Modeling of Vacuum Desorption in Freeze-Drying Process

Abstract

A mathematical model of multicomponent vacuum desorption, which occurs in vacuum freeze-drying process, was developed. In freeze-drying porous biomaterials and pharmaceuticals are considered and the vacuum freeze-drying process, especially the moisture desorption in its final stage, is investigated. In this article, the drying with conductive heating and constant contact surface temperature was considered. Pressure drop is taken into account in the model formulation but was neglected in process simulation because of thin material layers undergoing freeze-drying. Model equations were solved by numerical method of lines. Moisture content and temperature distributions within the drying material were predicted from the model as a function of drying time.     

Design of a Robust Soft-Sensor to Monitor In-Line a Freeze-Drying Process

This article deals with the in-line monitoring of a vital freeze-drying process using a soft-sensor that couples the experimental measurement of product temperature with a mathematical model of the process. This tool allows estimating in-line the residual amount of ice in the product and, thus, the duration of the primary drying stage, as well as some model parameters like the heat transfer coefficient between the shelf and the product and the resistance of the dried cake to vapor flow. As the performance of this sensor, based on the Extended Kalman Filter algorithm, strongly depends on the accuracy of the initial estimations of model parameters, an innovative algorithm based on a simple model of the freezing stage (and on product temperature measurement in this stage) is first used to roughly estimate the dried cake resistance to vapor flow. Then, a curvilinear regression algorithm is used in the first part of the primary drying stage with the goal of further refining model parameters' estimations. In this way, the robustness of the sensor is significantly improved, as confirmed by various experiments carried out to validate the soft-sensor and to investigate the effect of the accuracy of the initial estimations of model parameters on the performance of the system.     

Modeling and Experimental Studies of Adsorptive Dewatering of Selected Aliphatic Alcohols in Temperature Swing Adsorption System

Based on experimental work, closely coupled with mathematical modeling, an analysis was performed of the adsorptive drying of selected water-aliphatic alcohol solutions. The experimental work involved ethanol, n-propanol, and n-butanol dehydration using two adsorbents, 3A and 4A zeolite molecular sieves. The isothermal model developed in this paper incorporates an overall linear mass driving force, including liquid film mass transfer and intraparticle diffusion coefficients, a variable axial diffusivity, and experimentally determined Langmuir-Freundlich isotherms. Breakthrough curves generated by the model were compared with those obtained experimentally, giving a fairly good fit. The model simulations enabled determination of the water content profiles in adsorbent beds.     

Kinematic Model for a Far Infrared Vacuum Dryer

Abstract

Energy analyses in drying of welsh onion from one source of far infrared radiation at an absolute pressure of 2.6 and 5 kPa were carried out to determine the energy input at which the highest level of efficiency would be attained. The experimental results were used not only to formulate an advanced mathematical model for the prediction of moisture content of onion as a function of drying time but also to study the dryer efficiencies. Less than half of energy input was utilized for evaporating water from the onion. Approximately 73–99% of operating efficiency, which was dependent on the dryer configuration, was converted into radiant energy. The highest radiant efficiency was obtained at 40 W initial power supply, which was equivalent to the source temperature of about 100°C. An 80 W initial electrical power supply at a 10 cm distance of heater from the onion surface showed the highest drying efficiencies. At 80 W power, efficiency decreased with increasing distance from the heater source but at the expense of quality. For optimum drying efficiency without compromising quality, distance of heater from onion surface was proposed to be 10 cm.     

Modeling of Contact Dryers

Contact drying of stagnant or agitated beds can be reliably described by the penetration model under vacuum or inert conditions. However, the penetration model has disadvantages in the consideration of granular mechanics and statistics due its continuous nature. The fact that such disadvantages can be avoided by discrete approaches is illustrated by application of the discrete element method to the problem of heating of particles in a rotary drum. Important limiting cases are treated, along with conditions for equivalence between continuous and discrete model. Time constants and scaling aspects are addressed and opportunities of combined product and process engineering are pointed out.     

A Mathematical Model for Vacuum Far-Infrared Drying of Potato Slices

A mathematical model of mass and heat transfer for vacuum far-infrared drying of potato slices is introduced in this study on the basis of energy and diffusion equations. The finite difference method is used to mathematically simulate the sample temperature and moisture content in different drying conditions. Calculated results are compared with the experimental findings at varying conditions of heater temperature (120°C, 140°C, and 160°C), chamber pressure (1500, 8000, and 15000 Pa), sample thickness (0.004, 0.006, and 0.008 m), and radiation distance (0.08, 0.12, and 0.16 m). Comparison results show that the model fits well the changes in sample temperature and moisture content at different times of drying, with the values of the coefficient of determination close to 1.0 and the relative error values less than 10%.     

Studies on Decreasing Energy Consumption for a Freeze-Drying Process of Apple Slices

The shape, color, flavor, and rehydration capacity of freeze-dried (FD) products are all better than other dried products. However, the energy consumption during FD is very high, which limits the application of this drying method for common materials. In this article, microwave vacuum drying (MWVD) was applied before or after FD to decrease the energy consumption during FD. Moreover, energy consumption was divided into two parts: valid and invalid energy consumption. Apple slices were used as an example to calculate the saving percentage of invalid energy consumption by comparing combination drying with FD. Apple slices freeze dried for 8.28 h first and then dried by MWVD have the best appearance, with a savings of 39.20% in invalid energy consumption. But apple slices freeze dried for 6 h first followed by MWVD have the highest savings of invalid energy consumption, 54.02%, while still maintaining an acceptable appearance.     

The Basics of a Reaction Engineering Approach to Modeling Air-Drying of Small Droplets or Thin-Layer Materials

In this article, the development of a reaction engineering approach (REA) to modeling air drying of thin-layer materials or solids droplet/particles, a 10-year-old approach, is critically reviewed. This approach for drying data reduction has been seen to be successful in several applications (droplet drying and layer drying). The historical aspects and its possible relations to the characteristic drying rate curve (CDRC) model, one of the most well-known drying kinetics models, have been articulated. Possible improvements and future prospects are discussed.     

Infrared Drying: From Process Modeling to Advanced Process Control

The article surveys the drying of solids materials and polymer solutions when infrared radiation (IR) is employed as the main heating source. The study reviews the current research trends of IR drying of specific applications. A case study similar to an industrial setting is presented to illustrate a model development and control scheme of an IR drying unit. The design and online implementation of an internal model controller (IMC) is discussed. The study demonstrates the controller capabilities to suppress random variations of the moisture content in the material entering the dryer. Simulation results also showed the success of model predictive control (MPC) multivariable controller ability, while handling process interactions and process constraints, to track setpoint changes in the humidity and temperature of the material exiting the dryer and to reject unmeasured stochastic disturbances in the inlet humidity stream.     

Infrared Drying: From Process Modeling to Advanced Process Control

The article surveys the drying of solids materials and polymer solutions when infrared radiation (IR) is employed as the main heating source. The study reviews the current research trends of IR drying of specific applications. A case study similar to an industrial setting is presented to illustrate a model development and control scheme of an IR drying unit. The design and online implementation of an internal model controller (IMC) is discussed. The study demonstrates the controller capabilities to suppress random variations of the moisture content in the material entering the dryer. Simulation results also showed the success of model predictive control (MPC) multivariable controller ability, while handling process interactions and process constraints, to track setpoint changes in the humidity and temperature of the material exiting the dryer and to reject unmeasured stochastic disturbances in the inlet humidity stream.     

黑加仑真空冷冻与微波真空联合干燥工艺研究

以黑加仑为原料,对其进行了真空冷冻与微波真空联合干燥工艺的研究。结果表明：先真空冷冻后微波真空干燥（FDMV）的组合方式是可行的;联合干燥合理工艺参数为：微波功率1．34kW。绝对压力11kPa,转换含水率为20％（wb）;通过试验验证,联合干燥生产的脱水黑加仑的感官品质和营养成分接近真空冷冻干燥,联合干燥方式对节省干燥时间和降低能耗是有效的。     

真空冷冻干燥在食品中的应用

介绍了真空冷冻干燥技术的原理、工艺流程和应用。通过水的相平衡图及三相点示意图。阐述了真空冷冻干燥技术的原理;分析了真空冷冻干燥过程中各阶段的特点;论述了真空冷冻干燥在食品加工中的应用。     

Foam-Mat Freeze Drying of Egg White—Mathematical Modeling Part II: Freeze Drying and Modeling

Foam-mat freeze drying is one of the promising methods of drying, which utilizes advantages of both freeze drying and foam-mat drying. Egg white with its excellent foaming properties makes a suitable candidate for foam-mat freeze drying. Experiments were conducted to study foam-mat freeze drying of egg white, in an effort to determine the suitability of this method. Xanthan gum (XG) at 0.125% concentration was used as stabilizer for foaming. The results showed that the addition of xanthan gum during foaming has a positive impact in reducing the total drying time and also produces excellent quality egg white powder. The addition of stabilizer also plays an important role in improving drying. Simple models were applied for determining drying time and diffusion coefficients during freeze drying.     

Spray Drying of Lactobacillus plantarum WCFS1 Guided by Predictive Modeling

Shelf life of probiotic microorganisms can be retained by drying. Spray drying is an economically interesting alternative to freeze drying with that respect. However, the viability can decrease due to the drying process and testing it is laborious and expensive. This research shows that the viability of Lactobacillus plantarum WCFS1 during pilot scale drying can be predicted with kinetics gathered at a single droplet level. Using this approach, it could be demonstrated that the viability of L. plantarum WCFS1 during spray drying is mainly determined by the combination of temperature and moisture content during the first 0.5 seconds after atomization. The combination of a high moisture content and a high temperature appeared most detrimental to the residual viability. Moreover, it was found to be important to take into account the particle size distribution during atomization when predicting viability, since this has a large effect on the moisture content during this first 0.5 seconds. Finally, it was observed that shelf life during storage was mainly determined by the moisture content of the powder. A lower moisture content resulted in a higher viability. Above a moisture content of 6%, shelf life stability rapidly decreased in the applied maltodextrin (DE = 16) matrix.     

Modeling and simulation of a beet pulp dryer for a training simulator

This paper deals with the modeling of a high-temperature rotatory sugar beet pulp dryer for training simulators. This model adds some aspects to traditional drum dryer models; particle size distribution, detailed modeling of the solid phase, and the inclusion of malfunctions in the model. An object-oriented simulation package is selected to implement this model in a library, together with models of other components of a drying plant. Using this library, the complete plant and its control system are built and simulated. Finally, the simulation of the plant integrated together with a SCADA makes up the training simulator.     

冷冻干燥过程的数学模型

本文以物料衡算和热量衡算为基础，作适当的简化，导出了所需参数较少，但能准确地预测冷冻干燥全过程时间的数学模型，通过对胡萝卜和土豆的实验研究，检验了模型的适用性和准确性。     

Modeling Superheated Steam Vacuum Drying of Wood

Abstract

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^?1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

Drying Characteristics of Thick Lumber in a Laboratory Radio-Frequeocy/Vacuum Dryer

ABSTRACT

A series of forty two drying runs of two wood species and two cross-sectional dimensions of wood squares were carried out in a laboratory radio-frequency/vacuum (RF/V) dryer. The experimental temperature, pressure and moisture content levels as functions of space and time are presented. The results showed that western red cedar and western hemlock can be dried to a final moisture content of 15% in about 24 and 32 hours, respectively. The quality of the dried specimens was exceptional- Detailed analysis revealed the absence of internal drying stresses, internal and external checking and surface discoloration. Furthermore, evaluation of moisture content distribution in the longitudinal and transverse direction showed minimum variation compared to conventional kiln drying. The experiments also revealed that RF/V drying rates are directly affected by the level of the electrode plate voltage. Drying rates decreased with time when the voltage remained constant throughout the drying cycle thus resulting in long drying times. That was because of the changing dielectric properties of wood due to moisture content reduction during drying. Raising the voltages with time though, resulted in constant drying rates and shorter diying times.     

Modeling Moisture Loss during Vacuum Belt Drying of Low-Fat Tortilla Chips

A continuous vacuum drying method was used to develop low-fat tortilla chips with good sensory properties. To better understand the process, drying models were developed to determine the effects of drying thickness and temperature on drying rate. Drying rates were determined at three conduction plate temperatures (80, 90, and 100°C) and three product thicknesses (0.8, 1.5, and 2.3 mm). An effective diffusion model and semi-empirical models were used to fit the data. In addition, a model was developed from the drying rate curves that incorporated a drying coefficient [k(t)] that varied with time and could be described by a two-term Lorentzian model. All models had good agreement between experimental data and predicted data, with R ² > 0.98. With consideration of other goodness-of-fit indicators (sum of squared errors [SSE] and χ²), the Page and variable coefficient models provided the best fit. The average effective moisture diffusivity was calculated using nonlinear regression and ranged from D _eff = 1.19 to 1.54 × 10^?9 m²/s. D _eff increased with temperature and was described by an Arrhenius equation with E _a  = 14.1 kJ/mol.

Continuous vacuum drying of a presteamed corn dough can be used to produce low-fat tortilla chips with high crispness and acceptable sensory properties. The drying rate models presented in this study will help predict appropriate drying times, optimize process conditions, and better understand the mechanisms of drying.     

Heat Pump Drying of Green Sweet Pepper

Thin-layer drying experiments under controlled conditions were conducted for green sweet pepper in heat pump dryer at 30, 35, and 40°C and hot air dryer at 45°C with relative humidities ranging from 19 to 55%. The moisture content of sweet pepper slices reduced exponentially with drying time. As the temperature increased, the drying curve exhibited a steeper slope, thus exhibiting an increase in drying rate. Drying of green sweet pepper took place mainly under the falling-rate period. The Page equation was found to be better than the Lewis equation to describe the thin-layer drying of green sweet pepper with higher coefficient of determination and lower root mean square error. Drying in heat pump dryer at 40°C took less time with higher drying rate and specific moisture extraction rate as compared to hot air drying at 45°C due to lower relative humidity of the drying air in a heat pump dryer though the drying air temperature was less. The retention of total chlorophyll content and ascorbic acid content was observed to be more in heat pump–dried samples with higher rehydration ratios and sensory scores. The quality parameters showed a declining trend with increase in drying air temperature from 30 to 45°C. Keeping in view the energy consumption and quality attributes of dehydrated products, it is proposed to dry green sweet pepper at 35°C in heat pump dryer.