Distributed Activation Energy Model Research Articles

Distributed activation energy model for lignocellulosic biomass torrefaction kinetics with combined heating program

Torrefaction kinetics is fundamental for the theoretical investigation and industrial application of torrefaction processes. Most of biomass torrefaction kinetic studies focused on kinetic modelling under either isothermal or linear heating programs with one or several activation energies, which couldn't accurately reflect its reaction mechanisms. A distributed activation energy model (DAEM) was proposed to analyze logging residue torrefaction kinetics with a combined heating program at different temperatures. The model parameters were efficiently optimized by using the pattern search method. The results showed that the DAEM could excellently describe the experimental data of logging residue torrefaction at various conditions. The obtained activation energy distributions for logging residue torrefaction with the combined heating program at final temperatures of 240, 270 and 300 °C lay in the range of 154–172 kJ mol−1, 160–177 kJ mol−1 and 165–185 kJ mol−1, respectively. These findings indicated that major reactions occurring during torrefaction were the devolatilization and carbonization of biomass's hemicellulose constituents and partial decomposition of biomass's cellulose constituents. The experimental kinetic data of mesocarp fiber torrefaction at final temperatures of 220, 250 and 270 °C from the literature was also successfully described by the DAEM.

Torrefied herb residues in nitrogen, air and oxygen atmosphere: Thermal decomposition behavior and pyrolytic products characters

The thermal decomposition behavior and pyrolytic products characters of herb residue (HR) torrefied in N2, air and O2 were investigated in present work. The clear gradual regularity of samples in Van Krevelen diagram exhibited the severity and some similarities of torrefaction. The activation energy (E) calculated by distributed activation energy model (DAEM) found that the E values of torrefied samples was higher than raw HR if the conversion is below 0.8. Torrefaction treatment would beneficial to increase the yield of gas but inhibit the formation of oil, and the compounds of gas and bio-oil under different torrefaction conditions are also quite different. It should be noticed that the presence of oxygen in the torrefaction atmosphere would reduce the torrefaction temperature significantly, while maintaining the severity of torrefaction and pyrolytic products distribution.

The kinetic analysis of lignite and waste biomass during co-combustion process by general distributed activation energy model

In this work, the new general distributed activation energy model (G-DAEM) was employed to obtained kinetic parameters during co-combustion process. Four pseudo-components for both lignite and waste biomass were optimized and the simulation results demonstrated excellent match. The results suggested that the G-DAEM is an effective and comprehensive kinetic model for complex solid-state thermal reaction. Assume the pre-frequency factor A is not a fixed number, the real kinetic mechanism may be obtained by the G-DAEM method.

Comparison of pyrolysis behavior between pure coal and mixture of coal/CaO

The pyrolysis of coal mixing with CaO can produce uniform mixture of residual char and CaO, which can be further converted into calcium carbide for providing alternative way of ethyne production. Therefore, knowledge on the pyrolysis behavior of coal at the presentation of CaO is important for the industrial production of such mixture of residual char and CaO. By comparing the TG/DTG curves of pure coal and mixture coal (with CaO), it was found that the addition of CaO can promote the release of volatiles especially at lower temperature. The Distributed Activation Energy Model (DAEM) were developed for pure coal and mixture coal separately for analyzing their corresponding pyrolysis kinetics. While 2-DAEM with two-Gaussian functions is accurate enough for describing the pyrolysis of pure coal, 3-DAEM is more suitable for capturing the main pyrolysis characteristics of mixture coal. DAEM results show lower average activation energy for the pyrolysis of mixture coal than that of pure coal, further demonstrating the catalysis effect of CaO on coal pyrolysis.

A validated Distributed Activation Energy Model (DAEM) to predict the chemical degradation of biomass as a function of hydrothermal treatment conditions

This study proposes a DAEM (Distributed Activation Energy Model) approach to predict the chemical alterations of lignocellulosic biomass as a function of hydrothermal treatment conditions. The model is first tuned by an original device allowing the sample shrinkage to be continuously assessed during hydrothermal treatment in saturated water vapor up to 190 °C. The shrinkage dynamic is supplied in the DAEM model as an indicator of the degree of biomass conversion. A set of chemical analyses was performed at selected residence times and treatment temperatures to correlate this degree of conversion with the resulting chemical molecules. A set of functions was then derived from this database to correlate the degree of conversion with the components concentrations. Finally, a validation database was built with different combinations of temperature levels and residence times. The model was proved to be predictive on this new dataset.

Kinetics and characteristics of activator-assisted pyrolysis of municipal waste plastic and chlorine removal using hot filter filled with absorbents

Pyrolysis of municipal waste plastic was conducted using a two-stage pyrolysis process with auger and fluidized bed reactors. The current study comprises two parts: a kinetic study and pyrolysis experiments using activator-assisted pyrolysis. The kinetic study was performed using the distributed activation energy model, and it revealed that the average activation energy for activated molecules was 7 kJ/mol lower than that for unactivated molecules. The pyrolysis experiment confirmed that the activation of molecules resulted in an enhanced gas production. In particular, the methane and ethene yields increased by 11 and 8 wt%, respectively, when molecules were activated. A higher flow rate of the product gas used as the fluidizing gas resulted in a decrease in the gas yield. CaO and Na2CO3 were used as absorbents for chlorinated compounds produced during pyrolysis to reduce the level of Cl in the oil. The absorbents, at first, changed the product distribution, enhancing the production of mono-aromatics. In particular, the benzene yield with Na2CO3 amounted to 10 wt%. The two absorbents were excellent in reducing the Cl content in oil. Between the two absorbents, Na2CO3 proved to be the better, reducing the Cl content to 65 ppm.

Pyrolysis of furfural residue pellets: Physicochemical characteristics of pyrolytic pellets and pyrolysis kinetics

Biomass pelletization technology has recently gained significant interest, where pyrolyzed pellets have a very wide range of applications (e.g., as pellet fuels and adsorbents). In this study, furfural residue pellets (FRPs) were pyrolyzed at temperatures of 200–850 °C in a tube furnace. The physical and chemical properties of the pyrolyzed FRPs (PFRPs) obtained at various temperatures were compared, and the kinetic parameters of the pyrolysis process were calculated using the distributed activation energy model (DAEM). The PFRPs prepared at 450, 650, and 850 °C had higher volumetric energy densities than coal, whereas other properties (e.g., H/C and O/C ratios) were found to be similar to those of coal. The maximum iodine adsorption value (i.e. 317.8 mg/g) and methylene blue adsorption value (i.e. 96.4 mg/g) were achieved by pyrolysis at 650 °C and 450 °C, respectively, indicating that pyrolysis promoted the formation of micropore structures at 650 °C. Two-dimensional correlation spectroscopy (2D-COS) was employed to explore the temperature-sensitivity of the surface functional groups of the PFRPs. Based on comparison of the volumetric energy density, hydrophobicity, particle density, and strength, the PFRPs prepared at 250–300 °C afforded the best overall performance, where the sample prepared at 300 °C exhibited the maximum hydrophobicity.

Thermokinetic analysis and product characterization of waste tire-hazelnut shell co-pyrolysis: TG-FTIR and fixed bed reactor study

The synergetic effects during co-pyrolysis of waste tires and hazelnut shell biomass were investigated concerning the product distribution and reaction kinetics. The components were blended at different ratios and investigated using a thermogravimetric analyzer coupled with a Fourier Transform Infrared spectrometer. Kinetic parameters were calculated for the blends by Distributed Activation Energy Model, Straink, and Ozawa-Flynn-Wall; activation energies varied between 100 and 300 kJ mol−1. Theoretical mass loss and activation energy results showed a synergetic interaction between components, especially for the 80% waste tire and 20% hazelnut shell biomass blends. Pyrolytic oil obtained from fixed bed experiments was analyzed by GC/MS, 1H NMR, and FTIR. Although the contents were similar, significant variations in intensities were observed. Elemental analysis showed the deoxygenation effect of co-pyrolysis with lower oxygen content and higher heating value for pyrolytic oil. The results showed that co-pyrolysis of these types of waste has the potential to be co-processed for liquid fuel production with improved properties.

Application of general third-order Gaussian distribution activation energy model in the combustion of solid waste

ABSTRACT Solid waste had a variety of components, and its complex and obscure combustion behavior brought challenges to calculate the kinetic parameters accurately. Therefore, the thermogravimetric experiments of municipal solid waste and sewage sludge were carried out and a general third-order Gaussian distributed activation energy model was built. The combustion components of solid waste could be divided into three categories: light volatile components, heavy volatile components, and fixed carbon. The kinetic model matched the experimental data well, the adjR2 was above 0.9994 and the global activation energy was within a reasonable range of 54.85 kJ/mol-178.04 kJ/mol. Local sensitivity analysis found that the average activation energy had a strong influence on the stability of the model, and the degree of influence was positively correlated with the content of combustion components. In addition, the model had the ability to predict experimental data under unknown conditions.

Catalytic pyrolysis kinetic behaviour and TG-FTIR-GC–MS analysis of waste fishing nets over ZSM-5 zeolite catalyst for caprolactam recovery

Caprolactam is the main compound of nylon 6 waste fishing nets (WFNs) and its recovery conserves natural resources, maximizes WFNs economic performance, and closes the circular economy loop of the fishing net industry. Within the framework and as a part of the Healthy Seas’ initiative to clean the oceans from waste fishing nets (WFNs), and to valorise it, this research aims to study the catalytic pyrolysis behaviour of the WFNs extracted from oceans in order to study their potential applications in the energy conversion field. The catalytic pyrolysis experiments of WFNs over ZSM-5 Zeolite catalyst (2.5, 5, 10, 20, 50 wt%) were conducted using thermogravimetry (TG) coupled with Fourier-transform infrared spectroscopy (TG-FTIR) and gas chromatography–mass spectrometry (GC-MS) at different heating rates (5–30 °C/min). Also, the kinetics of ZSM-5/WFNs catalytic pyrolysis was studied by model-free methods (KAS, FWO, and Friedman). In addition, the distributed activation energy model (DAEM) and the independent parallel reaction kinetic model (IPR) combined with the optimization algorithm were used to fit the TGA-DTG experimental data and to calculate the parameters that can achieve the minimum deviation. The TGA results showed that the main decomposition zone was located in the range 342–476 °C with a total weight loss 83-75 wt% (based on the amount of catalyst). Meanwhile, FTIR and GC-MS results manifested that alkyl C–H stretch functional group, carbonyl functional group (CO), and caprolactam (83.15%; at 20 wt% of ZSM-5) are the main groups and volatile compounds in the decomposed WFNs samples. The model-free kinetics analysis showed that all activation energies were estimated at 112 kJ/mol (WFNs) and 158, 230, 197, 201, and 220 kJ/mol for ZSM-5/WFNs samples (2.5, 5, 10, 20, 50 wt%). At the same time, DAEM and IPR models proved a high prediction to fit TG curves at all heating rates. Based on these results, catalytic pyrolysis using 20 wt% of ZSM-5 can be used as a promising technology for extracting caprolactam from WFNs with high yield (83%). The recovered caprolactam can be used in the production of nylon fibres, nylon thin films, carpets, textiles, resins, etc.

An investigation into the pyrolysis and oxidation of bio-oil from sugarcane bagasse: Kinetics and evolved gases using TGA-FTIR

Bio-oil produced from the pyrolysis of sugarcane bagasse has the potential to be used as a sustainable and renewable energy source. In the present study, a non-isothermal thermo-gravimetric analysis (TGA) of the pyrolysis (in N2 atmosphere) and combustion (in the air) of bio-oil from sugarcane bagasse was investigated at three heating rates: 5, 10, and 20 °C/min. The sample was heated from room temperature up to 900 °C and the evolved gases in the TG furnace were carried to a Fourier transform infrared (FTIR) cell where the composition of the gases and the functional groups present there were analyzed. A global kinetic analysis was performed to obtain the Arrhenius kinetic parameters for the pyrolysis and oxidation of the bio-oil using the distributed activation energy model. Three distinct stages, namely; low-temperature oxidation (LTO), fuel decomposition (FD), and high-temperature oxidation (HTO) were observed during the oxidation of bio-oil. The initial devolatilization of the oxygenated compounds observed during pyrolysis was similar to the LTO stage observed during combustion. The intensity of the CO2 FTIR peaks seen during the bio-oil combustion was 10 times the intensity of the CO2 peaks attained during pyrolysis. The TGA-FTIR analysis of the sugarcane bagasse bio-oil sheds new light on its thermal degradation/oxidation characteristics.

Pyrolysis kinetic behavior and TG-FTIR-GC–MS analysis of end-life ultrafiltration polymer nanocomposite membranes

This is the first research to be concerned with end-life ultrafiltration polymer nanocomposite membranes and their valorization into high added-value products using the pyrolysis treatment. Polysulfone membrane (PES) as a commercial product and their nanocomposites (CNTs/PES and graphene/PES) were used as a feedstock in the present research. The experiments started with fabrication of membranes loaded with 0.04 wt% of CNTs and graphene (GNs). The elemental analysis and proximate analysis of the fabricated membranes were studied. Subsequently, thermogravimetric coupled with Fourier-transform infrared spectroscopy (TG-FTIR) system was used to study the thermal and chemical decomposition of the membranes at different heating rates (5-30˚C/min). The volatile products released from the pyrolysis process of the membranes were analyzed using TG coupled with gas chromatography–mass spectrometry (GC–MS) unit. Finally, pyrolysis kinetic parameters of PES membrane and its nanocomposites were studied using model-free models. Also, thermogravimetry and differential thermal gravimetry (TG/DTG) experimental data were simulated using the distributed activation energy model and the independent parallel reactions kinetic model with high predictability. The results showed that sulfur dioxide, benzene, phenol, and diphenyl ether compounds represented the main compounds in the released volatile components with high total abundance, especially at high heating rate and estimated at 85% (PES), 94% (CNTs/PES), and 99% (GNs/PES). Meanwhile. the kinetics analysis showed that the whole activation energies decreased significantly in case of nanocomposites by this trend 206.4 kJ/mol (PES), 187.8 kJ/mol (CNTs/PES), and 139.30 kJ/mol (GNs/PES), what indicates that CNTs and GNs act as self-catalysts and end-life polymer membranes can be used as a new source for renewable energy.

Multi-distribution activation energy model on slow pyrolysis of cellulose and lignin in TGA/DSC

Developing a kinetic model to analyze the multi-step reaction of biomass pyrolysis is pivotal to elucidate the mechanism of the pyrolysis. For this purpose, a model-fitting method such as multi-distribution the Distributed Activation Energy Model (DAEM) is one of the most reliable methods. DAEM with 4 different distribution functions of Gaussian, Logarithmic, Gumbel, and Cauchy was utilized to characterize the pyrolysis of cellulose and lignin during Thermogravimetric Analysis/Differential Scanning Calorimetry (TGA/DSC) instrumentation. By comparing Derivative Thermogravimetry (DTG) and DSC profiles, determination of pseudo-components can be done more accurately. A kinetics analysis on the pyrolysis of cellulose with a single Gaussian distribution DAEM yielded a single activation energy of 178 kJ mol−1 with a narrow standard deviation. This result was justified by a single and dominant endothermic peak followed by minor exothermic peaks in the DSC result. For lignin pyrolysis, the presence of multiple peaks is characterized by four pseudo-components in DAEM with activation energies of 157, 174, 194, and 200 kJ mol−1. These pseudo-components were confirmed by the DSC result which indicated the occurrences of two exothermic peaks with two lesser exothermic or possibly endothermic peaks at the same temperature range. These findings imply the importance of DSC to support a kinetics study of thermogravimetric pyrolysis.

Estimation of the kinetic parameters of chlorinated polyvinyl chloride waste pyrolysis by particle swarm optimization

AbstractChlorinated polyvinyl chloride (CPVC) is a widely‐used material in various fields with excellent properties. However, CPVC waste is one of the most intractable solids to dispose of. With the development of pyrolysis technology, some advantages have been exhibited, for example, it is flexible to convert solid waste into clean products by pyrolysis, which can be used as energy. Therefore, pyrolysis is considered as an effective method to dispose of solid waste. Especially, kinetic parameters are significant for pyrolysis, which contributes to reactor design and waste management. To better apply the kinetic parameters of CPVC to dispose of waste, thermogravimetric experiments were conducted to obtain the kinetic parameters and establish the reaction mechanism. The Tang, distributed activation energy model, and Advanced Vyazovkin methods were used to calculate the activation energy, and the reaction order was obtained by the Coats‐Redfern method. The results showed that the reaction consisted of two stages, and the average activation energy of the corresponding stage was 153.27 and 290.55 kJ/mol, respectively. However, the abovementioned parameters by traditional methods were not enough to characterize the whole pyrolysis behaviors, then the obtained kinetic parameters were further optimized and extra parameters were computed by the Particle Swarm Optimization algorithm.

Influence of carbon black filler on pyrolysis kinetic behaviour and TG-FTIR-GC–MS analysis of glass fibre reinforced polymer composites

Recently, several filler materials, such as carbon black (CB), have been added to glass fibre reinforced polymers (GFRP) to enhance their mechanical and electrical performance. So far, we have insufficient information on the effect of these additives on the recyclability of GFRP and the resulting products. Within this context, this is the first research developed to study the effect of these additives on pyrolysis behaviour of GFRP. The experiments were started with dispersion of CB in epoxy resin solution, then CB/GFRP panels were prepared using vacuum-assisted resin transfer technique, followed by grinding to prepare the feedstock. The ultimate, proximate, and morphological properties of the CB/GFRP samples were analysed. Afterwards, TG-FTIR-GC measurements were conducted on the milled samples at several heating rates. Depending on the TG analysis, the pyrolysis kinetics of CB/GFRP were studied using both linear and nonlinear isoconversional methods (i.e., Kissinger, KAS, FWO Friedman, Vyazovkin, and Cai). Also, TGA-DTG data was simulated using the distributed activation energy model and the independent parallel reactions kinetic model. The results show that the fibre is rich in volatile content (45%), while aromatic benzene and C–H bond were the major groups in the TG-FTIR analysis. In addition, phenol and p-Isopropenylphenol were the major compounds in the GC-Ms measurements with abundance of 67% (with improvement of 146% compared with neat GFRP) and 33%. Meanwhile, the pyrolysis kinetic showed that KAS, Vyazovkin, and Cai models are the most appropriate isoconversional methods that can be used to study of the pyrolysis kinetic of CB/GFRP with estimated activation energies in the ranges of 198–209 kJ/mol (with improvement of 64% compared with neat GFRP). Based on that, the filler materials added to GFRP composites, including CB filler, act as self-catalysts during the pyrolysis treatment leading to increased yield and better quality of the formulated volatile compounds.

A predictive PBM-DEAM model for lignocellulosic biomass pyrolysis

Pyrolysis is a promising and attractive way to convert lignocellulosic biomass into low carbon-emission energy products. To effectively use biomass feedstock with size distribution to produce biofuels, a comprehensive kinetic model of the process, occurring at particle level, is important. In this study, the population balance model (PBM)-distributed activation energy model (DAEM) coupled model is first time developed to predict biomass pyrolysis. The Population balance model is used to present the variable size distribution of solid, decomposed from virgin biomass to porous char. Two different kinetic models are embedded into the conservation equations of mass and energy. They are compared to demonstrate the prediction performance of heating-up time during the pyrolysis process of biomass with a normal size distribution. It is found that non-isothermal kinetics without and with DEAM capture the intra-particle temperature distribution. There is a noticeable difference of heating-up time between single and distributed particle size.

Mixed biochar obtained by the co-pyrolysis of shrimp shell with corn straw: Co-pyrolysis characteristics and its adsorption capability

The co-pyrolysis characteristics of shrimp shell (SS) with corn straw (CS) were investigated by comprehensive characterization to reveal the synergistic effects and further discuss the adsorption capability. TGA results showed that pyrolysis behavior and reactivity were improved with the increase of heating rate and doping ratio of CS. Flynn-Wall-Ozawa (FWO) and distributed activation energy model (DAEM) indicated that co-pyrolysis can effectively reduce energy consumption and promote the decomposition of CaCO3. TG-FTIR and Py-GC/MS analysis indicated that the release of CH4, CO2, CO and NH3 at the doping ratio of 25% CS (75SS+25CS) was higher than that at other doping ratios, and the relative proportions of N-heterocyclics and oxygenates were lower, which was conducive to the development of pore structure for mixed biochar and effectively alleviated the pollution during co-pyrolysis process. The structure of mixed biochar was improved, confirmed by the characterizations of BET, SEM, FTIR and XRD. The mixed biochar prepared at 800 °C (75SS+25CS800) exhibited optimal porosity, aromatization and the most thorough CaCO3 decomposition. Batch adsorption experiment showed that the removal rate of 50 mg/L Cu(II) by 75SS+25CS800 was close to 100% under the dosage of 1 g/L and pH = 3–6. The adsorption process was well described by Langmuir, pseudo-second-order and Webber-Morris model, illustrating diffusion monolayer chemisorption was the main adsorption mechanism of Cu(II) on 75SS+25CS800. The maximum adsorption capacity of 75SS+25CS800 for Cu(II) was 79.77 mg/g at 35 °C. In short, this study provided a reference in optimizing the preparation process and improving the adsorption performance of mixed biochar.

An evaluation of the reactivity of synthetic Fe-Ni oxygen carriers: CO oxidation, H2O reforming, and toluene cracking

NiFe2O4 is an ideal oxygen carrier for the chemical looping process. This study focused on the evaluation of NiFe2O4 reactivity in relation to CO oxidation, H2O reforming and toluene (model tar) cracking. The NiFe2O4 was synthesized by the coprecipitation (CP), solid state (SS) and sol–gel (SG) methods for the TG and fixed bed experiments. We proposed a distributed activation energy model of the time integral, namely, DAEM-TI, for the evaluation of the reactivity of NiFe2O4 for CO oxidation (nonisothermal condition) and H2O reforming (isothermal condition). The goodness of the model fitting agreed well with the experimental data for CO oxidation (nonisothermal condition) but was slightly worse for H2O reforming (isothermal condition). The average activation energy, Emean, obtained by DAEM-TI was successfully used to determine the reactivity rank for different oxygen carriers. Emean analysis showed that the reactivity rank for CO oxidation was determined to be sample SG, sample SS and sample CP, and for H2O reforming, the rank determined to be sample CP, sample SG and sample SS. These results agreed well with TG analysis, and this finding will inspire the applications of the DAEM. In general, the sample SG showed better reactive performance for CO oxidation, H2O reforming and toluene cracking compared to the other samples. The inert support significantly increased the multiple redox cycle reactivity of NiFe2O4, and the improvement due to the inert support was ranked as follows: ZrO2≈Al2O3 > TiO2(anatase) > TiO2(rutile) > SiO2.

Pyrolysis kinetics of wildland vegetation using model-fitting methods

Slow-heating pyrolysis experiments of 14 plant species native to forests in the southern United States were conducted in a TGA to find the kinetic parameters for slow pyrolysis of all live and air-dried plant samples. Kinetic coefficients were determined from the data using model-fitting methods, resulting in single kinetic parameters for the entire pyrolysis process which can be used by wildland fire modelers. The model forms explored here are a simple one-step model and single and multiple reaction distributed activation energy (DAE) models. The mass loss and derivative mass loss data were fitted simultaneously at heating rates of 10, 20, and 30 °C min−1 to find kinetic parameters for these model forms.The multiple-reaction DAE model gave the best fit to the pyrolysis data at multiple heating rates when multiple peaks were observed. The multiple pyrolysis peaks were attributed to decomposition of hemicellulose, cellulose, and lignin, based on literature observations for biomass. The order of activation energies for pyrolysis of all plant species indicated that hemicellulose and extractives decompose more readily than cellulose and finally lignin.

A two-dimensional distributed activation energy model for pyrolysis of solid fuels

Pyrolysis kinetic models are pivotal for understanding and optimizing the gasification, distillation, and combustion processes. This paper proposes a novel two-dimensional distributed activation energy model (2D-DAEM), which is achieved via extending the classical DAEM to the 2D plane of activation energy E and pre-exponential factor A. The performance of the proposed model was evaluated based upon comprehensive analyses of complex reactions such as co-pyrolysis. The results show that the 2D-DAEM outperforms the classical DAEM in terms of efficiency and accuracy. Specifically, the co-pyrolysis analysis of pine woodchips (PINE) and polyethylene terephthalate (PET), shows that the classical DAEM tends to underestimate the lnA values (i.e., 43.0 for PINE pyrolysis; 42.0 for PET pyrolysis; but 39.2 for PINE&PET co-pyrolysis), while the lnA value of 2D-DAEM (about 43.0 for all) is more reasonable. Additionally, the 2D-DAEM is employed to study the influence of coal particle size on pyrolysis. It is observed that the 25 μm coal has the highest reaction rate under both 500 K and 1500 K iso-thermal processes. As a more normative, reasonable, and accurate model, the proposed 2D-DAEM is bound to enhance the practice of reaction prediction, material analysis, and process design.