A new predictive PID controller for the processes with time delay

A new proportional-integral-derivative (PID) controller is proposed based upon a simplified generalized predictive control (GPC) control law. The tuning parameters of the proposed predictive PID controller are obtained from the simplified GPC control law for the 1 ^st -order and 2 ^nd -order processes with time delays of integer and non-integer multiples of the sampling time. The internal model technique is employed to compensate the effect of time delay of the target process. The predictive PID controller is equivalent to the PI controller when the target process is 1 ^st -order and to the PID controller when the target process is an integrating process. The performance of the proposed predictive PID controller is almost the same as that of the simplified GPC. The main advantage of the proposed control scheme over other control methods is the ease of tuning and operation.     

A Predictive Model for Assessment of the Risk of Mold Growth in Rapeseeds Stored in a bulk as a Decision Support Tool for Postharvest Management Systems

Reliable prediction of the risk of mold development in a stored bulk of rapeseeds may help to maintain seed quality and ensure the highest quality and safety of cooking oil. Mathematical models based on predictive microbiology that are able to assess the risk of fungal growth and the mycotoxins formation in a stored seed ecosystems are promising prognostic tools, which may improve postharvest management systems. The aim of the study was to develop a predictive model of fungal growth in bulks of rapeseeds stored under conditions, in which seeds are at risk of quality deterioration. It was formulated on the basis of data reflecting actual seed ecosystems with a hazardous initial level of mold spores (characteristic of seeds that vegetate and are harvested under adverse weather conditions) stored at a wide range of temperature (12–30 °C) and humidity (seed water activity, a_w = 0.80–0.90). The predictive model was based on the modified Gompertz equation, whose coefficients are related with biological parameters of mold growth (i.e., lag phase duration, maximum growth rate and fungal population level at the stationary phase). The biological parameters of the model were described using the second-degree polynomial functions of temperature and water activity. The criteria used to assess the model efficiency pointed to its good predictive quality (R² = 0.90; RMSE =0.547). Moreover, the model was characterized by high accuracy (bias factor B _f = 1.045 and accuracy factor A _f = 1.050). The formulated model of fungal growth can be used as a decision support tool to improve systems managing postharvest seed preservation processes.     

New models for the binary interaction parameters of nitrogen–alkanes mixtures based on the cubic equations of state

In this study, the goal was to derive a new purely predictive model to obtain binary interaction parameters based on intermolecular theories. The Lorentz–Berthelot and Halgren HHG molecular combining rules were coupled with the vdw1 mixing rule to derive the new equations for binary interaction parameters. These equations were used with the PR and ER EoSs to calculate the vapor–liquid equilibria of 14 binary mixtures of nitrogen with either methane, ethane, propane, iso-butane, n-butane, iso-pentane, n-pentane, n-hexane, n-heptane, n-octane, n-nonae, n-decane, n-dodecane, or n-tetradecane over wide ranges of temperature and pressure. To increase the accuracy for all of the investigated systems, we have additionally suggested a new correlative mode for the proposed equations. For some of the systems, the proposed predictive equations enhance the accuracy of vapor–liquid equilibria predictions up to three times in comparison to the case where binary interaction parameters are set to zero.     

A generalized procedure for the prediction of multicomponent adsorption equilibria

Prediction of multicomponent adsorption equilibria has been investigated for several decades. While there are theories available to predict the adsorption behavior of ideal mixtures, there are few purely predictive theories to account for nonidealities in real systems. Most models available for dealing with nonidealities contain interaction parameters that must be obtained through correlation with binary‐mixture data. However, as the number of components in a system grows, the number of parameters needed to be obtained increases exponentially. Here, a generalized procedure is proposed, as an extension of the predictive real adsorbed solution theory, for determining the parameters of any activity model, for any number of components, without correlation. This procedure is then combined with the adsorbed solution theory to predict the adsorption behavior of mixtures. As this method can be applied to any isotherm model and any activity model, it is referred to as the generalized predictive adsorbed solution theory. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2600–2610, 2015     

Application of gain scheduling for modeling the nonlinear dynamic characteristics of NO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> emissions from utility boilers

A hierarchical gain scheduling (HGS) approach is proposed to model the nonlinear dynamics of NO _x emissions of a utility boiler. At the lower level of HGS, a nonlinear static model is used to schedule the static parameters of local linear dynamic models (LDMs), such as static gains and static operating conditions. According to upper level scheduling variables, a multi-model method is used to calculate the predictive output based on lower-level LDMs. Both static and dynamic experiments are carried out at a 360 MW pulverized coal-fired boiler. Based on these data, a nonlinear static model using artificial neural network (ANN) and a series of linear dynamic models are obtained. Then, the performance of the HGS model is compared to the common multi-model in predicting NO _x emissions, and experimental results indicate that the proposed HGS model is much better than the multi-model in predicting NO _x emissions in the dynamic process. This paper was presented at the 7 ^th China-Korea Workshop on Clean Energy Technology held at Taiyuan, Shanxi, China, June 25–28, 2008.     

Mathematical Model for the Extraction of Neodymium from Nitrate Media using Hollow Fiber Supported Liquid Membrane Operated in a Recycling Mode

A mathematical model for facilitated extraction of Neodymium (Nd³⁺) ions from nitrate media using microporous hollow fiber supported liquid membrane (HFSLM) operated in a recycling mode is presented. Extractant N,N,N′, N′-tetraoctyl diglycolamide (TODGA) diluted with n-dodecane was used as the membrane phase. Di-n-hexyl octanamide (DHOA) has been used as a phase modifier for the extractant. The model developed is not specific to the case considered and has a more general and wide applicability. The model has been developed using equilibrium-based approach. The complexation and de-complexation reactions were assumed to be fast and at equilibrium. Mass balance equations for both acid (HNO₃) and TODGA were also incorporated in the model. It was observed that the model results are in good agreement with the experimental data when diffusivity of metal-complex (D _m ) and acid-complex (D _hm ) through the membrane phase in the pore is 6 × 10^?12 m²/s and 1.2 × 10^?10 m²/s. Once the values of D _m and D _hm are estimated by simulation for one set of data, there are no further fitting parameters in the model. The model can then be used in a truly predictive mode for all the remaining data sets.     

Modeling and optimization of the process parameters in vacuum drying of culinary banana (Musa ABB) slices by application of artificial neural network and genetic algorithm

The influence of drying temperature, sample slice thickness, and pretreatment on quality attributes like rehydration ratio, scavenging activity, color (in terms of nonenzymatic browning), and texture (in terms of hardness) of culinary banana (Musa ABB) has been evaluated in the present study. A comparative approach was made between artificial neural network (ANN) and response surface methodology (RSM) to predict various parameters for vacuum drying of culinary banana. The effect of process variables on responses during dehydration were investigated using general factorial experimental design. This design was used to train feed-forward back-propagation ANN. The predictive capabilities of these two methodologies for optimization of process parameters were compared in terms of relative deviation (R_d). Results revealed that a properly trained ANN model is found to be more accurate in prediction as compared to RSM. The optimum condition selected from ANN/GA responses on the basis of highest fitness value revealed that culinary banana slices of 6 mm thickness pretreated with 1% citric acid and dried at 76°C resulted in a maximum rehydration ratio of 6.20, scavenging activity of 48.63% with minimum nonenzymatic browning of 25%, and hardness of 43.63 N. Results further revealed that, in the case of rehydration ratio, temperature and pretreatment showed a positive effect while thickness had a negative effect. On the contrary, for scavenging activity, temperature showed the highest negative effect followed by slice thickness and positive effect with pretreatment. For nonenzymatic browning, thickness showed the highest negative effect but temperature and pretreatment showed a positive effect. Similarly, for hardness, all three parameters showed a negative effect.     

Extending the UNIFAC model for ionic liquid–solute systems by combining experimental and computational databases

Considering that the predictive UNIFAC model is highly valuable for the solvent selection, process design and optimization of separation tasks, a large extension of this model to ionic liquid (IL)–solute systems is presented by combining experimental and COSMO-RS derived databases. The experimental infinite dilution activity coefficient (γ^∞) data of different solutes in ILs are first collected exhaustively to extend UNIFAC-IL to cover all involved IL and conventional functional groups. Afterwards, the experimental and COSMO-RS calculated γ^∞ are compared for different types of solutes to evaluate the potential of using COSMO-RS predictions as quasi-experimental data for further UNIFAC-IL extension. In the cases where COSMO-RS can provide quantitatively accurate predictions after calibration, additional γ^∞ database is specifically generated to regress more group interaction parameters in the UNIFAC-IL model. Finally, a large experimental liquid–liquid and vapor–liquid equilibria database is collected and employed to evaluate the predictive performance of the obtained γ^∞-based UNIFAC-IL model.     

The glass transition of compatible blends

In a thermodynamic model of the glass transition, general but circular relations for the compositional variation of the glass-transition temperature, T_g, can be derived from the entropy, the volume, and the enthalpy. The circumstances necessary for each of these to reduce to predictive relations are stated. Of these relations, that derived from the entropy should be the most general because of the expected rather wide applicability of the random mixing assumption, with which it is associated. The entropic theory is used to account for several aspects of the compositional variation of T_g, including problems not of solutions per se.     

Development of kinetic model for the reaction between SO2/NO and coal fly ash/CaO/CaSO4 sorbent

Sorbents for semidry-type flue gas desulfurization (FGD) process can be synthesized by mixing coal fly ash, calcium oxide, and calcium sulfate in a hydration process. As sorbent reactivity is directly correlated with the specific surface area of the sorbent, reacting temperature, concentration of the reacting gas species and relative humidity, two major aim in the development of a kinetic model for the FGD process are to obtain an accurate model and at the same time, incorporating all the parameters above. Thus, the objective of this work is to achieve these two aims. The kinetic model proposed is based on the material balance for the gaseous and solid phase using partial differential equations incorporating a modified surface coverage model which assumes that the reaction is controlled by chemical reaction on sorbent grain surface. The kinetic parameters of the mathematical model were obtained from a series of experimental desulfurization reactions carried out under isothermal conditions at various operating parameters; inlet concentration of SO₂ (500 ppm  C_0,SO2  2000 ppm), inlet concentration of NO (250 ppm  C_O,NO  750 ppm), reaction temperature (60 °C  T  80 °C) and relative humidity (50%  RH  70%). For a variety of initial operating conditions, the mathematical model is shown to give comparable predictive capability when used for interpolation and extrapolation with error less than 7%. The model was found useful to predict the daily operation of flue gas desulfurization processes by using CaO/CaSO₄/coal fly ash sorbent to remove SO₂ from flue gas.     

Local Likelihood for non‐parametric ARCH(1) models

Abstract. We propose a non‐parametric local likelihood estimator for the log‐transformed autoregressive conditional heteroscedastic (ARCH) (1) model. Our non‐parametric estimator is constructed within the likelihood framework for non‐Gaussian observations: it is different from standard kernel regression smoothing, where the innovations are assumed to be normally distributed. We derive consistency and asymptotic normality for our estimators and show, by a simulation experiment and some real‐data examples, that the local likelihood estimator has better predictive potential than classical local regression. A possible extension of the estimation procedure to more general multiplicative ARCH(p) models with p > 1 predictor variables is also described.     

A general correlation for the minimum spouting velocity

A new general correlation is presented for the minimum spouting velocity based on the annular pressure gradient at the top of the bed at minimum spouting. The correlation fits a wide range of experimental data to 11.6% on average. The normalized minimum spouting velocity ratio. u_mS/u_mF, is shown to be a function of three dimensionless parameters.     

Solid Solubilities of Sulfonamides and Use of Rapid Expansion of Supercritical Solutions for Microparticle Production

The solubility of solid active pharmaceutical ingredients in supercritical fluids is a major thermodynamic criterion for selection and screening of microparticle generation processes. To develop an efficient method for solubility prediction, a solution model was adopted to establish the correlations of the solid solubilities of six sulfonamides in supercritical CO₂. The model was capable of determining solubility correlations. Accordingly, it was attempted to simplify and generalize the model, yielding a predictive solution model, which provided order-consistent solubility predictions. A case study for model extrapolation was conducted. After understanding the mechanisms underlying the solubility of sulfonamides, the rapid expansion of supercritical solutions (RESS) process was applied to produce microparticles of p-toluenesulfonamide, an anticancer drug. The effects of RESS process parameters were investigated.     

Correlative models for perovskites with rock salt B-site ordering

Empirically derived predictive models describing synthesis-structure relationships have the potential to significantly improve and guide future research in a more cost-effective and timely manner; however, few of these models exist for cation ordering in perovskites. In this study, four compositions within the AZn_0.5Ti_0.5O₃ system (A = Nd, Sm, Nd_0.5La_0.5, Nd_0.5Gd_0.5) were synthesized using a conventional solid-state mixed-oxide method. X-ray diffraction data show evidence of long-range 1:1 rock salt cation ordering on the B site for all compositions. Additional data for other rock salt B-site ordered compositions were mined from literature. Correlative models for the B-site shrinkage (Δr_B) have been derived for each B-site ordered system, and a general model has been developed for rock salt B-site ordering from these specific models. This general model allows for the prediction of the room-temperature volume shrinkage resulting from rock salt B-site ordering using only published ionic radii data.     

Correlation and estimation of solubilities of fatty acids in supercritical carbon dioxide using solution model approach

In this study, solid solubility data of five fatty acids in supercritical carbon dioxide (CO₂) at different temperatures and pressures are correlated using a two-parameter solution model developed from the regular solution model coupled with the Flory⿿Huggins equation. The developed solution model with fewer parameters yields correlated results comparable to those from commonly used semi-empirical equations. In addition, both parameters in the solution model can be further generalized with the chain length of fatty acids and a new predictive solution model is proposed for solubility prediction. The predictive solution model proposed in this study provides better predicted results and yields average deviation in predicted solubilities of 22.1%. To further apply this solution model to other compounds, solid solubility data of three triglycerides in supercritical CO₂ at 313 K are also correlated. After model simplification and generalization, a new predictive solution model for triglycerides is also proposed, which yields average deviation in predicted solubilities of 29.8%. These results demonstrate that the solution model used in this study is applicable for correlation and prediction of solid solubilities of structure-related compounds in supercritical CO₂.     

Physicochemical criteria for reverse osmosis separation of monohydric and polyhydric alcohols in aqueous solutions using porous cellulose acetate membranes

Reverse osmosis data using different samples of Loeb-Sourirajan-type porous cellulose acetate membranes and single-solute aqueous solution systems involving 16 monohydric alcohols, 4 phenols, 18 polyhydric alcohols, pyrogallol, ethylene glycol monoethyl ether, 6 aldehydes, and 8 carbohydrates (sugars) have been studied. The solute concentrations used were in the range of 0.0005 to 0.003 g mole/l. (～100 ppm), and operating pressure used was 250 psig in all cases. The results show that correlations of acidity and basicity parameters (obtained from IR spectra) with solute separation data are equivalent, and they have predictive capability. A method is given for estimating Taft numbers (Σσ^*) for monohydric and polyhydric alcohols from available data based on the additive nature of σ^*. Data on solute transport parameters (D_AM/Kδ) for the different solutes were calculated from membrane performance data. For all the alcohols studied, the Σσ^*-versus-log (D_AM/K)δ correlation was found to be a straight line with a slope different for different ranges of Σσ^*, but independent of the porous structure of the membrane. Based on this result, it is shown that the parameters of the Taft equation can serve as a basis for expressing solute transport parameter, and this basis offers a means for predicting membrane performance for all alcohol–water systems from a single set of experimental data for a reference solute system. This prediction technique is illustrated using experimental data for 1,3-butanediol taken as the reference solute. The general applicability of the technique has been tested for predicting the separation of some aldehydes and carbohydrates.     

A model for the devolatilization of EPDM rubber in a series of steam stripping vessels

A mathematical model was developed for the multitank stripping section of industrial ethylene propylene diene monomer (EPDM) rubber processes. Experiments were conducted to determine Henry's law coefficients and diffusivities for hexane solvent and 5‐ethylidene‐2‐norbornene (ENB) comonomer in EPDM particles. Equivalent radii for diffusion within the particles were also determined. A model was developed to predict solvent and comonomer concentrations in a single particle as it moves through a series of tanks with different operating conditions. A second, more‐complicated model was then developed to account for a continuous flow stirred tank residence time distribution for the particles in the tanks. Data from three industrial plants were used to estimate parameters and assess the models' predictive ability. Typical prediction errors are 0.90 wt % for residual hexane and 0.14 wt % for residual ENB. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2596–2606, 2014     

The rigid adsorbent lattice fluid model for pure and mixed gas adsorption

The ability of macroscopic models to predict correctly multicomponent systems from pure component isotherms alone remains a major challenge in adsorption engineering. A new fundamental thermodynamic model for multicomponent adsorption of molecules of different size in nanoporous materials is derived from a modified lattice fluid model. Expressions for the fugacity coefficients are derived and the resulting equilibrium relationships are shown to be consistent with a type I adsorption isotherm. Expressions are obtained for the saturation capacity, the Henry law constant and the adsorption energy. The model is applied to silicalite and the parameters for the adsorbent are obtained from crystal properties, the adsorption energy of n-alkanes and Henry law constants for six gases. Model predictions for gas adsorption up to 20 bar are shown to be comparable to empirical adsorption isotherm equations. Extension to binary and quaternary systems shows good a priori predictive capability when compared to experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1304–1314, 2019     

Kinetic model for cloud-point blending of diesel fuels

A semi-empirical model, with two adjustable parameters, has been developed for predicting the cloud points following the blending of diesel fuel components. The model is based on a kinetic argument deduced from the cloud-point dependence of the cooling rate. By either using a constant cooling rate or standardizing the cloud point to a constant cooling rate, blended cloud points can be accurately predicted from the equation

where T_j are the component cloud point (K), v_j are the component volume fractions, and T_c is the blended cloud point. The two adjustable parameters, α and β are associated with the concentration of nucleating sites in the components. The contribution of the β term to the prediction is small and is insignificant if component cloud points are evenly distributed. In general, the larger the cloud point the larger the number of nucleating sites, but this also appears to be dependent on the type of molecules involved in the nucleating sites.