Accelerated successive substitution schemes for bubble-point and dew-point calculations

The accelerated successive substitution (SS) algorithms developed by Mehra et al. for flash calculations have been extended to the prediction of saturation points. A transformation matrix which is used to calculate the acceleration parameter has been rewritten in a form that is applicable at the saturation conditions. Simple equations for estimating the initial values and recursive formulae according to which the iterates can be updated are presented. The proposed schemes were compared with the conventional SS method and a multivariate Newton's method. The comparison suggests that the accelerated SS schemes are more tolerant of poor initial values and sometimes more efficient than Newton's method.     

A modified “inside-out” algorithm for simulation of multistage multicomponent separation processes using the UNIFAC group-contribution method

A computational procedure using a modification of Boston and Sullivan's “inside-out” multistage multicomponent separation algorithm (1974) is developed. In order to improve convergence behavior for problems involving mixtures with highly nonideal liquid phases, a two-parameter model is used to describe liquid-phase compositional effects upon the K-factor. The quasi-Newton methods of Mehra et al. (1983) and Nghiem (1983) are applied to solving various sets of solution variables in the proposed algorithm. Activity coefficients are calculated using the UNIQUAC activity-coefficient model (1975) with parameters obtained from the UNIFAC group-contribution method (1975). The computational procedure is applicable to distillation, absorption and reboiled-absorption configurations. The proposed algorithm was implemented in a FORTRAN 77 program and tested on the Honeywell DPS 8/70M computer at the University of Calgary. Inclusion of the liquid-phase model resulted in improved convergence behavior for nonideal systems in which the original “inside-out” method failed to converge.     

A modified general dominant eigenvalue method for convergence acceleration of cyclic systems

In this paper, a new derivation is presented for the General Dominant Eigenvalue Method (GDEM) for Convergence Acceleration of cyclic systems described by a set of non-linear algebraic equations. Through the derivation a modification which improves the convergence of the GDEM is suggested. Two examples are used to show the kind of improvement, one might expect using the modified version.     

Sedimentation of polydisperse concentrated suspensions

Gravity sedimentation of bidisperse and tridiperse concentrated suspensions have been studied both theoretically and experimentally. Experimental data were collected from batch settling tests using fully-characterized colored spherical particles. Ten sizes of particles with three different densities were used in the sedimentation experiments. Varying proportions of each size were used and total solids concentration ranged from 13% to 45% by volume. Previously published and newly collected data were compared with predictions from six available models. These models include those of Lockett and Al-Habbooby (1973), Mirza and Richardson (1979), Masliyah (1979), Reed and Anderson (1980), Selim et al. (1983a, 1983b), and Patwardhan and Tien (1985). Based on the present study and a similar study by Law et al. (1987) on bidisperse suspensions of heavy (sinking) and light (buoyant) particles, it is found that the Selim et al. model represents the data more accurately as compared to the other models.     

Phase equilibria calculations for ill-defined mixtures using the prsv equation of state

A method for the calculation of vapor-liquid equilibria (VLE) for multicomponent systems using continuous thermodynamics is presented. The Extended Spline Fit Technique (ESFT) is used to represent the molar distribution curve of petroleum fluids. A continuous version of the Peng-Robinson-Stryjek-Vera (PRSV) equation of state (EOS) with Generalized Single Carbon Number Properties (GSCNP) is utilized. For continuously distributed components, following the suggestion of Hendriks (1987), the number of equations solved is reduced through integration over the range of the distributing variable using Legendre-Gauss quadrature. Integrated equations are solved using accelerated successive substitution. Flash, dew and bubble point calculations for an imaginary and a real system yield satisfactory results.     

A linear model predictive control algorithm for nonlinear large‐scale distributed parameter systems

This work provides a framework for linear model predictive control (MPC) of nonlinear distributed parameter systems (DPS), allowing the direct utilization of existing large‐scale simulators. The proposed scheme is adaptive and it is based on successive local linearizations of the nonlinear model of the system at hand around the current state and on the use of the resulting local linear models for MPC. At every timestep, not only the future control moves are updated but also the model of the system itself. A model reduction technique is integrated within this methodology to reduce the computational cost of this procedure. It follows the equation‐free approach (see Kevrekidis et al., Commun Math Sci. 2003;1:715–762; Theodoropoulos et al., Proc Natl Acad Sci USA. 2000;97:9840‐9843), according to which the equations of the model (and consequently of the simulator) need not be given explicitly to the controller. The latter forms a “wrapper” around an existing simulator using it in an input/output fashion. This algorithm is designed for dissipative DPS, dissipativity being a prerequisite for model reduction. The equation‐free approach renders the proposed algorithm appropriate for multiscale systems and enables it to handle large‐scale systems. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

A real-time algorithm for moving horizon state and parameter estimation

A moving horizon estimation (MHE) approach to simultaneously estimate states and parameters is revisited. Two different noise models are considered, one with measurement noise and one with additional state noise. The contribution of this article is twofold. First, we transfer the real-time iteration approach, developed in Diehl et al. (2002) for nonlinear model predictive control, to the MHE approach to render it real-time feasible. The scheme reduces the computational burden to one iteration per measurement sample and separates each iteration into a preparation and an estimation phase. This drastically reduces the time between measurements and computed estimates. Secondly, we derive a numerically efficient arrival cost update scheme based on one single QR-factorization. The MHE algorithm is demonstrated on two chemical engineering problems, a thermally coupled distillation column and the Tennessee Eastman benchmark problem, and compared against an Extended Kalman Filter. The CPU times demonstrate the real-time applicability of the suggested approach.     

MULTIPLE STEADY STATES IN NON-ISOTHERMAL FT SLURRY REACTOR

A model for a non-isothermal, semi-balch (stagnant slurry and flowing gas), laboratory scale Fischer-Tropsch (FT) slurry reactor is developed. The model assumes the existence of FT and water-gas shift (WGS) reactions. The reactor configuration is assumed to be the same as one used by Bhattacharjee et at. (1986). Gas-slurry mass transfer coefficients, solubility parameters and other physical transport and kinetic parameters used in the model are obtained from the reported studies of Lieb and Kuo (1984), Bhattacharjee et al. (1986), Deckwer et al. (1982, 1986) and Karandikar et al. (1987( for the FT slurry system

The model is used to evaluate the relevant kinetic constants and the heat generation parameters for the FT reaction from the experimental data of Bhattacharjee et al. (1986). The nature of the heat generation curves indicates that multiple steady states are likely to occur in a non-isothermal FT slurry reactor. The ignition temperatures are calculated as functions of gas hourly space velocity, activation energy for the FT reaction, reactor pressure, and coolant temperature and flow rate. In general, these temperatures are in good agreement with those reported by Bhattacharjee et al. (1986). The exact values of the ignition temperature are strongly affected by the magnitudes of the activation energy and the heat of FT reaction. Once the reactor is ignited, the catalyst changes its character leading to the multiple branches of heat generation and product distribution curves. The extinction temperature was, therefore, not observed in Bhattacharjee's experiments.     

Impregnation of Hardboard with Poly(methyl methacrylate)

The increasing deficiency of natural woods has led to the use of agricultural residues in the preparation of pulp and boards. The important agricultural residues are bagasse, straws, and cotton stalks, which accumulate in vast amounts. Some studies concerning the use of bagasse (Lumen et al., 1963), rice straw (Mobarak et al., 1975; Fadl et al., 1984), cotton stalks (Mobarak and Nada, 1975), and other agricultural residues (Lathrop and Naffziger, 1949; Aronosky and Lathrop, 1949) for producing hardboards are available. Actually, resins are added to pulp before board formation to give a final board of high strength and water resistance. The common resins are phenol-formaldehyde, urea-formaldehyde, and melamine- formaldehyde. Also, in one of our previous works, whole black liquor (Nada et al., 1982), produced from rice straw pulping process or its separated components (lignin, hemicellulose, and silica) (El-Saied et al., 1982) in the presence or absence of phenol-formaldehyde resin during hardboard preparation, was used to improve the strength properties of board. Other treatments are used to modify the hardboard or paper sheet properties, by impregnation of the sheets in resin solution (Plomely and Cottstein, 1968; Nada et al., 1981) or by polymer solution (Calleton et al., 1970; Youssef et al., in press). In addition, chemical modifica-tions such as acetylation, grafting (Smraishi et al., 1982). and cyanoethylation are carried out on wood and hardboard to improve their dimensional stability.     

Atmospheric spouted bed combustion: The role of hydrodynamics in emissions generation and control

Recent studies have reaffirmed the utility of spouted beds as potential combustion devices for a variety of fuels: solid, liquid and gaseous fuels (Arbib and Levy, 1982; Weinberg et al., 1988; Zhao et al., 1987; Altwicker et al., 1989; Altwicker and Lin, 1991; Altwicker et al., 1993; Konduri et al., 1994). In this study, the role of annulus residence time on the performance of such a spouted bed combustor is investigated. The experiments presented here show that fluid hydrodynamics in the annulus of a spouted bed combustor can significantly influence the overall performance; changing the residence time in the annulus significantly affects the concentrations of products due to incomplete combustion at the exit of the combustor. The annular residence time is varied by changing the shape of the bottom of the reactor, by introducing a draft tube and by changing the bed heighn. Propane is used as the fuel and sand as the bed medium. Inferences from the combustion results are supported by pressure and temperature profiles. A streamtube model (Lim and Mathur, 1976) was used to obtain an estimate of the residence time in the annulus. It is concluded that the flame processes taking place at the top of the annulus play a critical role in the emission generation and that more information is needed to understand the annulus-flame.     

COMPARISON AMONG TECHNIQUES TO RETRIEVE KINETIC PARAMETERS FROM THERMOGRAVIMETRY DATA

A statistical comparison of methods used to retrieve kinetic information from thermogravimetric analysis (TGA) data was done. The objective of this work was to try to establish if there is a difference between the kinetic parameters predicted using: Coats and Redfern (1964), and its modifications: Fischer, el al. (1987), Chen and Nuttal (Nutall et al. 1983), Reich and Stivala (1980), and Horowitz and Metzger (1963). All these methods were tested using data obtained by numerical integration of a first order irreversible reaction under typical TGA conditions, and to study the effects of experimental error in parameter estimation these data were perturbed by introducing a random error variation in the numerical data. From the results, the first three methods are statistically similar, while the last two produce significantly erroneous values even with no error present in the data     

大型稀疏代数方程组的分解

大型稀疏代数方程组是稳态过程模拟与过程设计数学模型的典型形式.与联立求解法相比,迭代求解的长处在于可解算包括非线性在内的方程,而且即使中途停顿也会得到解算过程的信息.此外,占内存少,计算时间短.在迭代之前,须预先确定设计变量(如果变量数多于方程数)、迭代变量、输出集和迭代次序.本文提出一种将给定方程组的关联矩阵重新排序的简便方法,根据重排后的关联矩阵优先决定迭代变量,然后决定输出集和设计变量.这种方法可以确保可行迭代顺序的产生,也比现有的方法简便.     

EVALUATION OF LAGRANGIAN PARTICLE DISPERSION MODELS IN TURBULENT FLOWS

This work evaluates the performance of Lagrangian turbulent particle dispersion models based on the Langevin equation. A family of Langevin models, extensively reported in the open literature, decompose the fluctuating fluid velocity seen by the particle in two components, one correlated with the previous time step and a second one randomly sampled from a Wiener process, i.e., the closure is at the level of the fluid velocity seen by the particle. We will call those models generically the “standard model.” On the other hand, the model proposed by Minier and Peirano (2001) is considered; this approach is based on the probability density function (PDF) and performs the closure at the level of the acceleration of the fluid seen by the particle. The formulation of a Langevin equation model for the increments of fluid velocity seen by the particle allows capturing some underlying physics of particle dispersion in general turbulent flows while keeping simple the mathematical manipulation of the stochastic model, avoiding some pitfalls, and simplifying the derivation of macroscopic relations. The performance of the previous dispersion models is evaluated in the configurations of grid-generated turbulence (Snyder and Lumley, 1971; Wells and Stock, 1983), simple shear flow (Hyland et al., 1999), and confined axisymmetric jet flow laden with solids (Hishida and Maeda, 1987).     

Continuous prediction technique for fast determination of cyclic steady state in simulated moving bed process

In the simulation of cyclic processes, such as simulated moving bed (SMB), the system should be equilibrated to reach a cyclic steady state (CSS) before evaluating the process performance. However, the conventional method of successive substitution is quite time-consuming. In this work, a continuous predicting method (CPM) is developed for fast determination of CSS in SMB. In CPM, the direct prediction of state variable at CSS and solving model equation are conducted alternately until CSS is reached. In order to give a guideline for the selection of the acceleration factor, CPM is applied on SMB process for enantioseparation of 1,1′-bi-2-naphtol racemate and with the optimized acceleration factor, 59% of computation time saved compared with successive substitution. In addition, this method is further successfully used in a sugar separation process. Given its efficiency and simplicity, this method could provide a useful tool for SMB simulations.     

Maleic anhydride formation from 1, 3-butadiene oxidation over a vanadia molybdate catalyst

Steady-state and transient studies of the partial oxidation of butadiene to maleic anhydride were performed over a Te-promoted vanadia molybdate catalyst previously used by Fiolitakis et al. (1983) for a study of maleic anhydride production from benzene. Inhibition of the partial oxidation by butadiene was observed. Pathways for CO₂ and maleic anhydride formation are different. False-start behaviour for some products was observed and attributed to conflicting contributions of adsorption and catalyst reduction or oxidation. The reaction mechanism for butadiene differs from that reported from benzene oxidation by Fiolitakis et al. (1983).     

Improved sequential and accelerated sequential Procedures for estimating the scale parameter in a aniform distribution

Ghosh and Mukhopadhyay (1975a) and more recently Mukhopadhyay et al.(1983) have consideredsequential minimum risk point estimation of θ in a uniform (0,θ)population.The loss function has been squared error plus linear cost and θ has beencustomarily estimated by the sample maximum.In this paper,we consider instead the best scalarmultiple of the sample aximum as the estimator of θ.The percentage saving in the fictitious optimal fixed sample size as well as the percentage reduction in the corresponding minimum risk ar seen to be about 20.6X when compared with the Mukhopadhyay et al.(1983) cedure.Since thisamount of saving is quite substantial,we set out to develop     

Modelling of hydrodynamics in a type I turbulent bed contactor

A simple model for the hydrodynamics in Type I TBC is developed for the prediction of hydrodynamic variables such as the phase holdups, bed expansion and pressure drop based on the model by Chern et al. (1983. Hydrodynamics of constrained inverse fluidization and semifluidization in a gas-liquid-solid system. Chemical Engineering Science 38, 1167). This is done by modelling the TBC as a packed bed with large porosities carrying countercurrent gas-liquid flow. The process parameters considered are gas and liquid velocities, particle size and density. The dependence of hydrodynamic variables on process parameters predicted by simulation agrees well with that reported in literature.     

A regularization approach to the reconciliation of constrained data sets

A new iterative solution to the statistical adjustment of constrained data sets is derived in this paper. The method is general and may be applied to any weighted least squares problem containing nonlinear equality constraints. Other methods are available to solve this class of problem, but are complicated when unmeasured variables and model parameters are not all observable and the model constraints are not all independent. Of notable exception, however, are the methods of Crowe (1986) and Pai and Fisher (1988), although these implementations require the determination of a matrix projection at each iteration which may be computationally expensive. An alternative solution which makes the pragmatic assumption that the unmeasured variables and model parameters are known with a finite but equal uncertainty is proposed. We then re-formulate the well known data reconciliation solution in the absence of these unknowns to arrive at our new solution; hence the regularization approach. Another procedure for the classification of observable and redundant variables which does not require the explicit computation of the matrix projection is also given. The new algorithm is demonstrated using three illustrative examples previously used in other studies.     

Prediction of the maximum spoutable height in spout-fluid beds

The development of the semi-theoretical correlation in Hadzisdmajlovic et al. (1983) for predicting the maximum spoutable height in a spout-fluid bed, is observed to involve certain discrepancies. Based on their experimental data, a new correlation is proposed.     

受扰双线性系统的近似最优扰动抑制方法

研究具有外界持续扰动作用下双线性系统的最优控制问题.关于二次型性能指标给出了一种设计最优扰动抑制控制律的逐次逼近方法.利用该算法可将在扰动作用下双线性系统的最优控制问题转化为求解一组线性非齐次两点边值序列问题.通过迭代序列得到的最优扰动抑制控制律由解析的线性前馈-反馈项和序列极限形式的非线性补偿项组成.通过截取非线性补偿序列的有限项,可以得到近似最优扰动抑制控制律.仿真结果表明,该方法抑制外部持续扰动的鲁棒性优于经典反馈最优控制.