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A comparison of a novel robust decentralized control strategy and MPC for industrial high purity, high recovery, multi-component distillation

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Abstract: In this work we have developed a novel, robust practical control structure to regulate an industrial methanol distillation column. This proposed control scheme is based on a override control framework and can manage a non-key trace ethanol product impurity specification while maintaining high product recovery. For comparison purposes, an MPC with a discrete process model (based on step tests) was also developed and tested. The results from process disturbance testing shows that, both the MPC and the proposed controller were capable of maintaining both the trace level ethanol specification in the distillate (XD) and high product recovery (β). Closer analysis revealed that the MPC controller has a tighter XD control, while the proposed controller was tighter in β control. The tight XD control allowed the MPC to operate at a higher XD set point (closer to the 10 ppm AA grade methanol standard), allowing for savings in energy usage. Despite the energy savings of the MPC, the proposed control scheme has lower installation and running costs. An economic analysis revealed a multitude of other external economic and plant design factors, that should be considered when making a decision between the two controllers. In general, we found relatively high energy costs favor MPC.

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A comparison of a novel robust decentralized control strategy and MPC for industrial high purity, high recovery, multi-component distillation

  1. 1. Research article A comparison of a novel robust decentralised control strategy and MPC for industrial high purity, high recovery, multicomponent distillation Isuru A. Udugama a,b , Florian Wolfenstetter a , Robert Kirkpatrick a , Wei Yu a,b , Brent R. Young a,b,n a Chemical & Materials Engineering, The University of Auckland, New Zealand b Industrial Information and Control Centre, The University of Auckland, New Zealand a r t i c l e i n f o Article history: Received 19 July 2016 Received in revised form 19 January 2017 Accepted 10 April 2017 Available online 14 April 2017 Keywords: High purity Practical control Distillation control Override control MPC a b s t r a c t In this work we have developed a novel, robust practical control structure to regulate an industrial methanol distillation column. This proposed control scheme is based on a override control framework and can manage a non-key trace ethanol product impurity specification while maintaining high product recovery. For comparison purposes, a MPC with a discrete process model (based on step tests) was also developed and tested. The results from process disturbance testing shows that, both the MPC and the proposed controller were capable of maintaining both the trace level ethanol specification in the dis- tillate (XD) and high product recovery (β). Closer analysis revealed that the MPC controller has a tighter XD control, while the proposed controller was tighter in β control. The tight XD control allowed the MPC to operate at a higher XD set point (closer to the 10 ppm AA grade methanol standard), allowing for savings in energy usage. Despite the energy savings of the MPC, the proposed control scheme has lower installation and running costs. An economic analysis revealed a multitude of other external economic and plant design factors, that should be considered when making a decision between the two controllers. In general, we found relatively high energy costs favour MPC. & 2017 ISA. Published by Elsevier Ltd. All rights reserved. 1. Introduction and background The determination of control system structure is an important step in distillation control. In general, there are two main branches of control structures available: a centralized multi-input multi- output (MIMO) controller, or a set of single-input single-output (SISO) controllers. Either one of these systems can be used to control a distributed or decentralized process. In the chemical industry, a decentralized type of control system is more common than the centralized control system, as it has more captivating advantages: it is easy to understand, uses uncomplicated hard- ware, and employs simple working algorithms [1–3]. However, decentralized control schemes lack the ability to operate a system at optimal levels. Conversely, centralized types of controls, in particular Model Predictive Controllers (MPC), have the potential to operate systems at optimal levels. Despite this, there are lim- itations to using centralised controllers, some of these limitations are: higher maintenance cost, difficulties in operation, complicated structure and lack of flexibility that can result in a fragile controller that is not profitable [4–6]. In addition, the actual data gathering process required to create an MPC model in an industrial environment can be difficult and can be further complicated as it might require techniques other than simple plant step tests [7]. However, in many situations plant step testing are still the most convenient method to capture the dynamics of the process [8]. Once the relevant data is gathered, the design and tuning process of MPC type controllers are also more complex and time con- suming [9]. Even with recent advances in computer technology, the field implementation of MPC still requires specialist high-end computer platforms [10]. In methanol distillation a multi-component feed of methanol, water and ppm levels of ethanol, is refined to achieve a tight high purity product and bottoms (ppm levels) and high methanol product recovery (β) (≥97.5%). For decades, operators and control schemes only focused on maintaining product ethanol specifica- tion (XD) below the industrial AA grade limit of 10 ppm [11], while β was not actively pursued. As a safety buffer, the operators also used excess reboiler duty to create a higher than required reflux ratio which, in turn, produced product methanol with a XD of ∼4 ppm. This action provides the operators with a sufficient XD buffer and can negate the non-linear behaviours of the column. With plant management's goal of improving profitability, these Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/isatrans ISA Transactions http://dx.doi.org/10.1016/j.isatra.2017.04.008 0019-0578/& 2017 ISA. Published by Elsevier Ltd. All rights reserved. n Corresponding author at: Industrial Information and Control Centre, The University of Auckland, New Zealand. E-mail address: b.young@auckland.ac.nz (B.R. Young). ISA Transactions 69 (2017) 222–233
  2. 2. distillation columns now need to operate at improved product recoveries ( ∼99.5%) using “normal” levels of reboiler duty while maintaining the AA grade product methanol specification. New control structures will need to be developed to meet this objective of increasing profitability. To operate the column at high purity and recovery while minimizing the use of reboiler duty requires a control structure that can deal with non-linear behaviour, where a small deviation from the operating point can have a significant influence on the operability and process dynamics. As such, a linear process model and linear SISO control structure might be insufficient to describe the system dynamics and control of the column over changing operating conditions [12,13]. Thus, a classic distillation column control arrangement, such as DV control [14], can have difficulty in controlling this type of process. In [15], these difficulties were confirmed; DV control was unable to operate an industrial me- thanol distillation process at required specifications. In contrast, MPC, which was specifically developed to control complex multi- variable processes [13] should be able to control the column at new specifications. In recent years much research has been car- ried out on implementing MPC on complex distillation units. In [16] the authors had looked into the tuning parameters of MPC for an industrial crude oil distillation unit. In [17], the authors compared a MPC and decoupled PID control structure on a Me- thyl Tert-butyl Ether distillation process and found MPC was able to better control the process. In [18], the authors formulated a multi-objective optimization procedure to operate a heavy crude oil fractionator. Despite these applications and improvements, the drawbacks described previously means MPC might not be the best choice commercially. Thus, there is an incentive in the methanol industry to develop control structures that use decentralized control schemes that can operate methanol distillation columns at high recovery and high purity without the use of excess reboiler duty. The conceptual framework of override control might be one al- ternative to deal with the complex process dynamics of methanol distillation. Override control is generally used to either protect equipment from harmful conditions or to detect and correct faulty process variables from effecting controllability [3,19,20]. In both these variations, the override control “sits” above the regulatory layer and uses logic operations in determining if an intervention is necessary [20]. In this manuscript, we have developed a novel, robust, prac- tical and easy to maintain control structure, that is able to meet the tight specifications of industrial methanol distillation without the use of excess reboiler duty. The proposed scheme has two layers that consist of a PID based regulatory layer and a super- visory layer inspired by override control. The regulatory layer, together with supervisory control maintain both XD and β at their tight specifications. In this control structure, the supervisory layer addresses the “root cause” of the non-linear process dy- namics and allows the PID regulatory layer to control the process. For comparison purposes, a generic MPC with a discrete non linear process model was also developed. Once completed, both the proposed control strategy and the MPC were tested against a range of process disturbances. To conclude, the economic im- plications of choosing between MPC and the proposed control scheme were discussed. 2. Set-up In methanol refining, a multi-component feed (methanol, wa- ter, ppm level of ethanol) is refined to achieve tight high purity product and bottoms at high methanol recovery ratio (≥97.5%). In this paper, we have looked into developing control schemes that can operate the column at ≥99.5% recovery and below the 10 ppm AA grade industrial methanol specification. The feed conditions for the high-purity column are given in Table 1. To produce AA grade methanol, the distillate needs to have a methanol purity of 99.85 wt% and, more importantly, <10 ppm ethanol [11]. From a fundamental and a process control point of view, product ethanol is the “lower key” in this distillation process, meeting this specification will guarantee the necessary product methanol purity. There are also limits on other trace compounds [11]; but these compounds are distilled out of the crude methanol prior to its arrival in the main methanol refining column. Bottom discharge mainly consists of water and must not contain more than 10 ppm of methanol to satisfy waste water discharge re- strictions. To accomplish such a high distillate and bottoms purity, most of the ethanol entering the column needs to be taken out via the fusel side draw. To satisfy both the operating stability of the column and limitations on the disposal system, the mass flow of this fusel stream must be kept within −2600 3700 kg h . To maximize the profitability of the methanol production it is important to recover as much of the methanol entering the col- umn as possible in the product methanol stream. In general the ratio of methanol in the feed to methanol in the product must be at a high level (≥ )97.5% . In this paper we would call this the pro- duct recovery ratio (β) and define it as: β = ̇ ̇ · ( ) m m 100% 1 MeOH Dist MeOH Feed , , where the component mass flow rate of methanol in distillate is ̇mMeOH Dist, and the component mass flow of methanol in the feed stream is ̇mMeOH Feed, . Table 1 Industrial plant data. Value Units Feed Mass Flow 142,500 kg h Temperature 80 °C Pressure 170.8 kPa Methanol Content 82.5 wt% Water Content 17.5 wt% Ethanol Content 150 ppm Distillate Mass Flow 115,150 kg h Methanol Content 99.99 wt% Water Content 85 ppm Ethanol Content 8 ppm Fusel Mass Flow 3015 kg h Methanol Content 65 wt% Water Content 34.4 wt% Ethanol Content 0.66 wt% Bottom Mass Flow 25,485 kg h Methanol Content 5 ppm Water Content 99.94 wt% Ethanol Content 0 ppm Specifications Reflux Ratio 1.687 – Reboiler Duty 88.25 MW Methanol Recovery 98 % I.A. Udugama et al. / ISA Transactions 69 (2017) 222–233 223
  3. 3. 3. Modelling and validation Process modelling and simulation are well recognized tools for critical decision making, control design and optimization in pro- cess engineering [3,21]. In this paper, the commercial simulation software packages VMGSim and HYSYS were used to build and validate dynamic models based on the industrial plant data. In this instance the mass flow rate and reboiler duty of the industrial distillation column was used to set the mass flow rate of the dis- tillation column in the process simulation. The simulation achieved a good match in all three compositions simulated, with the all important ethanol profile being matched very closely even down at the ppm levels. This biggest miss matches are in product and bottoms water content, however, a closer looks reveals that these compositions are in ppm levels, as a large % error translates to a very small absolute error. Table 2 shows the comparison of mass fractions between the real plant and the process simulation. Once validated, the simulation was pushed towards 99.5 % re- covery and was then revalidated based on plant trials and other available data. The vapour liquid equilibrium (VLE) in the distillation column is described by an activity coefficient approach with a property package using the Wilson model. In this model, the activity coef- ficients (of each component in) the mixture were first determined to calculate the fugacity of the liquids, while a Virial equation of state was chosen to calculate the vapour fugacity. The column solver uses equilibrium and enthalpy models paired with rigorous thermodynamics in calculations. The column was simulated with sieve trays, the overall tray efficiency of the column was set at 80%, this figure was reached based on information provided by the tray manufacturer who based this estimate of the specific tray installed and the overall column loading. The Maximum flooding factor of 120% was set based on tray information received from the tray manufacturer who based this estimate on tray hydraulics. The basic PID controllers for pressure, flow and level control were also necessary to operate the column at a stable point. 4. Control configurations In this section, we will introduce both the proposed control and MPC scheme designed for the high-purity methanol distillation column. To run the plant at a maximum profit, methanol recovery needs to be maintained at a high level, while satisfying the con- straint of AA grade methanol in the distillate. In addition, the control schemes must also be able to operate the column in a stable manner. As such, both control schemes must meet the fol- lowing requirements: Maximizing/controlling methanol recovery Handling the AA grade constraint on distillate ethanol content Ability to reject disturbances in feed mass flow and composition. 4.1. Process dynamics The requirement for high β and tight XD where non key ethanol needs to be managed at ppm levels, creates unusual non-linear process behaviours. To understand these non-linearities we have plotted in Fig. 1 the response of XD to a change in β from a base case of 99.6 %. Fig. 1 shows that the process has a non-linear response for all deviations in β. Analysing the + −/ 0.07% incremental recovery curves, we can see that a positive change in β has a higher influ- ence on XD in comparison to a similar reduction in β. This confirms the non linearity of the system. The degree of non-linearity also tends to increase with bigger changes in β. Fundamentally, this behaviour is acceptable as larger positive deviations in β take the system closer to (and above) 100% β at which point the imbalance in the material and energy balance will result in a surge of XD. This phenomena is further confirmed by the comparatively steep rise of the +0.21% incremental recovery curve. Bigger negative deviations in β, however, result in a smaller influence on XD as we are already at ppm levels of ethanol. Further analysis shows that the process itself has a relatively large time constant; even after 2000 min, most of the plots have not yet reached steady state From a practical perspective, we are more interested in the time taken for XD to exceed the 10 ppm constraint if kept un- checked as AA grade product methanol needs to contain 10 ppm of ethanol. Even for a small increase in β of 0.14%, XD will exceed the 10 ppm constraint over time. As the deviation is increased to 0.21 %, the time taken for XD to reach 10 ppm reduces dramatically. 4.2. Proposed control scheme Control of a high purity industrial methanol distillation col- umn is complicated due to the high purity product specification xD, high product recovery requirements and need to minimize the reboiler duty usage. In addition, the control scheme developed needs to be industrially compatible. Standard control structures available in literature are incapable of meeting all these re- quirements. As such, in this work we developed a novel control structure that can meet all these requirements. The proposed control scheme in this paper was developed with the aim of achieving high recovery and high purity while minimizing re- boiler duty usage and in turn reducing the costs of operation. The proposed control scheme comprises of two layers: a regulatory primary layer and a supervisory secondary layer. The secondary Table 2 Plant data Vs Simulation results. Plant data Simulation Units % Error Distillate Methanol 99.99 99.99 Mass Frac (%) 0 Ethanol 8 8 ppm 0 Water 85 56 ppm 34 Bottom Methanol 5 3.2 ppm 36 Ethanol 0 0 ppm 0 Water 99.94 99.94 Mass Frac(%) 0 Fusel Methanol 65 63.4 Mass Frac (%) 2.5 Ethanol 0.66 0.66 Mass Frac (%) 0.3 Water 34.4 35.6 Mass Frac (%) 3.5 Fig. 1. Process response of product ethanol specification for changes in product recovery ratio (β). I.A. Udugama et al. / ISA Transactions 69 (2017) 222–233224
  4. 4. layer consists of a recovery constraint controller (RC) and a dy- namic reboiler controller (DR). We have used the control struc- ture developed in [15] as a start point. We will call this proposed control scheme by the acronym RCDR in the following sections. Recovery Constraint Controller - RC. The RC controller acts as a central supervisory controller that takes measurements of the current recovery ratio and the ethanol content in the distillate stream. The set point of the composition controller YSP QC, will be set depending on the state of the system. To avoid sudden set point changes of the composition controller, a rate limiter is added to the output signal of the RC controller. The maximum rate of change is set to 0.1 % min , this value was set experimentally to allow for a relatively rapid yet smooth transitions between set-points, even during quick product ethanol set point changes. The calcu- lation of the set point is based on two different cases according to the following equations. ⎡⎣ ⎤⎦ β β β β= − · · − ≤ ( ) − Y Y MHigh recovery case: 10 % if 2 SP QC SP H SP SP, 6 ⎡⎣ ⎤⎦ β β β β= − · · − ( ) − Y Y MLow recovery case: 10 % if 3 SP QC SP L SP SP, 6 Eq. (2) represents the high recovery case, where the current recovery β is higher than the specified recovery set point (βSP). In this case, the RC controller will take advantage of this beneficial situation and produce higher grade methanol with a ethanol content of 7.8 ppm. Accordingly, the set point of the composi- tion controller will be lowered. This action also ensures that the system is not running at recoveries of β 100% over long periods of time, which would be infeasible. MH, the gradient in Eq. (2), dictates the rate at which the set point will be increased for a given increase in β. Where, a large MH represents an aggressive controller. In a situation where β 99.6% we require the RC controller to bring β back to out set point in a timely manner. However, we do not require a very aggressive response as β 99.6% is financially favourable (more methanol produced), but needs to be managed as it can create potential control pro- blems in future. Based on disturbance rejection tests carried out MH is set to 2 to achieve timely response. The low recovery case is represented by Eq. (3). If the system is running at a recovery of β β SP , the RC controller will try to in- crease β by increasing the set point for the composition controller. The set point can only be increased up to the maximum ethanol content of 10 ppm. Unlike the high recovery case, the low recovery case represents a situation that is economically unfavourable. This requires the controller to intervene aggressively. To enable this, ML, the gradient in Eq. (3), has to been set to high value to enable an aggressive control response. Based on disturbance rejection tests this value has been set to 6. Fig. 2 shows a control schematic of the overall control scheme. The low recovery and high recovery equations ensure that the β is managed to be around 99.6 %. Even during sharp disturbances (as discussed in Section 6), these equations will bring β back to set point before the non-linearities can effect the column. As such, these equations deal with the reasons for non-linearities rather than their effects. Fig. 3 illustrates the overall structure of the RC controller and discusses how these two controllers act together. The flow rate of the fusel stream is also set by the RC controller element. The necessary fusel flow rate is determined by Eq. (4). In methanol distillation, 95 % of the ethanol entering the column needs to be extracted at this side draw. If this term is not met for a long period of time, there can be a major column upset due to the build-up of ethanol in the tower. ̇ = ̇ ( ) m m X 4 Fusel EtOH Feed EtOH Fusel , , In this equation, fusel mass flow rate ( ̇mFusel) is determined by the mass flow of ethanol in the feed ( ̇mEtOH Feed, ) and the con- centration of ethanol in the fusel draw ( XEtOH Fusel, ). Depending on the current feed composition, the amount of ethanol in the dis- tillate and the fusel composition, an optimal fusel flow rate can be calculated according to Eq. (4). This flow rate is implemented as the set point of the fusel flow controller. Minimum and maximum set point values of 2000 Kg/h and 3700 Kg/h respectively are en- forced to reflect practical limitations. The express objective of setting the side draw flow rate is to maintain column stability by ensuring there is no major ethanol build up in the column and not used as a manipulated variable for optimization. To better illustrate the function of the controller, we have constructed a control diagram of the RC controller in Fig. 3. The RC controller consists of two parallel controller modules. The top module deals with setting the XD controller set point, where it uses the distillate methanol flow rate and feed methanol flow rate are used as process inputs (PVs). It also requires the plant operator to set the recovery ratio (β) and product ethanol (XD) set point limits. In addition, a maximum ethanol limit also needs to be specified. Generally, this can be the AA grade me- thanol limit of 10 ppm. The dotted circle in this diagram shows the logic switch and equations used to determine the relation- ship between the recovery ratio and product ethanol specifica- tion at a given process condition. The fusel flow rate set point module is much simpler: feed ethanol mass flow and fusel ethanol concentration, together with maximum and minimum fusel flow limits, are used to determine the fusel flow set point. In addition to these functions, the RC controller also sends the current recovery ratio and recovery ratio set point information to the DR controller, as discussed below. Dynamic Reboiler Controller - DR. The DR controller comprises of a feed forward controller and a feedback trim controller. The feed forward controller increases or decreases reboiler duty based on the feed flow rate. Eq. (5) has been empirically derived to Fig. 2. Schematic of the proposed control scheme (including regulatory controllers). I.A. Udugama et al. / ISA Transactions 69 (2017) 222–233 225
  5. 5. achieve a product recovery of 99.6% while achieving a 7.5 ppm product ethanol specification. This equation was validated during plat trials where the collumn was held at 99.6% recovery for a short time period. ⎡⎣ ⎤⎦ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ̇ = · ̇ − ( ) Q m h kW 0.6707 kg 4200 5 Reb Feed In cases where feed disturbances can be measured, the feed forward controller can improve column stability. In addition, a simple feed back trim controller is used to keep track of and maintain β at set point by carrying out minor adjustments in re- boiler duty. The feedback trim controller is a basic PI type controller. Fig. 4 illustrates the control architecture of the DR controller, where a feed forward element together with a feed back trim controller is used to set reboiler duty. The controller also takes current recovery and recovery set point information from the RC controller. The feed forward element in this instance acts as a “coarse” controller, while the feed back trim acts as a “fine” con- troller. This means a simple feed forward controller is sufficient as the trim controller can deal with correcting offsets and re- acting to unmeasured disturbances. The trim controller also al- lows the DR controller to operate at different product ethanol specifications and at different recovery rates. Since the trim controller receives recovery information from RC controller, the users only have to set the desired product ethanol and product recovery ratio at the RC controller. Overall Performance. From a chemical engineering perspective the RC controller and DR controller manipulates the mass and energy balance of the column respectively. This allows RC and DR controllers to work together to achieve on specification product recovery and ethanol specification. If a process disturbance influ- ences the product recovery, the RC controller will actively manipulate the product ethanol set point to bring the product recovery back to acceptable values. At the same time DR controller would change the reboiler duty to bring the recovery rate back to set point. For example, a process disturbance which reduces pro- duct recovery, the RC controller will relax the product ethanol specification up to 10 ppm. This action allows the controller to increase product recovery rate for a short time period without breaking the product ethanol specification. If the DR controller is switched off, the RC controller will remain at ethanol set point of 10 ppm and the recovery rate will drop down to a new steady state, as the reboiler duty (energy) supplied to the column is not able to maintain the desired product recovery rate at product specification below 10 ppm. If we now switch on the DR controller, it will now increase the reboiler duty to bring the recovery back to the set point. As this happens the RC controller will slowly reduce its set ethanol set point back to its steady state level (the level is was at before the disturbances). In reality the RC and DR con- trollers work at the same time and will simultaneously increase product ethanol specification and reboiler duty to bring back the product recovery back to specification as soon as possible. As time progresses the RC controller will settle back down while the DR controller will settle to a higher reboiler duty Robustness and application. The relatively straight forward lo- gic used in the supervisory control structure was built with the ideology that if and when plant operations (control engineer/ su- pervisor) can change the heuristically tuned parameters to fit plant requirements at that time. It is authors experience that many advanced process control solutions including MPC's tend to taken off-line due to the relatively complex nature of them which re- quires routine expert support to retune. Further, disturbance tests performed in Section 6 illustrates the proposed controller is suf- ficiently robust to handle large process swings. 4.3. Model predictive controller (MPC) This section will give a more detailed overview of the im- plementation of the model predictive controller(MPC). The choice of tuning parameters for the MPC, as well as the tests conducted to obtain the dynamic process model will be discussed. The methanol distillation column can be controlled by a 2x2 multi-input multi- output (MIMO) controller, with each input affecting both outputs. The two inputs are the methanol recovery β and the ethanol content in the distillate stream. The recovery is calculated ac- cording to Eq. (1). The two outputs of the MPC are the set point for the XD controller and the reboiler duty. Process model. To build the process model, we carried out open Fig. 3. Control Diagram of the RC controller illustrating the inputs, outputs and the information flow within the controller. Where (1), (2), (3) and (4) refer to Eqs. (1), (2), (3) and (4) that are used in the RC controller calculations. Fig. 4. Control diagram of DR controller illustrating the inputs out puts and the information flow with in the controller. Where (5) refers to Eq. (5) used to in the DR controller calculations. I.A. Udugama et al. / ISA Transactions 69 (2017) 222–233226
  6. 6. loop step tests on our dynamic simulation, where we changed reboiler duty and distillate flow rate and observed its effect on XD and β. As expected, the process dynamics were relatively complex and could not be accurately estimated by a simple first order plus dead time model. Since industrial MPC modules allow the user to input the actual set response (step response data points that de- scribes a discrete transfer function), we normalised our responses and created transfer functions that were then inserted into the MPC module as the process model.The MPC module used in this particular instance is a commercial system. Tuning parameters and process variable. One distinctive fea- ture of MPC is the large amount of tuning parameters and vari- ables that needs to be set [22]. The first variable that needs to be set is the control or sampling interval k. This denotes the time interval in which the MPC will take actions. The large time con- stant of the process means a long time interval between MPC execution would be sufficient to regulate the process. The sam- pling interval value k was first set to 100 min, as this is was 1/10 th of the time constant of the smallest process time constant. However, this resulted in unfavourable results during the short term disturbances. Thus a k value of 10 min has been set based on short term cyclical disturbance tests carried out. From a practical point of view, k of 10 min is still significantly long enough for the MPC application to execute and subsequent real time measure- ments needed (especially composition measurements) can be updated within this time frame. The prediction horizon P represents the number of sampling intervals into the future where predictions are made. The predic- tion horizon was set to P¼50 to account for the large time con- stant of the process. The control horizon M is the number of control moves into the future the MPC considers when predictions are made. The default value of M¼2 was chosen, as this gave the best responses in initial testing. The last parameters are the pro- cess variable and manipulated variable weighting matrices Γy and Γu respectively. We found that at low Γu values, the controller took large controller actions that affected its stability, but was better at rejecting sharp disturbances. Conversely, a high Γu re- sulted in stable steady state performance, but with bad dis- turbance rejection characteristics. Since we desire both stability and disturbance rejection properties we have set Γy and Γu to 1 which gives equal priority to both. Implementation. A schematic of the MPC scheme is shown in Fig. 5. As previously described, the two inputs are the ethanol content in the distillate XD and the methanol recovery β. The re- covery is governed by the distillate stream which is adjusted by the composition controller. The fast actions of this controller can lead to a noisy signals for the MPC. In order to reduce the signal noise, a rate limiter is used. The maximum rate of change on the recovery input signal is set to 0.1 % min . A material balance is solved at every sampling interval k following Eq. (4). The fusel flow in this instance was kept at the default value of 3113 kg h 5. Feed step tests To understand the behaviour of the control schemes to process disturbances, it was necessary to carry out disturbance step tests. Based on analysis and operators experience, it was determined that the feed flow rate and composition are the most likely process variables to introduce process disturbances into the column. 5.1. Feed flow rate step test To start off with, the feed flow rate was changed from ̇ =M 142.5Feed t h to 147.5 t h . This represents an extreme scenario where it is demanded that the collumn take extra feed flow in a short period of time. The response of MPC and the proposed control scheme to this step test are illustrated in Figs. 6 and 7. Where the reboiler duty is the manipulated variable, while pro- duct ethanol composition and product recovery are process variables. As expected, both the control schemes counter the increase in feed flow rate by increasing reboiler duty. The proposed control scheme reacts with an “impulse” like response due to the feed forward controller. The feedback trim controller then reduces the reboiler duty to achieve 99.6% recovery. In comparison, the MPC controller has a far more gradual response and reaches a similar steady state as the proposed control scheme. This behaviour can be attributed to the ratio of Γy and Γu which is set at 1 (balanced approach). Both control schemes are able to tightly maintain XD and β, while the MPC returns to set point quicker than the proposed control scheme. It is also important to note the increase in XD specification for the proposed control scheme is rapid. This be- haviour can be attributed to the proposed control scheme trying to “sacrifice” XD specification in order to maintain recovery at the desired set point of 99.6%, This fact is further confirmed by Fig. 5. Schematic of the high-purity methanol distillation column with model predictive control (MPC). Fig. 6. Reboiler duty response of MPC and proposed control scheme (RCDR) to changes in feed flow rate. I.A. Udugama et al. / ISA Transactions 69 (2017) 222–233 227
  7. 7. analysing the results from Table 3. Examining Table 3, we can conclude that, in terms of the re- covery, the proposed control scheme does a better job at “arrest- ing” the initial drop in recovery. As explained, the nature of the proposed control scheme is to “sacrifice” XD in the short term, which, in turn, enables β to quickly return to specified recovery. However, this quick recovery comes at the cost of XD stability where the total integral error for MPC controller is much lower than the proposed control scheme. Further analysing Fig. 6 illustrates that the rebiler duty ma- nipulated by the proposed control scheme initially overshoots its new steady sate settling point. From a industrial point of view the overshoot in reboiler duty requires additional steam to be gener- ated. In methanol production plants this additional steam re- quirement can be generated with auxiliary natural gas firing at the reforming section of the plant, which will allow the reboiler duty to move above its new steady state during the transient periods. 5.2. Feed methanol content step tests In this test, we have increased the methanol concentration of the feed stream by 2wt%. To compensate, the water concentration in the feed has been decreased by 2 wt%. This represents an ex- treme situation where, a sudden change in feed gas or catalyst has rapidly changed the methanol concentration. Analysing Figs. 8 and 9 shows both the MPC and proposed control scheme has increased the reboiler duty to deal with the excess methanol concentration. Thermodynamically, this makes sense as an increase in methanol concentration means a higher mass of methanol needs to be distilled to keep the recovery ratio at specification. Both control schemes have similar rise times while the proposed control scheme seems to be increasing the reboiler duty slightly more than MPC in the initial stages, but re- turns to a similar steady state. In feed flow disturbance testing, we looked at how the two control schemes react to a measured dis- turbance, as the proposed control scheme had some degree of “advanced” information through the feed forward controller. By contrast, in the methanol content step test, both control schemes get the same information through the process variable β. As such both control schemes are on an “equal footing”. In terms of ethanol ppm, the proposed controller seems to have a bigger “swing” in ethanol concentration in comparison to MPC. Table 4 confirms this observation, as MPC has a lower integral absolute error in controlling XD. However, this is an expected outcome, as the proposed control scheme sacrifices the short term ethanol ppm stability (up to 10 ppm) to stabilize the recovery. This is also evident as MPC has a bigger “swing” in recovery in com- parison to the proposed control scheme and has a higher integral error in controlling β. This test clearly shows that the proposed control scheme can better stabilize the recovery (which is of fi- nancial importance), while MPC is better at stabilizing the product ethanol specification. Fig. 7. Responses in β and XD of MPC and proposed control scheme (RCDR) to changes in feed flow rate. Table 3 Integral Absolute Error of XD and β for a feed disturbance (expressed as a percen- tage of absolute integral error of the proposed control). Variable Control Scheme Integral Absolute Error XD Proposed Control 100 % MPC 38.5 % β Proposed Control 100 % MPC 450 % Fig. 8. Reboiler duty response of MPC and proposed control scheme (RCDR) to changes in feed methanol content. Fig. 9. Responses in β and XD of MPC and proposed control scheme (RCDR) to changes in feed methanol content. Table 4 Integral Absolute Error of XD and β for a feed methanol disturbance (expressed as a percentage of absolute integral error of proposed control). Variable Control Scheme Integral Absolute Error XD Proposed Control 100 % MPC 38.5 % β Proposed Control 100 % MPC 180 % I.A. Udugama et al. / ISA Transactions 69 (2017) 222–233228
  8. 8. 6. Disturbance tests In order to compare the different control schemes in re- sponse to real world conditions, their performance under cyclic process disturbances was tested. The tests were designed to reflect realistic disturbance scenarios in plant operation. The main source of disturbances in this particular process is the feed stream. Three different series of disturbance tests were per- formed on each control system. They were feed mass flow var- iations, feed methanol/water ratio variations, and finally, feed ethanol content variations. 6.1. Disturbances in feed flow rate To compare the ability of the two control schemes to handle oscillating disturbances in feed flow rate, a sinusoidal variation of ̇ = −m 137500 147500Feed kg h was introduced. To model both long time period process variations and short time period plant up- sets, two different time periods of =t 50minshort and =t 2000minlong were examined. Fig. 10 shows the controlled variables XD, β and the reboiler duty ̇QReb for the MPC and the proposed control scheme. For long time period fluctuations, it can be seen that there are only minor differences in both the energy input and the disturbance reactions of the MPC and the proposed control scheme, as illustrated in Fig. 10a and c. However, for short time period fluctuations, as shown in Fig. 10b, the reboiler duty for the MPC is delayed by 15 min and the actions are very small compared to the proposed control scheme. These observations are confirmed in the amplitude of deviation results in Table 5, where all variables, except the short time period reboiler duty reaction, are the same. For short time period disturbances the proposed control scheme has a 7 Â greater amplitude in its reboiler duty reaction compared to the MPC controller. Closer observation of the tabulated results Fig. 10. The effect of short time period and long time period feed flow rate fluctuations on reboiler duty, XD and β. Table 5 Process and manipulated variable fluctuation for feed flow fluctuation. Process Variable Control Scheme Long time period Short time period XD amplitude (ppm) Proposed Control 0.19 0.88 MPC 0.30 0.11 β amplitude (%) Proposed Control 0.05 0.34 MPC 0.36 0.37 Reboiler amplitude (kW) Proposed Control 4.19 3.28 MPC 3.12 0.30 I.A. Udugama et al. / ISA Transactions 69 (2017) 222–233 229
  9. 9. also shows that the proposed control scheme is slightly better at β fluctuations, while MPC is slightly better at controlling the ethanol specification. This behaviour can be explained by analysing the way the two schemes work. The proposed control scheme uses a feed forward element that adjusts the reboiler duty directly with the feed flow rate. For this reason, the reboiler duty for both short and long time period disturbances will always reflect the change in feed flow rate for the proposed control scheme. MPC, on the other hand, measures changes in recovery and ethanol content in distillate to calculate the output. This means that disturbances in the feed have to affect β and XD before the MPC will take action. Since fluctuations in feed flow rate take some time to affect β and XD, the response in reboiler duty has a slight delay of 1.5 min, compared to the proposed control scheme's 15 min. For short time period disturbances this effect becomes visible. Also, the objective function of the MPC pe- nalizes large control moves (changes in manipulated vari- ables). Since the time period of the sine wave is only ten times bigger than the sampling interval, the MPC does not have sufficient time to carry out big changes in reboiler duty. The response of the controlled variables are displayed in Fig. 10c and Fig. 10d and tabulated in Table 5. For both long and short time period disturbances, the recovery is almost constant and very close to the set point of β = 99.6% for both MPC and the proposed control scheme. The deviation of XD in the distillate stream from set point is roughly the same for MPC and the proposed control scheme under long time period disturbances. Since MPC takes smaller control actions in reboiler duty for short time period disturbances, one would assume that MPC would preform poorly in controlling XD in comparison to the proposed control scheme. However, analysing Table 5 we can see that proposed control scheme preforms 8 Â worse than MPC for XD control and only slight better at β control. We can conclude from this that the proposed control scheme slightly overreacts for short time period cyclical process disturbances. To remedy this issue, we can use a rate-limiter in the design of the DR controller, which would slow down the rate at which the reboiler duty can change. However, this type of a rate limiter will make the proposed control scheme more vulnerable during sharp feed flow disturbances as illustrated in Section 5.1. The average values of the variables in Fig. 10 are summarized in Table 6. From the average values in Table 6, it can be seen that the reboiler duty used by both control schemes is the same. However, since MPC causes a smaller fluctuation amplitude in the all im- portant XD variable, we can look to increase the XD set point to closer to the 10 ppm limit. Based on further analysis we have found 9 ppm would be an acceptable and reasonable new set point. The results and potential energy savings will be discussed in Section 7. In [15], we carried out similar feed flow disturbance tests on a DV control configuration. These tests illustrated that a DV con- figuration cannot maintain the recovery or meet the bottoms methanol composition, which must be met in operations. For comparison, both proposed control scheme and MPC controllers are able to maintain this composition 6.2. Disturbances in feed methanol content In this set of disturbance tests, the methanol content in the feed stream was varied from =X 80%MeOH Feed, to =X 85%MeOH Feed, . This disturbance was implemented as a varied methanol feed mass flow ̇mMeOH Feed, . The mass flow of ethanol was unchanged, while the water mass flow was adjusted to ensure a constant overall feed mass flow of ̇ =m 142500Feed kg h . The time periods tshort and tlong were used for the sinusoidal disturbance. Fig. 11 and Table 7 show the reaction of the proposed control scheme and MPC to short and long time period feed methanol variations. During the short term variations, both proposed control scheme and MPC show minor fluctuations in reboiler duty. This behaviour can be attributed to the rate limiter on proposed control scheme and the Γu of the MPC which prevents rapid changes in control variables. In general, both controllers are keeping XD spe- cification and maintaining a normal recovery. During the long time period disturbances we can see both the controllers changing re- boiler duty accordingly. In terms of the XD specification and re- covery, we can see more variation during the short time period disturbances. Again, both controllers are maintaining specifica- tions. A look at Table 7 also confirms that the key process and controlled variables are not fluctuating too much and have similar amplitudes of fluctuation. As expected, the proposed control scheme is doing a better job at controlling β while the MPC con- troller is doing a better job at controlling XD. 6.3. Disturbances in feed ethanol content In the last test series, the ethanol content in the feed stream was changed using a sinusoidal wave from =X 100 ppmEtOH Feed, to =X 200 ppmEtOH Feed, . The mass flows of the other components were unchanged, since variations in ethanol mass flow have no major effect on the overall feed mass flow. Fig. 12 and Table 8 show the reaction of the proposed control scheme and the MPC to short and long time period feed ethanol variations. During the short time period variations, both proposed con- trol scheme and MPC show no control actions. This behaviour can be attributed to the requirement for ethanol to accumulate/de- plete for a long period of time to affect the column performance. For the long time period disturbances, both control schemes react in a similar manner, where reboiler duty is increased for in- creases in feed ethanol content and decreased for decreases in feed ethanol content. We can also see that both control schemes have a 200 min lag. 7. Energy savings and economic benefits In Section 6, tests illustrated that both MPC and the proposed controller scheme have similar performance characteristics, where MPC is able to control the XD tighter than the proposed control scheme during process fluctuations, while maintaining similar recovery. As such, the XD of the MPC controller can be pushed closer towards the 10 ppm industrial AA grade methanol Table 6 Average values of the variables displayed in Fig. 10. Variable Controller type Average for tshort Average for tlong Feed flow rate in kg h MPC 142,538 142,515 Proposed Control 142,538 142,515 Reboiler duty in kW MPC 91,300 91,392 Proposed Control 91,126 91,549 XD in ppm MPC 8.0 7.9 Proposed Control 8.1 7.8 Recovery β in % MPC 99.62 99.61 Proposed Control 99.60 99.61 I.A. Udugama et al. / ISA Transactions 69 (2017) 222–233230
  10. 10. specification, which enables the column to reduce reboiler duty usage. In further analyses we concluded that the XD set point for MPC can be increased up to 9 ppm. Table 9 shows the net energy benefit of using MPC over the proposed control scheme for this particular case. 8. Economic implications of MPC vs the proposed control scheme So far in this manuscript, we have compared MPC with proposed control scheme in terms of controller performance. But this comparison does not cover the underlying economic im- plications that inevitably would decide which control scheme would be implemented in an industrial situation. Operating MPC over operating the proposed control scheme allows energy savings of ∼400 kW, even during steady periods of plant operations. In general, the plant is likely to operate at steady state for 90% of the time. In the other 10%, the plant might experience process dis- turbances, in this instance the MPC would save ∼550 kW. 8.1. Monetizing energy savings Assuming the plant operates throughout the year, we can cal- culate the amount of energy we can save (ESaving) by implementing MPC. = ( · + · )· = ( ) E 0.4 MW 0.9 0.55 MW 0.1 8760 h a 3635.4 MWh a 6Saving Before converting the calculated energy savings into saved costs we need to consider the following factors: Does the plant have an internal need for extra steam? Can the plant reduce the gas usage? (Many methanol plants require some auxiliary natural gas to supplement the steam Fig. 11. The effect of short time period and long time period methanol concentration fluctuations on reboiler duty, XD and β. Table 7 Process and manipulated variable fluctuation for feed methanol fluctuation. Process variable Control Scheme Long time period Short time period XD amplitude (ppm) Proposed Control 0.12 0.39 MPC 0.17 0.10 β amplitude (%) Proposed Control 0.09 0.10 MPC 0.24 0.39 Reboiler amplitude (kW) Proposed Control 2.33 0.18 MPC 1.99 0.32 I.A. Udugama et al. / ISA Transactions 69 (2017) 222–233 231
  11. 11. generated by waste heat recovered at the reforming process). Can the plant sell this energy to the electricity market? (By converting excess steam to electricity in a steam turbine- generator). Can the excess steam be used to process more methanol? Taking these options into consideration, we can come up with two extreme scenarios. In the first scenario, the steam saved can be used to make more product methanol, this is the most profit- able scenario. In contrast, the worst case scenario can be where the plant generates all its steam from waste heat and the savings Fig. 12. The effect of short time period and long time period feed ethanol concentration fluctuations on reboiler duty, XD and β. Table 8 Process and manipulated variable fluctuation for feed ethanol fluctuation. Process variable Control Scheme Long time period Short time period XD amplitude (ppm) Proposed Control 0.19 0.22 MPC 0.11 0.04 β amplitude (%) Proposed Control 0.09 0.01 MPC 0.17 0.11 Reboiler amplitude (kW) Proposed Control 1.05 0.16 MPC 1 0.07 Table 9 Comparison of energy consumption at different set points for the composition controller. Disturbance XD Set point ̇QReb for tshort ̇QReb for tlong Flow rate disturbance 7.84 ppm 91,300 kW 91,392 kW 9.00 ppm 90,812 kW 90,867 kW Energy savings 488 kW 525 kW Methanol content disturbances 7.84 ppm 91,364 kW 91,454 kW 9.00 ppm 90,817 kW 90,841 kW Energy savings 547 kW 613 kW Ethanol content disturbances 7.84 ppm 91,532 kW 91,398 kW 9.00 ppm 90,871 kW 90,858 kW Energy savings 661 kW 540 kW I.A. Udugama et al. / ISA Transactions 69 (2017) 222–233232
  12. 12. in steam cannot be converted into additional revenue. All practical scenarios fall in between these two extremes. 8.2. Cost of implementation and other considerations When MPC is chosen as a control scheme, the following addi- tional costs need to be considered: Cost of equipment Cost of setting up Cost of maintenance In some cases, the net benefit provided by MPC would be “wiped out” by the cost of implementation and maintenance. Again, the net cost per column will be reduced based on the size of the methanol producer, as implementation of MPC on multiple (similar) columns would reduce set up and maintenance costs. Additionally, we also need to consider the following factors: General resistance of plant operations to implement MPC Implications of operating MPC during major process upsets/ catastrophic events In general MPC would be favoured over the proposed control scheme during times of high energy costs, not withstanding the above. In current market conditions of low energy prices the proposed control scheme will be favoured. It is also important to note that both the proposed controller and MPC would require additional process measurements (e.g accurate composition of the feed), which will require costly gas chromatograph to be installed. However, the increase in recovery provided by both the control structures would more that offset any additional costs of measurement. From an industrial point of view, the conceptual ideology used in the development of the proposed controller can be used as a template and a road map to develop supervisory controllers for other distillation applications where similar high recovery and quality constraints are common. Especially in the chemicals in- dustry where older generation plants are getting pushed to make tight product specifications at highest possible recoveries. 9. Conclusions In this manuscript we have developed a novel, industry friendly control structure that is capable of operating an industrial me- thanol distillation column at high product recovery, whilst main- taining a tight product ethanol specifications and minimising en- ergy usage. To facilitate the development and the testing process a validated process simulation of an industrial methanol distillation column was employed. A MPC with a discrete model was also developed for comparison purposes. Both the proposed control scheme and the MPC were subjected to a multitude of disturbance tests, that included disturbance step tests, cyclical feed fluctua- tions and set point changes. In all tests, the proposed control scheme and MPC were able to maintain both recovery and XD specifications using similar levels of reboiler duty. As such, both control schemes can be potentially implemented in this applica- tion. In addition, it was observed that MPC was able to control to the XD specification tighter than the proposed control scheme. This enabled the XD set point to be set closer to the 10 ppm industrial AA grade methanol limit, allowing the average energy usage of MPC to be reduced by ∼500 kW, which is ∼0.5% of total reboiler duty. An economic analysis of the proposed control scheme and MPC illustrated that many other factors, such as the value of en- ergy savings and the costs of implementing MPC, need to be considered in deciding between the two controllers. In general however,we found that plants with low value for reboiler duty (steam) savings would prefer proposed control scheme over MPC. Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.isatra.2017.04.008. References [1] Morari M, Evanghelos Z. Robust Process Control. Englewood Cliffs, NJ: Prentice Hall.; 1989, 205–215. p. 359–389. 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