Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011 Modelling, Validation, and Control of an Industrial Fuel Gas Blending System 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.