In this work, we present the estimation techniques used to update the model parameters in a reduced kinetic model describing the oxidation-reduction re- actions in a hydrothermal oxidation reactor. The model is used in a nonlinear model-based controller that minimizes the total aqueous nitrogen in the reac- tor effluent. Model reduction is accomplished by com- bining similar reacting compounds into one of four component groups and considering the global reac- tion pathways for each of these groups. The reduced kinetic model developed for thk reaction system pro- vides a means to characterize the complex chemical reaction system without considering each chemicaJ species present and the reaction kinetics of every pos- sible reaction pathway. For the reaction system under study, model reduction is essential in order to reduce the computational requirement so that on-line imple- mentation of the nonlinear model-based controller is possible and also to reduce the amount of a priori information required for the model

Dellorco, Phillip C.

Flesner, Raymond L.

Le, Loan A.

Littell, Jonathan D.

Muske, Kenneth R.

UNT Digital Library

LA-UR- 99-910 Approved forpublic release; distdbution is unlimited. Title: Author(s): Submitted to: Parameter Identification and On-Line Estimation of a Reduced Kinetic Model WCEtVED Muske, Kenneth R., Villanova University- Littell, Jonathan D.-Villanova University Dellorco, Phillip C.-DX-2 Le, Loan A,- CST-6 Flesner, Raymond L.-DX-2 O S T I  MAY 0 3 899 1999 American Control Conference June 2-4, 1999 San Diego, CA Los Alamos N AT I 0 N A L LAB 0 R A T 0  RY Los Alamos National Laboratory, an affirmative actiodequal opportunity employer, is operated by the University of California for the US. Department of Energy under contract W-7405-ENG-36. By acceptance of this article, the publisher recognizes that the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher's right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness. Form 836 (1 0196) DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. Parameter Identification and On-line Estimation of a Reduced Kinetic Model Jonathan D. Littell and Kenneth R. Muske Department of Chemical Engineering, Villanova University, Villanova, PA 19085 Phillip C. Dell’Orco, Loan A. Le, and Raymond L. Flesner High Explosives Science and Technology Group Los Alamos National Laboratory, Los Alamos, NM 87545 Abstract In this work, we present the estimation techniques used to update the model parameters in a reduced kinetic model describing the oxidation-reduction re- actions in a hydrothermal oxidation reactor. This model is used in a nonlinear model-based controller that minimizes the total aqueous nitrogen in the reac- tor effluent. Model reduction is accomplished by com- bining similar reacting compounds into one of four component groups and considering the global reac- tion pathways for each of these groups. The reduced kinetic model developed for this reaction system pro- vides a means to characterize the complex chemical reaction system without considering each chemical species present and the reaction kinetics of every pos- sible reaction pathway. For the reaction system under study, model reduction is essential in order to reduce the computational requirement so that on-line imple- mentation of the nonlinear model-based controller is possible and also to reduce the amount of a priori information required for the model. 1. Introduction The parameter estimation techniques used with a re- duced kinetic model describing the hydrothermal ox- idation of hydrolysate solutions obtained from base hydrolysis of the high explosive PBX-9404 are pre- sented in the sequel. The combination of base hy- drolysis and hydrothermal oxidation is used for the destruction of this material at the Pantex Depart- ment of Energy facility in Amarillo, Texas. In this process, the high explosive material is first hydrolyzed in a batch reactor using a concentrated sodium hy- droxide solution to yield non-energetic, water soluble compounds. The result is a high pH base hydrolysate solution with reaction products that include a series of carboxylic acid salts, glycolates, primary and sec- ondary amines, and nitrites. The hydrolysate solu- tion contains from two to ten wt% of organic carbon and nitrogen compounds that must be further treated before disposal. Hydrothermal oxidation is used to eliminate the organic compounds present in the base hydrolysate solution. The oxidation reaction is carried out in a tubular reactor in which hydrogen peroxide is in- jected with the feed and at a second injection point downstream. Hydrothermal oxidation is very effec- tive at removing organic carbon compounds, how- ever, aqueous nitrogen compounds tend to be more difficult to completely remove. The resuit is the pres- ence of nitrate and ammonium ions in the aqueous effluent stream of the reactor. Since elevated con- centrations of aqueous nitrogen compounds prevent the direct discharge of the aqueous effluent, a model- based controller is used to minimize the total aqueous nitrogen in the effluent while ensuring complete de- struction of the organic carbon compounds. The model-based controller contains a plug flow reactor model that incorporates the reduced kinetic model of the hydrothermal oxidation reactions. Us- ing this model, the hydrogen peroxide injection rates required to miniiize the total aqueous nitrogen com- pounds and maintain a desired excess oxygen concen- tration in the reactor effluent are determined. The effluent aqueous nitrogen concentration is measured by nitrate and ammonium ion-selective sensors. Ex- cess oxygen is inferred from the oxygen concentration of the gas effluent stream. These measurements are used for on-line estimation of the model parameters. 2. Reduced Kinetic Model The chemical components considered in the kinetic model are total organic carbon (TOC), nitrate/nitrite (NO,), ammonia/ammonium (NH:), and oxygen ( 0 2 ) .  TOC and NO, are present in the base hydrol- ysis feed to the reactor. NH; is generated from the oxidation of the organic carbon compounds by both oxygen and NO,. Oxygen is generated from decom- position of the hydrogen peroxide injected into the re- actor. Since the hydrogen peroxide is completely de- composed in the injection line before it enters the re- actor, only oxygen is considered. The following three reactions are included in the reduced kinetic model. Each reaction is assumed to be a second order oxidation-reduction reaction. The reaction rates for each of the chemical components are in which p r  is the reactor fluid density and the con- centrations are in the units of mole/kg. The fluid density at reactor conditions is computed using the cubic form of the Peng-Robinson equation of state. The Arrhenius pre-exponential factor and activa- tion energy for the reaction rate constants and the reaction ratios are shown in Table 1. These values were determined from hydrothermal oxidation exper- iments conducted at Los Alamos National Laboratory on PBX-9404 hydrolysate solutions at temperatures between 350 C and 480 C. A complete discussion of the kinetic model development and determination of the parameter values is contained in [l]. I Ratio I Value 1 0.750 Table 1: Kinetic model parameters. Although it is possible to develop a detailed hy- drothermal oxidation reaction kinetic model that dis- tinguishes between each of the different organic car- bon and nitrogen compounds in the hydrolysate feed, a model of this scale would result in a significant increase in complexity and computational require- ments. Since the hydrolysate composition can vary depending on the operation of the hydrolysis reac- tor, characterization of the feed components would be necessary after each hydrolysis reaction in order to use this model. Due to the difficulties in accu- rately characterizing the hydrolysate feed at Pantex, this model would provide limited improvement over the simpler reduced kinetic model for the prediction of the effluent aqueous nitrogen compounds. In ad- dition, the significant increase in the computational requirements would preclude the use of this model in the model-based controller. For these reasons, a reduced kinetic model was developed for this process. 3. Optimal Reactor Operation The optimal reactor operation is achieved when the production of NH: from the T O G 0 2  reaction and the TOC-NO, reaction balances the destruction of NH: from the NHi-NO, reaction. At low perox- ide injection rates, the TOC-NO, reaction removes NO, from the system resulting in a high NH: effluent concentration. At high injection rates, the TOC-02 reaction predominates resulting in an elevated NO, effluent concentration. Figure 1 presents the efflu- ent nitrogen component concentrations as a function of the initial hydrogen peroxide injection rate for an average reactor temperature of 435C, a reactor pres- sure of 990 bar, and a hydrolysate feed rate of 150 gallday. A constant effluent excess oxygen concen- tration of 0.1 mol/kg is maintained by adjusting the second peroxide injection rate. 0 05 1 1.5 2 25 3 35 4 4.5 5 55 6 6.5 7 75 0 85 9 9.5 Wet hdrcgen PemMe K i  Rate (galMay) Figure 1: Effluent nitrogen component concentrations. 4. Model-based Controller The model-based controller solves a steady-state non- linear optimization problem to find the hydrogen per- oxide injection rates that minimize the model pre- dicted effluent total aqueous nitrogen at the desired * excess oxygen concentration target for the current hy- drolysate feed rate and operating conditions. In this optimization, HI and H2 are the first and second hy- drogen peroxide volumetric injection rates, [.]e is the effluent concentration of component c, and [O& is the excess oxygen target. (5) [021e = [@It Subject To: Reactor Model The reactor model consists of a series of four differ- ential equations, one for each of the chemical compo- nents discussed in Section 2, that describe the steady- state concentration profile in a plug flow reactor in which F is the total volumetric feed flow rate, pf is the feed density, pr is the fluid density at reactor conditions, A,  is the reactor cross-sectional area, and R(c) is the rate of reaction of component c from Eqs. 1 through 4. The excess oxygen concentration can be determined from the following expression (7) H2 [021f + (Fh + Hl) (LO21 - d [TOCI) Fh+Hl +H2 [021e = in which [02]f is the concentration of oxygen in the peroxide feed, [ 0 2 ]  and [TOC] are the model pre- dicted oxygen and total organic carbon concentra- tions in the reactor prior to the second peroxide in- jection point, and Fh is the hydrolysate volumetric feed rate. The difference between the model predicted excess oxygen concentration, [OZ]~ ,  and the concen- tration determined by the oxygen analyzer, [02],, is used to make an adjustment to the second peroxide injection rate to control the effluent excess oxygen. Q: = [O2le - [021, (8) AH2 = 2 (9) 4% + Hl) ([OZIf - [ 0 2 1 +  W O C I )  ([OZIf - [021,) - 0 ( P 2 I f  - bit) Further detail on the model-based controller is pre- sented in [2]. 5. Parameter Estimation The simplified hydrothermal oxidation reactions in the reduced kinetic model provide an adequate repre- sentation of the effluent aqueous nitrogen concentra- tions for the experimental data used to generate the model parameters [l]. However, the model must be adapted on-line to accurately predict the minimum effluent nitrogen concentration for the current reac- tor operating conditions. Due to the limited number of analytical measurements on the process, it is not possible to update each of the parameters in the re- duced kinetic model. Therefore, only the feed TOC and NO, concentrations used by the model are esti- mated on-line. The effect of changes in these param- eters on the calculated NO, and NH; effluent con- centrations are similar to the effect of changes in the kinetic parameters in Table 1 121. Accurate measure- ments of these concentrations are also not available for each hydrolysis batch. Determination of the feed concentrations based on the measured aqueous nitrogen effluent concentra- tions is performed by steady-state batch estimation using an initial estimate approach [3] N + ([NO;] e- [NO;] yt) j=1 in which [cIe is the predicted effluent concentration for component c at the current operating conditions, [c]iAt is the measured effluent concentration at time jAt, A[TOC]f and A[NOJf are the changes to the feed concentrations, At is the sample period of the es- timator, N is the number of samples in the batch, and wc and w,, are tuning parameters. The predicted ef- fluent concentrations are determined from the steady- state plug flow reactor model in Eq. 6 using the nomi- nal kinetic model parameter values in Table 1. Initial estimates of the feed concentrations are determined from analysis of the base hydrolysis solution. The ion-selective sensors used to determine the ef- fluent nitrate and ammonium concentrations measure the activity of these ions in solution. The activity co- efficient of these ions is a function of the ionic strength and temperature of the solution [4]. The concentra- tion measurements are therefore subject to error due to variation in the aqueous effluent stream tempera- ture and ionic strength. Since it is not possible to es- timate the activity coefficients from the ion-selective sensor readings and analytical corrections based on the Nernst and Debye-Huckel equations would not be reliable in the process environment, these sensor errors are not accounted for. This omission has no effect on the model-based con- troller because minimizing the activity of the nitrate and ammonium ions is equivalent to minimizing their concentration. However, these errors do effect mon- itoring the performance of the reactor. In order to - address this issue, calibration of these sensors is per- formed prior to processing a hydrolysate batch us- ing standard solutions at the expected ionic strength of the effluent. Sodium bicarbonate, the principal electrolyte in the effluent, is used to adjust the ionic strength of the standard solutions. Since the effluent nitrate and ammonium concentrations are so small, changes in their concentration have little effect on the ionic strength of the solution and, consequently, little effect on the activity coefficient. 6. Closed-loop Control The estimated feed concentrations from Eq. 10 are used to provide feedback to the model-based con- troller in Eq. 5. After the feed concentrations are estimated, the controller uses these concentrations to determine a new set of hydrogen peroxide injection rates that minimize the model predicted total aque- ous nitrogen. After a delay of one reactor residence time, the parameter estimation collects effluent sensor readings and then estimates updated feed concentra- tions. This cycle is continuously repeated during the operation of the reactor. In order to determine the effectiveness of this feed- back scheme, a Monte Carlo simulation study was first carried out before implementation on the reac- tor. The reactor operating conditions for this study were the nominal operating conditions at an average reactor temperature of 435 C, a reactor pressure of 990 bar, a hydrolysate feed rate of 150 @/day, and feed compositions of 0.9 mol/kg total organic carbon and 0.3 mol/kg nitrate/nitrite. The effluent excess oxygen concentration target was 0.1 mol/kg. A se- ries of process models were developed by randomly varying each of the reduced kinetic model parame- ters in Table 1 with normally distributed white noise. Table 2 presents the nominal values at the reactor op- erating conditions, standard deviations of the white noise sequences, and bias values for each of the model parameters. Model Parameter ~ ki Icz k3 a b d C Nominal Value 0.108 742.6 0.222 0.567 0.078 0.496 0.750 0.025 250.0 0.025 0.10 0.10 0.01 Table 2: Kinetic model parameter variation. Figure 2 compares the effluent total aqueous nitro- gen concentration probability density between open- loop and closed-loop operation. The open-loop con- troller implements the optimal hydrogen peroxide in- jections using the nominal model parameters and feed concentrations. The closed-loop controller uses the nominal model parameters with updated feed concen- trations based on the parameter estimator in Eq. 10 with no penalty on the feed concentration changes. As shown in the figure, closed-loop operation results in a lower mean effluent total aqueous nitrogen con- centration and a smaller variance. Feedback reduced the mean effluent concentration from 0.075 mol/kg to 0.065 mol/kg and the variance from 0.05 mol/kg to 0.03 mol/kg. 0 I I I I I 0.05 0.07 0.09 0.11 0.13 0.15 Concenlrab3nofTotalAqumu E61rogen(mVkg) Figure 2: Open and closed loop effluent total aqueous nitrogen. Figure 3 presents the probability density of the de- viation from the minimum achievable effluent total aqueous nitrogen concentration for the open-loop and closed-loop operation. Open-loop operation shows a significant variation of this deviation. The closed- loop operation essentially achieves the minimum ef- fluent concentration within the tolerance of the simu- lation for each of the runs. The result of feedback is a reduction in the average deviation from 0.01 mol/kg to 1 x mol/kg. The number of iterations of the model-based controller and parameter estimation scheme is also an important consideration for closed- loop operation. 7. Conclusions The reduced kinetic model in this work allows for the implementation of model-based control and on- line parameter estimation for a hydrothermal oxida- tion reaction system. A steady-state reactor model is used for the model-based control and parameter esti- mation because the computational requirements nec- 02 : I  i :  i :  0.1 ; j Figure 3: Open and closed loop deviation from minimum values. essary for a dynamic reactor model exceed the limited computational resources available. Normal operation of the hydrothermal oxidation reactor is to process a single batch of hydrolysate solution at a given set of operating conditions. Under these conditions, steady- state algorithms are adequate since the reactor feed and operation remains constant for each hydrolysate batch processed. Acknowledgments We would like to thank the Department of Energy and the DoD/DOE Memorandum of Understanding for funding this research. References [l] P. C. Dell’Orco, et al. Hydrothermal treatment of C-N-0-H wastes: Reactions of high explosive hydrolysis products. Submitted. Ind. Eng. Chem. Res., 1999. [2] K. R. Muske, et al. Implementation of model pre- dictive control on it hydrothermal oxidation reac- tor. In Proc. 1998 American Control Conference, pages 2946-2950,1998. [3] K. R. Muske and J. B. Rawlings. Nonlinear mov- ing horizon state estimation. In R. Berber, editor, Methods of Model Based Process Control, pages 349-365,1995. [4] P. W. Atkins. Physical Chemistry. W. H. Fkee- man, San Franciso, 1978. 

Parameter Identification and On-Line Estimation of a Reduced Kinetic Model

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