Humidity Ratio Research Articles

Analytical solution for heat and mass transfer in desiccant coated heat exchangers

• Heat and moisture transfer in a desiccant-coated heat exchanger (DC-HX) is studied. • A new closed-form analytical solution is proposed. • Linear and exponential profiles are assumed for air temperature and humidity ratio. • A new DC-HX coated with AQSOA™-FAM-Z02 is also fabricated and tested. Due to the complicated nature of desiccant-coated heat exchangers (DC-HXs), solving the highly-coupled transient heat and mass transfer equations using numerical simulations are rather time-consuming and as a result may be impractical for real-time system optimization and seasonal simulations. On the other hand, the approach of majority of studies associated with DC-HXs is numerical and experimental analyses and there is no analytical model that can accurately predict the heat and moisture transfer in a DC-HX in the literature. Thus, in this paper, a new closed-form analytical solution is proposed to accurately predict the heat and moisture transfer in a DC-HX for the first time. The governing equations are simplified to a set of linear ordinary differential equations with initial conditions and then solved analytically. In the present analytical model, both linear and exponential profiles are assumed for the air temperature and humidity ratio along the DC-HX and the results are compared to experimental data collected in our lab. A new DC-HX coated with AQSOA™-FAM-Z02 is also fabricated and tested in our custom-built testbed under a wide range of operating conditions for model validation and performance assessment. Our results indicate that the present analytical solution with exponential profile assumption predicts the experimental data with an average relative difference of less than 10%, while the linear profile assumption results in a relative difference of ∼ 20% with the experimental data. The new analytical solution is capable of predicting the performance of DC-HXs, which is crucial for design, optimization and operating dehumidification systems in a variety of applications.

Composting plants as a technology for the transformation of agro-industrial residue into organic fertilizer

The increase in the consumption of ready-to-eat foods has also increased the generation of agro-industrial waste. The organic matter present in these residues causes damage to the environment when they are improperly disposed of. Composting is a technology that uses these residues to obtain a sustainable material that can be used as a biofertilizer, without harming the environment. The objective was to collect and analyze data related to composting as a technology capable of transforming agro-industrial waste into organic fertilizer. For this, keywords were defined and a survey of information in the SciELO database was carried out. The keyword [composting AND (“agro-industrial waste” OR “agro-industrial waste”)], in English, obtained the best representation and refinement. Annual evolution data were observed between 2007 and 2020, with the number of publications fluctuating over the period. Considering the 13 selected scientific articles, a total of 4 countries were highlighted as the headquarters of the research executing institutions, namely: Brazil, Chile, Mexico and Portugal. The thematic area “Agrarian Sciences” and the journal “Engenharia Agrícola” have the largest number of publications in their respective groups. There was no relationship between the number of publications of scientific articles and the impact factor presented by the journal. The relevance of the control of humidity, aeration, temperature, pH, carbon and nitrogen ratio (C:N) and granulometry was verified. Therefore, composting is a potential technology to transform agro-industrial waste into organic fertilizer.

On the performance study of a hybrid indirect evaporative cooling and latent-heat thermal energy storage system under commercial operating conditions

In this paper, a hybrid evaporatively-enhanced cooling system is proposed under commercial operating conditions. The indirect evaporative cooler (IEC) is first employed as a pre-cooling equipment to treat ambient air by recovering energy from the indoor exhaust air. The pre-cooled air is then treated to achieve the required thermal condition by employing the latent-heat thermal energy storage (LHTES) containing spherical balls encapsulated with a synthesized phase change material (PCM). Such a novel hybrid process takes full advantage of the IEC’s high cooling efficiency and LHTES’s power peak load shifting capability. Experimental system comprising the IEC integrated with the LHTES is designed and tested under various air conditions. Additionally, mathematical models are developed to simulate transport phenomena behind the system. Employing experimentally-validated models, thermodynamic analyses are conducted to study the system's performance. Results indicate that (1) the proposed hybrid system is able to pre-cool and dehumidify the ambient air in the tropics simultaneously; (2) the ambient air temperature and humidity ratio can be respectively reduced by 6–10 °C and 2–11 g/kg dry air under specific operating ranges; (3) the evaporative cooling technology facilitates the use of a higher chilled water supply temperature which results in an improvement on the chiller efficiency; and (4) a higher water flow rate leads to faster cold energy storage and release rates during the respective charging and discharging periods.

Reusing maintenance monitoring data on preventive conservation

The indoor climate of libraries and archives is determinant for the preservation of their collections, as temperature and relative humidity can trigger other damage factors. Standards and literature recommend to perform long term monitoring to understand the climatic history where the goods were kept, instead of follow rigid and arbitrary conditions. This trend is sustainable and environmentally friendly, but adds a new duty to the overloaded staff. We present two technical advices sustained in monitoring records produced to assess the HVAC equipment and reused to preservation purposes. The first is a library collection transferred from a historic building to a new building, and the second is a deposit room supplied with de-humidificators, where the analysis evidenced a very low humidity ratio. The main conclusion is that a synergetic use of monitoring data can improve the indoor climate of the collections and reduce the energy demand for preservation.

Liquid desiccant-based deep dehumidifier working with a novel ionic liquid: Prediction model and performance comparison

Deep dehumidification system with energy conservation and stable operation is expected to be used in industrial occasions with low-humidity environment. Compared with solid desiccant dehumidification, liquid desiccant-based dehumidification is a promising alternative because of its advantages of continuous operation and low regeneration temperature. However, corrosion and crystallization problems exist with liquid desiccant-based deep dehumidifier (LDDD) using salt solutions. In this work, LDDD using a novel ionic liquid (IL) was introduced, and the heat and moisture transfer model was established based on the finite difference method. Meanwhile, the moisture transfer characteristics were numerically simulated under different operating parameters (i.e., inlet humidity ratio wa,in, air velocity va, solution mass concentration X, solution temperature ts and solution volume flow Vs). Besides, the significance of various factors and their interactions were analyzed based on response surface methodology. The numerical model is validated against the experiment of the LDDD test bench with a relative deviation of 3%-8%. Numerical results show that the LDDD using IL can achieve deep air dehumidification, and outlet humidity ratio of less than 4 g/kgda is possible. In particular, the order of significance for influencing factors of outlet humidity ratio is: wa,in > X > ts > va > Vs. Moreover, it is found that dehumidification rate of 60% LiBr solution (saturated state) is less than that of 90% IL. This study establishes a prediction model of moisture transfer between IL and air under the coupling of multiple physical fields, and provides guidance for the application of LDDD using ILs.

Mass transfer study on high-pressure membrane dehumidification applied to aircraft environmental control system

Expected to replace conventional condensing dehumidification, pressure-driven membrane dehumidification is an alternative to the high-pressure air dehumidification in aircraft environmental control system (ECS). A high-pressure membrane dehumidification experiment is conducted on a counter-flow hollow fiber membrane module to investigate the dehumidification performance under various operating conditions including feed flow rate, feed pressure and sweep ratio. The experiment achieves the dehumidification rate of 1007 g/h at highest. Taking account of the variation of mass transfer driving force along the flow direction, the theoretical model reaches a good agreement with the experiment data. Based on the validated model, a numerical simulation study is conducted to explore the detailed mass transfer characteristics. The simulation reveals the outstanding distinction between the high-pressure and normal-pressure membrane dehumidification. Driven by water vapor partial pressure difference, the mass transfer in the latter one is determined by humidity ratio only, while that in the former one depends on humidity ratio and pressure altogether. Various combination modes of multiple membrane modules are also investigated for more flexible arrangement in the compact space of aircraft, and it is found that the pure parallel mode performs the best. Finally, exergy analysis is employed to compare with the condensing method. In comparison, the membrane method performs the less exergy destruction especially at low desired outlet humidity ratio.

Analysis of Preferential Flow at the Front Mesh Cartridge of the Gas Mask Filter: Cases in Malaysia Climate Environment

A gas mask respirator is essential for human protection from the hazardous and toxic chemical environment. The gas mask filter should be regularly checked, and the filter must be changed abruptly based on the temporal exposure to the toxic environment. Furthermore, the filter is exposed to a highly humid climate, and the high gas concentration speeds up the expiry cycle of the gas mask filter. Thus, this study aims to investigate the preferential flow absorbed into the gas mask filter and predict the potential area that presents the dead zone. In this study, a three-dimensional model of the commercial gas mask filter was modeled using the computational aided design (CAD) software. Four different humidity ratios of 50%, 60%,70%, and 80% as well as Five different filter concentrations of 20ppm, 100ppm, 200ppm, 300ppm, and 1000 ppm were simulated. The computational fluid dynamic (CFD) method was governed by continuity and Navier-stokes equation to investigate the presence of the dead zone based on several flow parameters. The result showed that the effects of the pressure, velocity, temperature, humidity, and concentration on the gas mask filter were analyzed. The pressure drop is seen in the charcoal filter region which experiences high-velocity circulation. The highest effect on the pressure drop, humidity, and concentration was seen for the case V filter. The high humidity ratio with the pressure drop in the gas mask filter also decreases the efficiency of filter concentration even though the temperature is constant. The high humidity ratio in the mask filter will retain the heat inside the gas mask filter, thus reducing the life cycle of the filter.

Robust Nonlinear Control Design for the HVAC System Based on Adaptive Sliding Mode Control

Control of Heating, Ventilating, and Air Conditioning (HVAC) aims to provide a comfortable environment for human life in terms of temperature and humidity and improve indoor air quality. The HVAC system is multi-input multi-output, where the control design of this system is challenging due to its strong nonlinearity and the coupled influence of both system controllers on the temperature within the thermal zone. The aim of this study is to design a dual-controller for the HVAC system. The first controller is a non-linear feedback controller which is devoted to control the humidity ratio of the thermal zone with the desired characteristic. While for the second one, a robust controller is designed to maintain the desired thermal zone temperature based on the adaptive sliding mode controller (ASMC). Using the ASMC enabled us to design the second controller without the need to know the uncertainty bound on the HVAC system model. Additionally, the stability of the proposed control system was verified using the Lyapunov theory. To construct the sliding variable for the temperature control, the error state which is the difference between the thermal zoon temperature and the desired value and its derivative is needed. Due to the uncertainty in the error state derivative, a robust differentiator was designed using the approximate classical sliding mode differentiator (ACSMD). Finally, the performance of the control system is confirmed via numerical simulation. The results showed the robust ability of the control system to make the humidity and temperature of the thermal area follow the required values and with high accuracy.

Evaluation of Split-Type Air Conditioner Performance under Constant Outdoor Moisture Content and Varied Dry-Bulb Temperature

An experimental investigation on the performance of an air conditioner and its operating conditions under constant outdoor moisture content and varied dry-bulb temperature has been accomplished. The test was conducted on an air conditioner using R32 with a nominal cooling capacity of 2.6 kW and the test was carried out in a controlled and standardized test room. During the test, the outdoor temperature was varied from 24 to 36℃ while maintaining the humidity ratio at 14.9 kg vapor per 1 kg of dry air. The indoor compartment was maintained at 27℃ dry-bulb temperature and 19℃ wet-bulb temperature. Generally, as the temperature of outdoor air increases by 1℃, the input power increases by 1.4%, the cooling capacity decreases by 0.9%, and the coefficient of performance decreases by 1.95%. In addition, the outdoor air temperature has a more significant effect on the refrigerant discharge and liquid line temperature than that of refrigerant suction temperature.

Three-dimensional numerical analysis of fin-tube desiccant-coated heat exchanger for air dehumidification in tropics

High-performance desiccant-coated heat exchangers (DCHEs) can be employed in air-conditioning systems to improve energy efficiency. While there are significant developments in experimental studies, theoretical approaches for analyzing the DCHE are impeded by the complex and coupled heat and mass transport mechanisms. Therefore, a 3D mathematical model has been developed in this work to study the dehumidification performance of a DCHE. Unlike other works reported in the literature, the developed model is able to simulate the complex coupling between heat and mass transfers in the entire volume of the heat exchanger. The model is calibrated and validated with experimental data, and a maximum discrepancy of ±8 % is recorded. A time-dependent study on the performance of the DCHE is carried out to understand the distribution of temperature, reaction rates, and water uptake in the heat exchanger. Effects of key influencing operational factors are investigated and discussed. It is indicated that the DCHE enters a stable performance state regardless of its initial adsorption state. The regeneration time should be equal to the dehumidification time to optimize the performance. A higher thermal COP is achieved under lower cooling/regeneration temperature, lower air flowrate, and shorter half-cycle time, while higher inlet air humidity ratio. Higher coated desiccant mass also provides a higher thermal COP, but this enhancement levels off once the coating grows. For DCHEs with less coating, reducing cycle time is recommended over increasing the coating amount.

Research on anti-frosting potential of air source heat pump evaporator in hot-summer and cold-winter zone

In this paper, the performance curve of a heat pump evaporator under critical frosting conditions was fitted. The functional relationship between the refrigerant evaporation temperature and the absolute air humidity ratio was obtained. In addition, the transfer unit model of the air source heat pump (ASHP) evaporator was established. The inlet air temperature, humidity ratio, velocity, fin pitch, and row number of evaporators were considered as input parameters. The anti-frosting potential of the heat transfer unit was simulated under critical frosting conditions. The results showed that, based on the heating potential of moist air unit mass under critical frosting conditions, the heating potential is at its minimum at an air humidity ratio of 3.39 g/kga. The maximum difference between the minimum temperature on the fin surface and the refrigerant evaporation temperature was found to be only 0.06 °C. The study findings highlighted that controlling the refrigerant evaporation temperature above the critical frosting temperature is an important method to prevent the evaporator from frosting. Under a low temperature environment, with the increase in the fin pitch and the inlet air velocity, the anti-frosting regulation performance of the two tube rows evaporator was found to improve compared to the single tube case. The aim behind increasing the inlet air velocity is to increase the heat transfer temperature difference between the inlet air and the critical frosting conditions. After optimizing the evaporator’s structural and operational parameters, the evaporator’s fin pitch is set according to the ambient air temperature. This was successful in meeting the requirement that the evaporator does not frost most of the time. Moreover, by adjusting the inlet air velocity, the evaporator will not frost at other times. In hot-summer and cold-winter zone, the operation of the ASHP evaporator with no frost can be achieved.

Thermal Insulation of Protective Clothing Materials in Extreme Cold Conditions

BackgroundThermophysiological comfort in a cold environment is mainly ensured by clothing. However, the thermal performance and protective abilities of textile fabrics may be sensitive to extreme environmental conditions. This article evaluated the thermal insulation properties of three technical textile assemblies and determined the influence of environmental parameters (temperature, humidity, and wind speed) on their insulation capacity. MethodsThermal insulation capacity and air permeability of the assemblies were determined experimentally. A sweating-guarded hotplate apparatus, commonly called the “skin model,” based on International Organization for Standardization (ISO) 11092 standard and simulating the heat transfer from the body surface to the environment through clothing material, was adopted for the thermal resistance measurements. ResultsIt was found that the assemblies lost about 85% of their thermal insulation with increasing wind speed from 0 to 16 km/h. Under certain conditions, values approaching 1 clo have been measured. On the other hand, the results showed that temperature variation in the range (−40°C, 30°C), as well as humidity ratio changes (5 g/kg, 20 g/kg), had a limited influence on the thermal insulation of the studied assemblies. ConclusionThe present study showed that the most important variable impacting the thermal performance and protective abilities of textile fabrics is the wind speed, a parameter not taken into account by ISO 11092.

A four-step method based on sequential solution of relevant model equations to predict condensation risk for a radiant cooling system

The problem of surface condensation constraints widespread application of radiant cooling (RC) system. Although, a dehumidification system is reported as a solution, the viability of using dehumidification for different climates is not conclusive. This study is conducted to determine the appropriation of dehumidification process for RC systems in different climates. An office building with an embedded RC system is modelled and simulated in EnergyPlus v9.6. Eighteen Asian cities are chosen based on ASHRAE's moisture zone classification for the simulation. Initially, the attainment of thermal comfort is assessed followed by an assessment of condensation. The results show that the system maintains required thermal comfort without an occurrence of condensation in eight cities with both dry and humid climates. It is noted that the condensation of an area does not depend on dry or humid zone of the area. Conversely, it is found that the outdoor humidity ratio is a major contributor towards the occurrence of condensation. A novel method is developed and validated that involves solving relevant model equations in a specific sequence to predict condensation risk based on outdoor humidity ratio. Results show that if the value of condensation risk is up to 20%, an RC system would provide thermal comfort without a dehumidification system and surface condensation. The proposed method will enable the designers and engineers to decide on provision of dehumidification for an RC system without going through rigorous simulation or experimental work.

Thermal performance analysis of a mixed-flow indirect evaporative cooler

This study experimentally investigates the performance of an indirect evaporative cooler based on the Maisotsenko cycle. It consists of a heat and mass exchanger (HMX) with a novel mixed-flow configuration. The de-sized cellulose rich cotton fabric is used as water-absorbing material, and aluminum sheets are used to fabricate the heat mass exchanger unit. The cooling performance indices of the system, namely dew point effectiveness (DPE), wet bulb effectiveness (WBE), and the coefficient of performance (COP), are evaluated at different inlet air temperatures (24 to 35 °C), volumetric flow rates (600 to 1050 m 3 /h), relative humidity (35 to 65%) and the extraction ratio (0.1 to 0.6). The results of the experimental study show that at a relative humidity of 35%, and inlet air temperature of 35 °C, the magnitude of the wet bulb and dew point effectiveness are highest and higher dew point and wet bulb effectiveness are observed at lower mass flow rates. The best cooling capacity and COP were obtained at an extraction ratio of 0.3 and are found to be highest at DBT of 35 °C. The maximum magnitude of CC was 2 kW with a COP of 16. Additionally, the convective heat transfer coefficient is calculated theoretically and compared with the experimental value. Further, a comparison of the obtained results for the mixed flow configuration considered in this study with those for other configurations reported in the literature reveals that the indirect evaporative cooler with mixed-flow configuration yields comparably good effectiveness. • Performance of indirect mixed flow evaporative cooler evaluated experimentally. • Effect of temperature, flow rate, relative humidity and extraction ratio are studied. • The optimum extraction ratio is observed to be 0.30. • Better performance is at higher inlet air temperature with lower humidity. • The maximum COP of 16 was observed at 35 °C with 35% relative humidity.

Thermal analysis and optimization of indirect flat evaporative coolers

• Analyzing the energy and exergy performance of indirect flat evaporative coolers on the basis of a verified numerical model and experimental correlation • Investigating the mechanism and theory of operation of indirect flat-panel evaporative coolers based on X-analysis • Calculating the entropy production rate of the flat-plate heat exchanger of the cooler Less attention and analysis have been given to cooling indirect evaporative coolers with different configurations and working air sources so far. This paper investigates the mechanism and theory of operation of indirect flat-panel evaporative coolers based on X-analysis. Then, based on the second law of thermodynamics analysis, the entropy production rate of the flat-plate heat exchanger of the cooler is calculated. As a result of this analysis, the optimal energy efficiency-evaporation efficiency and cooling capacity values are presented in terms of effective parameters in the design. It was concluded that dew point effectiveness and COP of the proposed system change monotonously with inlet mass flow rate, temperature and humidity ratio of primary air, respectively. The dew point effectiveness also varies monotonously with the mass flow rate ratio of secondary air to primary air. However, there exists an optimal mass flow rate ratio resulting in a maximum COP.

Research on improving dynamic response ability of 30kW real fuel cell system based on operating parameter optimization

The dynamic response performance of fuel cell has a great significance on the output power and reliability of the system, which works mainly under load change conditions. This paper is aimed at the dynamic response of 30 kW fuel cell system. Combined with the mechanism analysis method and empirical method, a fuel cell system model including stack, air supply system, hydrogen supply system and thermal management system is established. The reliability of the model is verified from three aspects: polarization curve, load change condition and road spectrum. The method of improving the dynamic response capability of the system is qualitatively studied through simulation. The results show that the best dynamic performance and output performance can be obtained by increasing the inlet pressure to 2.5 bar, relative humidity to 80% and the stoichiometric ratio to 3, while the effect of the temperature is not significant. The coupling relationship between gas pressure and temperature, humidity and stoichiometric ratio is preliminarily studied, and the influence law is explained combined with the mechanism. It is found that increasing the stoichiometric ratio is conducive to increasing the oxygen pressure, while humidity and temperature have the opposite effect. This model can be further used to explore the coupling relationship of internal parameters of PEMFC under load change condition.

Modelling Analysis of a Membrane-Based Fresh Air Processing System.

The current standard of residential buildings is based on well-insulated and airtight construction as an effective way to reduce primary energy consumption. On the other hand, this intensifies the issue of the indoor air quality. In this paper, the applicability of a hybrid dehumidification/evaporative cooling system for the processing and supply of fresh air is evaluated. The proposed novel system employs cross-flow hollow-fiber membrane modules. To provide a better insight into this novel approach, the system’s performance is numerically investigated using a validated mathematical model. The proposed fresh air processing system provides supply air parameters in or close to the summer comfort range. The analyzed system is characterized by a high coefficient of performance (COP) of up to 33.2 at an outdoor air temperature in the range of 30 °C to 38 °C and a humidity ratio in the range of 8 g/kg to 14 g/kg. Moreover, a temperature difference of up to 9.7 °C can be obtained after the two-stage membrane processing and the mixing process.

Numerical prediction of spatio-temporal frosting patterns of curved surface considering varying working parameters

Accurate numerical prediction of frosting patterns is essential for the efficient layout and timing defrosting of heat exchangers under frosting conditions. In this study, a numerical model is developed to predict the spatio-temporal frosting habits on curved surfaces in combination with the correlations of frost density and thermal conductivity. In the model, frost melting is considered. After verification, the frosting and heat transfer characteristics along the flow path are investigated under various structural and operating conditions. Frost thickness along the path is mainly affected by the cooling surface temperature, while the heat and mass transfer rates are strongly correlated with the humidity ratio. The proportions of latent heat and sensible heat are distributed more unevenly in parallel flow case than in counter flow case. Frost deposition is facilitated by a smaller radius of curvature of the cooling surface. More uniform frosting characteristics along the path and smaller heat transfer obstruction are presented with a smaller length-to-height ratio of the flow path.

Air dehumidification performance study of a desiccant wheel by a three-dimensional mathematical model

Hitherto air-conditioners have severe shortcomings because of the inherent need to maintain the cooling coil temperature significantly below the air's dew point. Their energy efficiency can be improved by employing desiccant wheel dehumidifiers that offer independent humidity control. Although numerous experimental and theoretical studies have evaluated desiccant wheels’ performance, no existing investigation yields a detailed account of its localized temperature and humidity distributions. Therefore, a new three-dimensional mathematical model was developed to study the time-dependent and steady-state temperature, humidity, and reaction distributions. The model predicted the performance with the maximum discrepancy of ±10% in both temperature and humidity ratio. It also revealed that the countercurrent airflow configuration has a more uniform reaction distribution than the concurrent configuration. The parametric analysis using the model revealed that higher regeneration temperatures require smaller regeneration angles. With the regeneration temperatures ranging between 110 and 50 °C, the optimal regeneration angles span 120–180°. Additionally, the dehumidification performance could be easily improved by increasing the wheel's rotation speed at low desiccant mass since coating more desiccant on the wheel is costly and inconvenient.

Hierarchically nanostructured Ag/ZnO/nBC for VOC photocatalytic degradation: Dynamic adsorption and enhanced charge transfer

The adsorption-photodegradation strategy can achieve continuous enrichment and efficient oxidation of volatile organic compounds (VOCs), but it requires a trade-off among adsorption, mass transfer, and charge transfer in this dynamic process. Therefore, the construction of an effective and stable catalytic system remains an immense challenge. Here, we report a strategy for constructing a hierarchically structured photocatalyst for efficiently degrading VOCs by assembling nanobiochar (nBC, ∼ 6.25 µm), the active center of ZnO (∼ 460 nm), and plasmonic-Ag nanoparticles (Ag NPs, ∼ 10 nm). Benefiting from its abundant surface functional groups (–OH, –CO, and –CO) and hierarchical structure-induced mesopores and macropores, VOCs can be quickly captured and dynamically diffused. Furthermore, Ag NPs build a charge transfer bridge and accumulate electrons to nBC from both the photogenerated electrons that are induced by ZnO and hot electrons from the local surface plasmon resonance (LSPR) effect of Ag NPs. Afterward, a desirable spatial separation of charge carriers and visible-light response can be achieved. Therefore, Ag/ZnO/nBC maximizes the reactive oxygen species (e.g., ·OH and ·O2−) and shows a 7.8 times higher degradation rate of formaldehyde than ZnO, and it also displays universality and stability with high photocatalytic efficiency. The photocatalytic performance was comprehensively determined based on the relative humidity, initial concentration, catalyst dose, and mass ratio of Ag NPs. This facile and universal strategy for architecting hierarchically structured photocatalysts provides an approach for enhancing photocatalytic performance for VOC degradation and environmental pollution treatment.