Reaction Rate Equation Research Articles

Exploring tubular steady‐state laminar flow reactors with orthogonal collocation

AbstractThe laminar flow reactor (LFR) is one of the most comprehensive problems in chemical reaction engineering, as its modeling involves mass, heat, and momentum conservation equations coupled with chemical reaction rate equations. It is relatively easy to grasp its basic operation, but the solution of the problem is far from trivial. Although there are analytical solutions that simplify the problem, students and tutors must use efficient numerical strategies to appropriately solve some LFR problems. In the present investigation, we solve several different cases of two‐dimensional cylindrical LFR, beginning with the isothermal case, as a benchmark. Calculations were performed using the Chebyshev orthogonal collocation technique by custom scripts in Scilab, Mathematica©, and Matlab®, and were compared with solutions available from the ECRE Version of COMSOL®, which was used as the reference, as well as available analytical solutions in the literature. After analyzing the case of the isothermal LFR with Newtonian fluid, we explored non‐Newtonian fluids, including Carreau and Bingham fluids, whose LFR results are not available in the preceding literature. For Newtonian fluids, besides (a) the isothermal case, we also explore other three nonisothermal design cases: (b) cooling jacket with a fixed heat exchange coefficient at the wall, (c) adiabatic operation, (d) nonisothermal LFR with isothermal wall. Through a performance criterion, the different operation models are compared and we show that nonisothermal design cases perform better than the isothermal case. Computation times, for different scenarios, are quite short and taking 25 nodal points or more suffice for an accurate and timely solution of the more complex problem Case (b). The numerical modeling approach is useful from a pedagogical standpoint, as one can compare numerical results with classical assumptions, and progress from a more restrictive conceptual model (segregated flow) to an array of different kinds of operation with the LFR in which one needs to consider diffusion and temperature distribution.

Modeling of Lithium-Flow Batteries with Aqueous Electrolyte

Flow batteries with aqueous electrolyte at the cathode are safe, low-cost and ecofriendly energy storage systems. When the aqueous cathode is coupled with a Li-metal anode with organic electrolyte, these batteries have extremely high energy densities (over 4,000 Wh/Kg), which makes them attractive not only for grid applications (where flow batteries are often used) but also in maritime applications such long endurance surface vessel systems and wave gliders [1-4]. In this presentation, we derive the mathematical model for lithium-flow batteries and use this model to predict the performance of the batteries under different discharge conditions, cathode microstructures, water flow velocities, etc. The results are then compared to experimental data already available in the literature. The mathematical model is based on coupling the flow equations (Navier-Stokes) with electrochemical equations for reaction rates and using average microscopic models for the cathode. For instance, Fig. 1 shows the voltage of a flow battery as a function of time for different water velocities in a flow battery simulated by solving the above model. For low water velocities, the water is not able to provide enough oxygen in the cathode and the voltage of the battery collapses after a few seconds. However, as long as the water velocity is above approx. 1.2 cm/s, the battery will have enough oxygen to operate continuously; in this case, the higher the flow of the water, the higher the voltage of the battery in the stationary state will be because of lower overpotential losses. In these simulations, the anode contained Li-metal. The cathode had a length of 1 cm (measured in the direction of water flow) and a thickness of 100 μm. The cell was discharged at a small rate of 0.01 mA/cm2. The incoming water had an oxygen concentration of 5 mg/l (which is equal to the oxygen concentration in seawater) and was pumped through the cathode at different velocities. A detailed derivation of the mathematical model and more simulation results and predictions will be presented at the meeting.

A theory of phonon-induced friction on molecular adsorbates

In this manuscript, we provide a general theory for how surface phonons couple to molecular adsorbates. Our theory maps the extended dynamics of a surface's atomic vibrational motions to a generalized Langevin equation, and by doing so captures these dynamics in a single quantity: the non-Markovian friction. The different frequency components of this friction are the phonon modes of the surface slab weighted by their coupling to the adsorbate degrees of freedom. Using this formalism, we demonstrate that physisorbed species couple primarily to acoustic phonons while chemisorbed species couple to dispersionless local vibrations. We subsequently derive equations for phonon-adjusted reaction rates using transition state theory and demonstrate that these corrections improve agreement with experimental results for CO desorption rates from Pt(111).

A clean metallurgical process for vanadium precipitation from vanadium-rich solutions

Ammonium salt vanadium precipitation process has excellent performance in industrial production, but its shortcomings such as high cost and environmental impact are not conducive to sustainable development. In this paper, ethylenediamine was selected as the precipitant, and vanadate was precipitated from acidic simulated vanadium-rich solutions by the ammonium salt precipitation process. The high purity V2O5 product was obtained after calcination. Under optimal conditions, the precipitation rate of vanadium reached 94.8 %, and the purity of vanadium was as high as 99.1 %. The vanadium precipitation product was hexamethyl ammonium, and the vanadium product was V2O5. It can be derived by the differential method that the reaction order was n = 2.4, the reaction rate equation was CV-1.4=kt+a, and the apparent activation energy was 27.8097 kJ/mol, which can be classified as the diffusion-controlled reaction. This innovative process enables a savings of 5050 yuan per ton of V2O5. On this basis, a complete V2O5 production process with zero waste discharge was designed.

ELECTROSYNTHESIS OF Cu2O IN THE Cu(s)|CuSO4(aq)|Fe(s) REACTOR AND DEGRADATION POTENT FOR METHYLENE BLUE

Research on Cu synthesis2O uses the electrolysis method in the Cu(s)|CuSO4(aq)|Fe(s) system and degradation tests on methylene blue. Cu2O is a blackish-red solid which has properties as a semiconductor with a band gap of around 2-2.2 eV. These transition metal oxides are widely used as catalysts, solar cell components, and photodetectors. This research aims to synthesize Cu2O with variations in electrolysis time, determine the characteristics of Cu2O using FTIR and XRD, and test the degradation of methylene blue. The method used is electrolysis with a fixed potential and time variations. Research stages include solution preparation, determination of decomposition potential, electrolysis of samples under various conditions, and analysis. The results of determining the decomposition potential are used as the application potential value in the copper electrolysis process, namely 3.25 V. Sample electrolysis was carried out at a potential of 3.25 V, solution pH 4.0 in a volume of 100 mL at 30, 60, 90, and 120 respectively. and 150 minutes. The products obtained were analyzed using Fourier Transform Infra-Red (FTIR) and X-ray diffraction (XRD). The results of FTIR analysis show that before calcination there is a Cu-O functional group with a wave number of 477.23 cm-1 and after calcination, there is a Cu-O functional group with a wave number of 538.28 cm-1 which indicates the formation of oxide. The results of XRD analysis show that the value of 2θ before calcination is 36.553; 50,481 ; 62.855 which shows the peak of Cu and after calcination 29.928; 36,027 ; 61.568 shows the Cu2O peak. The highest photocatalytic activity test results for Cu2O against methylene blue were 85.96%. The rate of degradation of methylene blue by Cu2O follows the second order reaction rate equation with the R2 value and reaction rate constant being 0.9418 and 0.00769572 L mol-1 s-1, respectively.

Expansion displacement mechanics model of concrete under seawater corrosion

In this study, the variation in the expansion displacement of concrete samples with different water-cement ratios under five corrosion solutions (single sulfate salt and coupled sulfate-chloride salt) is explored. The expansion displacement evolution of these concrete samples under sulfate corrosion (single salt corrosion) and sulfate-chloride corrosion (double salt corrosion) is comprehensively examined. The results reveal that the continuous accumulation of corrosion damage eventually manifests in the form of expansion displacement. Based on the experimental results and the chemical reaction rate equation of the delayed ettringite formation and Friedel’s salt generation, an evolution model of expansion force is established. According to this model and the Weibull distribution law of damage, a expansion displacement mechanics model is proposed to predict the expansion displacement behavior of concrete under sulfate corrosion as well as combined sulfate-chloride corrosion.

Synthesis of Propylene Glycol Methyl Ether Acetate: Reaction Kinetics and Process Simulation Using Heterogeneous Catalyst

Propylene glycol methyl ether acetate (PGMEA) serves as a crucial solvent in semiconductor and display material processes, demanding high purity and low acidity. Despite its significance, its conventional synthesis method using homogeneous catalysts requires extensive purification. Our study explores the use of Amberlyst-15, a stable solid catalyst, to streamline this process. Through batch reactions with a 1:1 reactant ratio at various temperatures and modeling using an integrated reaction rate equation, we obtained kinetic parameters. These parameters were used to predict the kinetics under different reactant ratios and different catalyst amounts, and the predictions match well with experimental results, especially when we used the catalyst amount scaled by the amount of the limiting reactant (PGME) rather than the total amount of the reactants. This highlights the importance of reporting kinetic parameters with proper scaling for catalyst used. Furthermore, we integrated these parameters into process simulations to determine the length of a plug flow reactor (PFR), constructed a PFR system, and confirmed that the simulation results matched well with experimental data obtained from the PFR system. Our findings suggest Amberlyst-15’s potential in simplifying PGMEA synthesis, promising advancements in industrial applications.

Liquid Hot Water (LHW) and Hydrothermal Carbonization (HTC) of Coffee Berry Waste: Kinetics, Catalysis, and Optimization for the Synthesis of Platform Chemicals

Colombia is the world’s leading producer of mildly washed arabica coffee and produces 12.6 million bags of green coffee, but at the same time, 784,000 tons of waste biomass are dumped in open fields, of which only 5% is recovered or used. The objective of this project was to evaluate the production of platform chemicals from these coffee wastes for sustainable resource management. To achieve this, biomass characterization was carried out using proximate analysis, ultimate analysis, and structural analysis. Hydrothermal valorization was carried out at a temperature range of 120–180 °C (LHW) and 180–260 °C (HTC) for one hour. The platform chemicals obtained were quantified by HPLC-RI and monitored by pH and conductivity, and the solid fraction was characterized by monitoring the functional groups in IR spectroscopy and elemental analysis. Hydrolysis processes were obtained at 150 °C, production of platform chemicals at 180 °C, and maximum concentration at 180 °C-4 h; over 200 °C, degradation of the products in the liquid fraction starts to take place. Homogeneous basic and acid catalysts were used to improve the yields of the reaction. The kinetics of the hydrolysis of lignocellulosic structures to sugars were also analyzed and described, and reaction orders of 1 (LHW), 3 (HTC), and their respective reaction rate equations were reported.

The Impact of Effective Matter Mixing Based on Three-dimensional Hydrodynamical Models on the Molecule Formation in the Ejecta of SN 1987A

To investigate the impact of matter mixing on the formation of molecules in the ejecta of SN 1987A, time-dependent rate equations for chemical reactions are solved for one-zone and one-dimensional (1D) ejecta models of SN 1987A. The latter models are based on the 1D profiles obtained by angle-averaging of the three-dimensional (3D) hydrodynamical models, which effectively reflect the 3D matter mixing; the impact is demonstrated, for the first time, based on 3D hydrodynamical models. The distributions of initial seed atoms and radioactive 56Ni influenced by the mixing could affect the formation of molecules. By comparing the calculations for spherical cases and for several specified directions in the bipolar-like explosions in the 3D hydrodynamical models, the impact is discussed. The decay of 56Ni, practically 56Co at later phases, could heat the gas and delay the molecule formation. Additionally, Compton electrons produced by the decay could ionize atoms and molecules and could destroy molecules. Several chemical reactions involved with ions such as H+ and He+ could also destroy molecules. The mixing of 56Ni plays a nonnegligible role in both the formation and destruction of molecules through the processes above. The destructive processes of carbon monoxide and silicon monoxide due to the decay of 56Ni generally reduce the amounts. However, if the molecule formation is sufficiently delayed under a certain condition, the decay of 56Ni could locally increase the amounts through a sequence of reactions.

A parameter determination method of powder burn model based on Levenberg-Marquardt optimization

ABSTRACT The powder burn model is a mathematical model used to characterize the combustion behavior of energetic materials. In this paper, a parameter determination method for the powder burn model is proposed based on the Levenberg-Marquardt (L-M) optimization algorithm, establishing connections between internal ballistics parameters and powder burn model parameters. Taking a 4/1 single-base propellant as an example, the detailed fitting process is presented, and error analysis is conducted. The fittings of the gas state equation and reaction rate equation of powder burn model converge at the 15th and 22nd iterations, respectively. Both fittings displayed a high level of accuracy, with an R-squared value of 0.999. The comparison with the results of the closed bomb experiments demonstrates excellent agreement between pressure-time curves calculated by the powder burn model and the internal ballistics model, confirming their suitability for describing the combustion behavior of propellants. This method provides a foundation for numerically simulating the internal ballistics combustion behavior of energetic materials.

Correct Use of the Bhatia and Perlmutter Random Pore Model under Nonisothermal Conditions.

The classic random pore model (RPM) of Bhatia and Perlmutter [A random pore model for fluid-solid reactions: I. Isothermal, kinetic control. AIChE J.1980, 26, 379-386], which has been used in the kinetic analysis of numerous gas-solid processes involving porous materials under reaction control, was originally derived only for isothermal conditions. This has not prevented many researchers from using it in nonisothermal conditions, a frequent procedure whose validity has not been demonstrated until now. In this work, different questions are answered: Are the isothermal equations of the RPM valid under nonisothermal conditions? And, related to this question, is the commonly used conversion function correct? This work provides the scientific basis that was missing until now for the use of the RPM in nonisothermal conditions, as well as the correct conversion function for such use over the entire particle size range. The said RPM conversion function has been obtained from the exact formulation of the reaction rate equation, and as it should have been originally, it has the grain model function as one of its particular solutions. In this way, the gap that prevented the use of the random pore model for very low particle size values has finally been closed.

Kinetics of Homogeneous Reaction of Potassium Methoxide Based on K2CO3 Catalyst in Transesterification of RBDPO to Biodiesel

Biodiesel production is generally catalyzed by potassium methylate or sodium methylate catalysts based on KOH and NaOH and these catalysts are still imported. The search for a cheap and effective catalyst continues to be carried out by researchers. One of the catalyst support materials currently in use involves impregnating K2CO3 with various substances, resulting in a heterogeneous catalyst. In this study, it was tried to use K2CO3 dissolved in methanol to produce a homogeneous potassium methylate catalyst. Potassium methylate-based homogeneous catalyst K2CO3-methanol is proven to have a very high function in the transesterification reaction of Refined Bleached Deodorized Palm Oil (RBDPO) into biodiesel, this is evidenced by the use of a catalyst percentage of 2% w and 30% w methanol to the weight of RBDPO resulting in an acid content in biodiesel of only 0.12% and a total glycerol of 0.124% in reaction time 3 hours, with the purity of the methyl ester in biodiesel reaching 98.80%. Meanwhile, for the calculation of homogeneous reaction kinetics, a reaction rate equation is produced where the order of the RBDPO transesterification reaction is order 2 (two) and the reaction rate constant is 0.0044.

BioModME for building and simulating dynamic computational models of complex biological systems.

Molecular mechanisms of biological functions and disease processes are exceptionally complex, and our ability to interrogate and understand relationships is becoming increasingly dependent on the use of computational modeling. We have developed "BioModME," a standalone R-based web application package, providing an intuitive and comprehensive graphical user interface to help investigators build, solve, visualize, and analyze computational models of complex biological systems. Some important features of the application package include multi-region system modeling, custom reaction rate laws and equations, unit conversion, model parameter estimation utilizing experimental data, and import and export of model information in the Systems Biology Matkup Language format. The users can also export models to MATLAB, R, and Python languages and the equations to LaTeX and Mathematical Markup Language formats. Other important features include an online model development platform, multi-modality visualization tool, and efficient numerical solvers for differential-algebraic equations and optimization. All relevant software information including documentation and tutorials can be found at https://mcw.marquette.edu/biomedical-engineering/computational-systems-biology-lab/biomodme.php. Deployed software can be accessed at https://biomodme.ctsi.mcw.edu/. Source code is freely available for download at https://github.com/MCWComputationalBiologyLab/BioModME.

First-principles-based microkinetic modeling of methanol steam reforming over Cu(111) and Cu(211): structure sensitive activity and selectivity.

The development of hydrogen energy is widely recognized as a key approach to addressing the energy and carbon emission challenges. Methanol steam reforming is a promising hydrogen production scheme that can provide high-purity hydrogen. In this work, we studied the primary reaction mechanisms of methanol steam reforming over the Cu(111) and Cu(211) surfaces using density functional theory (DFT) calculations and microkinetic simulations. A detailed kinetic perspective on the reaction mechanism, which is often overlooked in previous research that relies solely on DFT calculations, is provided in the current work. Our findings reveal that under typical experimental conditions, the dominant mechanism on the Cu(111) surface is the methyl formate mechanism, while the H2COO dehydrogenation mechanism is dominant on Cu(211). The activity over the Cu(111) surface was slightly higher than that over Cu(211). Based on the degree of rate control analysis results, a reaction rate equation was derived to quantitatively explain the trend of activity under different operating conditions. It was also found that CO2 selectivity was significantly higher over Cu(211) than over the Cu(111) surface. Furthermore, based on the Wulff construction scheme, copper nanoparticle models with different sizes were constructed, and a detailed structure sensitivity study was executed. This comprehensive investigation sheds light on the mechanisms of methanol steam reforming reactions over the Cu(111) and Cu(211) surfaces, providing essential insights for the design of high-performance catalysts for hydrogen production.

First principle based rate equation (1pRE) for reduction kinetics of Fe2O3 with syngas in chemical looping

Chemical looping combustion (CLC) of solid fuel is a promising technology with inherent CO2 separation and low energy penalty for CO2 capture. Syngas is main intermediate species of solid fuel conversion in CLC, the reduction kinetics of oxygen carriers with syngas play a crucial role in CLC systems. However, the current research obtains the reaction rate constants by fitting the apparent models with the experimental data, and cannot explain the reduction kinetics behavior from a microscopic level. It remains a challenge to compute the reduction kinetics of oxygen carriers with syngas directly from first-principles density functional theory (DFT) without fitting experimental data. This study proposes a first-principle-based rate equation (1pRE) theory and integrates it into the random pore model (RPM) to predict the kinetics of Fe2O3 reduction by syngas in CLC. The developed 1pRE theory utilizes DFT calculations to search for reaction pathways and energy barriers of elementary reactions. Then the DFT data are introduced into the statistical mechanics partition function and transition state theory (TST) to calculate the reaction rate constants. Microkinetic rate equations of elementary reactions occurring at the surface scale are developed to describe the change of surface coverage of different surface species. The 1pRE theory is integrated into the RPM to account for the influence of particle-scale structural changes on the overall conversion rate during the reduction process. The theory can predict the reduction kinetics of oxygen carriers without fitting experimental data and establishes a connection between microscopic insights and macroscopic phenomena. The accuracy was validated by experimental data of Fe2O3 oxygen carriers obtained from the thermogravimetric analyzer (TGA) in the atmosphere of syngas. The developed 1pRE predicts the reduction kinetics of oxygen carriers accurately and can be used to optimize the design of oxygen carrier materials and the scale up of CLC reactors.

Rate Equations for Reversible Disproportionation Reactions and Fitting to Time-Course Data.

Integrated rate equations are straightforward to fit to experimental data to verify a proposed mechanism and to extract kinetic parameters. Such equations are derived for reversible disproportionation/comproportionation reactions with any set of initial concentrations. Extraction of forward and reverse rate constants from experimental data by fitting the rate law to the data is demonstrated for the disproportionation of 2,2,6,6-tetramethyl-1-piperidinyl-N-oxyl (TEMPO) under acidic conditions where the approach to equilibrium is observed.

Mechanistic analysis of the electro-reduction of oxygen to water on electrode surfaces partially inhibited by electro-oxidation

A mechanistic model for the oxygen reduction reaction (ORR) on noble-metal electrodes was proposed, which considers the possible inhibition of active sites by electro-oxidation and the electro-reduction of dissolved oxygen to water on non-inhibited sites through the simultaneous occurrence of two parallel routes. Equations for describing steady state ORR polarization curves were derived by solving this mechanism without aprioristic restrictions on rate-determining steps. In this model the electro-oxidation of the metallic surface sites occurs in parallel with the ORR, causing the formation of subsurface oxides that block the active sites capable to adsorb ORR intermediates. For accounting the potential-dependent inhibition, metal electro-oxidation was described through a single-step reaction, assuming Frumkin-type interactions of the oxidized metal sites. On the other hand, reaction-rate equations were derived for the ORR operating through the simultaneous occurrence of two routes, so-called the dissociative (DP) and the associative (AP) pathways, which involve the adsorption of oxygen on the non-inhibited active sites as Oad and OOHad, respectively. An analysis of the effects of elementary kinetic and adsorption parameters allowed to visualize the effects that the electro-oxidation reaction causes, together with the ORR kinetics, on the polarization curves, particularly at low overpotentials. The obtained expressions were used to correlate reported experimental polarization curves measured on polycrystalline Pt microelectrodes in acid and alkaline media. It was verified that the DP is operative at low overpotentials and the current tends to reach a kinetically controlled limiting current just before the AP becomes effective. Additionally, it was concluded that while the ORR performance of Pt could be improved by shifting the electro-oxidation reaction toward more anodic values, it would be more efficient to increase its kinetic capacity for cleaving oxygen as Oad and for reducing its protonated form (OHad) to water.

The Effect of Sr<sup>2+</sup> and Fe<sup>3+</sup> Cations and the Stirring Speed on The Precipitation of Barium Sulfate in a Batch System

The batch system investigation explored the effect of Sr2+ and Fe3+ cations and the stirring speed on the characteristics of precipitated barium sulfate. A series of experiments were conducted to evaluate the rate of barium sulfate precipitation in laboratory equipment from brines containing barium ions (3500 ppm) and varying amounts of Sr2+ and Fe3+ ions (10 and 20 ppm). Kinetic analysis was also performed to explore how stirring speeds (240 and 480 rpm) affect barium sulfate scales' crystallization by increasing the stirring speed and promoting Sr2+ and Fe3+-cation solubility while decreasing the precipitation rate. All solid crystals obtained were mostly pure barite, as the X-ray diffraction (XRD) method confirmed. The SEM micrograph of barite morphology revealed particles with tablet-shaped crystals 2 to 5 nm in size. With the presence of Sr2+ and Fe3+-cation, the shape of barium sulfate was modified into spherical tablets or flower-like clusters of tablets. Meanwhile, the morphological changes could result from increased stirring rates. Moreover, the kinetic results yielded a general reaction rate equation that might be used to estimate barium sulfate deposition in pipelines for various brine, supersaturation, and mixing time durations.

A novel bimetallic Fe-Cu-CNT catalyst for effective catalytic wet peroxide oxidation: reaction optimization and mechanism investigation

Treatment of organic wastewater is of great importance and can be carried out by catalysis technologies such as catalytic wet peroxide oxidation (CWPO). A novel bimetallic Fe-Cu-CNT catalyst was first developed by a facile hydrothermal method; Fe species (Fe (Ⅱ) and Fe (Ⅲ)) and Cu species (Cu (Ⅰ) and Cu (Ⅱ)) were used to fabricate the catalyst with the CNTs, which was stable during testing. Methylene blue (MB) was chosen as model compound for the study; the optimization for treatment by the Box-Behnken design indicated that a combination of low pH, high MB concentration and intermediate temperature led to better treatment performance. The CWPO reaction obeyed the 2nd-order kinetic equation and the catalyst activity increased with an increase in the Cu content. The reaction induction period was shortened with decreasing Fe:Cu ratio. The cycling reaction between Fe3+/Fe2+ and Cu2+/Cu+ pairs generated a large number of oxidative radicals and improved the pollutant degradation efficiency. Finally, the reaction rate equation of CWPO over Fe-Cu-CNT was derived, and it was experimentally illustrated that hydroxyl radicals played a crucial role in the treatment. This study demonstrates that the optimized Fe-Cu-CNT has great potentials for treatment of organic wastewater with higher efficiency and lower cost.

Aminoalkyl organosilicon with dual chemical sites for SO2 absorption and analysis of site-specific absorption entropy and enthalpy

Wet flue gas desulfurization is widely used for its high efficiency, however, the low absorption capacity, high viscosity and poor thermal stability of absorbents remains an open question. Herein, a low viscosity and high thermal stability SO2 absorbent with dual interacting sites was synthesized by introducing phenyl into organic silicon. The thermal stability of 1,5-bis (diethylamino)− 1,1,5,5-tetramethyl-3,3-diphenyltrisiloxane (BADPS) is comparable to ILs, while its viscosity is much lower than that of ILs. For the first time, we use a variant of the pseudo-first-order reaction rate equation obtained the reaction rate constant and the saturation absorption capacity. In addition, the optimal absorption and desorption temperatures were obtained based on an objective function. Mostly importantly, the absorption enthalpy change (ΔH) and entropy change (ΔS) of BADPS absorption reaction show the highest absolute values of SO2 absorbents reported so far. These results indicated that the prepared amine alkyl organosilicon could serve as a promising desulfurizing agent with low-energy consumption.