details (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +91-512-2597513. Fax: 0512-2597432. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support from the Ministry of Human Resource Development, Government of India, is gratefully acknowledged. REFERENCES

(1) Wang, X.; Zheng, D.-Z. Diffrence Control of Parallel Stream Temperatures. J. Process Control 2005, 15 (5), 531−536. (2) Wang, X.; Zheng, D.-Z. Load Balancing Control of Furnace with Multiple Parallel Passes. Control Eng. Practice 2007, 15 (5), 521−531. (3) Roffel, B.; Rijnsdorp, J. E. Dynamics and Control of a Gas-Fired Furnace. Chem. Eng. Sci. 1974, 29 (10), 2083−2092. (4) Shinskey, F. G. Process Control Systems: Application, Design, and Tuning, 4th ed.; McGraw Hill Inc.: New York, 1996. (5) Cutler, C. R.; Ramkar, B. L. Dynamic Matrix ControlA Computer Control Algorithm. In Proceedings of Joint Automatic Control Conference; San Francisco, CA, 1980. (6) Garcia, C. E.; Morari, M. Internal Model Control. A Unifying Review and Some New Results. Ind. Eng. Chem. Process Des. Dev. 1982, 21 (2), 308−323. (7) Qin, S. J.; Badgwell, T. A. An Overview of Industrial Model Predictive Control Technology. AIChE Symp. Ser. 1997, 93 (316), 232− 256.

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Control System Design for Furnaces with Multiple Parallel Passes

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