Pseudo-steady State Assumption Research Articles

Transient Interporosity Flow in Shale/Tight Oil Reservoirs: Model and Application.

The dual-porosity model has been used widely to describe the fracture network in well test or numerical simulation due to the high computational efficiency. The shape factor, which can be used to determine the capability of mass transfer between the matrix and fracture, is the core of the dual-porosity model. However, the conventional shape factor, which is usually obtained under pseudo-steady state assumption, has certain limitation in characterization of the mass transfer efficiency in a shale/tight reservoir. In this study, a new transient interporosity flow model has been established by considering the influence of nonlinear flow, stress sensitivity, and fracture pressure depletion. To solve this new model, a finite difference and Newton iteration method was applied. According to the Duhamel principle, the solution for time-dependent fracture pressure boundary condition has been obtained. The solution has been verified by using the fine-grid finite element method. Then, the influence of nonlinear flow, stress sensitivity, and fracture pressure depletion on shape factor and interporosity flow rate has been studied. The study results show that constant shape factors are not suitable for unconventional reservoirs, and the interporosity flow in the shale/tight reservoir is controlled by multiple factors. The new model can be used in test interpretation and numerical simulation, and also provides a new approach for the optimization of the perforation cluster number.

The MINC proximity function for fractured reservoirs flow modeling with non-uniform block distribution

Reservoir simulation is a powerful technique to predict the amount of produced hydrocarbon. After a solid representation of the natural fracture geometry, an accurate simulation model and a physical reservoir model that account for different flow regimes should be developed. Many models based on dual-continuum approaches presented in the literature rely on the Pseudo-Steady-State (PSS) assumption to model the inter-porosity flow. Due to the low permeability in such reservoirs, the transient period could reach several years. Thus, the PSS assumption becomes unjustified. The numerical solution adopted by the Multiple INteracting Continua (MINC) method was able to simulate the transient effects previously overlooked by dual-continuum approaches. However, its accuracy drops with increasing fracture network complexity. A special treatment of the MINC method, i.e., the MINC Proximity Function (MINC–PF) was introduced to address the latter problem. And yet, the MINC–PF suffers a limitation that arises from the existence of several grid-blocks within a studied cell. In this work, this limitation is discussed and two possible solutions (transmissibility recalculation/adjusting the Proximity Function by accounting for nearby fractures) are put forward. Both proposed methods have demonstrated their applicability and effectiveness once compared to a reference solution.

Conversion of Glucose to 5-Hydroxymethylfurfural by Co-catalysis of p-Toluenesulfonic Acid (pTSA) and Chlorides: A Comparison Based on Kinetic Modeling

Hydroxymethylfurfural (HMF) has been considered as one of the most promising biomass derived precursors for producing bio-based materials. Lewis acids are usually used to facilitate the isomerization of glucose to fructose in order to improve the HMF yield. In this study, glucose was converted to HMF with p-toluenesulfonic acid (pTSA) and chlorides as Bronsted and Lewis acids catalysts in the DMSO medium at 120 °C under atmospheric pressure. Kinetic modeling of the process was investigated with consideration of glucose isomerization, dehydration of fructose, rehydration of HMF and formation of humin. NH4Cl was screened as the most efficient co-catalyst for glucose conversion with HMF yield of 47%. The developed model could be well used to simulate the process with satisfying goodness of fit. The activation energies for glucose isomerization, condensation, dehydration of fructose, and rehydration of HMF were determined to be 39.8, 18.1, 55.2, and 19.0 kJ/mol, respectively. However, because the fructose concentration was very low and the reaction rate of fructose dehydration was much higher than that of glucose isomerization, a pseudo-steady state assumption could be employed, by which the observed activation energy for a lumped reaction of glucose to HMF conversion (EHMF) was determined as 45.6 kJ/mol. The developed observed kinetic model could be well used to describe the kinetics of pTSA and chloride co-catalyzed conversion of HMF. Isomerization of glucose to fructose, condensation of glucose to form humin, dehydration of fructose to form HMF, and rehydration of HMF to LA were the major reactions in the system. To improve the HMF selectivity, efforts should be made to reduce the rate of glucose condensation to form humin

Adaptive Flux Variability Analysis: A Tool To Deal With Uncertainties

Abstract Underdetermined metabolic networks are usually investigated using Flux Variability Analysis (FVA) under the pseudo-steady state assumption of the internal metabolites. When a dynamic overview of the flux map is sought, the time variation of the cell uptake and excretion rates is deduced from extracellular dynamic mass balances and smoothing of the measurement data of the time evolution of the extracellular concentrations. Nevertheless, the resulting system of equations does not always admit a feasible solution under these constraints. Indeed, measurement data is affected by noise, whose processing (smoothing, etc) always entails some subjective user choices, and the network itself might not be perfectly suited to explain the several culture phases. To alleviate these adverse effects, the constraints can be relaxed by introducing coefficients of variation of the external fluxes, and by considering an interval representation of the fluxes. This work presents a systematic method to determine these coefficients of variation, along the time course of the culture, leading to an adaptive scheme where the coefficients are set to the tightest bounds. The methodology is applied to experimental data of cultures of hybridoma in batch and perfusion modes and compared to previously published results.

Kinetic model for surfactant-induced pore wetting in membrane distillation

Appendix CMembrane pore wetting is a unique and important technical challenge for membrane distillation (MD). While the general principle of pore wetting is well known, the detailed mechanism of pore wetting induced by surfactants that can actively adsorb onto membrane pore surface has not been theoretically elucidated. In this study, we developed a theoretical model, based on surfactant transport in a partially wetted membrane pore under the pseudo-steady state assumption, to quantify the kinetics of pore wetting. The theoretical model predicts several key dependences of wetting kinetics on operating parameters and solution properties, which are highly consistent with results from MD experiments using feed solution containing sodium dodecyl sulfate. It was found that kinetics of pore wetting is strongly dependent on vapor flux, surfactant concentration, but relatively independent of the transmembrane hydraulic pressure. The critical surfactant concentration below which pore wetting does not occur was also predicted by the wetting model. Finally, the impact of surfactant species on wetting kinetics was also discussed.

Kinetic models of Fischer-Tropsch synthesis reaction over granule-type Pt-promoted Co/Al2O3 catalyst

Kinetic models of CO hydrogenation to paraffinic hydrocarbons through Fischer-Tropsch synthesis (FTS) reaction were studied by using Langmuir-Hinshelwood Hougen-Watson (LHHW) model of 16 different reaction steps with a pseudo steady-state assumption (PSSA) on the prototype Pt-promoted Co/Al2O3 catalyst having a granule size of ∼1 mm of spherical γ-Al2O3 support (surface area of 149m2/g). The derived kinetic models from ten sets of experimental data by altering the reaction conditions such as temperatures, pressures, space velocities and H2/CO molar ratios were found to be well fitted with reasonable kinetic parameters and small errors of conversion of CO and hydrocarbon distributions in terms of mean absolute relative residual (MARR) and relative standard deviation error (RSDE). The derived reaction rates and CO activation energy of -86 kJ/mol well correspond to the our previously reported results using power-type catalysts. Based on the LHHW model with PSSA, the possible chemical intermediates on the granule ball-type Co-Pt/Al2O3 surfaces were precisely considered to explain the typical adsorption, initiation, propagation and termination steps of FTS reaction as well as to derive elementary reaction rates with their kinetic parameters and hydrocarbon distributions. The derived kinetic models were further used to verify temperature-profiles in a pilot-scale fixed-bed tubular FTS reactor with a packing depth of 100 cm catalyst, and it confirmed that the temperature gradients were less than 10 °C in a length of reactor by effectively removing the generated heat by an exothermic FTS reaction.

Glycosylation flux analysis reveals dynamic changes of intracellular glycosylation flux distribution in Chinese hamster ovary fed-batch cultures

N-linked glycosylation of proteins has both functional and structural significance. Importantly, the glycan structure of a therapeutic protein influences its efficacy, pharmacokinetics, pharmacodynamics and immunogenicity. In this work, we developed glycosylation flux analysis (GFA) for predicting intracellular production and consumption rates (fluxes) of glycoforms, and applied this analysis to CHO fed-batch immunoglobulin G (IgG) production using two different media compositions, with and without additional manganese feeding. The GFA is based on a constraint-based modeling of the glycosylation network, employing a pseudo steady state assumption. While the glycosylation fluxes in the network are balanced at each time point, the GFA allows the fluxes to vary with time by way of two scaling factors: (1) an enzyme-specific factor that captures the temporal changes among glycosylation reactions catalysed by the same enzyme, and (2) the cell specific productivity factor that accounts for the dynamic changes in the IgG production rate. The GFA of the CHO fed-batch cultivations showed that regardless of the media composition, galactosylation fluxes decreased with the cultivation time more significantly than the other glycosylation reactions. Furthermore, the GFA showed that the addition of Mn, a cofactor of galactosyltransferase, has the effect of increasing the galactosylation fluxes but only during the beginning of the cultivation period. The results thus demonstrated the power of the GFA in delineating the dynamic alterations of the glycosylation fluxes by local (enzyme-specific) and global (cell specific productivity) factors.

Assessing and Resolving Model Misspecifications in Metabolic Flux Analysis.

Metabolic flux analysis (MFA) is an indispensable tool in metabolic engineering. The simplest variant of MFA relies on an overdetermined stoichiometric model of the cell’s metabolism under the pseudo-steady state assumption to evaluate the intracellular flux distribution. Despite its long history, the issue of model error in overdetermined MFA, particularly misspecifications of the stoichiometric matrix, has not received much attention. We evaluated the performance of statistical tests from linear least square regressions, namely Ramsey’s Regression Equation Specification Error Test (RESET), the F-test, and the Lagrange multiplier test, in detecting model misspecifications in the overdetermined MFA, particularly missing reactions. We further proposed an iterative procedure using the F-test to correct such an issue. Using Chinese hamster ovary and random metabolic networks, we demonstrated that: (1) a statistically significant regression does not guarantee high accuracy of the flux estimates; (2) the removal of a reaction with a low flux magnitude can cause disproportionately large biases in the flux estimates; (3) the F-test could efficiently detect missing reactions; and (4) the proposed iterative procedure could robustly resolve the omission of reactions. Our work demonstrated that statistical analysis and tests could be used to systematically assess, detect, and resolve model misspecifications in the overdetermined MFA.

Unsteady dissolution of particle of various shapes in a stagnant liquid

The dissolution of planar, cylindrical, and spherical particles in a stagnant liquid is analyzed theoretically. Assuming that the diffusion of solute molecules is the rate-determining step, the temporal variation in the particle size is derived. The transient nature of the phenomenon under consideration is taken account of by solving a moving boundary problem through regular perturbation, and a perturbation parameter assessing if the pseudo-steady state assumption made in previous analyses is proposed. The applicability of the analytical result derived is verified by fitting it to the experimental data in the literature. We show that neglecting that transient nature may yield appreciable qualitative and quantitative deviations, especially if a particle has a high solubility, large molecular weight, or low density.

Integrating Flux Balance Analysis into Microalgae Growth Kinetics for Dynamic Simulation

Most of the microalgae growth models are based on modified Monod kinetics, which often involve many parameters to identify. Some fundamental questions about the validity of such empirical growth rate still remain. On the other hand, flux balance analysis (FBA) can compute a steady-state flux distribution of metabolic networks within a feasible flux space constrained by fundamental laws including mass balances. This work proposes how to set up various constraints as boundary conditions in FBA, relate the resulting flux distribution to the growth rate, and dynamically simulate the microalgae growth kinetics. In order to relate mass balances of the bioreactor to the FBA solution, accumulation rates as well as uptake and production rates are used. Dynamic simulations were performed by modifying pseudo-steady state assumption for FBA and integrating the ordinary differential equations for bioreactor model over time, leading to a two-time scale description. The proposed scheme can reduce the number of parameters and explain adaptation to the changing environment. A Chlamydomonas reinhardtii culture system is illustrated to present the applicability of the proposed scheme.

Simplifying Complex Computer-Generated Reactions Network to Suppress Its Stiffness

Creation of mathematical model of complex radical processes manually is a very time-consuming process. Steam-cracking model created automatically by automated reaction network generation, on the other hand, becomes very large and complex for bigger molecules. This work was aimed at applying pseudo-steady state assumption automatically to components inside generated reactions network. The details of simplifying procedure are provided and the comparison of experimental data (lab-scale) to simulations by original and simplified model is presented. In overall, the simplification procedure lead only to marginal deviations in the simulated results, but the model ability to simulate bigger molecules has substantially improved.

Structure and Dynamics of Bio-Networks : Robustness of Metabolic Networks

We investigated the robustness of cellular metabolism by simulating the system-level computational models, and also performed the corresponding experiments to validate our predictions. We address the cellular robustness from the “metabolite”-framework by using the novel concept of “flux-sum”, which is the sum of all incoming or outgoing fluxes (they are the same under the pseudo-steady state assumption). By estimating the changes of the flux-sum under various genetic and environmental perturbations, we were able to clearly decipher the metabolic robustness; the flux-sum around an essential metabolite does not change much under various perturbations. We also identified the list of the metabolites essential to cell survival, and then “acclimator” metabolites that can control the cell growth were discovered. Furthermore, this concept of “metabolite essentiality”' should be useful in developing new metabolic engineering strategies for improved production of various bioproducts and designing new drugs that can fight against multi-antibiotic resistant superbacteria by knocking-down the enzyme activities around an essential metabolite. Finally, we combined a regulatory network with the metabolic network to investigate its effect on dynamic properties of cellular metabolism. [Proc. Nat. Acad. Sci. USA. 104 13638 (2007)]

Optimal time-dependent operation of seawater reverse osmosis

The operation of seawater reverse osmosis (SWRO) plants is systematically optimized with the objective to reduce the electricity charges, which constitute the largest portion of the operation costs. Variable operating conditions and a time-of-use electricity tariff rate schedule are considered. A well-established model is extended to model a reverse osmosis (RO) system equipped with highly efficient pressure exchangers (PXs) and variable frequency drives (VFDs). All major performance factors are considered, including membrane's permeability, concentration polarization, temperature effects, membrane fouling, and efficiency dependency of the VFD on the loading conditions. The proposed formulation minimizes the electricity cost per day, given a desired daily production rate. The problem is formulated as a mixed-integer nonlinear program (MINLP), allowing for periods without operation. The time domain (24 h) is discretized into 0.5 h increments, and a pseudo steady-state assumption is used. The optimal operation plan resulting in maximum electricity cost-savings is established with standard global optimization tools. The results show significant electricity and production cost-saving potentials. More savings in electricity can be achieved by oversizing the plant, thus allowing shutting-off at periods of high electricity cost. The cost-saving potentials are particularly promising in electricity markets in which the electricity rate schedule is widely distributed.

Modeling and simulation of unstirred dead end ultrafiltration of macromolecules

A mass transfer model based on unsteady state component balance over the concentration boundary layer has been developed in the present study. The model uses semi-infinite consideration in order to solve the governing partial differential equation by Laplace transform that gives an analytical expression for the concentration profile. During the solution procedure, pseudo steady state assumption has been used, as a consequence of which permeate flux and membrane surface concentration have been taken constant over any small time interval. Once the expression for concentration profile is known, a time evolution loop has been developed to simulate the permeate flux, membrane surface concentration and permeate concentration under specified operating conditions of transmembrane pressure drop and bulk concentration. The prediction of the proposed model was found to be in good agreement with experimental results obtained during unstirred dead end ultrafiltration of polyethylene glycol (of average molecular weight 6000) solution using a cellulose acetate membrane of 5000 Da molecular weight cut-off.

Kinetic behavior of photo-polymerization of UV-curable resins with carboxylic acid and amino groups

Photo-polymerization behaviors of bisphenol-A epoxy diacrylate (EPA) and six kinds of EPA-derived resins containing different amounts of carboxylic acid, urethane, amide, and imide groups were studied by a photo differential scanning calorimetry. The dark polymerization was performed and pseudo-steady state assumption of growing radicals was made to obtain the kinetic constants for propagation, bimolecular termination, monomolecular termination, and the concentration of growing radicals of different resins as a function of extent of reaction. Compared with EPA, it was found that the rate of polymerization and kinetic constants of the six resins were relatively small because the mobility of reacting species in resins was restricted by carboxylic acid, urethane, amide, and imide groups. Finally, three different photo-initiators were used to initiate the polymerization, and their kinetic behaviors were compared. The effect of tertiary amine group of photo-initiator on the rate of polymerization of resins having carboxylic acid group and the initiator efficiency were discussed. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010

Oxidative degradation of dimethyl phthalate (DMP) by UV/H 2O 2 process

The photochemical degradation of dimethyl phthalate (DMP) in UV/H 2O 2 advanced oxidation process was studied and a kinetic model based on the elementary reactions involved was developed in this paper. Relatively slow DMP degradation was observed during UV radiation, while DMP was not oxidized by H 2O 2 alone. In contrast, the combined UV/H 2O 2 process could effectively degraded DMP, which is attributed to the strong oxidation strength of hydroxyl radical produced. Results show that DMP degradation rate was affected by H 2O 2 concentration, intensity of UV radiation, initial DMP concentration, and solution pH. A kinetic model without the pseudo-steady state assumption was established according to the generally accepted elementary reactions in UV/H 2O 2 advanced oxidation process. The rate constant for the reaction between DMP and hydroxyl radical was found to be 4.0 × 10 9 M −1 s −1 through fitting the experimental data to this model. The kinetic model could adequately describe the influence of key factors on DMP degradation rate in UV/H 2O 2 advanced oxidation process, and could serve as a guide in designing treatment systems for DMP removal.

Stoichiometric modelling of cell metabolism

There are several methodologies based on representations of cell metabolism that share two characteristics: the use of a metabolic network and the assumption of pseudosteady state. These methodologies have different purposes, employ different mathematical tools and are based on different assumptions; however, they all exploit the properties of a similar mathematical description. In this article we use the term stoichiometric modelling to encompass all these methodologies and to describe them within a common framework. Although the information about reaction stoichiometry embedded in metabolic networks is highly important, the framework encompasses methodologies not limited to the use of stoichiometric information. To highlight this fact, the definition of the framework is approached from a constraint-based perspective. One of the reasons for the success of stoichiometric modelling is that it avoids the difficulties that arise in the development of kinetic models: a consequence of the lack of intracellular experimental measurements. Thus, it makes it possible to exploit the knowledge about the structure of cell metabolism, without considering the still not very well known intracellular kinetic processes. Stoichiometric models have been used to estimate the metabolic flux distribution under given circumstances in the cell at some given moment (metabolic flux analysis), to predict it on the basis of some optimality hypothesis (flux balance analysis), and as tools for the structural analysis of metabolism providing information about systemic characteristics of the cell under investigation (network-based pathway analysis).

Diffusion of mobile products in reactive barrier membranes

Diffusion of mobile products produced in reactive barrier membranes was studied theoretically and experimentally. A diaphragm cell in which a reactive solute challenges a reactive membrane was adopted for this purpose. A diffusion equation with a reaction term describes the behavior of a mobile product before breakthrough of the solute, while the common diffusion equation governs the system after the breakthrough. An approximate, analytical solution was derived to this diffusion problem based on a pseudo-steady state assumption, and the result agreed closely with a numerical solution without assumptions. A poly(vinyl alcohol) membrane containing zinc oxide particles was challenged by hydrochloric acid in a diffusion experiment to validate the theoretical predictions. Diffusion of zinc chloride, the mobile reaction product, was monitored using a colorimetric method. The experimental results matched the analytical model.

β- d-Glucosidase reaction kinetics from isothermal titration microcalorimetry

The cellobiase activities of nine thermal stable mutants of Thermobifida fusca BglC were assayed by isothermal titration microcalorimetry (ITC). The mutations were previously generated using random mutagenesis and identified by high-temperature screening as imparting improved thermal stability to the β- d-glucosidase enzyme. Analysis of the substrate–saturation curves obtained by ITC for the wild-type enzyme and the nine thermally stabilized mutants revealed that the wild type and all the mutants were subject to binding of a second substrate molecule. Furthermore, the “inhibited” enzyme–substrate complexes were shown to retain catalytic activity. In the case of three of the BglC mutants (N178I, N317Y/L444F, and N317Y/L444F/A433V), binding of a second substrate molecule resulted in improved cellobiose turnover rates at lower substrate concentrations. No correlation between denaturation temperatures of the mutants and activity on cellobiose at 25 °C was evident. However, one particular mutant, BglC S319C, was significantly improved in both thermal tolerance and cellobiase activity with respect to those of the wild-type BglC. The triple mutant, N317Y/L444F/A433V, had a 5 °C increase in denaturation temperature while maintaining activity levels similar to that of the wild type at higher substrate concentrations. ITC provided a highly sensitive and nondestructive means to continuously monitor the reaction of BglC with cellobiose, resulting in abundant data sets that could be rigorously analyzed by fitting to known enzyme kinetics models. One distinct advantage of using data from the ITC was the empirical validation of the pseudo steady state assumption, a necessary condition for obtaining solutions to the proposed mechanisms.

Structured kinetic model for Xanthomonas campestris growth

A structured kinetic model for Xanthomonas campestris growth is proposed. The formulation of the model is made according to those steps employed for kinetic modeling of reaction networks. First, simplified reaction schemes are proposed, which are formed by four or five reactions using lumping and pseudosteady-state assumption for different compounds. Several expressions for the kinetic equations have been considered, checking their validity with the evolution of experimental data taking into account the different reactions in the scheme of reactions assumed. Afterwards, parameter values are calculated by regression to experimental data, using simple and multiple non-linear techniques. Then, model discrimination is carried out using both statistical and physical restrictions. The model finally proposed has four key compounds: ammonium, RNA, DNA and intracellular proteins. The analysis of the intracellular compounds (RNA, DNA and proteins) has been carried out using an experimental technique based in flow cytometry. Three experiments (under the same operational conditions but with different initial nitrogen concentrations in the medium) have been fitted to the model to obtain the values of the parameters, showing a prediction very close to the experimental data. The model is able to predict different system evolutions for different nitrogen initial concentrations.