Removal of heat of adsorption from adsorbent by forced convection

An analytical mathematical model is used to investigate the effectiveness of forced convection for removal of the heat of adsorption from an adsorbent mass undergoing a differential adsorption process in a flow system. An example of such a process is measurement of gas adsorption kinetics using a differential adsorption bed. Isothermal operation may not be achieved even when a high gas flow rate is used, particularly if the sorption kinetics is relatively fast. Very small changes in the adsorbent temperature can cause significant departure from the isothermal uptake behavior when the heat of adsorption is moderately large. A criterion for validity of isothermal data analysis is given.     

Real-time image analysis and numerical simulation of isothermal spherulite nucleation and growth in polyoxymethylene

A method of analysing nucleation and crystallization kinetics, based on real time image analysis and hot stage optical microscopy, has been used to investigate the isothermal crystallization of different grades polyoxymethylene. The data were compared with results from differential scanning calorimetry (DSC), using a simple numerical simulation to model the effects of finite smaple thickness on the form of the isothermal DSC curves. This simulation was then used to predict the microstructural development in a bulk sample for different boundary conditions, taking into account latent heat evolution and diffusion during crystallization.     

Phenomenological study on heat and mass coupling mechanism of waxy crude oil pipeline transport process

Based on the phase equilibrium model of the paraffin wax precipitation in the process of oil pipeline transportation, theory and method of non-equilibrium thermodynamics were applied to obtain the linear phenomenological equations for the cross-interaction of heat and mass transfer during pipeline transport, which were derived from the irreversible entropy production rate equation. Then, the analysis of the irreversible heat flow and the mass flow were carried out, and the mathematical expressions of the phenomenological coefficient of liquid phase, the phenomenological coefficient of solid phase flow, and the heat flow phenomenological coefficient were obtained. Taking a waxy crude oil transportation pipeline in Daqing Oilfield as an example, based on the analysis of liquid–solid phase equilibrium, the irreversible linear phenomenological mechanism of heat and mass coupling in waxy crude oil pipeline transportation was analyzed in detail from three levels: phenomenological coefficients which reflect characteristic of the effect of force on flow in heat and mass transfer; thermodynamic forces which trigger heat and mass transfer; transmitted heat and mass flow density, providing a theoretical basis for the further study of the wax deposition in the process of pipeline transportation.     

恒温过程的热量传递

目前,基于物化教材上对"恒温过程"和"热"的定义,初学者在理解恒温过程的热量传递时往往会产生很大困惑。对概念的孤立和片面理解是造成该结果的根本原因。本文借助数学上的极限思想,以理想气体的恒温可逆膨胀过程为例,对该过程的能量传递做出详细剖析,以消除物理化学初学者在入门期的学习障碍。     

Mathematical Simulation of Plasma-Chemical Coal Conversion

A mathematical model that describes the conversion of a coal-dust flow in a cylindrical plasma reactor is presented. The model describes a two-phase (coal particles + air) chemically reacting flow, which propagates in a channel with or without an internal heat source (an electric arc, a plasmatron torch, or exothermic chemical reactions). The model is based on the assumption that the process is quasi-stationary and one-dimensional; coal particles are taken isothermal, and ash is assumed an inert component. The model represents the composition of coals by their organic and mineral constituents. The model was implemented as a program for personal computers; calculations performed with the use of this program are in satisfactory agreement with experimental data.     

Wax deposition rate model for heat and mass coupling of piped waxy crude oil based on non-equilibrium thermodynamics

In this paper, wax deposition in waxy crude oil transportation process was regarded as an irreversible process. Based on the entropy production rate equations, the linear phenomenological equations for the diffusion of wax molecules were derived by using the theory and method of non-equilibrium thermodynamics and heat-mass transfer. Combined with the mass and energy conservation laws, the differential equations of heat and mass transfer in the process of pipeline transportation were established, and the molecular diffusion rate of dissolved wax was solved. On the basis of this, the mathematical model of actual wax deposition rate was established by considering the attachment process and scouring process of the wax molecules. Taking an oil pipeline in Daqing as an example, the change law and influencing factors of the wax molecular diffusion coefficient, the wax deposition rate, and the net wax deposition rate were studied by numerical simulation. The wax deposition rate test results of the laboratory loop test were compared with the theoretical calculation results in order to analyze the accuracy and the adaptability of heat and mass coupling mechanism and to provide a theoretical basis for further study of wax deposition in the process of waxy oil pipeline transportation.     

Degradation of substrate and/or product: mathematical modeling of biosensor action

Mathematical model for evaluation of the multilayer heterogeneous biocatalytic system has been elaborated. The model consists of nonlinear system of partial differential equations with initial values and boundary conditions. An algorithm for computing the numerical solution of the mathematical model has been applied. Two cases: when product diffuses out of the biosensor and when the outer membrane is impermeable for product (product is trapped inside the biosensor) have been dealt with by adjusting boundary conditions in the mathematical model. Profiles of the impact of the substrate and product degradation rates on the biosensor response have been constructed in both cases. Value of the degradation impact has been analyzed as a function of the outer membrane thickness. The initial substrate concentration also affects influence of the degradation rates on the biosensor response. Analytical formulae, defining approximate values of relationships between the degradation rates and the outer membrane thickness or the initial substrate concentration, have been obtained. These formulae can be employed for monitoring of the biosensor response.     

Influence of particle size and kinetic parameters on tire pyrolysis

One of the most important parameters that can significantly affect the cost of the tire pyrolysis process is the time needed for thermal decomposition of the tire material. In this work, the influence of particle size and kinetics of thermal decomposition on the pyrolysis time was studied. The apparent kinetic parameters of tire thermal decomposition were estimated using three different approaches based on thermogravimetry measurements. In separate experiments, tire particles with different sizes were pyrolyzed under isothermal conditions in a laboratory flow reactor at different residence times of the particles in the reactor and the data recorded were employed in the determination of tire conversion during the thermal decomposition. A mathematical model of tire pyrolysis considering heat conduction in the tire particles was developed. All three types of estimated kinetic parameters were used to determine the conversion behavior at isothermal conditions and the results were compared with experimental data obtained. The model was used also to calculate the pyrolysis time in an industrial scale reactor at different temperatures and particle sizes.     

Modelling a flow of a highly viscous liquid with the boundary layer of low viscosity in an extruder

Features of the flow of a highly viscous liquid in an extruder with boundary layer of low viscosity liquid at the cylinder wall and at the endless screw surface are considered. The liquid flow is modeled under conditions of isothermal simple shift using cylindrical model of a screw canal. The profiles of rates for the stream of a highly viscous liquid with the ring boundary layer of low-viscous liquid at the cylinder wall and at screw in the both presence and absence of a counter pressure are calculated. Consideration of computer calculations shows that increase in the flow rate is possible when the counter pressure tends to zero and the low-viscous liquid forms a ring boundary layer at the cylinder wall.     

A Dynamic Model for Cellulosic Biomass Hydrolysis: a Comprehensive Analysis and Validation of Hydrolysis and Product Inhibition Mechanisms

The objective of this study is to perform a comprehensive enzyme kinetics analysis in view of validating and consolidating a semimechanistic kinetic model consisting of homogeneous and heterogeneous reactions for enzymatic hydrolysis of lignocellulosic biomass proposed by the U.S. National Renewable Energy Laboratory (Kadam et al., Biotechnol Prog 20(3):698–705, 2004) and its variations proposed in this work. A number of dedicated experiments were carried out under a range of initial conditions (Avicel® versus pretreated barley straw as substrate, different enzyme loadings and different product inhibitors such as glucose, cellobiose and xylose) to test the hydrolysis and product inhibition mechanisms of the model. A nonlinear least squares method was used to identify the model and estimate kinetic parameters based on the experimental data. The suitable mathematical model for industrial application was selected among the proposed models based on statistical information (weighted sum of square errors). The analysis showed that transglycosylation plays a key role at high glucose levels. It also showed that the values of parameters depend on the selected experimental data used for parameter estimation. Therefore, the parameter values are not universal and should be used with caution. The model proposed by Kadam et al. (Biotechnol Prog 20(3):698–705, 2004) failed to predict the hydrolysis phenomena at high glucose levels, but when combined with transglycosylation reaction(s), the prediction of cellulose hydrolysis behaviour over a broad range of substrate concentrations (50–150 g/L) and enzyme loadings (15.8–31.6 and 1–5.9 mg protein/g cellulose for Celluclast and Novozyme 188, respectively) was possible. This is the first study introducing transglycosylation into the semimechanistic model. As long as these type of models are used within the boundary of their validity (substrate type, enzyme source and substrate concentration), they can support process design and technology improvement efforts at pilot and full-scale studies.     

Product desorption rate influence on catalytic reactivity of spatially inhomogeneous surfaces

We investigate numerically a phenomenological mathematical model of unimolecular reactions proceeding on inhomogeneous planar surfaces in the two-dimensional space case taking into account: the bulk diffusion of the reactant from the bounded vessel toward the adsorbent and the product bulk one from the adsorbent into the same vessel, the adsorption and desorption of reactant particles, long-range surface diffusion of the adsorbate, and a slow product desorption from the adsorbent. Simulations were performed using the finite difference technique. The influence of the long-range surface diffusion and product desorption rate on the kinetics of processes catalysed by inhomogeneous surfaces with different arrangements of reactive and nonreactive adsorption sites are studied.     

Estimation of the curing rate of acrylamide used as a consolidant in heritage sandstone conservation

An investigation of the curing (polymerisation) rate of acrylamide was carried out using isothermal and non-isothermal DSC in order to estimate the time for complete conversion of monomer at ambient temperatures. The non-isothermal data were used to model the rate using integral isoconversional and incremental isoconversional kinetic methods. Applying the equations for integral isoconversional methods and extrapolating to ambient temperatures resulted in non-sensical conversion–time curves, where the time estimated decreased for increasing degree of conversion to be reached. This odd behaviour was attributed to the incorrectness of the integration where the kinetic parameters (e.g. the activation energy) are a function of conversion. The problem was addressed by applying incremental methods which provided more reasonable results as the integration is carried out over small conversion increments where the kinetic parameters are assumed to be constant. Estimates of the conversion were compared to isothermal measurements and, although isothermal DSC produced significant variability in the data, extrapolated estimates from non-isothermal kinetic analysis produced, at best, an upper boundary for the estimation of the time to reach a fixed degree of conversion.     

Influence of viscous dissipation and thermophoresis on Darcy-Forchheimer mixed convection in a fluid saturated porous media

Mixed convection flow, heat, and mass transfer about an isothermal vertical flat plate embedded in a fluid-saturated porous medium and the effects of viscous dissipation and thermophoresis in both aiding and opposing flows are analyzed. The similarity solution is used to transform the problem under consideration into a boundary value problem of coupled ordinary differential equations, which are solved numerically by using the shooting method. Numerical computations are carried out for the non-dimensional physical parameter. The results are analyzed for the effect of different physical parameters such as thermophoretic, mixed convection, inertia parameter, buoyancy ratio, and Schmid number on the flow, heat, and mass transfer characteristics. Two cases are considered, one corresponding to the presence of viscous dissipation and the other to the absence of it.     

A computer model of the nonstationary gas flow in a long multilayer-insulated high-pressure subsea gas pipeline

For the non-stationary gas flow in a long multilayer-insulated high-pressure subsea gas pipeline, an original computer model was developed that takes into account transient heat-transfer processes in the long multilayer wall of the pipeline. These processes may influence the energy balance of the flowing gas, leading to a change in the gas temperature down to negative values, which may cause frosting of the pipe and reduction of its strength characteristics up to rupture. The adequacy of the model was checked on an industrial subsea pipeline more than 300 km long. Computational experiments on the developed computer model under essentially unsteady boundary conditions for pressure, mass flow rate, and temperature showed that the developed model gives more accurate values of flow velocity, pressure, and temperature throughout the pipeline.     

Heat conduction in a two-dimensional spherulite

The anisotropy of thermal conduction in a spherulite is calculated for a two-phase model. The problem of the temperature distribution due to cooling of a spherulite suddenly heated at one point is solved. An analytical result is given and isothermal contours are calculated for wide ranges of thermal conduction anisotropy and cooling time. Experiments with spot-heated isotactic polypropylene (i-PP) and isotactic polystyrene (i-PS) spherulites were conducted using a laser pulse and a needle as heat sources. The isotherms were recorded using a thin coating of a heat-sensitive indicator substance, and then by comparison with theoretical isotherm patterns the heat conduction anisotropy of a PP spherulite was estimated. Additional measurements of heat conduction coefficients of at least two polymer films characterized by different crystallinity permit calculation of the thermal conductivity of the amorphous phase, and the conductivities of single crystals along chains and perpendicular to the chains. The results show that the heat is transferred mainly along the primary bonds of polymer chains. However, the morphology of sperulites and lamellas plays an important role.     

Toward a statistical mechanical theory for water: analytical theory for a short-ranged reference system

Starting from a realistic Hamiltonian and making use of recent findings that the properties of associating fluids are determined primarily by short-ranged interactions, this methodology has been implemented using statistical mechanical approaches and thermodynamic perturbation theory for the TIP4P model of water. We focus on the short-range reference system for which an analytic expression for the Helmholtz free energy is derived. It is found that the model (reference system) exhibits, in addition to a faithful representation of the structure of water, the same features that are characteristic for real water, namely, (i) the temperature of the density maximum and its pressure dependence, including the inflection point at high pressures and (ii) the temperature minima of the constant pressure heat capacity and the coefficient of isothermal compressibility.     

Wax phase equilibria: developing a thermodynamic model using a systematic approach

Reservoir hydrocarbon fluids contain heavy paraffins that may form solid phases of wax at low temperatures. Problems associated with wax formation and deposition are a major concern in production and transportation of hydrocarbon fluids. The industry has directed considerable efforts towards generating reliable experimental data and developing thermodynamic models for estimating the wax phase boundary.The cloud point temperature, i.e. the wax appearance temperature (WAT) is commonly measured in laboratories and traditionally used in developing and/or validating wax models. However, the WAT is not necessarily an equilibrium point, and its value can depend on experimental procedures. Furthermore, when determining the wax phase boundary at pipeline conditions, the common practice is to measure the wax phase boundary at atmospheric pressure, then apply the results to real pipeline pressure conditions. However, neglecting the effect of pressure and associated fluid thermophysical/compositional changes can lead to unreliable results.In this paper, a new thermodynamic model for wax is proposed and validated against wax disappearance temperature (WDT) data for a number of binary and multi-component systems. The required thermodynamic properties of pure n-paraffins are first estimated, and then a new approach for describing wax solids, based on the UNIQUAC equation, is described. Finally, the impact of pressure on wax phase equilibria is addressed.The newly developed model demonstrates good reliability for describing solids behaviour in hydrocarbon systems. Furthermore, the model is capable of predicting the amount of wax precipitated and its composition. The predictions compare well with independent experimental data, demonstrating the reliability of the thermodynamic approach.     

Applied computer model of the non-stationary gas flow in a long multilayer-insulated high-pressure subsea gas pipeline

An applied fluid-dynamics model of the non-stationary flow in a long multilayer-insulated high-pressure subsea gas pipeline was developed. Instead of a complex partial differential heat conduction equation, which represents the heat flux between the flowing gas and the environment in the energy balance equation, the model uses a first-order ordinary differential equation. The applied model allows one to significantly increase the speed of numerical computation of the fluid-dynamics parameters of the gas flow in the pipeline, which is necessary for multivariate computations in design and operation of gas pipelines.     

Morphology Evolution During Polymer Crystallization Simultaneous Calorimetric and Optical Measurements

The crystallization of the isotactic poly(propylene) (I-PP) has been studied carrying out measurements by means of a special calorimeter connected to a microscope and a digital acquisition system of images. To authors' knowledge, this is the first time that simultaneous calorimetric and optical measurements are carried out on polymers. The analysis of Polarized Optical Microscopy images has allowed the appraisal of nucleation density and growth rate in isothermal and non isothermal conditions. The results obtained in isothermal conditions have been analyzed through the Kolmogoroff model and the crystallinity calculated from the model has been compared with that obtained from the calorimetric measurements.