Biodegradation and sorption of nutrients and endocrine disruptors in a novel concrete-based substrate in vertical-flow constructed wetlands.

Removing phosphorus and endocrine-disruptors (EDC) is still challenging for low-cost sewage treatment systems. This study investigated the efficiency of three vertical-flow constructed wetlands (VFCW) vegetated with Eichhornia crassipes onto red clay (CW-RC), autoclaved aerated concrete (CW-AC), and composite from the chemical activation of autoclaved aerated concrete with white cement (CW-AAC) in the removal of organic matter, nutrients, and estrone, 17ß-estradiol, and 17α-ethinylestradiol. The novelty aspect of this study is related to selecting these clay and cementitious-based materials in removing endocrine disruptors and nutrients in VFCW. The subsurface VFCW were operated in sequencing-batch mode (cycles of 48-48-72 h), treating synthetic wastewater for 308 days. The operation consisted of Stages I and II, different by adding EDC in Stage II. The presence of EDC increased the competition for dissolved oxygen (DO) and reduced the active sites available for adsorption, diminishing the removal efficiencies of TKN and TAN and total phosphorus in the systems. CW-RC showed a significant increase in COD removal from 65% to 91%, while CW-AC and CW-AAC maintained stable COD removal (84%-82% and 78%-81%, respectively). Overall, the substrates proved effective in removing EDC, with CW-AC and CW-AAC achieving >60% of removal. Bacteria Candidatus Brocadia and Candidatus Jettenia, responsible for carrying out the Anammox process, were identified in assessing the microbial community structure. According to the mass balance analysis, adsorption is the main mechanism for removing TP in CW-AC and CW-AAC, while other losses were predominant in CW-RC. Conversely, for TN removal, the adsorption is more representative in CW-RC, and the different metabolic routes of microorganisms, biofilm assimilation, and partial ammonia volatilization in CW-AC and CW-AAC. The results suggest that the composite AAC is the most suitable material for enhancing the simultaneous removal of organic matter, nutrients, and EDC in VFCW under the evaluated operational conditions.

Effects of temperature and HRT on biogas production in moving and fixed bed of a novel upflow anaerobic hybrid (UAHB) reactor.

The upflow anaerobic hybrid (UAHB) reactor combines the advantages of a upflow anaerobic sludge blanket (UASB-type) reactor and an anaerobic filter in a single compartment. A novel configuration of the UAHB reactor, composed of two three-phase separators (3PHS), was proposed to evaluate the biogas production in the moving and fixed bed in the treatment of synthetic sewage at a temperature range of 14-21 °C and hydraulic retention time (HRT) of 12, 10 and 8 h. The bench-scale reactor was operated in three different phases with organic loading rate (VOLR) of 0.6 (0.3-0.7), 0.7 ± 0.2, and 1.1 ± 0.1 kg COD m-3 d-1, respectively, for 225 days. The average removal efficiency of chemical oxygen demand (CODt) was 78 (42-89)%, and the total biogas yield was 3090 (1704-4782) mL d-1, with 66% of the lower 3PHS (moving bed) and 34% of the upper 3PHS (fixed bed). However, no significant difference was observed between the biogas yield on the 3PHS (p-value = 0.5048), thus confirming the influence of temperature in the biogas production. The average percentage of methane was 76 (60-82)% for both beds, and the filter media increased the production by 21%. Thus, it can be concluded that the fixed bed suppressed the instability of the moving bed regarding the biogas production and contributed to the final quality of the effluent.

Recovery of methane dissolved in the effluent of a novel upflow anaerobic hybrid reactor (UAHB) submitted to temperature variation.

Recent studies point out losses of 30-40% of the produced methane in the effluent of anaerobic reactors treating sewage, reducing the renewable energy potential and the environmental footprint. A novel bench-scale upflow anaerobic hybrid (UAHB) reactor combining a sludge blanket at the bottom and a filter media at the top, both with three-phase separators, was proposed to evaluate the recovery of dissolved methane. UAHB was operated with volumetric organic loading rate of 1.24 kg COD m-3 d-1 and hydraulic retention time of 8 h for 218 days to evaluate the influence of temperature (18°C, 23°C, and 28°C) in the methane dissolved in the effluent and collected from three-phase separators. Chemical oxygen demand (COD) and total suspended solids (TSS) removals efficiencies remained constant during the operation and equal to 90 and 95%, respectively, related to the activity of biomass retained in the filter media. Temperature increase influenced more the methane production in the sludge blanket rather than in the upper bed. The volume of recovered methane increased about 20% with the installation of the support media and the upper three-phase separator (3PHS). The loss of methane dissolved in the effluent was strongly influenced by the temperature, and higher with the decrease of this parameter. Non-statistically significant correlations were observed between the temperature and the methane production in the upper bed (p-value = 0.0943) and total (p-value = 0.0930). Thus, it can be concluded that the evaluated temperatures did not influence the global efficiency and the total methane yield of the UAHB reactor.

Performance of an anaerobic-oxic-anoxic (AOA) system in the simultaneous removal of nutrients and triclosan and bacterial community.

The constant presence of triclosan (TCS) in surface water and wastewater has been verified due to its application in several pharmaceutical and personal care products. Thus, removing this emerging contaminant is essential to minimize the contamination of water bodies. The anaerobic-aerobic-anoxic (AOA) system is an innovative alternative that combines the removal of nutrients and triclosan. This study focuses on the simultaneous removal of carbonaceous matter, nitrogen, phosphorus, and triclosan in a continuous pilot-scale AOA system from synthetic wastewater. The upflow system, in series, was operated at hydraulic retention time (HRT) of 8 h and a flowrate of 2.40 L h-1. Glucose (190 mg L-1) was added to the anoxic reactor as the external carbon source. Besides that, bacterial community structure was investigated using 16S rRNA sequencing in each reactor. The system achieved average removal efficiencies of 96% (14.03 g d-1) for Chemical Oxygen Demand (COD), 85% (2.64 g d-1) for Total Kjeldahl Nitrogen (TKN), 88% (1.40 g d-1) for Total Ammonia Nitrogen (TAN), 20% (0.12 g d-1) for Total Phosphorus (TP), and 93% (1.87 µg d-1) for Triclosan (TCS). The phyla Proteobacteria, Firmicutes, Bacteroidetes, and Chloroflexi were found in greater abundance. The main genera identified were Anaeromusa, Aeromonas, Azospira, Clostridium, and Lactococcus. The organisms related to phylum and genus corroborate the involved processes and the removal performance achieved. In addition, Lactococcus, Thermomonas, Ferruginibacter, and Dechloromonas were involved in triclosan biodegradation. The anaerobic-oxic-anoxic system successfully removed carbonaceous, nitrogenous matter, and triclosan, with glucose increasing the denitrifying activity.

Removal of micropollutants by UASB reactor and post-treatment by Fenton and photo-Fenton: Matrix effect and toxicity responses.

Literature is scarce on the performance of Fenton-based processes as post-treatment of municipal wastewater treated by upflow anaerobic sludge blanket (UASB) reactor. This study aims to perform Fenton and photo-Fenton from UASB influent and effluent matrices to remove micropollutants (MPs) models: atrazine (ATZ), rifampicin (RIF), and 17α-ethynylestradiol (EE2). A UASB reactor at bench-scale (14 L) was operated with these MPs, and the AOPs experiments at bench-scale were performed on a conventional photochemical reactor (1 L). A high-pressure vapor mercury lamp was used for photo-Fenton process (UVA-Vis) as a radiation source. Microcrustacean Daphnia magna (acute toxicity) and seeds of Lactuca sativa (phytotoxicity) were indicator organisms for toxicity monitoring. The UASB reactor showed stability removing 90% of the mean chemical oxygen demand, and removal efficiencies for ATZ, RIF, and EE2 were 16.5%, 45.9%, and 15.7%, respectively. A matrix effect was noted regarding the application of both Fenton and photo-Fenton in UASB influent and effluent to remove MPs and toxicity responses. The pesticide ATZ was the most recalcitrant compound, yet the processes carried out from UASB effluent achieved removal >99.99%. The post-treatment of the UASB reactor by photo-Fenton removed acute toxicity in D. magna for all treatment times. However, only the photo-Fenton conducted for 90 min did not result in a phytotoxic effect in L. sativa.

Influence of HRT and carbon source on the enhancement of nutrient removal in an Anaerobic-Oxic-Anoxic (AOA) system.

The eutrophication and increase in toxicity promoted by the continuous or abundant supply of nutrients in water bodies threaten the safety of drinking water and human health. In this regard, this study proposes the investigation of wastewater treatment focusing on the simultaneous removal of nitrogen and phosphorus in the anaerobic-oxic-anoxic (AOA) system. The AOA system was operated in three different stages to verify the influence of the external carbon source addition in the anoxic reactor and the reduction of hydraulic retention time (HRT) in the anaerobic and oxic reactors for nutrient removal optimization. Results showed that the best performance of the AOA system on nutrient removal was obtained in Stage 3, with the reduction of the HRT in the anaerobic and oxic reactors (HRT = 4 h) while maintaining HRT of 6.4 h in the anoxic reactor with no addition of the external carbon source. Under these conditions, the average removal efficiencies reached 98% for Chemical Oxygen Demand (COD), 88% for Total Ammonia Nitrogen (TAN), 81% for Total Kjeldahl Nitrogen (TKN), and 70% for Total Phosphorus (TP). The results also demonstrate that the highest phosphorus removal efficiency was achieved in the anoxic reactor, thus indicating the occurrence of denitrifying phosphorous removal by Denitrifying Phosphate Accumulating Organisms (DNPAOs). This configuration was efficient regarding the simultaneous removal of nitrogen and phosphorus; besides, the advantages of this system include robust configuration and excellent performance on the nutrient removal.

Nitrogen removal from poultry slaughterhouse wastewater in anaerobic-anoxic-aerobic combined reactor: Integrated effect of recirculation rate and hydraulic retention time.

The aim of this work was to assess the nitrogen removal from slaughterhouse wastewater in an anaerobic-anoxic-aerobic combined reactor, evaluating the integrated effect of recirculation rate and hydraulic retention time. The recirculation of the liquid phase from the aerobic zone to the anoxic zone was applied to promote the denitrification through the use of endogenous electron donors. Three recirculation rates (R: 0.5, 1 and 2) and three hydraulic retention times (14, 11 and 8 h) were applied. The operation of the reactor was divided into 3 steps (I, II, and III) according to the factors evaluated (recirculation rate and HRT), to achieve operational conditions that would allow satisfactory performance in the different compartments of the reactor. During the experiment the reactor was fed with average total nitrogen (TN) and chemical oxygen demand (COD) of 65 mg L-1 and 580 mg L-1, respectively. The denitrification efficiency (theoretical) and kinetics parameters for COD decay were calculated. The highest performance was verified in the Step III (R = 2) and HRT of 11 h with NH4+ and TN removals of 84% and 65%, respectively. The TN removal efficiency (65%) was considered satisfactory, since the theoretical denitrification efficiency expected for this condition (R = 2) is 67%, without addition of an external carbon source. The lowest nitrification efficiency values were obtained in HRT of 8 h in the Step I and II (R = 0.5 and 1, respectively), indicating that the nitrification time (3 h - aerobic phase) may be the limiting factor in this HRT. The COD removal efficiency was high in all assays (>95%). The values of the kinetic degradation constants of organic matter were close for all recirculation rates, and the highest values were recorded for the HRT of 8 h and R = 1 and R = 2 (-0.48 and -0.43, respectively).

Influence of the flooded time on the performance of a tidal flow constructed wetland treating urban stream water.

A vertical subsuperficial tidal flow constructed wetland (TFCW) operated under flooded time (FT) variation, was evaluated in the removal of carbonaceous, nitrogenous, and phosphorous matter from urban stream water. The TFCW downflow (117 L) was filled with bricks (44% porosity) and vegetated with Althernanthera philoxeroides (32 plants m-2). The TFCW was operated under different flooded times - Stage A (48 h), B (36 h), C (24 h), and D (12 h), organic loading rates of 19.58-43.83 gCOD m-2 d-1, 3.68-6.94 gTN m-2 d-1 and 0.93-2.00 gTP m-2 d-1 and volumetric load rates of 46.8, 58.5, 78.0 and 11.7 L d-1. No significant differences were observed in the removal efficiencies to Chemical Oxygen Demand (COD 66 to 94%), Total Ammonia Nitrogen (TAN 58 to 87%), and Total Nitrogen (TN 53 to 78%) among the stages, and nitrate concentrations lower than 6 mg L-1 in the effluent. High Total Phosphorus removal was obtained in FT of 48 h (TP 79%). Total phosphorus loading rate was a limiting factor in TP removal, which reduced along with the reduction of FT. The nitrifying community was present over time since ammonia-oxidizing bacteria (Nitrosospira) and nitrite-oxidizing bacteria (Nitrobacter and Nitrospira) were identified in operational stages with variation in relative abundance, but TAN removal efficiency did not show significant differences. There was no change in the denitrifying community structure, indicating that FT did not influence the TN removal. A. philoxeroides was responsible for phytoextraction of 2.1% of TN and 2.7% of TP from the total removed by TFCW. TN removal (65%) was attributed to adsorption in the filtering material and microbial metabolism during the rest time. The findings of this study suggest FT of 12 h to remove COD and TN, and equal to or higher than 48 h to remove TP.

Construction waste as substrate in vertical subsuperficial constructed wetlands treating organic matter, ibuprofenhene, acetaminophen and ethinylestradiol from low-strength synthetic wastewater.

This study aimed to evaluate the removal of chemical oxygen demand (COD), total Kjeldahl nitrogen (TKN), total ammonia nitrogen (TAN), total phosphorus (TP), ibuprofen, acetaminophen and ethinylestradiol of synthetic effluent simulating low-strength sewage by sequencing-batch mode constructed wetlands (CWs). To verify the feasibility of using a floating macrophyte in CWs and compare different substrates, three CWs containing light expanded clay aggregates (CWL), expanded clay with porcelain tiles (CWLP) and bricks (CWB) were planted with Pistia stratiotes. The results showed that CWB achieved the highest removals of TKN (78%), TAN (70%) and TP (46%), and CWLP achieved the highest COD removal (75%). LECA favored the removal of ibuprofen (92%, p < 0.05) when compared to bricks (77%), probably by the combination of biodegradation and sorption in the systems. The highest acetaminophen removal (71% to 96%) was observed in CWL, probably via biodegradation, but no significant differences were found between the CWs (p > 0.05). Ethinylestradiol was removed 76% in CWLP and 73% in CWB, both differing statistically from CWL (p < 0.05), demonstrating that brick and the combination of clay with porcelain were better than just clay in this hormone removal. After 188 days of operation, P. stratiotes was able to uptake nitrogen and phosphorus of approximately 0.28 g and 0.25 g in CWL, 0.33 g and 0.21 g CWLP, and 0.22 g and 0.09 g in CWB of, respectively. Adsorption of nitrogen and phosphorus onto the substrates was 0.48 g and 6.84 g in CWL, 0.53 g and 5.69 g in CWLP, and 0.36 g and 10.18 g in CWB, respectively. The findings on this study suggest that adsorption was possible the main process for TP removal onto the evaluated substrates whereas microbial activity was the most probable mechanism for TN removal in the evaluated CW systems.

Anaerobic co-digestion of industrial landfill leachate and glycerin: methanogenic potential, organic matter removal and process optimization.

The objective of this study was to evaluate the performance of the anaerobic co-digestion of different concentrations of industrial landfill leachate associated with crude residual glycerin, in relation to the methanogenic potential, COD removal, accumulated methane production, the effects of the factors (food/microorganism ratio and percentage of glycerin added to the leachate) and their interactions on kinetic parameters of methane production (CH4) using the modified Gompertz model. Co-digestion tests were carried out in bench scale (400 mL of useful volume) under batch mode at 30 ± 1°C during 30-day incubation of anaerobic sewage sludge as inoculum. The parameters glycerin addition to the leachate (v/v) (0%, 1.5%, 5%, 8.5% and 10%) and F/M ratio (0.3, 0.5, 1, 1.5 and 1.7) were investigated using Central Composite Rotational Design method (CCRD). The results indicated significant effect to the response variables: methanogenic potential, COD removal, accumulated production of CH4 and maximum estimated production of CH4, considering a confidence interval of 95% (p < .05). The ideal mixture of 95.13% of leachate with 4.87% of raw glycerin was obtained by desirability test to F/M of 1.61 gCOD of substrate per gVSS (volatile suspended solids) of sludge. Methanogenic potential was 0.19 LNCH4 gTVSrem -1, and the average removal of COD was 92%, resulting in accumulated production and maximum estimated production of CH4 of 74 and 80 mL, respectively. It was noted that the process of co-digestion of the industrial landfill leachate with the crude residual glycerin is promising, due to is potential of complementing and balancing organic materials, nutrients and other components that influence the biological process. Abbreviations: AN: ammoniacal nitrogen; BMP: biochemical methane potential; CCRD: central composite rotational design; COD: chemical oxygen demand; F/M ratio: food/microorganism ratio; FSS: fixed suspended solids; NTP: normal temperature and pressure; TSS: total suspended solids; TA: total alkalinity; TFS: total fixed solids; TKN: total Kjeldahl nitrogen; TP: total phosphorus; TS: total solids; TVA: total volatile acids; TVS: total volatile solids; VSS: volatile suspended solids; WWTP: wastewater treatment plant.

Materiais alternativos como meio suporte de filtros anaeróbios para tratamento de esgoto sanitário sintético / Alternative materials as support medium of anaerobic filters for the treatment of synthetic sanitary sewage

RESUMO O tipo de material utilizado como recheio em filtros anaeróbios pode ser determinante na eficiência do tratamento, então a avaliação de novos materiais se torna importante. Assim, o objetivo deste trabalho foi estudar o comportamento de três filtros anaeróbios de fluxo ascendente, operados de modo contínuo, preenchidos com carvão ativado, cerâmica de argila e borracha de pneu, no tratamento de água residuária sintética com glicose como substrato. Os filtros, em escala de bancada (1,3 L), foram operados com tempo de detenção hidráulica (TDH) de oito e quatro horas, em duas etapas. Seu desempenho, avaliado com o emprego dos parâmetros pH, alcalinidade total e bicarbonato e ácidos voláteis, foi estável nas duas etapas de operação. O filtro que obteve maior eficiência em termos de remoção de demanda química de oxigênio (DQO) foi o com carvão ativado, 94 e 81% nas etapas I e II, respectivamente, seguido do com borracha de pneu, 88 e 63%, e do com cerâmica de argila, 81 e 61%, ambos nas etapas I e II, respectivamente. As principais morfologias encontradas nos meios suportes foram bacilos, cocos, filamentos, Methanosaeta sp. e Methanosarcina sp. As diferenças obtidas entre os filtros podem ser relacionadas com as características distintas de cada material utilizado como meio suporte, e as diferenças entre as etapas ocorrem pelo aumento da carga hidráulica, que diminui o tempo de retenção celular, assim como eventuais diferenças de temperatura.

ABSTRACT The type of material used as packing in anaerobic filters may be a determinant factor in the treatment efficiency, so the evaluation of new materials is important. Thus, the objective of this study was to study the behavior of three upflow anaerobic filters, filled with charcoal, clay pottery and tire rubber, in the treatment of synthetic wastewater with glucose as substrate. The filter, in bench scale (1.3 L), was operated at a HRT of 8 and 4 hours, in two phases. The performance of the filters, in terms of pH, total alkalinity and bicarbonate and volatile acids was stable during the two operational phases. The best filter in terms of COD removal efficiency was the one with activated carbon, 94 and 81%, in Phases I and II, respectively, followed by tire rubber filter, 88 and 63%. The lowest efficiency obtained was the ceramic clay filter, with 81 and 61%, in Phases I and II, respectively. The main morphologies found were bacilli, cocci, filaments, Methanosaeta sp. and Methanosarcina sp. The differences obtained between filters are related to the different characteristics of each material, and the differences between phases are due to the hydraulic load increase and subsequent cellular retention time decrease, as well as an eventual temperature difference.

Avaliação do comportamento hidrodinâmico de reator anaeróbio de manta de lodo e fluxo ascendente com diferentes configurações do sistema de distribuição do afluente utilizando fluidodinâmica computacional / Hydrodynamic performance evaluation of an upflow anaerobic sludge blanket reactor with different configurations of the influent distribution system using computational fluid dynamics

RESUMO Compreender o comportamento hidrodinâmico de reatores biológicos pode auxiliar na detecção de problemas associados a falhas operacionais e de projeto, situações que prejudicam a eficiência do tratamento. Neste artigo, realizaram-se simulações da fluidodinâmica computacional (CFD) de escoamento de duas fases sólida-líquida de um reator anaeróbio de manta de lodo e fluxo ascendente (UASB), em escala piloto (160 L), com tempo de detenção hidráulica (TDH) de 10 h e vazão de 16 L.h-1. Um modelo Euler-Euler simplificado foi formulado para simular o comportamento hidrodinâmico da zona de reação, influenciada pela configuração do sistema de distribuição do afluente. Foram avaliadas quatro configurações do sistema de distribuição do afluente no reator: uma entrada na parte central (1) e duas entradas centrais (2), de fluxo ascendente; duas entradas nas laterais (3), de fluxo radial; e três entradas de fluxo descendente (4), utilizando geometrias bidimensionais e tridimensionais para verificar a formação de zonas mortas, curtos-circuitos hidráulicos e caminhos preferenciais. As melhores características hidrodinâmicas e a melhor distribuição do afluente foram verificadas na configuração 4, com melhor perfil de mistura do lodo com a fase líquida, na comparação com as demais configurações. Foi notada formação de vórtices na parte inferior do reator com maior concentração do lodo anaeróbio nessa configuração e de caminhos preferenciais nas laterais do reator na configuração 3, indicando mistura ineficiente do afluente com o lodo anaeróbio. O modelo demonstrou que a configuração do sistema de distribuição do afluente influencia significativamente o comportamento hidrodinâmico do reator UASB.

ABSTRACT Understanding the hydrodynamics behavior of biological reactors can help in the detection of problems related to operational failures and design that adversely affect the efficiency of the treatment. In this paper, computational fluid dynamics (CFD) simulations of two-phase liquid-solid flow were carried out in an upflow anaerobic sludge blanket reactor in pilot scale (160 L), with hydraulic retention time (HRT) of 10 h and flowrate 16 L.h-1. The Euler-Euler approach was formulated to simulate the reaction zone hydrodynamics. Four configurations of the influent distribution system in the reactor were evaluated: one central inlet (1) and two central inlets (2), upflow; two lateral inlets (3), radial flow; and three inlets, downflow (4), using two and three-dimensional geometries to verify the formation of dead zones, hydraulic short-circuiting and preferential pathways. Better influent distribution and greater mixture profile of the sludge with the liquid phase were found in the configuration 4, compared to the others by the formation of vortices in the bottom part of the reactor with higher concentration of anaerobic sludge. Formation of preferential pathways was noted in the lateral inlets of the reactor in the configuration 3, indicating an inefficient mixture of the influent with the sludge. The model demonstrates that the configuration of the influent distribution system significantly influences the hydrodynamics behavior of the UASB reactor.

Avaliação hidrodinâmica de reator UASB submetido à variação cíclica de vazão / Hydrodynamic evaluation of a UASB reactor submitted to cyclical flowrate variation

Um reator UASB em escala piloto (160 l) foi usado com o objetivo de estudar seu comportamento hidrodinâmico quando submetido a variações cíclicas senoidais da vazão afluente. Os ensaios foram realizados com traçador eosina Y para as condições operacionais: vazão média afluente constante e igual a 16 l.h-1 e tempo de detenção hidráulica de 10 h (ensaios 1 e 2), e para vazão afluente submetida à variação senoidal de 40 por cento (ensaios 3 e 4) e de 60 por cento (ensaio 5). A variação da concentração do traçador no efluente foi ajustada pelos modelos teóricos de dispersão de fluxo e de reatores em série. O reator UASB apresentou comportamento similar ao de reator de mistura completa para vazão média afluente constante e similar ao reator de fluxo pistonado com a aplicação das variações senoidais cíclicas, sendo que o modelo de pequena dispersão apresentou melhor ajuste matemático.

A bench scale UASB reactor (160 l) was used in stimulus-response assays in order to evaluate its behaviour when submitted to cyclical sinusoidal variations of the influent flow rate. Assays were carried out with eosin Y as the tracer in different operational conditions: constant mean influent flow rate of 16 l.h-1 and hydraulic residence time of 10 h (assays 1 and 2), and influent flow rate submitted to sinusoidal variation of 40 percent (assays 3 and 4) and 60 percent (assay 5). The variation of tracer concentration in the effluent was adjusted by the theoretical models of dispersion (low and high) and N-continuous stirred tank reactors in series. Complete mixture behaviour was noted to the application of the constant influent flow rate and a plug flow one to the application of the cyclical sinusoidal variations of the influent flow rate. The low dispersion model demonstrated the best mathematical adjustment in the RTD.