Mass Balance Relationships Research Articles

An estimation method for bias error of measurements by utilizing process data, an incidence matrix and a reference instrument for data validation and reconciliation: Part 2 Extension to the energy balance relation

Abstract Ensuring data reliability is becoming increasingly important for further applications of AI, IoT, and digital twins. One promising technology for ensuring data reliability is data validation and reconciliation (DVR), which minimizes the uncertainty of measurements based on statistics. DVR has been widely used for the operation and maintenance of nuclear power plants in Europe and the United States in recent years. The most important input for DVR analysis is measurement uncertainty. The catalog value provided by sensor manufacturers includes the measurement uncertainty, but in reality, the actual measurement uncertainty is often smaller. Previous studies have proposed several methods for evaluating the actual measurement uncertainty based on process data, which have been confirmed to be effective for evaluating random errors. It is important to note that bias errors also contribute significantly to the measurement uncertainty. In our previous paper, we proposed a method for estimating bias error using process data, an incidence matrix, and a reference instrument. The proposed method was limited to a mass balance relation, i.e., flow rate measurements. In this paper, we extend the method to include an energy balance relation by considering energy conservation in addition to mass conservation. This extension enables the evaluation of measurement uncertainty for flow rate and temperature. The proposed method was validated with two benchmark problems. It was found to be applicable to various flow conditions, including physically fluctuating flow, such as that observed in the feedwater flow in nuclear power plants.

Study on Hydrochemical Characteristics and Interactions between Groundwater and Surface Water in the Dongting Lake Plain

The Dongting Lake Plain is a major ecological reserve for river and lake wetlands in the Yangtze River Basin, with complex river and lake relationships and frequent water flow exchange. Studies on the hydrochemical characteristics and the mechanism of interaction between groundwater and surface water will actively promote the scientific management, utilization of water resources, and protection of the ecological environment in the Dongting Lake Plain. Based on hydrogeochemical statistics, Gibbs diagrams, ion ratios, rock weathering end-element diagrams, hydrogen–oxygen isotope relationship diagrams, and other technical methods, the chemical characteristics, ion sources, and the distribution of hydrogen–oxygen isotopes of groundwater and surface water in “the Three Inlets” and “the Four Rivers” water system areas as well as the Dongting Lake water were analyzed. Additionally, the interactions between groundwater and surface water and the proportions of these contributions were discussed. The results show that both groundwater and surface water in the Dongting Lake Plain are weakly acidic or alkaline, and the anions are mainly HCO3−, the cations are mainly Ca2+and Mg2+, with the hydrochemical types being mainly HCO3−Ca−Mg and HCO3−Ca. The chemical characteristics of groundwater and surface water are mainly affected by the interaction between water and rock; the ions in surface water mainly come from the weathered dissolution of carbonate and silicate rocks, while the ions in groundwater mainly come from the weathered dissolution of carbonate and silicate rocks, with the dissolution of evaporite rocks locally. Groundwater and surface water are mainly distributed near the local meteoric water line (LMWL), and the slope of the local evaporation line is less than that of the LMWL, which indicates that atmospheric rainfall is an important recharge source for groundwater and surface water and that at the same time, it is affected by evaporation to a certain extent. Part of the groundwater in the Dongting Lake Plain is discharged into the surface rivers in “the Three Inlets” and “the Four Rivers” water system areas, and the other part is directly discharged into Dongting Lake. According to the mass balance relationship of isotopes, the proportions of surface water in “the Three Inlets” and “the Four Rivers” water system areas contributing to Dongting Lake’s water are 18.48% and 60.38%, respectively, and the proportion of groundwater in the lake plain contributing to Dongting Lake water is 21.14%.

Theoretical and operational investigation of the temperature of the glass surface, floor and effluent inside the solar desalination pond

The purpose of this research is to investigate the effect of salinity percentage on the performance of a solar pond, experimentally and mathematically. Experiments are designed to find the temperature of different parts of the solar desalination pond. Using the mass and energy balance relationships for different components of the solar pond, the temperature of the glass surface, bottom and effluent has been reported operationally. The laboratory results state that if the flooring made of nano aluminum oxide is used, the amount of fresh water production reaches a maximum of 6.67 L. Also, when using nano oxide zinc flooring, the amount of fresh water production reaches a maximum of 6.6 L, and if using a simple flooring, it reaches a maximum of 5 L. The average intensity of sunlight and the average temperature of the environment in this month is approximately 0.285 kW/m2 and 33.7 °C.

Why is the film model fundamentally wrong but still able to correlate the experimental data in membrane processes?

The film model that predicts a logarithmic dependence of permeate velocity on feed solute concentration in membrane separation processes is fundamentally wrong because the primary mass balance equation in the model is inapplicable to the total solute. Based on mass balance relationships on the retained solute, The permeate velocity in crossflow membrane separation processes can be rigorously shown to be a cube root function of the retained solute concentration. Furthermore, the reported good fitness of the film model to the experimental permeate velocities can be shown just to be a delusion of curve fitting mainly due to the adjustable parameters in the model.

Effects of mass balance, energy balance, and storage-discharge constraints on LSTM for streamflow prediction

We investigate the effects of physics-based constraints, added to the loss function of a Long Short-Term Memory (LSTM) network, on its performance in daily streamflow prediction. Three types of constraints (mass balance, energy balance, and storage-discharge relationship), along with their combinations, are tested across 34 river basins in Nebraska. We found that the addition of constraints improves the model performance in several basins, but there are also cases where the performance drops or does not differ significantly. Mass and energy balance constraints improve the performance in 38% and 32% of catchments, respectively, while storage-discharge constraints improve the performance in 12% of catchments. The combination of mass and energy balance constraints has a positive effect on 41% of catchments, while the combination of mass balance and storage-discharge constraints improves the performance in 26% of catchments. We recommend the use of constraints in cases where they boost the LSTM performance.

Origin of sodium bicarbonate groundwaters, Southern Hills Aquifer System, USA by silicate hydrolysis

Groundwaters dominated by sodium-bicarbonate represent an important end-member continental water type. The Southern Hills aquifer system in southwestern Mississippi and southeastern Louisiana, USA provides an excellent field laboratory for studying the origin and evolution of Na–HCO3 groundwaters in siliciclastic aquifers. Our research, which is based on establishing spatial variations in water chemistry, mass balance relations, and thermodynamic considerations, supports the hypothesis that the process of generating Na–HCO3 groundwaters in the Southern Hills aquifer system is driven by irreversible dissolution-precipitation reactions primarily involving silicate minerals, not by calcite dissolution and cation exchange, as has been proposed by others. The evidence supports the following scenario: oxidation of organic carbon produces organic acids which react with detrital plagioclase feldspars having an average bulk composition of approximately Ab0.70An0.30. In the up-gradient part of the system, the incongruent dissolution of plagioclase produces a kaolinite phase and releases dissolved silica, Na, Ca, and HCO3 into solution. As the silica concentration and the sodium/hydrogen ion activity ratio in the waters increase down gradient, the waters become saturated with respect to a (Na,Ca)-smectite. As plagioclase hydrolysis continues as a result of production of carbonic acid, there is a progressive increase in (Na+/H+) and (Ca2+/(H+)2) activity ratios and now a progressive decrease in dissolved H4SiO40 as a result of buffering by kaolinite-smectite. It is likely that some Ca is preferentially removed from solution over Na by adsorption on newly-formed smectite. In the most distal parts of the aquifer system the high bicarbonate alkalinity and high pH result in the waters becoming saturated with respect to calcite, and the precipitation of calcite is another probable sink for Ca. Using dissolved bicarbonate as a reaction progress variable provides a useful technique for evaluating controls on groundwater compositions. It is also clear that the evolution of groundwater compositions in this and similar systems cannot be understood without understanding the controls on dissolved silica.

Estimating glacier mass balance in High Mountain Asia based on Moderate Resolution Imaging Spectroradiometer retrieved surface albedo from 2000 to 2020

AbstractGlacier surface albedo is a key parameter of the glacier mass and energy balance process. Many scholars have used the albedo method to study mass balance for an individual glacier, but less attention has been given to large‐area glaciers. Based on Moderate Resolution Imaging Spectroradiometer (MODIS) retrieved glacier surface albedo and in situ mass balance, the correlations between albedo and mass balance are reported. The minimum/mean method (the whole glacier albedo is calculated by averaging the minimum/mean albedo of each grid cell), the MODIS snow albedo products (MxD10A1) and the MCD43A3 shortwave albedo were tested during the melt season (June–August) for four glaciers in the High Mountain Asia (HMA). Results reveal that albedo is well correlated with mass balance, the correlation (r) ranging from 0.41 to 0.90. Overall, the minimum method is better than the mean method, and MxD10A1 is better than MCD43A3. The albedo changes were calculated based on the MxD10A1 and the mean method, and a linear relationship is established between albedo changes and digital elevation models (DEMs) calculated mass balance from 2000 to 2016. A strong linear correlation (r = .9) is found between albedo changes and mass balance while excluding some areas that have insignificant seasonal variation in albedo, and the reconstructed albedo–mass balance relationship can be used to retrieve mass balance in large‐scale glaciers. Furthermore, the average loss of mass from 2000 to 2020 is calculated as −0.225 ± 0.040 m w.e.a−1. The greatest glacier mass loss is concentrated in the southeastern part of HMA, the mass loss in the north and west is less than that in the southeast, and the glacier mass is in a state of aggravated loss in recent years. Our study also offers a new method for estimating the large‐scale glacier mass balance.

Glacier mass balance estimation in Garhwal Himalaya using improved accumulation area ratio method.

Water requirements of the mountain communities living in the Himalaya are supported by snow and glacier melt. The availability of water from the source depends on numerous climatic and glacier parameters. One key parameter is mass balance, which helps to assess the glacier health and future water availability. We have used the improved accumulation area ratio (IAAR) method to estimate mass balance in Alaknanda and Bhagirathi basins, constituting 1055 glaciers covering ~1609 km2. The mean Equilibrium Line Altitude (ELA) of the Alaknanda and Bhagirathi basins are estimated as 6147 ± 130 and 5985 ± 130m.a.s.l, respectively. The mass balance is estimated using the accumulation area ratio (AAR)-mass balance relationship. The mean specific mass balance of the Alaknanda and Bhagirathi for 2001-2013 is estimated as -1.1 ± 0.03m.w.e.a-1 and -1.01 ± 0.07m.w.e.a-1, respectively. Total mass loss from the study area is calculated as ~21.4 ± 1.1Gt during this period. The loss of glaciers in the mountain area will increase the vulnerability of communities living in the region. It suggests a need for better adaptation strategies to improve the resilience of high mountain communities.

Production of Styrene from Dehydrogenation of Ethylbenzene

AbstractA pseudo‐homogeneous model based on intrinsic rate equations for dehydrogenation of ethylbenzene to styrene in an adiabatic fixed‐bed reactor is developed. Steam and ethylbenzene are the main reactants with styrene as the desired product, and benzene and toluene as by‐products. Styrene production is an endothermic reaction depends on various factors such as temperature, pressure, steam to ethylbenzene ratio, styrene to ethylbenzene ratio in feed. These factors affects the properties like styrene selectivity, ethylbenzene and by‐product conversion etc. The development of the mathematic model includes the application of mass balance, energy balance, and basic thermodynamic relations, momentum balance, Langmuir and Hinshelwood model, Ergun relation, etc. The effects of temperature as well as of the steam‐to‐ethylbenzene and styrene‐to‐ethylbenzene molar ratios in the feed on the selectivity for styrene, ethylbenzene conversion, and conversion to by‐products are also evaluated. The maximum selectivity for styrene can be achieved at increased steam‐to‐ethylbenzene feed ratio and a lower ethylbenzene conversion.

Thermo-Economic Analysis of a Coal-Fired Power Plant (CFPP) Using Turbine Cycle Heat Rate and Plant Net Heat Rates at Various Operating Loads

Evaluating Coal-Fired Power Plant (CFPP) performance is a complex process involving the determination of the turbine cycle Heat Rate (TCHR). This study focuses on determining the TCHR by developing a mathematical model. The model, which incorporates economic analysis of the plant, is developed using energy and mass balance relationships of the turbine cycle, validated using plant commissioning data from a 700MWn CFPP located in Perak, Malaysia. Actual plant data from a 700MWn CFPP is utilized to improve the accuracy and increase the confidence of the results of this study. It was found that at the nominal operating load of 729MWg, there is a Heat Rate (HR) deviation of -1,135 kJ/kWh, leading to daily losses of RM240,447 or USD 60,112. Furthermore, it is possible to utilize the developed model at lower loads as the plant is now being used to operate on “cyclic” loads. The daily losses at a lower load of 431MWg are RM125,767 or USD31,442. Thus, the model is able to compare the plant HR at various loads against commissioning data, and economic analysis is able to be carried out effectively. Valuable information for plant operations and performance engineers could be obtained using this model to determine plant HR.

Functioning of glacierized catchments in Monsoon and Alpine regimes of Himalaya

Glacier mass balance (MB) and runoff relationship is poorly explored in the Himalaya due to limited in-situ data. A simplified glacio-hydrological model is used to reconstruct the long-term MB and runoff on Dokriani Bamak Glacier (DBG) in the Monsoon regime and Chhota Shigri Glacier (CSG) catchments in the Alpine regime of the Himalaya. Since 1950, DBG and CSG show limited mass wastage with mean annual glacier-wide MB of –0.09 ± 0.35 m w.e. a−1 and –0.12 ± 0.28 m w.e. a−1, respectively. The mean annual catchment-wide runoff are also almost similar 0.13 ± 0.01 106 m3 a−1 and 0.14 ± 0.01 106 m3 a−1 from DBG and CSG catchments, respectively over 1950–2020. Available in-situ short-term MB and runoff data from eight glacierized catchments do not show any significant MB-runoff relationship, except for CSG. The long-term modelled MB and runoff data on both DBG and CSG catchments suggest that the higher catchment-wide runoff corresponds to more negative MB, and vice versa. This is in contrast to the previously suggested MB-runoff relationship on DBG catchment. Present detailed analysis also indicates that the hydrology of the DBG catchment is mainly dominated by the summer precipitation, while in CSG catchment, it is mainly controlled by the glacier-wide annual MB. In dry years, the corresponding negative annual MB on both the glaciers provides additional glacier-degraded runoff to the catchment streams that can be as high as 13% and 38% of total runoff on DBG and CSG catchments, respectively.

Active food packaging to control carbon dioxide

AbstractKeeping certain level of carbon dioxide concentration along with a desired oxygen concentration in food packages is helpful in preserving a variety of foods, and thus, active packaging technology to control CO2 has been reviewed here in perspective of optimized package design. For whatever product packages, tailoring interaction among the gas, food product and packaging material is essential for realization of positive role and function of CO2: antimicrobial activity, prevention of oxidation, preferred sensory quality, maintenance of package integrity and extension of shelf life. Gas absorbers, emitters or active valves may be applied for this purpose, and commercial products are available in market. However, these active devices should be applied in harmony with food's CO2 production and dissolution. Elements or factors involved in the design process are examined by looking over scientific literature. Mass balance relationship combined with dissolution equilibration for active food package has been presented to control CO2 concentration and package wholesomeness in beneficial and desired way. Atmosphere estimation of roasted coffee packages was presented as case study for tackling the task of attaining the desired condition.

Metallurgical Research and Its Contribution to Industrial Development

Metallurgical Research and Its Contribution to Industrial Development

Appraisal of Super-Fast Membrane Bioreactors by MASM—A New Activated Sludge Model for Membrane Filtration

The structure of existing activated models is inherently deficient in reflecting the major role of the membrane filtration. The study developed a novel model, MASM, for the membrane activated process. The effective filtration size imposed by the membrane module, entrapping larger particles, was adopted as the basis of the proposed model. The model defines a modified form of COD fractionation that accounts for the captured COD fractions as additional model components and utilizes related mass-balance relationships. It was implemented to test the fate of soluble hydrolyzable COD and the system performance of super-fast membrane activated sludge based on real data for the characterization and process kinetics of domestic sewage and denim processing effluents. Model evaluation was carried out for parallel systems with gravity settling and membrane filtration operated at a sludge age range of 0.5–2.0 d. Results reflected significantly better performance by the super-fast membrane activated sludge system for both wastewaters, underlining that it was crucially important to account for the captured COD fractions to provide an accurate evaluation of system behavior and effluent quality. This should also be identified as the major shortcoming of the ASM models for evaluating and predicting the system performance of activated sludge configurations with membrane separation.

Particle size distribution of chemical oxygen demand in industrial effluents: impact on effective filtration size and modelling of membrane bioreactors

AbstractThis study reviews particle size distribution (PSD) analysis for industrial effluents. Evaluation of available experimental data indicated that the approach started with arbitrary selection of size distribution. Following a pioneering study on pulp and paper effluent, sequential filtration and ultrafiltration has established itself as a prescribed methodology complementing respirometric assessment of chemical oxygen demand (COD) fractionation based on biodegradation characteristics. Results indicated that most industrial effluents exhibited a COD distribution where soluble fractions accounted for the majority of the total COD, with significant implications for the understanding of membrane bioreactor (MBR) systems. Observations on the accumulation of soluble COD in the reactor to levels much higher than the permeate COD paved the way to define an experimental PSD methodology for assessing the effective filtration size for the membrane module. This novel parameter considered in the light of reported PSD analyses showed that a portion of what was conventionally considered soluble COD would be retained by the size barrier of the membrane and recycled back to the reactor. Thus, MBR systems require a new mathematical model structure that would include a modified COD fractionation, account for the retained COD fractions as additional model components and utilize related mass balance relationships in order to yield an accurate mechanistic description of microbial reactions taking place in the system. © 2021 Society of Chemical Industry (SCI).

Removal of Turbidity and Assessment of Groundwater Contribution during Riverbank Filtration

Indian rivers carry large sediment loads. During monsoon season when river discharge is high, rivers carry suspended particles, silt, clay, and organic substances, causing river water turbidity that is not suitable for drinking. Riverbank filtration (RBF) is a natural process in which one can abstract good quality water from a highly polluted river through abstraction wells. As RBF water is a mixture of riverbank filtered water and groundwater, assuming no turbidity was picked up by the river water as it travelled through the soil matrix to reach the pumping well. A strategy-A was developed in which flow of groundwater contribution toward pumping well was neglected, while simultaneously measuring source water and abstracted water quality; it was observed that the variation of K, the kinetic coefficient, captured the variation in ln(C0), natural logarithm of influent quality, with R2 equal to 0.974. The kinetic coefficient, K, also captured the variation with ln(C0) of turbidity after travel times of 14 days and 21 days, having R2 equal to 0.991 and 0.989, respectively. A strategy-B was developed using the mass balance relationship, wherein the flow of groundwater contribution toward pumping well was utilized in refining the abstracted water quality. It was observed that K, the kinetic coefficient, of strategy-B captured the variation with ln(C0), the natural logarithm of the influent quality of turbidity with R2 equal to 0.972. If both the strategies were to be compared, strategy-B was found to be superior to strategy-A. However, one additional data of measurement on the groundwater turbidity was required for strategy-B. Further, strategy-C was developed with the assumption that there was no turbidity in groundwater, as a low value of turbidity was observed in groundwater. The variation of K, the kinetic coefficient, with ln(C0), the natural logarithm of influent quality of turbidity in strategy-C, showed that when the groundwater turbidity was ignored, the agreement between observed and computed turbidity was adversely affected. The average contribution of groundwater toward pumping well was observed nearly 12.43% and the average contribution of river water toward the pumping well was observed nearly 87.57%, considering the depth of river water. In strategy-C also, the agreement between simulated and observed values of turbidity was satisfactory.

A Mathematical Model of Two-Way Heterodiffusion Processes with Cascade Decay of Migrating Particles

We construct a mathematical model of mass transfer processes with regard for the local structure of the medium and cascade decay of foreign particles migrating in two different ways. For a specific scheme of cascade decay, we deduce the mass balance relations for the components of the system and obtain linear equations of state and kinetic relations. The conditions for the intensities of mass production in different components of the system are established. The key systems of the model equations of two-way heterodiffusion with cascade decay of migrating particles are obtained in the case where the decay of substance in the current stage serves as a mass source in the next stage.

Porosity and Water Saturation Estimation for Shale Reservoirs: An Example from Goldwyer Formation Shale, Canning Basin, Western Australia

Porosity and water saturation are the most critical and fundamental parameters for accurate estimation of gas content in the shale reservoirs. However, their determination is very challenging due to the direct influence of kerogen and clay content on the logging tools. The porosity and water saturation over or underestimate the reserves if the corrections for kerogen and clay content are not applied. Moreover, it is very difficult to determine the formation water resistivity (Rw) and Archie parameters for shale reservoirs. In this study, the current equations for porosity and water saturation are modified based on kerogen and clay content calibrations. The porosity in shale is composed of kerogen and matrix porosities. The kerogen response for the density porosity log is calibrated based on core-based derived kerogen volume. The kerogen porosity is computed by a mass-balance relation between the original total organic carbon (TOCo) and kerogen maturity derived by the percentage of convertible organic carbon (Cc) and the transformation ratio (TR). Whereas, the water saturation is determined by applying kerogen and shale volume corrections on the Rt. The modified Archie equation is derived to compute the water saturation of the shale reservoir. This equation is independent of Rw and Archie parameters. The introduced porosity and water saturation equations are successfully applied for the Ordovician Goldwyer formation shale from Canning Basin, Western Australia. The results indicate that based on the proposed equations, the total porosity ranges from 5% to 10% and the water saturation ranges from 35% to 80%. Whereas, the porosity and water saturation were overestimated by the conventional equations. The results were well-correlated with the core-based porosity and water saturation. Moreover, it is also revealed that the porosity and water saturation of Goldwyer Formation shale are subjected to the specific rock type with heterogeneity in total organic carbon total clay contents. The introduced porosity and water saturation can be helpful for accurate reserve estimations for shale reservoirs.

Reconciling the surface temperature–surface mass balance relationship in models and ice cores in Antarctica over the last 2 centuries

Abstract. Ice cores are an important record of the past surface mass balance (SMB) of ice sheets, with SMB mitigating the ice sheets' sea level impact over the recent decades. For the Antarctic Ice Sheet (AIS), SMB is dominated by large-scale atmospheric circulation, which collects warm moist air from further north and releases it in the form of snow as widespread accumulation or focused atmospheric rivers on the continent. This suggests that the snow deposited at the surface of the AIS should record strongly coupled SMB and surface air temperature (SAT) variations. Ice cores use δ18O as a proxy for SAT as they do not record SAT directly. Here, using isotope-enabled global climate models and the RACMO2.3 regional climate model, we calculate positive SMB–SAT and SMB–δ18O annual correlations over ∼90 % of the AIS. The high spatial resolution of the RACMO2.3 model allows us to highlight a number of areas where SMB and SAT are not correlated, and we show that wind-driven processes acting locally, such as foehn and katabatic effects, can overwhelm the large-scale atmospheric contribution in SMB and SAT responsible for the positive SMB–SAT annual correlations. We focus in particular on Dronning Maud Land, East Antarctica, where the ice promontories clearly show these wind-induced effects. However, using the PAGES2k ice core compilations of SMB and δ18O of Thomas et al. (2017) and Stenni et al. (2017), we obtain a weak annual correlation, on the order of 0.1, between SMB and δ18O over the past ∼150 years. We obtain an equivalently weak annual correlation between ice core SMB and the SAT reconstruction of Nicolas and Bromwich (2014) over the past ∼50 years, although the ice core sites are not spatially co-located with the areas displaying a low SMB–SAT annual correlation in the models. To resolve the discrepancy between the measured and modeled signals, we show that averaging the ice core records in close spatial proximity increases their SMB–SAT annual correlation. This increase shows that the weak measured annual correlation partly results from random noise present in the ice core records, but the change is not large enough to match the annual correlation calculated in the models. Our results thus indicate a positive correlation between SAT and SMB in models and ice core reconstructions but with a weaker value in observations that may be due to missing processes in models or some systematic biases in ice core data that are not removed by a simple average.

Phosgene formation via carbon monoxide and dichlorine reaction over an activated carbon catalyst: Reaction kinetics and mass balance relationships

The reaction of carbon monoxide and dichlorine over an activated carbon catalyst to produce phosgene is examined using a previously described micro-reactor arrangement. An activation energy of 34.1 kJ mol−1 is determined. The reaction profile at 323 K as a function of time-on-stream establishes steady-state operation to be achieved rapidly, with no deactivation evident within a reaction time of 300 min.. Phosgene production seemingly exhibits 100 % selectivity. However, mass balance measurements indicate a small degree of carbon and chlorine retention by the catalyst that is not directly coupled to the formation of gaseous phosgene. The molecular form of the retained moieties is unknown but, nonetheless, their presence reduces the atom economy of the process and, correspondingly, attenuates total phosgene selectivity. The order of reaction with respect CO, Cl2 and COCl2 is, respectively, 1, 0.5 and 0; leading to the determination of the rate law for phosgene production over this catalyst.