Concentrations Of Chemical Species Research Articles

A low-order coupled chemistry meteorology model for testing online and offline data assimilation schemes: L95-GRS (v1.0)

Abstract. Bocquet and Sakov (2013) introduced a low-order model based on the coupling of the chaotic Lorenz-95 (L95) model, which simulates winds along a mid-latitude circle, with the transport of a tracer species advected by this zonal wind field. This model, named L95-T, can serve as a playground for testing data assimilation schemes with an online model. Here, the tracer part of the model is extended to a reduced photochemistry module. This coupled chemistry meteorology model (CCMM), the L95-GRS (generic reaction set) model, mimics continental and transcontinental transport and the photochemistry of ozone, volatile organic compounds and nitrogen oxides. Its numerical implementation is described. The model is shown to reproduce the major physical and chemical processes being considered. L95-T and L95-GRS are specifically designed and useful for testing advanced data assimilation schemes, such as the iterative ensemble Kalman smoother (IEnKS), which combines the best of ensemble and variational methods. These models provide useful insights prior to the implementation of data assimilation methods into larger models. We illustrate their use with data assimilation schemes on preliminary yet instructive numerical experiments. In particular, online and offline data assimilation strategies can be conveniently tested and discussed with this low-order CCMM. The impact of observed chemical species concentrations on the wind field estimate can be quantitatively assessed. The impacts of the wind chaotic dynamics and of the chemical species non-chaotic but highly nonlinear dynamics on the data assimilation strategies are illustrated.

Aerosols Characterization during the Holi festival in Dehradun: Foothills of the Himalayas, India

In this study, Partisol 2300 speciation sampler and ICP-OES were used for determining the mass and elemental composition of fine particulate matter (PM2.5) during Holi festival week 13th March 2014 to 20th March 2014 at Dehradun, India. Chemical analysis for 15 elements (Fe, Ni, Cr, Mn, Cu, Zn, Cd, As, Pb, Na, K, Al, Mg, Sb and Ca) were carried out with the collected samples (n=8). The order of concentration of chemical species during holi festival days were K>Fe>Na>Mn>Mg>Cr> Zn>Ca>Al>Cu>As>Pb>Ni>Sb>Cd. Aethalometer was used for determining the Black Carbon (BC) concentration and percentage of black carbon contributed by the biomass burning (BB). The average mass concentration of PM2.5 and BC during holi festival week (pre-Holi (3 days), holi(holi festival days) (2 days) and post-holi (3 days)) period was found to be 41.58, 68.61, 42.96 µg/m3 and 4.97 ± 1.89, 7.61 ± 2.37, 3.20 ± 2.46 µg/m3 respectively. The percentage of BC contributed by BB during pre-Holi, Holi and post-Holi period was 15.05 %, 18.20 % and 17.24 %. On analyzing the concentration of PM2.5, BC, surface ozone (O3), oxides of nitrogen (NOx) during the sampling period, substantial increase in concentration was observed during Holi from pre-Holi period.

Simulation of particle diversity and mixing state over Greater Paris: a model-measurement inter-comparison.

Air quality models are used to simulate and forecast pollutant concentrations, from continental scales to regional and urban scales. These models usually assume that particles are internally mixed, i.e. particles of the same size have the same chemical composition, which may vary in space and time. Although this assumption may be realistic for continental-scale simulations, where particles originating from different sources have undergone sufficient mixing to achieve a common chemical composition for a given model grid cell and time, it may not be valid for urban-scale simulations, where particles from different sources interact on shorter time scales. To investigate the role of the mixing state assumption on the formation of particles, a size-composition resolved aerosol model (SCRAM) was developed and coupled to the Polyphemus air quality platform. Two simulations, one with the internal mixing hypothesis and another with the external mixing hypothesis, have been carried out for the period 15 January to 11 February 2010, when the MEGAPOLI winter field measurement campaign took place in Paris. The simulated bulk concentrations of chemical species and the concentrations of individual particle classes are compared with the observations of Healy et al. (Atmos. Chem. Phys., 2013, 13, 9479-9496) for the same period. The single particle diversity and the mixing-state index are computed based on the approach developed by Riemer et al. (Atmos. Chem. Phys., 2013, 13, 11423-11439), and they are compared to the measurement-based analyses of Healy et al. (Atmos. Chem. Phys., 2014, 14, 6289-6299). The average value of the single particle diversity, which represents the average number of species within each particle, is consistent between simulation and measurement (2.91 and 2.79 respectively). Furthermore, the average value of the mixing-state index is also well represented in the simulation (69% against 59% from the measurements). The spatial distribution of the mixing-state index shows that the particles are not mixed in urban areas, while they are well mixed in rural areas. This indicates that the assumption of internal mixing traditionally used in transport chemistry models is well suited to rural areas, but this assumption is less realistic for urban areas close to emission sources.

Chaos in the Belousov–Zhabotinsky reaction

The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov–Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle.

On the link between conformational changes, ligand binding and heat capacity

BackgroundConformational changes coupled to ligand binding constitute the structural and energetics basis underlying cooperativity, allostery and, in general, protein regulation. These conformational rearrangements are associated with heat capacity changes. ITC is a unique technique for studying binding interactions because of the simultaneous determination of the binding affinity and enthalpy, and for providing the best estimates of binding heat capacity changes. Scope of reviewStill controversial issues in ligand binding are the discrimination between the “conformational selection model” and the “induced fit model”, and whether or not conformational changes lead to temperature dependent apparent binding heat capacities. The assessment of conformational changes associated with ligand binding by ITC is discussed. In addition, the “conformational selection” and “induced fit” models are reconciled, and discussed within the context of intrinsically (partially) unstructured proteins. Major conclusionsConformational equilibrium is a major contribution to binding heat capacity changes. A simple model may explain both conformational selection and induced fit scenarios. A temperature-independent binding heat capacity does not necessarily indicate absence of conformational changes upon ligand binding. ITC provides information on the energetics of conformational changes associated with ligand binding (and other possible additional coupled equilibria). General significancePreferential ligand binding to certain protein states leads to an equilibrium shift that is reflected in the coupling between ligand binding and additional equilibria. This represents the structural/energetic basis of the widespread dependence of ligand binding parameters on temperature, as well as pH, ionic strength and the concentration of other chemical species. This article is part of a Special Issue entitled Microcalorimetry in the BioSciences — Principles and Applications, edited by Fadi Bou-Abdallah.

Geometry‐coupled reactive fluid transport at the fracture scale: application toCO2geologic storage

AbstractWater acidification followsCO2injection and leads to reactive fluid transport through pores and rock fractures, with potential implications to reservoirs and wells inCO2geologic storage and enhanced oil recovery. Kinetic rate laws for dissolution reactions in calcite and anorthite are combined with the Navier‐Stokes law and advection–diffusion transport to perform geometry‐coupled numerical simulations in order to study the evolution of chemical reactions, species concentration, and fracture morphology. Results are summarized as a function of two dimensionless parameters: the Damköhler numberDawhich is the ratio between advection and reaction times, and the transverse Peclet numberPedefined as the ratio between the time for diffusion across the fracture and the time for advection along the fracture. Reactant species are readily consumed near the inlet in a carbonate reservoir when the flow velocity is low (low transverse Peclet number andDa > 10−1). At high flow velocities, diffusion fails to homogenize the concentration field across the fracture (high transverse Peclet numberPe > 10−1). When the reaction rate is low as in anorthite reservoirs (Da < 10−1), reactant species are more readily transported toward the outlet. At a given Peclet number, a lower Damköhler number causes the flow channel to experience a more uniform aperture enlargement along the length of the fracture. When the length‐to‐aperture ratio is sufficiently large, sayl/d > 30, the system response resembles the solution for 1D reactive fluid transport. A decreased length‐to‐aperture ratio slows the diffusive transport of reactant species to the mineral fracture surface, and analyses of fracture networks must take into consideration both the length and slenderness of individual fractures in addition toPeandDanumbers.

Chemometrics applied to environmental systems

To understand the processes that give rise to the observed concentrations of chemical species in environmental samples, it is often useful to apply chemometric methods to help convert chemical data into environmental information. In this review, various chemometical methods including pattern recognition, mixture resolution methods, and probability estimation will be described, and their applications to a variety of environmental systems are presented. However, there are important differences between applying chemometrical methods in the laboratory as compared to environmental data. The environmental system can be monitored, but in general, it is not possible to plan experiments and use known distributional properties of the system under study. Given the complexity of these systems, large data sets are typically needed to provide the basis for obtaining a good understanding of its functioning. Expanding computer capabilities coupled with improved analytical methods have allowed the production and analysis of larger and larger data sets with more and more computationally intensive sophisticated algorithms that offer the promise of even greater information retrieval in the future.

Chaos control for Willamowski–Rössler model of chemical reactions

Real systems evolving towards complex state encounter chaotic behavior. This behavior is very important in chemical processes or in biological structures because it defines the direction of the evolution of the system. From this point of view, the capability of deliberate control of these phenomena has a great practical impact despite the fact that it is very difficult; this is the reason why theoretical models are useful in these situations. In order to obtain chaos control in chemical reactions, the analysis of the dynamics of Willamowski–Rössler system involving the synchronization of two Minimal Willamowski–Rössler (MWR) systems based on the adaptive feedback method of control is presented in this work. As opposed to previous studies where in order to obtain synchronization 3 controllers were used, implying from a practical point of view the control of the concentrations of three chemical species, in this study we showed that the use of just one is sufficient which in practice is important as controlling the concentration of a single chemical species would be much easier. We also showed that the transient time until synchronization depends on initial conditions of two systems, the strength and number of the controllers and we attempted to identify the best conditions for a practical synchronization.

A High Resolution Multi-Physics Numerical Model for Planar SOFC Stack

An SOFC stack is the basic functioning unit of SOFC as an electrical power generation device. The physical condition of an operating SOFC stack is vastly different from that of a laboratory button cell. The ability to analyze the performance characteristics of SOFC stacks is immensely helpful for advancing the SOFC technology for large scale commercial applications. Here we report a successful development of a high space resolution multi-physics mathematical model for full scale planar SOFC stacks which is, to the best of our knowledge, the first of its kind. This 3D stack model takes into account the coupled physical processes of mass, charge and heat transport, chemical and electrochemical reactions, applicable for both methane and hydrogen based fuels. The computational domain contains all components of the stack, including fuel and air channels, internal manifolds, cathode-electrolyte-anode assemblies, interconnects, seals and frames. The computational model is constructed using the commercial CFD software, FLUENT®, supplemented with in-house developed external subroutines to ensure all governing equations and physical properties are correctly coupled and solved successfully. Boundary conditions for the stack and that between material components are all properly incorporated into the computational model. To illustrate, Figure 1 shows a geometric model for a 30-cell stack with a counter- or co-flow design. The size of the stack is 136mm 143mm 133mm. The manifold consists of two/three gas inlet-outlet channels for each air or fuel flow. Every fuel cell consists of 30 channel-rib pitches, i.e., there are 900 repeating units for the electrochemically active area of the 30-cell stack. To properly resolve all the stack components involved, the computational model consists of a total of about 27 million grids. Multi-physics numerical simulations of this truly high resolution computational model of 30-cell stack have been successfully performed in a 2-CPU/16-core PC. Detailed information about the distributions of physical quantities is revealed, e.g., concentrations of chemical species, temperature profile, current density and electrical potential distributions, chemical and electrochemical reaction rates, etc. To summarize, the goal of performing detailed multi-physics simulations for realistic planar SOFC stacks has been achieved. Performance simulation with this high resolution, high computing efficiency numerical model can do much to advance the SOFC technology by improving the stack design and optimizing the operating parameters. Figure 1

Emulating cellular automata in chemical reaction–diffusion networks

Chemical reactions and diffusion can produce a wide variety of static or transient spatial patterns in the concentrations of chemical species. Little is known, however, about what dynamical patterns of concentrations can be reliably programmed into such reaction---diffusion systems. Here we show that given simple, periodic inputs, chemical reactions and diffusion can reliably emulate the dynamics of a deterministic cellular automaton, and can therefore be programmed to produce a wide range of complex, discrete dynamics. We describe a modular reaction---diffusion program that orchestrates each of the fundamental operations of a cellular automaton: storage of cell state, communication between neighboring cells, and calculation of cells' subsequent states. Starting from a pattern that encodes an automaton's initial state, the concentration of a "state" species evolves in space and time according to the automaton's specified rules. To show that the reaction---diffusion program we describe produces the target dynamics, we simulate the reaction---diffusion network for two simple one-dimensional cellular automata using coupled partial differential equations. Reaction---diffusion based cellular automata could potentially be built in vitro using networks of DNA molecules that interact via branch migration processes and could in principle perform universal computation, storing their state as a pattern of molecular concentrations, or deliver spatiotemporal instructions encoded in concentrations to direct the behavior of intelligent materials.

Chemical speciation of CO2 absorption in aqueous monoethanolamine investigated by in situ Raman spectroscopy

A quantitative analysis method of chemical species in liquid phase during CO2 absorption into monoethanolamine was developed for Raman spectroscopy. Band envelopes in the spectral region between 300 and 3100cm−1 were resolved with Gaussian Lorentzian function. Spectroscopic characterization of MEA, protonated MEA, carbamate, bicarbonate, carbonate and molecular CO2 in aqueous was performed. Calibration curves were constructed with area ratio plotted against species concentration. Concentration of individual chemical species in liquid phase can be systematically determined using the correlations introduced. Experiments of CO2 solubility in aqueous MEA were carried out for pressure ranges from 1 to 60bar and three temperatures (303.15, 313.15 and 323.15) K with in situ Raman measurement. Absorption capacity was determined with conventional gas pressure drop method and newly developed Raman spectroscopic analysis method based on total carbon containing species in liquid phase. Results depict good accuracy and reproducibility of Raman measurement method. Chemical speciation during CO2 absorption into aqueous solution of 30% MEA at pressure up to 60bar was evaluated. The findings from present work will improve the understanding of phase equilibrium behavior associated with absorption reactions and can be employed for monitoring, analysis and optimization of CO2 capture process.

Hybrid grid-particle method for fluid mixing simulation

In this paper, we propose a hybrid grid-particle method for the numerical simulation of fluid mixing problem. The method solves the incompressible Navier–Stokes equations using a grid method and the advection–diffusion equation of chemical species concentration using a particle method. With this framework, the fluid mixing problem at moderate Reynolds number ( $$\sim $$ 10 $$^2$$ ) and high Peclet number ( $$\sim $$ 10 $$^5$$ ), which is typical for liquid–liquid mixing in microsystem, can efficiently be solved utilizing the characteristics of each approach; the flow field is stably solved even with long time step, and the concentration field is accurately solved with minimal numerical diffusion. The proposed hybrid method is examined through three test cases, and the results show that the hybrid method provides substantial accuracy for simulating the fluid mixing problem at high Peclet number.

Study of monoprotic acid–base equilibria in aqueous micellar solutions of nonionic surfactants using spectrophotometry and chemometrics

Many studies have shown the distribution of solutes between aqueous phase and micellar pseudo-phase in aqueous micellar solutions. However, spectrophotometric studies of acid–base equilibria in these media do not confirm such distribution because of the collinearity between concentrations of chemical species in the two phases. The collinearity causes the number of detected species to be equal to the number of species in a homogenous solution that automatically misinterpreted as homogeneity of micellar solutions, therefore the collinearity is often neglected. This interpretation is in contradiction to the distribution theory in micellar media that must be avoided. Acid–base equilibrium of an indicator was studied in aqueous micellar solutions of a nonionic surfactant to address the collinearity using UV/Visible spectrophotometry. Simultaneous analysis (matrix augmentation) of the equilibrium and solvation data was applied to eliminate the collinearity from the equilibrium data. A model was then suggested for the equilibrium that was fitted to the augmented data to estimate distribution coefficients of the species between the two phases. Moreover, complete resolution of concentration and spectral profiles of species in each phase was achieved.

Influence of an urban canopy model and PBL schemes on vertical mixing for air quality modeling over Greater Paris

Impacts of meteorological modeling in the planetary boundary layer (PBL) and urban canopy model (UCM) on the vertical mixing of pollutants are studied. Concentrations of gaseous chemical species, including ozone (O3) and nitrogen dioxide (NO2), and particulate matter over Paris and the near suburbs are simulated using the 3-dimensional chemistry-transport model Polair3D of the Polyphemus platform. Simulated concentrations of O3, NO2 and PM10/PM2.5 (particulate matter of aerodynamic diameter lower than 10 μm/2.5 μm, respectively) are first evaluated using ground measurements. Higher surface concentrations are obtained for PM10, PM2.5 and NO2 with the MYNN PBL scheme than the YSU PBL scheme because of lower PBL heights in the MYNN scheme. Differences between simulations using different PBL schemes are lower than differences between simulations with and without the UCM and the Corine land-use over urban areas. Regarding the root mean square error, the simulations using the UCM and the Corine land-use tend to perform better than the simulations without it. At urban stations, the PM10 and PM2.5 concentrations are over-estimated and the over-estimation is reduced using the UCM and the Corine land-use. The ability of the model to reproduce vertical mixing is evaluated using NO2 measurement data at the upper air observation station of the Eiffel Tower, and measurement data at a ground station near the Eiffel Tower. Although NO2 is under-estimated in all simulations, vertical mixing is greatly improved when using the UCM and the Corine land-use. Comparisons of the modeled PM10 vertical distributions to distributions deduced from surface and mobile lidar measurements are performed. The use of the UCM and the Corine land-use is crucial to accurately model PM10 concentrations during nighttime in the center of Paris. In the nocturnal stable boundary layer, PM10 is relatively well modeled, although it is over-estimated on 24 May and under-estimated on 25 May. However, PM10 is under-estimated on both days in the residual layer, and over-estimated on both days over the residual layer. The under-estimations in the residual layer are partly due to difficulties to estimate the PBL height, to an over-estimation of vertical mixing during nighttime at high altitudes and to uncertainties in PM10 emissions. The PBL schemes and the UCM influence the PM vertical distributions not only because they influence vertical mixing (PBL height and eddy–diffusion coefficient), but also horizontal wind fields and humidity. However, for the UCM, it is the influence on vertical mixing that impacts the most the PM10 vertical distribution below 1.5 km.

A novel tracer technique to quantify the atmospheric flux of trace elements to remote ocean regions

AbstractAtmospheric input into the global ocean constitutes an important budgetary component of numerous chemical species and plays a key role in controlling biogeochemical processes in the ocean. Assessment of this input is difficult, however, because measurements of deposition rates to the ocean, particularly in remote areas, are rare and susceptible to problems of temporal and spatial variability. While the collection and analysis of aerosol samples is somewhat routine, the chemical concentration data collected from ship board or land‐based aerosol samplers in and of themselves cannot yield the deposition flux of trace elements; a method is required to transform concentration measurements into flux. The ability to derive the atmospheric flux of 7Be from its ocean inventory provides a key linkage between the atmospheric concentration of chemical species and their deposition to the ocean. We have demonstrated that estimates of the atmospheric flux of trace elements (TEs) can be made by multiplying the ocean inventory of 7Be x [TE/7Be] ratio in bulk aerosols. Flux estimates for trace elements made by the 7Be ocean inventory method were comparable to fluxes derived from rain samples collected on the island of Bermuda. The situation at Bermuda allows such testing to be made, where ocean‐based methods can be calibrated by convenient land locations. Our results suggest that this method would be useful for remote areas where fixed sampling stations do not exist; that is, the majority of the global ocean.

Effects of Thermal Radiation and Radiation Absorption on Flow Past an Impulsively Started Infinite Vertical Plate with Newtonian Heating and Chemical Reaction

A perfect solution to the present natural convective flow problem of a vertical transfinite plate owing to the impulsive motion in the ubiety of first ordered chemical reaction, radiation absorption, radiation, Newtonian heating and species concentration in its plane is evolved by applying the method of Laplace transforms in closed form at the plate. Exact results for velocity, temperature, concentration fields are prevailed and expressions for heat and mass transfer rates are also found. The effects are analyzed for the respective invariables for both ammonia and water vapor.

Light-addressable Potentiometric Sensor (LAPS) Combined with Multi-chamber Structures to Investigate the Metabolic Activity of Cells

LAPS are field-effect-based potentiometric sensors which are able to monitor analyte concentrations in a spatially resolved manner. Hence, a LAPS sensor system is a powerful device to record chemical imaging of the concentration of chemical species in an aqueous solution, chemical reactions, or the growth of cell colonies on the sensor surface, to record chemical images. In this work, multi-chamber 3D-printed structures made out of polymer (PP-ABS) were combined with LAPS chips to analyse differentially and simultaneously the metabolic activity of Escherichia coli K12 and Chinese hamster ovary (CHO) cells, and the responds of those cells to the addition of glucose solution.

Injectivity, multiple zeros and multistationarity in reaction networks

Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems are typically parametrized by many (unknown) parameters. A goal is to understand how properties of the dynamical systems depend on the parameters. Qualitative properties relating to the behaviour of a dynamical system are locally inferred from the system at steady state. Here, we focus on steady states that are the positive solutions to a parametrized system ofgeneralized polynomialequations. In recent years, methods from computational algebra have been developed to understand these solutions, but our knowledge is limited: for example, we cannot efficiently decide how many positive solutions the system has as a function of the parameters. Even deciding whether there is one or more solutions is non-trivial. We present a new method, based on so-calledinjectivity, to preclude or assert that multiple positive solutions exist. The results apply to generalized polynomials and variables can be restricted to the linear, parameter-independent first integrals of the dynamical system. The method has been tested in a wide range of systems.

Epilithon isotope composition as an environmental archive in rivers receiving wastewater

Epilithon is a complex community of autotrophic and heterotrophic organisms that includes inert, organic and inorganic material and is attached to the surface of submersed rocks. Water samples collected in the Grand River (southwestern Ontario) in April 2011 showed that ammonium concentrations decreased downstream, whereas nitrate varied, largely dependent on weather conditions (concentrations of both chemical species were higher during winter). Epilithon δ15N-TN downstream from the Kitchener wastewater treatment plant oscillated between 0.4 to 23.2‰, and δ13C-TC around -27‰. The wastewater treatment plant effluent consisted of δ15N-NO3- between 12 and 16‰, with a decreasing trend as it traveled downstream; δ15N-NH4+ became enriched downstream (as high as 31‰). Average values for δ13C-DIC were -10.1‰ and δ13C-DOC -26.8‰. It is proposed that the nitrogen and carbon isotope composition of epilithon could be used as a short- or medium-term environmental archive, as it reflects in-stream processes, such as ammonia oxidation, in a river impacted by treated wastewater. The interpretation provided here was limited due to the ample range of events and potential sources, specifically when the nitrogen isotopic composition of nitrate and ammonium was similar. Epilithon is easily collected, processed and analysed and proved to be valuable tool to describe changes in river and stream geochemistry.

New transformation proposed for improving CFD simulation of free radical polymerization reactions in microreactors

A new yet simple transformation is proposed to significantly improve the accuracy of computational fluid dynamics (CFD) modeling and simulations of free radical polymerization (FRP) reactions carried out especially in flow microreactors. The new transformation makes the kinetic rate coefficients dimensionless in terms of concentration. To that extent, the chemical data (chemical species concentration and kinetic rate coefficients values) can be fed in original molar form instead of usual mass form to CFD software package while simulating chemical species as passive scalars. The normalization of various variables (passive scalars) helps in reducing the numerical stiffness as well as numerical errors during simulations. Another advantage of this new transformation is that the expression for transformed reaction rate equations remains unchanged thus enabling an easy coding and debugging process. The new transformation was first validated through numerical simulation against theoretical analytical solution of FRP for homogeneous batch reactor. It was then validated through CFD simulation against published experimental data for FRP in coiled tube microreactor under steady-state flow condition. It has also been demonstrated that in CFD simulations of FRP in flow microreactors, significant error arises for the prediction of number-average chain length (and thus $${\text{MW}}_{n}$$ , number-average molecular weight) from the use of chemical data in mass form instead of original molar form. This new transformation is thus found to be more suitable for CFD simulations in flow reactors compared to previous Zhu’s transformation.