Modelling, Validation, and Control of an Industrial Fuel Gas Blending System

Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011

Cornelius J. Muller, ∗,∗∗ Ian K. Craig, ∗∗ N. Lawrence Ricker ∗∗∗

∗ Sasol Solvents RSA, Sasolburg, South Africa (e-mail: [email protected]), ∗∗ Department of Electrical, Electronic, and Computer Engineering, University of Pretoria, Pretoria, South Africa (e-mail: [email protected], [email protected]), ∗∗∗ Department of Chemical Engineering, University of Washington, Seattle, USA (e-mail: [email protected])

Abstract: In industrial fuel gas preparation, there are several compositional properties that must be controlled within specified limits. This allows client plants to use the fuel gas mixture without having to adjust and control the composition themselves. These properties are controlled by adjusting the volumetric flow rates of several inlet gas streams of which some are makeup streams (always available) and some are wild streams that vary in composition and availability (by-products of plants). The inlet streams need to be adjusted in the correct ratios to control all the controlled variables (CVs) within limits while minimising the cost of the gas blend. Furthermore, the controller needs to compensate for fluctuations in inlet stream compositions and total fuel gas demand (the total discharge from the header). This paper describes the modelling and model validation of an industrial fuel gas header as well as a simulation study of a Model Predictive Control (MPC) strategy for controlling the system while minimising the overall operating cost.

Keywords: dynamic model; model-based control; state-space model; validation.

1. INTRODUCTION FIC 001 Natural Gas FIC The fuel gas used in industrial plants must have sev- 002 eral compositional properties. These Controlled Variables Reformed Gas FIC r

(CVs or plant outputs) include the Higher Heating Value 003 e PI AI AI AI d 100 010 020 030 (HHV or gross caloriﬁc value) (Green et al. [1997]), Wobbe Hydrogen ea h FIC s

Index (WI), and Flame Speed Index (FSI, using Weaver’s 004 a g l

Nitrogen e

ﬂame speed factor) (Johnson and Rue [2003]), all of which u

FIC F must be controlled within predetermined ranges. In addi- 005 tion, the fuel gas blending header pressure must be kept Tail Gas 1 FIC within specified limits. These properties are controlled 006 by adjusting the flow rates of several inlet streams (the Tail Gas 2 Manipulated Variables (MVs) or plant inputs) consisting of makeup gasses as well as wild gas streams (by-products Fig. 1. Process diagram of blending header. from plants). These streams need to be adjusted so as to control the outputs within the specified ranges as well as 2. PROCESS OVERVIEW to minimise the overall unit cost of the fuel gas. To adjust these streams simultaneously and in correct ratios when Figure 1 shows a process diagram of the system. Although disturbances act in on the system is a challenging task, the header is depicted as a vessel, it is made up of the even for the most experienced operator. Although ratio volumes of the piping network. The flow rates are high control can improve matters somewhat, the compositions so it is assumed that turbulent flows facilitate perfect of the inlet streams vary, causing the required ratios to mixing such that the composition of the exit stream equals change as well. Model Predictive Control (MPC) is an the header composition which is assumed to be uniform. attractive alternative to PID control because the effects Six gas streams enter the fuel gas header (shown with of compositional and demand fluctuations can be included their fictional tag names in Figure 1). These six feed in the MPC formulation. There are many publications streams are Natural Gas (NG), Reformed Gas (RG, a on fuel gas in the literature, but there seems to be a Hydrogen to CO ratio of between 1.8:1 and 2:1), Hydrogen lack of publications on fuel gas blending control (although (H2), Nitrogen (N2), Tail Gas 1 (TG1), and Tail Gas industrial applications of this kind do exist). 2 (TG2). The first four streams are make-up streams

Copyright by the 12360 International Federation of Automatic Control (IFAC) Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011

Table 1. Controlled variable ranges. Table 3. Component characteristics.

Controlled Variable Abbr. Range Units HHV WI SG MWt A s Higher Heating Value HHV 16.5 – 18 MJ/Nm3 CH4 37.78 50.72 0.557 16.04 9.55 148 Wobbe Index WI 25 – 27 MJ/Nm3 C2-C6 126.5 87.62 2.018 58.12 31 514 Flame Speed Index FSI 39 – 46 - H2 12.10 45.88 0.069 2.016 2.39 339 Pressure P 2000 – 2200 kPa N2 - - 0.973 28.02 - - CO 11.97 12.17 0.968 28.01 2.39 61 Table 2. Typical inlet compositions (mol %). CO2 - - 1.528 44.01 - - 6 NG RG H2 N2 TG1 TG2 ui = 44.64 yF ,i.Fj (2) CH4 91.1 1.5 - - 5.5 15.0 X j =1 C2+ 6.8 0.0 - - 1.0 1.0 j H2 0.0 62.0 100 - 62.0 57.0 for i = 1 to 6 and where Fj is the volumetric flow rate N2 1.5 0.5 - 100 2.5 6.0 th 3 CO 0.0 31.0 - - 26.0 13.0 of the j inlet stream [kNm /h] and yFj ,i is the molar CO2 0.6 5.0 - - 3.0 8.0 fraction of component i in inlet stream j. The j index refers to the sequence shown in Figure 1. The outputs HHV 43.02 11.78 12.10 0.0 13.96 15.39 are calculated according to the molar fractions of the WI 52.62 17.87 45.73 0.0 21.60 22.92 components in the system (and the total number of moles in the case of pressure). The output calculations are whereas the two tail gas streams are wild streams, varying 6 in availability and composition. The streams need to be HHVfg = X HHVi.yfg,i (3) mixed in correct ratios and quantities to control the output i=1 composition and pressure. Table 1 shows the specified HHVfg ranges for the outputs. The NG, RG, and N2 streams W Ifg = (4) have costs associated with them whereas the H2 and tail √ρfg gas streams are free. Therefore, the use of the NG, RG, 6 Pi=1 yfg,i.si and N2 streams needs to be minimised in the optimisation F SIfg = 6 2 (5) yfg,i.Ai + 5 nfg,j 18.8xO2 + 1 problem whereas the use of the tail gas streams and H2 Pi=1 Pj=1 − should be maximised subject to its availability. Natural N RT P = T (6) gas is used continuously to increase the calorific value V up to specification. Nitrogen will only be used when the FSI is too high. Reformed gas is used as a substitute for where si is the flame speed factor for component i, Ai the tail gas streams when not available. Apart from these is the molar stoichiometric air demand factor (for total streams, several disturbances act on the system, including combustion) for component i, nfg,j is the molar fraction of

fluctuations in the feed stream compositions and total fuel inert component j in the fuel gas, xO2 is the mole fraction gas demand (i.e. the discharge flow rate from the header). of oxygen in the gas (usually zero in this application), NT Table 2 gives the typical compositions and characteristics is the total number of moles in the system, R = 8.314 is the of the inlet streams. gas constant, T is the header temperature (Kelvin) and V is the header volume (m3, estimated at 100m3). The Fuel Gas specific gravity, ρfg, is calculated as 3. MODELLING 6 i=1 MW ti.yfg,i ρfg = P (7) The HHV, WI, and FSI are functions of the molar com- MW tair position of the fuel gas. There are six states (the numbers of moles of the six components in the header), six inputs where MW ti is the molar weight of component i and (the volumetric flow rates of the six inlet streams), and MW tair = 28.8 is the standard molar weight of air. Table four outputs (HHV, FSI, WI, and Pressure). The state 3 lists some characteristics of the components (Green et al. equations are given by [1997]).

N˙ fg,i = ui yfg,i.uT (1) 3.1 Model validation − where i = 1to 6, Nfg,i is the number of moles of component The integrity of the process model needs to be determined i in the header, ui is the total molar flow of component i in order to support the validity of the simulation study. entering the header (summed over all inlet steams), uT is For the validation, a period of operation was identified in the total molar discharge rate from the header, and yfg,i is which all the flow measurements are reliable (either zero or the molar fraction of component i in the header. The inlet greater than the turn-down of the transmitters). The inlet flows are described in terms of volumetric flow rates and flow rates, feed stream compositions, and header discharge compositions. Therefore, these flows need to be converted rate were used as verification data and the simulation to molar flow rates of the individual components to get to output data compared to the plant measurements (the ui. This is done by converting the volumetric flow rates to system is at ambient temperature for which the effects molar flow rates. The volumetric flow rates are measured of diurnal fluctuations are negligible). The initial model in kNm3/h (i.e. under an ideal gas assumption). Therefore, states were the steady values corresponding to the average the individual component molar flow rates ui are feed flow rates and compositions. Analyser dead-times (for

12361 Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011

Table 4. Correlation coeﬃcients for output Table 5. Linearised model matrix. data. NG RG H2 Data set Correlation coeﬃcient (%) 24.61 e−s/180 −4.42 e−s/180 −5.04 e−s/180 HHV s+28.62 s+23.12 s+26.44 HHV 93.8 30.73 e−s/60 −6.23 e−s/60 2.25 e−s/60 WI s+28.69 s+23.39 s+26.29 WI 84.8 −59.21 e−s/180 11.05 e−s/180 32.26 e−s/180 FSI s+28.57 s+22.92 s+27.14 FSI 83.1 1120 1120 1120 P s s s

] 18 3 N2 TG1 TG2 HHV − − − Analyser HHV 13.27 e−s/180 3.31 e−s/180 1.66 e−s/180 17.5 HHV s+23.09 s+25.78 s+22.64 Sim −30.42 e−s/60 −4.04 e−s/60 −2.45 e−s/60 WI s+23.00 s+25.62 s+22.85 − 17 33.59 e−s/180 10.40 e−s/180 2.23 e−s/180 FSI s+23.00 s+26.72 s+22.17 P 1120 1120 1120 16.5 s s s and FSI and with integrating models for pressure. The Higher Heating Value [MJ/Nm 16 0 2 4 6 8 10 12 14 16 18 linearisation was performed around an operating point of Time [h] [HHV, WI, FSI, P] = [16.75, 25.32, 43.47, 2085] which is Fig. 2. HHV analyser data versus simulation data. a typical operating region for the plant. The resulting model matrix is shown in Table 5. The time unit for the 26.5 model is hours. WI ] Analyser 3 26 WI Sim 4. ITERATIVE LINEARISATION

25.5 The steady state values for the controlled variables can 25 be calculated directly from the volumetric ﬂow rates and Wobbe Index [MJ/Nm compositions of the inlet streams. Taking the derivatives of 24.5 0 2 4 6 8 10 12 14 16 18 these equations with regard to the individual inlet streams Time [h] give the instantaneous gains. These gains can then be Fig. 3. WI analyser data versus simulation data. used to update the model used in the MPC to provide a form of iterative linearisation. The gain calculations

45 are described in the next sections (Hughes [2008], Hughes [2010a], Hughes [2010b]). 44 43 4.1 Heating value 42 FSI Analyser The fuel gas heating value is calculated as Flame Speed Index 41 FSI 6 Sim F HHV 40 Pi=1 i Fi 0 2 4 6 8 10 12 14 16 18 HHVfg = · (8) Time [h] FT

Fig. 4. FSI analyser data versus simulation data. where Fi and HHVFi are the volumetric flow rate (kNm3/h) and heating value (MJ/Nm3) of the ith inlet measuring HHV, WI, and FSI) were initially estimated at i=1 stream and FT = P6 Fi is the total inlet volumetric 2 minutes and adjusted for better data correlation. The flow rate. The gains are then calculated as final dead-times were 20 seconds for HHV, 1 minute for ∂HHVfg HHVF HHVfg WI, and 20 seconds for FSI (the FSI is measured by a = i − (9) mass spectrometer which has a small dead-time but only ∂Fi FT samples every 10 minutes). The correlation coefficients for 4.2 Wobbe index a validation period of 18 hours are shown in Table 4. The presence of feedback control on the header pressure for The Wobbe index is calculated as shown in Equation 4) all plant data complicates the validation of the pressure where HHVfg is given in Equation 8 and ρfg is the relative model. The model is, however, based on well developed density of the fuel gas, calculated with regard to inlet flow physical models and will be assumed to be adequate for rates as the purposes of this simulation study. 6 i=1 Fi ρFi ρfg = P · (10) The data plots for the validation are shown in Figures 2 to FT 4. The sample rate for the plant data is 20 seconds (1/180 hours). where ρFi is the relative density of inlet gas i. Taking the derivative of W Ifg gives 3.2 Linearising the model for control purposes ∂W Ifg 1 ∂HHVfg HHVfg ∂ρfg = . 1.5 . (11) ∂Fi √ρfg ∂Fi − 2.ρfg ∂Fi In order to apply linear MPC, a linear dynamic model needs to be derived from the first principles model. Several with ∂HHVfg given in Equation 9 and types of LTI (Linear Time-Invariant) models were consid- ∂Fi ∂ρfg ρF ρfg ered and fitted. Finally, first order plus dead time transfer = i − (12) function models were selected and fitted for HHV, WI, ∂Fi FT

12362 Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011

4.3 Flame speed index Table 6. Relative costs (cost/kNm3), weights, and limits of inlet streams (kNm3). The flame speed formula is shown in Equation 5 with the Feed Relative Weight Rate High Low values for Ai and si given in Table 3. To calculate the FSI in terms of the inlet volumetric flow rates, the molar stream cost weight lim. lim. components in the fuel gas are calculated using NG 0.678 67 1 0 15 6 RG 0.254 25 1 0 20 Pj=1 Fj.yF j,i H2 0 0 1 0 5 yfg,i = (13) N2 0.068 7 1 0 5 FT TG1 0 0 1 0 30 TG2 0 0 1 0 30 where yF j,i is the molar fraction of component i inlet stream j. The derivative can then be determined as of dealing with large disturbances quickly (due to its in- 4 2 ∂F SIfg ∂F SIfg ∂yfg,x ∂F SIfg ∂nfg,k herent use of feed forward control). The main drawbacks in = X . + X . (14) using MPC are the computational burden associated with ∂Fi ∂yfg,x ∂Fi ∂nfg,k ∂Fi x=1 k=1 it (especially when considering large systems and large control and prediction horizons) and the need for a reliable where yfg,x refers to the molar fraction of combustible model of the process (Camacho and Bordons [2007]). component x in the fuel gas and nfg,j is the molar fraction of inert component j in the fuel gas. The individual terms 5.2 MPC application on fuel gas header in Equation 14 are given by ∂F SIfg sx Ax.F SIfg The interactive and multivariable nature of the fuel gas = 6 − 2 (15) ∂yfg,x blending system make it an ideal candidate for MPC. Pi=1 yfg,i.Ai + 5 Pj=1 nfg,j 18.8xO2 + 1 − The LTI model described in Section 3.2 was used as an ∂yfg,x yF ,x yfg,x = i − (16) initial model in the MPC algorithm. The relative costs are ∂Fi FT given in Table 6. The MPC was designed using the Model ∂F SIfg 5.F SIfg Predictive Control Toolbox in Matlab (Bemporad, Morari, = 6 − 2 (17) & Ricker [2010]). ∂nfg,k yfg,i.Ai + 5 nfg,j 18.8xO2 + 1 Pi=1 Pj=1 − The average settling time for the HHV, WI, and FSI is ∂nfg,k nF ,k nfg,k = i − (18) about 12 minutes (this can be determined by taking an ∂Fi FT average time constant of τ = 1/25 60 = 2.6 minutes ∗ and then calculating the settling time ts 5.τ = 12 5. PREDICTIVE CONTROL minutes (Seborg, Edgar, & Mellichamp [2004]).≈ The initial values for the prediction and control horizons were chosen 5.1 MPC overview according to the proposed guidelines in Seborg, Edgar, & Mellichamp [2004]. This resulted in a control horizon of Since the early description of MPC (Model Predictive 5 and a prediction horizon of 44. These values did not Control) in the late 1970’s by Richalet et al. [1976] and give the desired results. The values were changed by trial its application in the refining industry by Shell Oil (Cutler to arrive at a final prediction horizon of 39 samples and and Ramaker [1979]), significant attention has been given a control horizon of 2 sampling intervals (to prevent the to the development of this powerful advanced control tech- controller from being too aggressive). nique. MPC is a model-based control strategy that uses a dynamic model of a system to predict its future behaviour Weights were added to the inputs in relation to the relative and then calculate the optimal control moves to minimise a costs of the streams (given in Table 6) with identical cost function. This is done by performing optimal control rate weights. The weights are shown in Table 6. The over a finite time interval into the future based on cur- MV weights penalise the deviation from nominal values rent state/output measurements, implementing the first (which are set initially to [0 0 5 0 30 30]). The outputs control moves, and repeating the process using the latest were given weights (given in Table 7) for deviations from measurements (also known as receding horizon control). the nominal values which were chosen to be mid-range Only the first move is implemented due to model-process (i.e. HHVnominal = 17.25, WInominal = 26, FSInominal = mismatches and unmeasured disturbances that cause the 42.5, and Pnominal = 2100). In addition to the weights, predicted state trajectories to differ from the actual system constraints were put on the inputs and outputs. The behaviour. Although there are many MPC algorithms, the input constraints were chosen to be representative of the basic structure of MPC is common to most applications. availability of each stream and are shown in Table 6. The The different algorithms differ in the model used, the form output constraints correspond to the controlled variable of the cost function, and the way the controller handles ranges shown in Table 1. The MPC formulation can be noise and disturbances (Camacho and Bordons [2007]). An found in Bemporad, Morari, & Ricker [2010]. overview of the commercial technologies available for MPC application in industrial plants can be found in Qin and 5.3 Dealing with non-linearities Badgwell [2003]. Some of the advantages of using MPC include flexibility in formulating the objective function and The MPC algorithm used for the control is designed defining the process model, the ability to include equality for linear plants. The Fuel Gas system however is non- and inequality constraints directly in the control law, ac- linear which reduces the performance of the MPC when commodation of multivariable systems, and the possibility moving away from the design operating region. There

12363 Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011

Table 7. Weights on CVs.

/h] 30 CV Weight 3 HHV 150 28 WI 100 FSI 100 Flow [kNm 26 P 100 0 1 2 3 4 5 6 Time [h] are several possibilities for dealing with non-linearities. One option is to use non-linear MPC which requires the Fig. 5. Header discharge flow. use of a non-linear model and optimiser (which is more complex and computationally intensive than the linear case). Another option is to continuously linearise the The results of using a constant LTI model (the model given plant at the current operating point (Adetola and Guay in Table 5) versus the iterative linearisation case are shown [2010]). The latter is the technique followed in this study. in Figure 5 to 8. The operating costs (calculated from The iterative linearisation is performed by calculating the flow rates and normalised costs) for the two cases are the gains of the Transfer Function Matrix (TFM) at shown in Figure 9. The same controller was used in both every 30th iteration (every 10 minutes) and updating the cases (identical tuning settings). model used by the MPC accordingly (Hughes [2008]). The results illustrate that a seemingly small change in the The compositions of the inlet streams on the plant are composition of the feed streams can cause a significant measured by the same mass spectrometer mentioned in change in the optimal operating costs. In this case, an Section 3.1 which samples every 10 minutes. Therefore, increase in the HHV of Tail Gas 1 allows for a reduction the linearisation frequency was chosen to coincide with in the NG usage which gives rise to the significant cost this sampling frequency. The initial TFM is given in Table reduction. The total cost (the operating cost integrated 5. The gain calculations were discussed in Section 4. The over the 6 hour period) for the case of iterative liearisation linearisation involves normalising the TFM, updating it is 0.2172 whereas the cost for the constant LTI model with the newly calculated gain values, and updating the is 0.2501 (a 13.15% cost reduction for this simulation). MPC to use the new TFM. The transient behaviour of the Considering the composition change at 4 hours alone, the plant does not change significantly at different operating operating cost is reduced from about 0.0415 to 0.0225 per regions. Therefore, only the gains of the TFM are updated, 3 kNm (a reduction of 45.78%). The true optimal steady leaving the dynamic parameters (the time constants and state costs before and after this disturbance are 0.0325 and delays) unchanged. 0.0 respectively (calculated using a nonlinear optimiser with the steady state equations from Section 4), with an 5.4 Results ideal total cost of 0.1294. This indicates that, although the iterative linearisation improves performance, it still The controller was tested in a simulation study (using the falls short of the true optimal solution. This is mostly nonlinear model discussed in Section 3 to represent the due to the formulation of the optimisation problem in the plant) to demonstrate its ability to control the CVs within MPC algorithm so as to provide adequate dynamic control. limits in the presence of noise (the discharge flow signal The mid-range targets on the CVs, the rate weights on has a 2% peak to peak noise) and disturbances, while the MVs, and the weights on the CVs are examples of attempting to minimise operating cost. For simplicity, parameters necessary for proper dynamic performance actuator dynamics were not considered and perfect flow which also have an effect on the ability to reach the manipulation assumed. theoretical optimal cost. Further improvement could be Two demand disturbances (changes in the total dis- obtained by applying real-time optimisation (RTO). charge) were introduced after 1 hours and 3 hours respectively, each of a 3 kNm3/h magnitude. A composition disturbance was also introduced in the NG stream at time 2 hours, changing the composition from 6. CONCLUSION [CH4, C2+, H2, N2, CO, CO2] = [0.911, 0.068, 0.0, 0.015, 0.0, 0.006] to [0.841, 0.088, 0.01, 0.035, 0.01, 0.016]. The The first principle model provides an adequate represen- composition of the Tail Gas 1 stream was changed at time 4 tation of the system to gain insight in the behaviour of the hours from [CH4, C2+, H2, N2, CO, CO2] = [0.055, 0.01, fuel gas blending header for simulation purposes. The cor- 0.62, 0.025, 0.26, 0.03] to [0.075, 0.04, 0.57, 0.025, 0.26, relations between the simulation and plant values indicate 0.03]. This compositional change causes a change in the that the assumptions made (of ideal gas and perfect mix- HHV of TG1 from 13.98 to 17.98 which causes the gain of ing) are acceptable for this study. Despite the non-linearity the model from TG1 to HHV to change sign (from neg- and interactive nature of the fuel gas system, MPC is very ative to positive). This illustrates the effectiveness of the effective in controlling the outputs within the specified iterative linearisation. When a constant LTI model is used, ranges while minimising the operating cost. The controller the controller does not detect the change in composition is able to handle significant disturbances in demand and and continues with the same inlet flow rates (not utilising fluctuation in feed compositions. Furthermore, the itera- the TG1 to reduce the cost as it could do). When the gains tive linearisation allows the MPC to compensate for model are updated, the controller detects that the HHV of the changes resulting from feed flow and composition changes. TG1 stream is higher and can therefore be exchanged for Further improvement could be achieved by applying real- some NG, reducing the cost. time optimisation (which will be done in future work).

12364 Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011 ]

Natural gas (NG) 3 Heating value /h] 3 15 18 10 5 17 0 16 HHV [MJ/Nm Flow [kNm 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Time [h] Time [h] Wobbe index ] Reformed Gas (RG) 3

/h] 27

3 20 26 10 25

0 WI [MJ/Nm 0 1 2 3 4 5 6

Flow [kNm 0 1 2 3 4 5 6 Time [h] Time [h] Flame speed Hydrogen (H ) 48 2 46 44 /h] 6 3

FSI 42 40 4 38 2 0 1 2 3 4 5 6 0 Time [h]

Flow [kNm 0 1 2 3 4 5 6 Header pressure Time [h] 2200 2100 Fig. 6. NG, RG, and H2 ﬂows for the constant LTI model 2000 (dotted) versus using iterative linearisation (solid). Pressure [kPa] 0 1 2 3 4 5 6 The dashed lines indicate the limits. Time [h]

Nitrogen (N ) Fig. 8. Controlled variables for the constant LTI model 2

/h] 6 (dotted) versus using iterative linearisation (solid). 3 4 The dashed lines indicate the limits. 2 0 0.06 Flow [kNm 0 1 2 3 4 5 6 Time [h] 0.04

Tail Gas 1 (TG ) Cost 1 0.02 /h]

3 30 20 0 10 0 1 2 3 4 5 6 0 Time [h]

Flow [kNm 0 1 2 3 4 5 6 Time [h] Tail Gas 2 (TG ) Fig. 9. Operating cost and ideal optimal cost (dashed 2 line) for the constant LTI model (dotted) versus using /h]

3 30 20 iterative linearisation (solid). 10 0 Johnson, F. and Rue, D.M., 2003. Gas Interchangeability Flow [kNm 0 1 2 3 4 5 6 Tests: Evaluating the Range of Interchangeability of Va- Time [h] porized LNG and Natural Gas. Gas Technology Institute for Gas Research Institute, April 2003. Fig. 7. N2, TG1, and TG2 ﬂows for the constant LTI model Green, D.W. et al., 1997. Perry’s Chemical Engineers’ (dotted) versus using iterative linearisation (solid). Handbook, pages 2-7 – 2-44. Seventh Edition. McGraw- The dashed lines indicate the limits. Hill. ACKNOWLEDGEMENTS Hughes, P., 2008. Sasol Fuel Gas Optimiser: APC Con- troller Feasibility Study. Sasolburg: Sasol Technology, Thanks to Adolf Wolmarans from Sasol Infrachem for May 2008. giving permission to use the plant data and to Paul Hughes, P., 2010a. SCI Fuel Gas Optimiser: Engineering Hughes from Sasol Technology for his advice and guidance Documentation, pp. 30 – 32. Sasolburg: Sasol Technol- (especially with regard to the iterative linearisation). ogy, March 2010. Hughes, P., 2010b. Discussion on the derivatives of HHV, WI, and FSI. Personal communication, Sasolburg: Sasol REFERENCES Technology, June 2010. Adetola, V. and Guay, M., 2010. Integration of real-time S.J. Qin and T.A. Badgwell, 2003. A survey of industrial optimization and model predictive control. Journal of model predictive control technology. Control Engineer- Process Control, 20(2), pp. 125–133. ing Practice, Vol. 11, No. 7, pages 733-764, July 2003. Bemporad, A., Morari, M., and Ricker, N.L., 2010. Model J. Richalet, A. Rault, J.L. Testud, and J. Papon, 1976. Predictive Control Toolbox 3: User’s guide. The Math- Algorithmic control of industrial processes. In: IFAC, Works, Inc., 2010. Procedings of the 4th IFAC Symposium on identiﬁcation Camacho, E.F. and Bordons, C., 2007. Model Predictive and system parameter estimation, pages 1119–1167. Control, pages 1 – 10. Second Edition. London: Springer. Seborg, D.E., Edgar, T.F., and Mellichamp, D.A., 2004. Cutler, C.R. and Ramaker, B.L., 1979. Dynamic matrix Process Dynamics and Control. Second Edition. NJ: control a computer control algorithm. AICHE national Wiley. meeting. Houston, April 1979.

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