MODELING OF SPEARMINT OIL EXTRACTION IN A PACKED BED USING SC-CO2

The packed bed extraction of spearmint oil using supercritical carbon dioxide was studied by a two-phase mass transfer model on the basis of desorption and diffusion. Unsteady-state mass balance for solute in supercritical and in solid phases led to two partial differential equations that were solved numerically using a linear equilibrium relationship. The model has four parameters, axial dispersion, mass transfer, and diffusion and desorption coefficients. Diffusion and desorption coefficients were used as the model tuning parameters and the others were predicted applying existing experimental correlations. The tuning parameters were calculated by the fitting error between 5 and 15% by the genetic algorithm method. In addition, this model was compared with a model that did not account for the desorption rate, according to the model suggested by Goodarznia and Eikani (G&E). Moreover, the effects of operational parameters such as pressures, temperatures, CO₂ flow rates, and mean particle sizes on the extraction yield were evaluated. In order to obtain experimental data for spearmint oil, a facility was designed and constructed to conduct the experimental part of this study. The two models were also applied to the literature's experimental data for rosemary leaves, grape seeds, peanuts, and tomato seeds. Comparison of the results of the proposed model with results from the G&E model indicated that the proposed model had better predictability. Also, good agreement of the proposed model results and the experimental data confirmed the basic hypothesis of the model and the importance of the desorption rate.     

A dynamic object-oriented model for efficient simulation of fluid dispersion in turbulent flow with varying fluid properties

Dispersion coefficients for turbulent flow are commonly available, but the common models are not easily implemented for fast computation of dispersion in time-dependent large flow systems.Criteria were developed to aid in the choice of parameters for a model combining plug flow with the N-continuously stirred-tanks model to obtain the best agreement with the pure axial-dispersed plug-flow model, while simultaneously being computationally efficient. Solution accuracy and computational savings were demonstrated for a realistic food industry example. The proposed model includes a method of structuring the discretisation to handle the simulation of pressure drop and momentum balance simultaneously with simulation of dispersion.The criteria were derived from the analysis of Laplace transforms. It was also shown that the proposed model predicts the response to a step change in concentration in agreement with the exact solution of the axial-dispersed plug-flow model.The model was written in the object-oriented language Modelica as an object in a library structure which is being developed to simulate complex liquid food process lines and their control systems.     

颗粒流拟流体的本构关系

针对慢速密集颗粒流的特点,采用拟流体的方法,类比具有屈服应力的非牛顿流体,给出了适用于慢速密集颗粒流的本构方程表达形式,建立了用粗糙底面斜槽测量颗粒流当量粘性的数学模型,并以小麦颗粒为例,通过粗糙底面斜槽实验得出了小麦颗粒流的屈服应力及其本构方程的关键系数. 将实验得出的小麦颗粒流本构关系系数作为其当量粘性的特征值对斜面流进行解析计算,体积流量的模型预测值与实验值的相对误差在15%以内.     

THE GALERKIN METHOD FOR TWO-PASS CROSSFLOW HEAT EXCHANGER PROBLEM

The Galerkin method is applied to solve the two-pass crossflow heat exchanger problem in the case of neither fluid mixed throughout. Four variants of flow arrangements differing in identical and/or inverted order of coupling the passes in an overall counter-current scheme are considered. The passes are not necessarily equal with respect to the number of heat transfer units. The power of the method presented can be seen in the fact that the exchanger effectiveness can be predicted with less than 0.1% error even in the case of the first order approximation. The convergence toward the exact results by carrying out the computations to higher order terms is demonstrated. Four-significant-figure effectiveness tables based on the first order approximation are given for each type of flow arrangement for N_tu up to 10. The effectiveness deterioration caused by unequal N_tu's per pass (due to different heat transfer coefficients, different fining, different core length, etc.) is presented in the form of charts.     

A gas holdup model for cocurrent air-water-fiber bubble columns

A gas holdup model is developed for cocurrent air-water-fiber bubble column flows using the drift-flux model. The model coefficients are estimated using a nonlinear least square method and systematically acquired experimental data. The model correlates gas holdup with superficial gas and liquid velocity, and fiber type and mass fraction. The model reproduces most experimental data within ±10% error and all but 3 of the 3839 experimental data points within ±15% error. It also accurately predicts air-water bubble column gas holdup data; these data were not used in estimating the model coefficients. The physical implications of the model coefficients are also discussed.     

Single bubble formation at orifices submerged in viscous liquids

This paper concerns the slow formation of gas bubbles at circular orifices submerged in liquids with viscosities ranging from 10 to 1000 poise. A mathematical model is developed for predicting the bubble lift-off size as a function of, basically, Froude, Weber and Reynolds numbers; it is analytical and does not depend on semi-empirical coefficients. To check the validity of this model, experiments involving various gas flow rates and orifice diameters were performed in several liquids. The model consistently underestimates the experimentally obtained bubble size; the error of estimate varies from 10 to 25%. For bubble formation in a regime between the constant flow and constant pressure regimes, both the chamber pressure and the flow rate into the bubble vary. Furthermore, the instantaneous gas flow rate into the bubble can be many times greater than the average flow rate in the piping far upstream of the orifice exit. The former flow rate is important in determining the forces acting on the bubble and a method is given for obtaining its average value.     

使用同轴双圆柱流变仪获取Bingham流体流变参数

分析了使用同轴双圆柱流变仪测试Bingham流体流变参数(屈服应力和塑性黏度)时,非剪切区对转速–扭矩曲线的非线性和连续性的影响,以及非剪切区对Bingham流体剪切应变速率的影响。对使用转速–扭矩曲线的线性段来获取Bingham流体流变参数的可行性进行了分析,提出了使用同轴双圆柱流变仪,在考虑非剪切区存在与否的情况下,利用剪切应力–剪切应变速率曲线获取Bingham流体流变参数的方法。同时,提出了剪切应力–剪切应变速率计算过程中的去噪声方法,实现了剪切应力–剪切应变速率曲线的高精度获取。     

环隙内流动沸腾传热的计算

提出环隙内流动沸腾传热计算的数学模型和计算方法。将传热系数K与流动沸腾传热系数hb的计算结果与实测数据加以比较。对环隙与空管两种结构的流动沸腾传热性能也进行了分析对比。     

超临界CO2萃取丁香油的数值模拟

为了预测超临界CO₂萃取挥发油动态过程，根据挥发油在超临界CO₂与物料之间的质量传递平衡，采用集总参数法建立超临界CO₂萃取丁香油过程的数学模型。结合不同温度、压力、粒径和CO₂流速条件下的实验结果，对方程进行了合理的简化，并利用实验数据拟合出模型中CO₂密度、粒径和流速的系数。验证结果表明模型的计算值和实验值的平均相对误差在6. 88%～57. 78%之间，建立的数值模型能较好地描述实际的超临界CO₂萃取丁香油行为。     

A new approach to evaluate kinetic parameters and mass transfer coefficients in continuous stirred tank reactors. Application to antibiotic separation

A new method is proposed to evaluate kinetic parameters and mass transfer coefficients for adsorption processes carried out in continuous stirred tank reactors. This method, employing a biphasic model, does not linearize nonlinear solute concentration versus time data, nor does it assume the existence of equilibrium in a typical nonequilibrium situation as is currently done. For a nonlinear adsorption isotherm, the coupled differential equations need to be solved numerically, but using an elegant analytical solution it is possible to determine rate constants and mass transfer coefficients in the case of nonlinear kinetics with a linear adsorption isotherm. This solution (biphasic model, linear isotherm) is obtained and compared with solutions incorporating (i) a linear model (linear isotherm) and (ii) a numerical solution (nonlinear isotherm) for recovery of the antibiotic novobicoin in stirred tank reactors. For novobiocin adsorption versus time data, use of the biphasic model results in a lower mean percentage error than either the linear model or the numerical simulation; further, it provides a far superior fit of short-time adsorption behavior. Hence, we strongly advocate that the biphasic model be routinely employed along with linear models and numerical simulations of Langmuir/Freundlich isotherms for interpretation of adsorption data.     

Heat transfer coefficient in a high pressure tubular reactor for ethylene polymerization

Heat transfer in tubular reactors for the high pressure polymerization of ethylene is very complex, since these tubular reactors are usually divided into several zones that exhibit different flow patterns and critical fouling behavior. The correct estimation of the overall heat transfer coefficient along the reactor axial distance is a major issue when assessing the predictive capabilities of a mathematical model for the process. In general, previous models employed either constant heat transfer coefficients or the usual correlations for the Nusselt number. Neither of these two approaches is accurate enough to allow a correct prediction of the reactor behavior with respect to temperature profiles and product molecular properties. The present work performs a more comprehensive estimation of the heat transfer coefficient in these reactors. At a first stage the overall heat transfer coefficients were estimated by using approapriate energy balances and a good set of experimental data. Then, a predictive model was proposed for the overall heat transfer coefficient. All flow regimes, as well as fouling effects, were taken into account, and the parameter estimation was based on temperature profiles obtained from an industrial reactor. The temperature profiles, conversions, pressures and molecular properties calculated by means of the experimentally fitted heat transfer coefficients or with the predictive model showed good agreement with plant data.     

Non-newtonian flow through open channels

A general method is proposed for prediction of the flow rate and maximum velocity in the isothermal, steady, uniform, laminar flow of any incompressible, time-independent non-Newtonian fluid in straight open channels of arbitrary cross section. The method requires only a knowledge of two geometric coefficients and a function of shear stress, used to characterize the behavior of the fluid model. The slip effect at the solid boundary has been taken into consideration. Numerical values of the geometric parameters have been determined for flow through an inclined plane of infinite width, semi-circular, semi-elliptical, rectangular, and 90° and 60° symmetric triangular open channels. Applications have been made to various non-Newtonian fluid models such as the power-law, Bingham, Ellis, Meter and the Reiner-Rivlin general model. Numerical examples are presented. A generalization of the Fanning friction factor — Reynolds number is also presented. The problem of determining the point of transition from laminar to turbulent flow in the general case is examined, as is the problem of prediction of the friction factor in turbulent flow.     

ESTIMATION OF COEFFICIENTS OF TIME SERIES REGRESSION WITH A NONSTATIONARY ERROR PROCESS

Abstract. We treat a problem of estimating unknown coefficients of a time series regression when the variance of the error changes with time, i.e. when a process which the error term obeys is nonstationary. First, we show the weak consistency of the ordinary least squares estimator for the coefficients of a polynomial regression under some assumptions on the covariance structure of the error process. Next, we propose a nonparametric method for estimating the variance of the error process and a weighted least squares estimator of the regression coefficients, which is constructed by using the estimator of the variance. We investigate statistical properties of our proposed estimator in the following way. We consider the prediction of a future value of a linear trend by using our proposed estimator and evaluate its prediction error. By simulation studies, we compare the prediction error of the predictor constructed by using our proposed estimator with the prediction errors obtained for other estimators including the ordinary least squares estimator when the variance of the error process increases with time and the sample sizes are small. As a result, our proposed estimator seems to be reasonable.     

Transfert de matiere lors de l'impact normal de jets liquides circulaires immerges

Using an electrochemical method we have measured mean mass transfer coefficients when an immerged circular jet of liquid impinges at right angles on a surface. The method involves the cathodic reduction of potassium ferricyanide at the transfer surface. The results can be divided into two domaines depending on the distance h of the nozzle from the surface with respect to a critical distance h_c. An empirical correlation is proposed for each of these two domaines.     

Gas-powder flow and powder accumulation in a packed bed: II: Numerical study

A mathematical model is proposed to describe gas-powder flow in a bed packed with particles. The model is the same as the two fluid model developed on the basis of the space-averaged theorem in terms of the governing equations but extended to consider the interactions between gas, powder and packed particles, as well as the static and dynamic holdups of powder. In particular, a method is proposed to determine the boundary between dynamic and stagnant zones with respect to powder phase, i.e., the profile of the powder accumulation zone. The validity of numerical modeling is confirmed by comparing the predicted and measured distributions of powder flow and accumulation under various flow conditions. On this basis, the role of gas-powder and powder-particle forces relative to the gravity force in controlling the powder flow and accumulation is analyzed.     

Nonparametric regression with rescaled time series errors

We consider a heteroscedastic nonparametric regression model with an autoregressive error process of finite known order p. The heteroscedasticity is incorporated using a scaling function defined at uniformly spaced design points on an interval [0,1]. We provide an innovative nonparametric estimator of the variance function and establish its consistency and asymptotic normality. We also propose a semiparametric estimator for the vector of autoregressive error process coefficients that is consistent and asymptotically normal for a sample size T. Explicit asymptotic variance covariance matrix is obtained as well. Finally, the finite sample performance of the proposed method is tested in simulations.     

Prediction of mass transport profiles in a laboratory filter-press electrolyser by computational fluid dynamics modelling

A commercial computational fluid dynamics code (Fluent) has been used to analyze the performance of a unit cell laboratory; the filter-press reactor (FM01-LC) operating with characteristic linear flow velocities between 0.024 m s⁻¹ and 0.110 m s⁻¹. The electrolyte flow through the reactor channel was numerically simulated using a finite volume approach to the solution of the Navier-Stokes equations. The flow patterns in the reactor were obtained and the mean linear electrolyte velocity was evaluated and substituted into a general mass transport correlation to calculate the mass transport coefficients. In the region of 150 < Re < 550, mass transport coefficients were obtained with a relative error between 5% and 29% respect to the experimental k_m values. The differences between theoretical and experimental values are discussed.     

水平管内油气两相混合物的传热计算

随着油气田开发的不断深入,油气两相混输技术的使用越来越广泛,这就涉及到水平管内油气两相混合物的传热计算问题。鉴于水平管内油气两相流动的复杂性,以三种常用简化计算的假设为基础,分别建立均相传热模型、分相传热模型以及流型传热模型,同时运用Aspen EDR软件对油气两相传热进行计算。将计算结果与工程实际设计值进行对比分析可知,均相传热模型与实际值相差最大;而流型传热模型最接近实际值,其相对误差仅2.6%;分相传热模型与软件计算值误差则介于这两者之间。另外,通过改变流速,对各个模型得出的油气两相传热系数进行了对比分析。     

AIR ENTRAPMENT DURING LIQUID INFILTRATION OF POROUS MEDIA

Some aspects of the interfacial phenomena that occur during liquid infiltration of porous media are discussed. Experimental data are presented on the critical speed at which air bubbles are trapped when a horizontal liquid surface passes (from below) across an isolated cylindrical rod or filament whose axis is horizontal. The results are correlated over a wide range of liquid viscosities and surface tensions. We observe that bubble entrapment occurs when the Capillary number exceeds a value defined by $ where γ is the so-called Property number, defined by $ The coefficients A and m depend upon the wetting characteristics of the liquid with respect to the solid (filament). A simple physical model is proposed which is in qualitative agreement with the observations.

In a porous bed of nonwoven filaments the physical phenomena that occur during wetting are different from those that occur on a single filament. Discussion of flow through such a porous medium leads to a simple model that describes recent data of others on removal of the initially entrapped air from the medium     

Investigation of the steady state measurement process

Based on the role of steady state concept in the model of analytical chemical measurement and deduction, the definition of ‘practically sleady slate’ (PSS) has been inlroduced. The defnition does not require the process to be in steady state in a strictly mathematical sense. In order to fulfil the requiremenls of ‘practically steady state’ the random error and the syslematic error must vary within a suitable limit, and the expected fgure for the measured value must be within a specified range.The goal of the present investigation was to detect the steady state of the measurement process with respect to the analytical information (peak area ratio) based on the measured values. The method proposed proved to be useful for the determination of the simultaneously present systematic error and random error. Control based on the measured values of the internal standard is useful, but additional information is necessary. There are several advantages to the method described: the results for the internal standard indicate possible sources of disturbances and allow the end of the steady state measurement process to be predicted.