Dry Steam Research Articles

Numerical Modeling of Toe-to-Heel Air Injection and Its Catalytic Variant (CAPRI) under Varying Steam Conditions.

There are huge reserves of heavy oil (HO) throughout the world that can be energy-intensive to recover. Improving the energy efficiency of the recovery process and developing novel methods of cleaner recovery will be essential for the transition from traditional fossil fuel usage to net-zero. In situ combustion (ISC) is a less used technique, with toe-to-heel air injection (THAI) and catalytic processing in situ (CAPRI) being specialized novel versions of traditional ISC. They utilize a horizontal producing well and in the case of CAPRI, a catalyst. This paper aims to investigate the impact that injected steam has on both the THAI and CAPRI processes for the purpose of in situ HO upgrading and will help to bridge the gap between the extant laboratory research and the unknown commercial potential. This study also presents a novel method for modeling the THAI-CAPRI method using CMG STARS, proposing an in situ hydrogen production reaction scheme. THAI and CAPRI experimental-scale models were run under three conditions: dry, pre-steam, and constant steam. Starting from a reservoir American Petroleum Institute (API) of 10.5°, THAI reached an average API of ∼16 points, showing no increase in the API output with the use of steam injection. A decreased API output by ∼0.7 points during constant steam injection was achieved due to a high-temperature oxidation-dominant environment. This decreases the reactant availability for thermal cracking. The CAPRI dry run reached an API of 20.40 points and achieved an increased API output for both pre-steaming (∼21.17 points) and constant steaming (∼22.13 points). The mechanics for this increased upgrading were discussed, and catalytic upgrading, as opposed to thermal cracking, was shown to be the reason for the increased upgrading. Both processes produce similar cumulative oil (∼3150 cm3) during dry and pre-steamed runs, only increasing to ∼3300 cm3 with the constant steam injection during THAI and 3500 cm3 for CAPRI.

Energy, environment and economy assessment of sewage sludge incineration technologies in China

Sludge incineration attracts increasing interests in China. Different sludge incineration modes, incinerator types, auxiliary fuel and sludge drying heat sources can cause various energy, environmental and economic performances. In this study, seven sludge incineration technologies (i.e., rotary kiln incineration with coal or natural gas fuel, fluidized bed incineration with natural gas or biomass fuel, co-incineration in coal-fired power plant (CFPP), and co-incineration in waste-incineration power plan (WIPP) by electric drying or steam drying) were evaluated and compared via energy flow analysis (EFA), life cycle assessment (LCA), and life cycle cost (LCC) methods. EFA results show that energy utilization efficiency of individual incineration without full utilization of waste heat is lower than 28%. LCA results show that comprehensive environmental indicator of coal and natural gas are approximately 100 times as large as biomass. For different drying heat sources, steam instead of electricity shows superior environmental impact. LCC results demonstrate that individual incineration technologies are 2–4 times that of co-incineration technologies in investment cost. The results of decision alternative ratia evaluation showed that co-incineration in CFPP is the best in seven technologies, followed by co-incineration in WIPP with steam drying.

Superheated Steam Spray Drying as an Energy-Saving Drying Technique: A Review

Drying is an extremely energy-intensive process. Superheated steam as a drying medium can improve the energy efficiency of the drying processes. In superheated steam drying, waste heat can be recovered by condensing the exhaust steam or raising its specific enthalpy. Spray drying is widely used in industry, even though its energy efficiency is often low. Substitution of air by superheated steam as a drying medium in a spray dryer may reduce the energy consumption of the drying process by 20–30%; moreover, if excess steam generated by moisture evaporation is upgraded to a higher temperature level and reused for drying, the energy demand could be decreased by even 80%. A literature review showed that superheated steam spray drying was successfully applied for both thermally resistant and a wide range of thermally sensitive materials. Superheated steam drying gives a number of advantages in terms of product properties, i.e., higher particle porosity due to rapid moisture evaporation results in improved powder rehydration properties. Additionally, steam drying may be applied for in situ particle crystallization. Taking into account the advantages of superheated steam drying and the potential application of this technology in spray drying systems, there is a great need for further research in this field. This literature review aimed to present an energy-saving solution, i.e., superheated steam spray drying process, showing its advantages and potential applications, followed by drying kinetics, providing analysis of the research papers on experimental studies as well as mathematical modeling of this drying technique.

Impact of Thermal Processing on the Composition of Secondary Metabolites of Ginger Rhizome-A Review.

Ginger (Zingiber officinale Rosc.) is both a commonly used spice, and an ingredient of various dietary supplements and medications. Its diverse applications result from the range of health benefits that this plant brings thanks to the presence of active compounds (secondary metabolites) in the matrix. Even if several studies underline a stronger pharmacological activity of fresh ginger rhizomes, the unprocessed plant is relatively rarely used. Ginger rhizomes are subjected to thermal processing, such as boiling, blanching, steam drying and others, at different temperature and time settings. Additionally, freeze-drying of the rhizomes is used as the first step in the preparation of raw material. It was proved that the composition of secondary metabolites of the Zingiber officinale rhizome changes upon the influence of temperature. Therefore, the aim of the review was to put together scientific results on the impact of traditional and unconventional methods of heat treatment on ginger rhizomes and to show the compositional differences that they induce in the plant matrix. Variations in the content and the transformation of some compounds into other metabolites will be also discussed, with particular attention paid to two major groups of secondary metabolites present in the plant, namely, phenolics and terpenes.

The role of emerging technologies in the dehydration of berries: Quality, bioactive compounds, and shelf life.

Berries are among the fruits with the highest nutritional and commercial value. This paper reviews the conventional and emerging dehydration methods most commonly used as postharvest treatment and discusses their efficacy in maintaining and/or improving the nutritional and functional qualities of dried berries. The characteristics of the conventional methods (e.g., convective drying, freeze-drying, spray-drying, osmotic dehydration), their pre-treatments, their combination, and intermittent drying, as well as their potential disadvantages are discussed. The use of emerging dehydration techniques (e.g., electromagnetic radiation drying, explosion puffing drying, heat pump drying, low-pressure superheated steam drying, microwave drying) allows to improve the quality of the dried berries compared to conventional techniques, in addition to reducing drying times, increasing drying speed and energy efficiency. Finally, the use of pre-treatments and the combination of technologies can enhance the quality of the final product as a result of the improvement in the effectiveness of the dehydration process.

Earthworm Aporrectodea molleri (oligochaeta)'s coelomic fluid-associated bacteria modify soil biochemical properties and improve maize (Zea mays L.) plant growth under abiotic stress conditions.

This study evaluated the impact of Aporrectodea molleri's coelomic fluid-associated bacteria (CFB) on Zea mays L. growth and soil biochemical characteristics under abiotic stress conditions, including alkaline soil (pH = 8) and nitrogen (N), phosphate (P), and potassium (K) deficit. Compared to maize cultivated in uninoculated soil, the effect of CFB on boosting plant growth under abiotic stress was notably exceptional. Different CFB treatments increased significantly root and shoot length by 50% and 21%, respectively. Furthermore, the presence of isolates in soil resulted in a significant increase in plant fresh and dry weights (of up to 113% and 91% for roots, and up to 173% and 44% for shoots), leaf surface (78%), and steam diameter (107%). Overall, soil inoculation with CFB significantly (P < 0.05) enhanced chlorophyll and water content in the plant compared to the untreated soil. Despite the soil's alkaline condition, CFB drastically boosted soil quality by increasing nutrient availability (up to 30ppm for N, 2ppm for P, and 60ppm for K) and enzyme activity (up to 1.14μg p-NP h-1g-1 for acide phosphatase, 9μg p-NP h-1g-1 for alkaline phosphatase and 40μg NH4-N 2h-1g-1 for urease), throughout the early stages of the growth period. Interestingly, alkaline phosphatase concentrations were substantially greater in treatments with different isolates than acid phosphatase. Furthermore, the principal component analysis showed that the inoculation with bacteria strains CFB1 Buttiauxella gaviniae and CFB3 Aeromonas hydrophila had a significantly better stimulatory stimulatory and direct influence on maize growth than the other isolates had a substantial effect on soil's biochemical features. Thus, we assumed that the beneficial contribution of earthworms in the rhizosphere might be attributed in large part to associated microorganisms.

Hydrogen and ammonia production from low-grade agricultural waste adopting chemical looping process

Chemical looping hydrogen production (CLH2) is a new technology used to produce hydrogen (H2) from fuels while separating CO2 simultaneously. This research aims to build an integrated conversion system of rice husks, a high energy potential biomass, to H2 with high energy efficiency. The developed system mainly consists of superheated steam drying, steam gasification, chemical looping, and Haber-Bosch processes. Three different systems are developed and compared. The first and second systems employ direct chemical looping (DCL) using H2O and CO2 as gas enhancers for the reducer, respectively, while the third system adopts syngas chemical looping (SCL). Exergy recovery and process integration technologies are adopted to enhance energy and exergy efficiencies. A mixture of Fe2O3 and Al2O3 is used as oxygen and heat carriers in the CLH2 module. Process modeling, optimization, and evaluation of both energy and exergy efficiencies are conducted using Aspen Plus. Some crucial operating parameters, including reactor temperature, pressure, the oxygen carrier flow rate, and gas enhancer flow rate, are selected to evaluate the performance of the system, especially in terms of efficiency. The highest achievable H2, NH3, and net power efficiencies are 51.8%, 38.09%, 0.65%, respectively, when DCL is adopted with CO2 as a gas enhancer during the reduction.

The use of steam dryer with heat recovery to decrease the minimum exhaust flue gas temperature and increase the net efficiency of thermal power plant

Net power plant efficiency is the ratio of exportable electrical power output to the product of fuel consumption rate and fuel heating value. Conventionally, power plants are designed to attain the maximum net power plant efficiency by using regenerative feed water heating, in which extracted steam from steam turbine is used to increase feed water temperature. An important factor that determines the net power plant efficiency is the temperature of flue gas exhausted from the power plant. Decreasing this temperature increases the net power plant efficiency. However, exhaust flue gas temperature should not be lower than the lower limit in order to avoid the corrosion resulting from condensation of sulfuric acid vapor in flue gas on heat exchanger tubes. The lower limit can be raised by reducing fuel moisture content and raising air temperature at boiler inlet. In this paper, it is proposed that low-pressure extracted steam should be used for fuel drying in steam dryer, and vapor released from steam dryer should be used for air heating in heat recovery air preheater. By doing so, the lower limit of exhaust flue gas temperature is decreased, and the net efficiency of the power plant is increased. A case study of a 600-MW lignite-fired power plant is used to demonstrate that the integration of steam dryer and heat recovery air preheater is economically justified.

Drying Characteristics of a Combined Drying System of Low-Pressure Superheated Steam and Heat Pump

The present study aimed at investigating the use of a drying system combining the concept of low-pressure superheated steam drying and heat pump drying for fish. The effects of various drying medium pressures on the temperature field, airflow field, drying time, equipment performance as well as the power consumption of the drying process were investigated and discussed. Four comparative tests with different initial pressures were carried out according to a specified drying process by the combined drying system. The results showed that when the vacuum was high, the temperature field and airflow field in the drying chamber were more uniform. Due to the poor heat transfer performance of the drying medium at high vacuum, the drying time increased with a decrease in initial pressure. It was also found that with the decrease in drying medium pressure, the power consumption of the heat pump and the axial fans was reduced, while the power consumption of the electric heater went up. Overall, the total power consumption is directly proportional to the drying medium pressure.

Numerical study on the effect of superheat on the steam ejector internal flow and entropy generation for MED-TVC desalination system

The droplets formed by wet steam spontaneously condensation deteriorated the steam ejector performance for the Multi-Effect Distillation-Thermal Vapor Compression (MED-TVC) seawater desalination system. According to our numerical research, it was found that increasing the wet steam superheat was an effective method to suppress the steam spontaneously condensation behavior, especially when the superheat was increased by 50 K, the entrainment ratio was improved by 10.3% and the total entropy production was reduced by 9.8% for the steam ejector of MED-TVC system. In this paper, a wet steam model with entropy generation rate was built, the numerical simulation results of dry steam and wet steam models were compared, and the influence of five primary fluid superheat ranging from 10 K to 50 K on the wet steam flow behavior were also investigated. The irreversible analysis of wet steam flow revealed that the entropy generation was mainly concentrated in the initial mixing position of primary and secondary fluids near nozzle outlet and shock wave position in the diffuser, and the entropy generation relevant for the heat transport mechanism accounted for a much higher proportion (63%) of total entropy production than viscous dissipation (33%), phase change (4%), and wall boundary layer (ignored).

Comparative Efficacy of Superheated Dry Steam Application and Insecticide Spray Against Common Bed Bugs Under Simulated Field Conditions.

The common bed bug, Cimex lectularius L., is a difficult urban pest to control. A simulated field study was conducted to compare the efficacy of steam application and an insecticide mixture spray (0.05% acetamiprid and 0.06% bifenthrin mixture) against C. lectularius. Three types of furniture (desk chair, upholstered armchair, and wooden table) were treated in the laboratory. The efficacy of the treatments was evaluated by visual inspection and placement of interceptor traps under the legs of the furniture. One hundred mixed stages of an insecticide-resistant population of C. lectularius were released onto each furniture item. After a 10-day acclimation period, each furniture item received steam treatment, insecticide spray, or no treatment. The second application of treatment was conducted 14 d later. Bed bug counts from interceptors and visual inspections were recorded at 13 d and 28 d after the initial treatment. At 28 d, the mean (± SE) live bed bug count in the steam, spray, and control group was 1 ± 0, 2 ± 1, and 83 ± 10, respectively. Both treatment methods were highly effective in controlling bed bugs on furniture. The mean bed bug count from interceptors in the steam, spray, and control groups were 0.3 ± 0.2, 11 ± 7, and 47 ± 9, respectively. There was no significant difference in the efficacy between steam and spray treatments based on either visual inspection or bed bug counts from interceptors. However, based on interceptor counts, the steam treatment caused faster bed bug population reduction than insecticide sprays.

Novel drying techniques for controlling microbial contamination in fresh food: A review

Fresh foods such as fruits, vegetables, grains, nuts, and meats are generally rich in water and are susceptible to microbial contamination. Drying and dehydration processes can reduce water content, but low water activity foods may not be microbiologically safe. Several novel drying techniques have demonstrated varying degrees of effectiveness in microbial inactivation, including supercritical CO2 drying, low-pressure superheated steam drying, microwave drying, radio frequency drying, infrared drying, vacuum drying, freeze drying, etc. Some typical microorganisms used as indicators of microbial inactivation including natural present microorganisms (e.g., mesophilic bacteria and their spores, yeast and mold) and various pathogens (e.g., Escherichia coli O157:H7, Listeria monocytogenes and Salmonella spp.). This paper reviewed novel drying techniques for controlling microbial contamination of fresh foods and analyzed their advantages/disadvantages and microbial inactivation capabilities. These novel drying techniques have the potential to ensure microbiological safety during drying and have the prospect of shortening the food processing chain by integrating drying and sterilization/decontamination into the same process.

Comparison of the Saponins in Three Processed American Ginseng Products by Ultra-High Performance Liquid Chromatography-Quadrupole Orbitrap Tandem Mass Spectrometry and Multivariate Statistical Analysis

A method with ultrahigh performance liquid chromatography Quadrupole-Orbitrap tandem mass spectrometry (UHPLC-Q-Orbitrap-MS/MS) was applied for the quality evaluation of different processing and drying of American ginseng, including natural drying (ND), steam drying (SD), and vacuum freeze-drying (VFD). A total of 51 saponins were successfully identified in three processed products. Three processed American ginseng products were well-differentiated in orthogonal partial least-squares discriminant analysis (OPLS-DA). The S-plot also identified the marker compounds in each product, while the major ginsenosides of ND (malonyl (M)-Rd, M-Rb1, Rg1), SD (20 (S)-Rg3, 20 (S)-Rg2), and VFD (M-Rd, M-Rb1) were found. The results indicate that the method by vacuum freeze-drying can retain the content of rare ginsenosides and malonyl-ginsenosides. The marker compounds selected will benefit the holistic evaluation of related American ginseng products.

Effects of a Combined Processes of Low-Pressure Steam Enrichment and Low-Pressure Superheated Steam Drying on the γ-Aminobutyric Acid Content of Japonica Rice

In order to improve the content of GABA in japonica rice, so as to improve the nutritional composition and enhance the added value of rice, this study explored a combined process of low-pressure steam enrichment of γ-aminobutyric acid (GABA) content in japonica rice and low-pressure superheated steam (LPSS) drying of japonica rice. The low-pressure energy and the energy stored in rice grains were used to promote water absorption and activation of rice germs in a steam environment. Under the action of glutamate decarboxylase, the germ glutamate underwent an enzymatic reaction to generate GABA, which was transferred to and stored in the rice endosperm due to the concentration gradient and water gradient. After germination, LPSS was successively applied to dry the rice grains. The response surface method was used to optimize the parameters of low-pressure wet steam enrichment and LPSS drying of the rice grains. The experimental results showed that when the pressure was 0.026 MPa, the temperature was 60.66°C, the time was 5.01 h, and the flow rate was 0.31 L/h; the GABA content produced by low-pressure wet steam germination of japonica rice peaked at 94.1751 mg/100 g. When the germinated and enriched japonica rice was put through LPSS drying with a pressure of 0.021 MPa, a temperature of 66.55°C, a time of 1.57 h, and a flow rate of 0.28 L/h, the GABA content peaked at 104.161 mg/100 g. The results show that the combined process of low-pressure steam enrichment and drying continuously produced GABA in the soaking enrichment and drying stages, and the content of GABA in the drying stage accounted for 10% of the total content, which effectively increased the content of GABA in japonica rice and shortened the enrichment time. This study provides a technical reference for industrialized production of GABA-rich brown rice, embryonic rice, and polished rice.

A Review of the Geothermal Potential Hot Spots in Iraq Using Geophysics Methods

This review introduces the concept of geothermal energy and the technologies used to harvest this sustainable and clean source. Geothermal systems were explained in details in the review. They were classified into two major types, steam cycle and binary cycle. The steam cycle is always used at higher enthalpy, and a binary cycle is used at low enthalpy. The power generation methods used to produce geothermal power from geothermal resources, typically, comprises of well production, injection and steam and gas separators, heat exchangers, preheaters, turbines and condenser. The steam cycle type allows the water to evaporate and the steam will be separated from brine solution and expanded in a turbine, generally the salty water will have discarded out of system, or it is flashed again at lower system part. Power generation methods were divided into single Flash Steam Plant, Double Flash Steam Plant, and Dry Steam Plant. The components of the geothermal power plant were elucidated, namely, feed pump, heat exchanger, preheater, evaporator, turbine, and condenser. After surveying the geothermal energy worldwide briefly, the Iraqi geothermal energy was introduced. Thermal gradient in Iraqi tectonic zone was analyzed. There is a very limited available literature on Iraq geothermal. However, we were able to analyze the geothermal temperature gradient in Iraq by dividing it into two regions; the northern Iraq, and the southern Iraq. Our analysis shows that Iraq is a poor zone for geothermal with no significant hot spots all over the country. However, low temperature applications can be invested using the exhausted petroleum wells.

Syngas Generation Process Simulation: A Comparative Study

Methane reforming processes are of great importance for both the reduction of this greenhouse gas concentration in the atmosphere and for hydrogen production for energetic or chemical synthesis purposes. The use of Biogas in substitution for methane in reforming processes still provides a solution for the recovery of organic waste capable of producing Biogas. However, an in-depth analysis of the advantages of this substitution from the point of view of process yield is still lacking. Thus, the main contribution of the present research is the focus given to the comparison between methane and biogas as a reactant for the dry and steam reforming processes. In this work, a computational comparison of syngas production processes was performed, considering the system within the open-loop control. The software Aspen Hysys was used based on the minimization of Gibbs free energy in equilibrium. The parameters studied were: molar ratio of reagents (1-5), temperature (600-1000 °C), and pressure (1-5 bar). Dry methane reforming and steam methane reforming units were simulated, as well as both units using Biogas as a methane source. The plant was built in the simulator, and the results obtained indicated that high values in the molar ratio of CO2/CH4, CO2/Biogas, H2O/CH4, and H2O/Biogas, high temperatures, and low pressures favor the maximum conversion of methane. The use of Biogas in replacement of pure methane in the reform process proved to be advantageous for favoring the synthesis gas production reaction, besides adding value to a residue.

Hydrogen production via chemical looping dry reforming of methane: Process modeling and systems analysis

AbstractThe present study presents and analyses a family of “chemical looping dry reforming” (CLDR) processes that produce inherently separated syngas (H2 and CO) streams via a combination of methane cracking in a “cracker reactor” and the Boudouard reaction (i.e., conversion of the formed carbon with CO2 to CO) in a “CO2 reactor,” and then further maximize the H2 yield via conversion of the produced CO via water‐gas‐shift. Remaining CO2 emissions are minimized via CO2 capture and sequestration. Four different configurations are evaluated which differ in how the heat required for the highly endothermic dry reforming reaction is supplied: (i) combustion of additional CH4 feed (CLDR‐CH4); (ii) combustion of some of the CO produced in the CO2 reactor (CLDR‐CO); and combustion of some of the carbon produced in the cracker reactor with (iii) pure oxygen (CLDR‐C‐oxy); or (iv) with air (CLDR‐C‐air). Process models are developed to comparatively analyze the mass and energy balances of these configurations, and benchmark them against H2‐production via conventional dry reforming and steam reforming of methane. Our results show that CLDR‐C‐oxy is the most promising H2‐production pathway among the chemical looping and conventional technologies both in terms of chemical energy efficiency and in terms CO2 emissions. Thus, the unique flexibility offered by the production of inherently separated syngas streams in CLDR enables overcoming the disadvantage of the strongly endothermic dry reforming reaction by combusting carbon internally in the reactor and thus achieving highly effective heat integration. Overall, the results support the technical viability and demonstrate the promise for strong process intensification of CLDR compared to conventional dry reforming and even steam reforming, the most widely used H2‐production pathway to‐date.

Analyzing the combustion oscillation of a gas turbine for syngas based on the characteristic time-scale theory

When the ambient temperature is less than −10 °C in winter, the gas turbine for syngas in Huaneng Tianjin integrated gasification combined cycle (IGCC) power station has an evident combustion oscillation phenomenon, which seriously affects the production safety and efficiency. This study used the characteristic time-scale theory to guide the operation, thereby reducing the combustion oscillation of the gas turbine for syngas. The work progressed as follows. First, the boundaries of the combustion oscillation and maximum temperature safe limitations were defined based on the operational data from the extreme ambient temperature in summer and winter in the Huaneng Tianjin IGCC power station. Then, the mathematical model of combustion with critical parameters, such as ignition delay time, the adiabatic temperature of the flame, and flame speed, was constructed using the binary quadratic regression method under various combinations of dry syngas, natural gas, and steam flow rates. Finally, an operation scheme for reducing the combustion oscillation of the gas turbine for syngas in winter was designed, as well as the limitation boundary and computation model. This operation scheme can effectively reduce the combustion oscillation in winter; this was confirmed in actual operation. The results of this study should assist gas turbine designers in improving the safety, reliability, and stability of syngas turbines.

Superheated Steam Torrefaction of Biomass Residues with Valorisation of Platform Chemicals—Part 1: Ecological Assessment

Within the last decade, research on torrefaction has gained increasing attention due to its ability to improve the physical properties and chemical composition of biomass residues for further energetic utilisation. While most of the research works focused on improving the energy density of the solid fraction to offer an ecological alternative to coal for energy applications, little attention was paid to the valorisation of the condensable gases as platform chemicals and its ecological relevance when compared to conventional production processes. Therefore, the present study focuses on the ecological evaluation of an innovative biorefinery concept that includes superheated steam drying and the torrefaction of biomass residues at ambient pressure, the recovery of volatiles and the valorisation/separation of several valuable platform chemicals. For a reference case and an alternative system design scenario, the ecological footprint was assessed, considering the use of different biomass residues. The results show that the newly developed process can compete with established bio-based and conventional production processes for furfural, 5-HMF and acetic acid in terms of the assessed environmental performance indicators. The requirements for further research on the synthesis of other promising platform chemicals and the necessary economic evaluation of the process were elaborated.

Study and comparison of different drying processes of porous particle at high temperature

This work presents a comparative study of four drying processes of a porous media: superheated steam drying at atmospheric pressure (APSSD), humid air (HA), low pressure superheated steam drying (LPSSD) and vacuum drying (VD). A single porous particle model has been developed to simulate the four drying processes. The model is based on the method of averaging volume. Spherical porous particles of coal are used as the model material in this paper. The evaporation rates are equal for these processes in point called the inversion temperature. This temperature was calculated during the constant rate period (CRP) and the falling rate period (FRP). A variation in the values of inversion temperature was observed (363-503 K). The effect of drying parameters such as: particle radius, gas mass flux, permeability, porosity and operating pressure were investigated. Several researchers have reported the noticeable variation of the inversion temperature values according to the drying period used to calculate this key parameter. Our results are compared with those obtained from a front model reported in the literature. A good agreement is found.