Acid Gas Removal Unit in Waste-to-energy Plants: Data-driven Models for Advanced Control

Flue gas cleaning is a crucial step in waste-to-energy (WtE) plants that process municipal solid waste. This paper analyzes the acid gas removal line of an Italian WtE plant, based on the injection of dry alkaline solid sorbents (calcium hydroxide Ca(OH)2 and sodium bicarbonate NaHCO3) for the abatement of hydrogen chloride, HCl. The aim of the study is to develop different data-driven models for the description of the acid gas treatment process with the final goal of implementing them in model-based controllers for optimizing the feed rate of alkaline reactants thus minimizing solid waste production. System identification and validation techniques have been applied to process data. Different input-output and state-space models are identified by optimizing related model orders and validated on different routine data. The comparison of two system structures (sequential and holistic) evidenced the importance of measuring additional internal variables to maintain low system orders and delays. Anyway, results appear reliable and promising for control purposes, making different modeling approaches and control structures possible.


I. INTRODUCTION
The emission of pollutants by waste-to-energy (WtE) power plants has attracted increasing attention worldwide [1]. The flue gas can contain various toxic substances due to the composition of municipal solid waste (MSW) burnt, such as NOx, SO 2 , HCl, HF, particulate matter, and heavy metals. To effectively control the pollutants, a flue gas cleaning system is indeed necessary to comply with legislation in operating MSW incineration power plants [2]. Among different solutions, injection of alkaline dry sorbents and separation via bag filters is among the best available techniques [3]. This approach has been also recently proposed as a retrofitting option for a WtE plant in China to satisfy the international standards and near-zero-emissions goal [4]. Nevertheless, current industrial control practices choose to guarantee high safety margins to comply with stringent emission standards over optimally tracking a set-point of concentration of outlet pollutants [5]. For this reason, reactants are often fed in large excess to avoid possible overshooting in emission at the stack, generating a lot of waste products and related cross-media effects [6]. In addition, a simplified economic analysis showed that the advantages of dry technologies can be lost when considering This research was supported by Horizon Europe through the funding program "FrontSeat, Project 101079342" the costs of chemicals and the disposal of solid byproducts [7]. For this reason, optimizing the acid gas removal becomes a mandatory task to ensure environmental and economic feasibility. Recent works have focused on deriving process data to accurately define the flue gas composition via multipoint measurements [8] or to develop artificial neural network models for the formulation of appropriate WtE plants and pollutant emission control schemes [9]. Similarly, Zhang et al. [10] developed a flow model to estimate SO 2 and HCl concentration to provide the basis for the appropriate design and operation of the control system.
Our recent study has used system identification techniques to develop dynamic models to predict the HCl concentration exiting the first stage of the flue gas treatment unit within an Italian WtE plant to minimize the flow rate of calcium hydroxide [11]. However, for a future assessment of the environmental performance of the WtE plant under advanced control structures, a model which also describes the concentration of HCl at the stack is needed [12]. Therefore in the present paper, we aim at developing and comparing two dynamics models: the first one, named sequential, considers the two stages as two input-output structures, while the second one, named holistic, considers the whole acid gas treatment unit as a single block. This paper is organized as follows: Section II, in which the WtE plant under study is briefly described, while identification of the models, their validation, and comparison are illustrated in Section III. Finally, Section IV concludes the work by drawing the future addresses of the research.

II. SYSTEM DEFINITION
The WtE plant considered in this work is a medium-sized facility operating in Northern Italy. The plant has an acid gas removal unit comprised of a two-stage process with an alkaline dry sorbent injection system, which is a sequence of reaction and filtration taking place at ≃ 180 • C (see Figure 1). A tubular reactor is fed with calcium hydroxide (Ca(OH) 2 ); then, a reaction tower is injected with sodium bicarbonate (NaHCO 3 ). Reverse pulse jet cleaning is adopted in the two baghouse filters to separate unreacted sorbents and residual solid chemicals: i.e., the cake deposited on filter tissues is broken by calibrated blasts of compressed air. Flue gas composition is measured by three sensors placed at different This study considers both stages of treatment, and, for the sake of simplicity, we only focus on the removal of hydrogen chloride HCl. In particular, for the first stage of acid neutralization, the main gas-solid reaction is: while for the second stage, NaHCO 3 decomposes to porous sodium carbonate (Na 2 CO 3 ), which then neutralizes HCl [5]: 2 NaHCO 3(s) → Na 2 CO 3(s) + CO 2(g) + H 2 O (g) (2) Na 2 CO 3(s) + 2 HCl (g) → 2 NaCl (s) + CO 2(g) + H 2 O (g) The distributed control system (DCS) of the plant receives variables measured online and then imposes the flow rate of two solid sorbents, Ca(OH) 2 and NaHCO 3 . These two manipulated variables are varied by a feed-forward plus feedback control architecture which is designed to feed reactants in strong excess with respect to the stoichiometric values to ensure a complete abatement of acid flue gas and to allow compliance with the emission limits at stack. For this reason, the implemented control logic is suboptimal; as a matter of fact, alkaline sorbent dosage can be reduced and consequent solid waste can be limited, while still respecting the process set-points and fulfilling safety and environmental constraints. The natural solution is thus the adoption of an advanced model-based controller which can guarantee a good trade-off between all the previous variables exploiting suitable optimization algorithms. Therefore, a reliable model for the process must be identified and validated on operational data.
The following systems are considered to derive models for the two-stage HCl removal process ( Figure 1): • Stage I -a system with 2 inputs and 1 output: inputs (u) are i) C SMP1 HCl , the concentration of HCl measured at SMP1; ii) Q Ca(OH) 2 , the mass flow rate of Ca(OH) 2 ; output (y) is C SMP2 HCl , the concentration of HCl measured at SMP2. • Stage II -with 2 inputs and 1 output: inputs are: i) C SMP2 HCl ; ii) Q NaHCO 3 , the mass flow rate of NaHCO 3 ; output is C SME HCl , the outlet HCl concentration, measured at stack. • Stage I+II -a single 3×1 system: inputs are C SMP1 HCl and both alkaline reactants flow rate; output is C SME HCl . The concentrations of HCl are expressed in mg/Nm 3 and measured by Fourier-Transform infrared (FTIR) spectrometers [5]; sorbent flow rates are in kg/h, evaluated from the rotational speed of the corresponding dosing screw feeder. A sampling time T s = 60s is used for data collection. As said, the sequential approach considers the sequence of stages I and II, while the holistic model refers to a single stage I+II.

III. SYSTEM IDENTIFICATION AND VALIDATION
To identify suitable dynamic models of the two-stage HCl removal unit, input-output plant data are employed. To achieve this task, we adopted the open-source Systems Identification Package for PYthon (SIPPY) developed in our previous work [13]; we considered linear models by comparing various structures and orders.

A. Dataset selection
Since the inlet concentration C SMP1 HCl strictly depends on the composition of the solid waste fractions burnt in the combustion chamber, it is assumed as a disturbance variable; on the opposite, the flow rates of two alkaline sorbents are standard manipulated variables, which control room operators can eventually vary in manual mode. In [11] the control architecture of Figure 1 was partially deactivated and Generalized Binary Noise (GBN) sequences were imposed to Ca(OH) 2 flow rate to build suitable tests for process dynamic identification. It is well-known that GBN signals are very effective for identification purposes; nevertheless, in this case, it was not possible to consider the same dataset, since these GBN were specifically suited for the first stage, and, as a consequence, the corresponding data produced for the second stage were low informative.
Therefore, in this work, normal operation plant data were employed in the analysis. Two different datasets (A, B) were considered, as shown in Figure 2. A cross-validation approach was developed: scenario i) first dataset (A) was used for identification purposes, and the second dataset (B) was selected for model validation; scenario ii) the two datasets were swapped: B for identification and A for validation. Note that dataset A presents levels for the two sorbents close to minimum values at different time instants, while both datasets A and B show various null values of the concentration of HCl at stack (C SME HCl ). It is clear how model identification from these routine data is not an easy task. Nevertheless, the consistent results showed in Sections III-B and III-C proved the models to be reliable despite the challenging framework in which data were collected. Note also that data could be split into different ways; sets A and B are just the first and the second half of the selected data. Identification is indeed affected by the specific dataset used; for example, higher performance is awaited when the whole data set (A+B) is employed.

B. Model identification
We tested and then compared different model structures and various model orders. As input-output structures, AutoRegressive and AutoRegressive-Moving-Average with eXogenous inputs models, that is, ARX and ARMAX models were considered. A Multi-Input-Single-Output (MISO) approach was carried out; so that, for ARMAX holds: y k + a 1 y k−1 + · · · + a n a y k−n a = b 1,1 u k−θ m −n bm + e k + c 1 e k−1 + · · · + c n c e k−n c (4) where the subscript k denotes the k − th time sample, n a is the output order, and a j its j-th coefficient; n bi is the order of the i-th input, and b i, j its j-th coefficient and θ i the corresponding time-delay; n c is the error model order, and c j its j-th coefficient. ARX models, with n c = 0, are obtained via a simple linear regression in least-square sense (LLS). ARMAX models, for which a pseudo-linear regression is required, are identified by iterative LLS.
The innovation form is used for state-space (SS) models: where y k ∈ R p , x k ∈ R n , u k ∈ R m are the system output, state, input, respectively; A ∈ R n×n , B ∈ R n×m ,C ∈ R p×n , D ∈ R p×m are the system matrices, with n the model order; K is the steady-state Kalman filter gain, computed by Algebraic Riccati Equation.
An established subspace method with a parsimonious algorithm (PARSIM-K) was adopted as an identification method [14]. To avoid numerical issues and aid the regression algorithms, for all methods input-output data were centered on their mean values (ū andȳ), that is, the identification was carried out on vectors u −ū and y −ȳ. Tables I and II show the results obtained for different model orders in terms of output data fitting for the sequential and holistic approaches, respectively. In particular, the Explained Variance was chosen as the performance index: This metrics falls into (−∞, 100];ŷ is the model output, 2 is the variance of the output data y, with respect to its meanȳ, where N is the number of time samples. Note that EV is the mean value for different model orders and both datasets (A, B). Both input-output models and statespace formulations show good performance, as high values of EV are achieved. In particular, ARMAX models give the best outcomes, while the SS identification returns an openloop unstable system for two models of high orders so that EV values are not significant (n.a. in Tables I and II).
A further discussion is reported for the results obtained on dataset A for three selected ARX models: ARX[2, (2, 2), (1, 1)] for stages I and II; ARX[2, (2, 2, 2), (1, 1, 1)] for the holistic approach, that is, stage I+II. Figure 3 shows the different trends over time of HCl concentration; measured values at point SMP2 and at stack (SME) are compared with the values identified by the selected models. Note that data shown in this Figure are not mean-centered, and the output of various ARX models can assume also negative values since the identification is not constrained. Nonlinear optimization methods could be  used in the future to identify ARX models followed by a saturation block to obtain only positive values of concentration. Moreover, Figure 4 shows the unit step responses of the same selected ARX models. Note that expected results are obtained for the sequential approach. Single increases of dosage of two alkaline sorbents produce a decrease of the corresponding HCl concentration, that is, of C SMP2 HCl for Ca(OH) 2 in stage I, and of C SME HCl for NaHCO 3 in stage II; this means that both static gains are negative. On the opposite, an increase of inlet HCl concentration causes an increase of the corresponding outlet HCl concentration, that is, of C SMP2 HCl for C SMP1 HCl in stage I, and of C SME HCl for C SMP2 HCl in stage II; in this case, both static gains are positive. In addition, a response inverse is revealed; this transient feature could be associated with an approximation of a larger time-delay or due to local remixing effects which fasten reaction rates.
On the opposite, for what concerns the holistic approach, that is, stage I+II, results are misleading for the selected ARX model with orders [2, (2, 2, 2), (1, 1, 1)]. As a matter of fact, an increase in dosage of two alkaline sorbents seems to cause an increase of HCl concentration at stack; whereas, an increase of inlet HCl concentration shows to produce a decrease of C SME HCl . Only when increasing the model time-delay it is possible to identify the expected dynamics; the behaviour shown at the bottom of Figure 4 are indeed obtained with n a = 2 and θ i = 4, i.e., ARX[2, (2, 2, 2), (4,4,4)]. This result proves the superiority of the sequential approach with respect to the holistic one when considering low-delay models. As a matter of fact, when the middle concentration of HCl (C SMP2 HCl ) is measured, two separated models can be built and, therefore, a higher prediction of the emission level at stack can be obtained. Nevertheless, it has to be noted that this is still a controlled variable of stage I and thus less informative than the HCl concentration entering the whole cleaning unit (C SMP1 HCl ).

C. Model validation
The same datasets (A, B) were then used for validation; we here test and compare the different model structures just identified in Section III-B. The results of validation for the various model orders are summarized in Tables III and IV for the two considered approaches, sequential and holistic, respectively; the index EV is again employed as a performance index. Note that this analysis concerns standard validation, that is when the model response one-step ahead in the future is Step tests for selected ARX models. Top and middle are for ARX [2, (2, 2), (1, 1)] while the bottom plot is for ARX [2, (2, 2, 2), (4,4,4)].
computed by using input-output data. The following predictor is used for ARX and ARMAX models [15]: where G(z) and H(z) are the identified discrete-time transfer function matrices in z operator, relating the output y with the deterministic input u and the stochastic noise e, respectively. SS models are validated in the innovation form to exploit the K matrix previously identified. All tested model structures confirm good performance, especially the two input-output formulations, as they return higher values of EV . ARMAX models guarantee the best results, albeit for some model orders the validation failed, in particular for the holistic approach (Table IV). Concerning the validation on C SME HCl , in both the approach for stage II and stage I+II on dataset B, the EV values for SS models generally decay when increasing the model order until divergent behavior.
Some detailed results of validation on dataset B are reported in Figure 5 for the same selected ARX models of Figure 3. The various time trends of HCl concentration are reported for the two modeling approaches; measured values at point SMP2 and at stack (SME) are again compared with the responses obtained by the selected models. As for the identification phase, also the validation of such models proves to be satisfactory corresponding to the EV values of Tables III and IV. IV. CONCLUSIONS Given the great variability in municipal solid waste composition entering waste-to-energy (WtE) plants, controlling the emissions of the corresponding acid gas treatment units proves to be a significant and challenging control problem. To this aim and to aid the possible design and implementation of advanced model-based controllers, this paper has dealt with the identification of different data-driven models based on a two-stage acid gas neutralization line in an Italian WtE plant. Routine data of the concentration of hydrogen chloride and the flow rates of the two solid alkaline sorbents deputed to its abatement have been used to produce datasets for system identification. Two modeling approaches have been selected: the sequential one considered the two abatement stages separately, while the holistic one includes the whole line. Different input-output and state-space models were selected and tested in terms of identification and then cross-validation capability. Acceptable performance in terms of prediction was obtained   [9] by ARMAX, ARX, and also SS models, with higher results for the first ones. Among the two approaches, the sequential one proves to offer the best performances with low delay models, while the holistic one needs a higher number of coefficients to obtain comparable results; the measurable internal variable in the sequential approach seems to improve the fitting of the HCl concentration at stack. Future work will be focused on building models also for the second main pollutant in the plant which is sulfur dioxide SO 2 , as well as implementing such models in advanced controllers, e.g. MPC.