Granular Media Filtration Research Articles

Exploring granular filter media in sustainable drainage systems (SuDS) for stormwater pollutant adsorption: A pilot study

Granular filter media are integral to sustainable drainage systems (SuDS) for their efficiency in removing pollutants from urban runoff. This study focuses on understanding the filtration processes within these media by combining a pilot experimental study with a modeling approach. The experimental study involved characterizing the physical and hydraulic properties of various granular filter media materials, including sand, pea-gravel, gravel, and geotextile membranes. Three laboratory-scale stormwater filtration rigs were tested to evaluate the filter media's pollutant removal capacity and hydraulic performance. This work presents a phenomenological model that predicts the spatial variation in the concentrations of stormwater and urban runoff substances, specifically nitrate ions (NO3-), phosphate ions (PO43-), chemical oxygen demand (COD), and suspended solids, by studying their concentration profiles. The stormwater quality model was used to predict the concentration profiles for stormwater with an average inflow consisting of 2.9 mg/L nitrates, 3.4 mg/L phosphate ions, 225 mg/L COD, and 3.3 mg/L of suspended solids. The predicted outlet concentrations matched well with measured experimental data. The results showed that adding geotextile membranes to a granular filter significantly improves its ability to adsorb dissolved species for stormwater applications. This research highlights the importance of understanding the physical and hydraulic properties of granular filter media and their impact on stormwater pollutant removal efficiency. The developed model can assist in the design and optimization of stormwater treatment systems by predicting the performance of different filter media materials, allowing for informed decision-making and improved system functionality.

Comparative evaluation of different pre-treatment alternatives for granular media filters treating greywater and their ranking using analytical hierarchy process.

In this study, the performance of four different pre-treatment alternatives for granular media filtration, namely, settling, aeration, coarse media filtration and chemical coagulation were compared experimentally. Further, analytical hierarchy process (AHP) was used to compare their performance based on economic, environmental, technical and performance criteria. Performance of settling and aeration were evaluated up to 24 h duration. The coarse media filter was intermittently operated with 10 L of greywater in downflow mode while alum was used for chemical coagulation. Experimental results showed that settling up to 6 h did not show significant removal of different pollutants whereas 24 h settling resulted in moderate removal of turbidity and organic content but was not efficient in the removal of nutrients and faecal coliforms. Chemical coagulation reduced 93, 66, 48 and 97% of turbidity, COD, NH4-N and faecal coliforms, respectively from greywater but resulted in excessive sludge generation and is difficult to adopt on-site and requires skilled supervision. Coarse filtration of greywater resulted in 61, 41, 36 and 35% removal of turbidity, COD, PO4-P and faecal coliforms, respectively. Considering different criteria AHP gave coarse filtration as the best pre-treatment option to the granular media filters treating greywater.

Impact of harmful algal bloom severity on bacterial communities in a full-scale biological filtration system for drinking water treatment

The occurrence of harmful algal blooms (HABs) in freshwater environments has been expanded worldwide with growing frequency and severity. HABs can pose a threat to public water supplies, raising concerns about safety of treated water. Many studies have provided valuable information about the impacts of HABs and management strategies on the early-stage treatment processes (e.g., pre-oxidation and coagulation/flocculation) in conventional drinking water treatment plants (DWTPs). However, the potential effect of HAB-impacted water in the granular media filtration has not been well studied. Biologically-active filters (BAFs), which are used in drinking water treatment and rely largely on bacterial community interactions, have not been examined during HABs in full-scale DWTPs. In this study, we assessed the bacterial community structure of BAFs, functional profiles, assembly processes, and bio-interactions in the community during both severe and mild HABs. Our findings indicate that bacterial diversity in BAFs significantly decreases during severe HABs due to the predominance of bloom-associated bacteria (e.g., Spingopyxis, Porphyrobacter, and Sphingomonas). The excitation-emission matrix combined with parallel factor analysis (EEM-PARAFAC) confirmed that filter influent affected by the severe HAB contained a higher portion of protein-like substances than filter influent samples during a mild bloom. In addition, BAF community functions showed increases in metabolisms associated with intracellular algal organic matter (AOM), such as lipids and amino acids, during severe HABs. Further ecological process and network analyses revealed that severe HAB, accompanied by the abundance of bloom-associated taxa and increased nutrient availability, led to not only strong stochastic processes in the assembly process, but also a bacterial community with lower complexity in BAFs. Overall, this study provides deeper insights into BAF bacterial community structure, function, and assembly in response to HABs.

Contaminants of emerging concern reduction and microbial community characterization across a three-barrier advanced water treatment system

This research investigated the removal of contaminants of emerging concern (CECs) and characterized the microbial community across an advanced water treatment (AWT) train consisting of Coagulation/Flocculation/Clarification/Granular Media Filtration (CFCGMF), Ozone-Biological Activated Carbon Filtration (O3/BAC), Granular Activated Carbon filtration, Ultraviolet Disinfection, and Cartridge Filtration (GAC/UV/CF). The AWT train successfully met the goals of CECs and bulk organics removal. The microbial community at each treatment step of the AWT train was characterized using 16S rRNA sequencing on the Illumina MiSeq platform generated from DNA extracted from liquid and solid (treatment media) samples taken along the treatment train. Differences in the microbial community structure were observed. The dominant operational taxonomic units (OTU) decreased along the treatment train, but the treatment steps did impact the microbial community composition downstream of each unit process. These results provide insights into microbial ecology in advanced water treatment systems, which are influenced and shaped by each treatment step, the microbial community interactions, and their potential metabolic contribution to CECs degradation.

Optimize Granular Media Filtration

Effective filtration depends on a combination of complex physical and chemical mechanisms. It's important for operators to know how granular media filters work, the basics of how they are designed, and strategies for successful operation.

Backwashing of granular media filters and membranes for water treatment: a review

AbstractFilter backwashing is a supplemental part of a drinking water treatment (DWT) facility to wash the filter bed at regular intervals using water or air scour/water by fluidizing the filter bed. Deposited material induces clogging the filter pores and enhances head loss in the bed. Biofiltration has been extensively utilized to decrease organic matter and manage the occurrence of disinfection by-products within drinking water sources. Biological rapid sand filters are frequently utilized to eliminate ammonium from groundwater provinces with the purpose of meeting drinking water requirements. Biological activated carbon (BAC) filters need to be backwashed to wash and enhance the treatment capability by detaching both restrained materials and residual biomass. The reclamation of activated carbon-used backwash water (UBW) was managed by exercising an ultrafiltration (UF) procedure.

Improvements in the reduction coagulation filtration process for hexavalent chromium treatment

AbstractReduction coagulation filtration using ferrous iron (Fe(II)‐RCF), or reduction filtration using stannous tin (Sn(II)‐RF), for the removal of hexavalent chromium (Cr(VI)) from drinking water represent attractive alternatives to ion exchange or reverse osmosis. With a new maximum contaminant level for Cr(VI) anticipated in California, this study sought to expand on previous research by applying Fe(II)‐RCF and Sn(II)‐RF to multiple groundwaters under a variety of reductant dose and reduction time scenarios. Four different granular filter media were also tested for removal of total chromium (Cr(T)) following Cr(VI) reduction to trivalent chromium (Cr(III)). Sodium hypochlorite, instead of aeration, was used to oxidize excess Fe(II) to Fe(III) prior to filtration, with minimal Cr(III) to Cr(VI) reoxidation. Sn(II)‐RF was also able to achieve Cr(T) and Cr(VI) treatment goals without dedicated reduction time prior to filtration. Results of this study were used to develop more up‐to‐date, feasibility‐level, 20‐year annualized cost estimates.

Application of Palm Kernel Shell Granular Filter Medium for Decolourisation and COD Removal from Clarified Palm Oil Mill Effluent

Palm oil mill effluent (POME) is characterised by high colour, COD and solids. Extraction and drying of the suspended solids for reuse as solid fuel shows great promise. However, the clarified wastewater may require further treatment to meet discharge limits. This study was aimed at evaluating the efficiency and kinetics of COD and colour removal from clarified POME using palm kernel shell (PKS) granular filter media and a sand filter as reference. The wastewater was collected from a small-scale palm oil processing mill in the Abura Aseibu Kwamankese District of Ghana and clarified using a solid-liquid separation system. The filter media of particle size 1.18mm was packed into acrylic cylinders (6cm dia.) to a height of 35.4 cm. The characteristics of influent wastewater and filter media were determined prior to the experiment following standard methods. Each filter was run as a batch system under anaerobic conditions by maintaining a minimum supernatant height of 10cm. Effluents were drawn from the bottom of each filter after 0, 24, 48, 72, 96, and 120 h for analysis using standard analytical methods. The removal efficiencies for the PKS and sand filters were, respectively, 77% and 79% for COD and 69% and 62% for colour. The COD removal was consistent with first-order kinetics for both PKS and sand filters. However, colour removal in PKS and sand filters followed second- and zero-order kinetics respectively. The correlation coefficients of the selected kinetic models show a strong correlation between the experimental and predicted results. Further research is required to establish the retention time required to bring the pollutant levels below the allowable limits for discharge into the environment.

Media coalescence filtration as a novel method for pretreatment of refinery wastewater

Refinery wastewater is not only large in volume but also complex in composition. It requires multi-stage treatment to achieve discharge or reuse targets. Pretreatment plays an important role as a front-end treatment. In conventional pretreatment technologies, petroleum removal and suspension removal are carried out through inclined plate settlement combined with two-stage air flotation. This poses problems such as high energy and chemical consumption and large outputs of hazardous waste. In this study, a short-process physical pretreatment technology is designed in conjunction with combined fiber coalescer (CFC) and granular media filter (GMF). The results of the pilot test show that with no added chemicals, the treated refinery wastewater is clear and translucent, and the petroleum and suspended solids content could be reduced to less than 20 mg/L, which falls within the acceptable range of the biochemical influent index. This process could greatly reduce the generation and emission of scum and volatile organic compounds (VOCs) and provides a new technique for the low-carbon pretreatment of refinery wastewater.

Application of combined granular media with opposite wettability for demulsification of oily wastewater by microchannel filter

Oil-water separation with high efficiency and low energy consumption is a tremendous challenge in the green treatment of oily wastewater. In this paper, a novel filtration method with combined granular media for collaborative removal emulsified oil and suspended solids (SS) was proposed, followed by the exploration of demulsification feasibility and oil removal mechanism. The effect of the operation and structural parameters of the filter bed on oil separation performance was thoroughly investigated, and its feasibility for raw oily wastewater treatment was also explored. A remarkable demulsification performance was observed with the combined granular media filter, and a balance of separation efficiency and pressure drop in the emulsified oily wastewater filtration was also achieved subsequently. Effective oil droplet capture and coalescence were observed with a high speed camera system, and pore clogging could be avoided in combined media. The optimal parameters of the combined media filter (CMF) were concluded to be a combined media ratio of 1:1, a superficial velocity of 0.20 m min−1, and a bed porosity of 58.1%. The average oil and suspended solids concentrations in raw oily wastewater was decreased to 8.4 mg/L and 23.3 mg/L during the pilot-scale operation, which indicated that the novel filter composed of combined media had better performance in collaboratively removing oil and SS, even in the period of fluctuating influent parameters. It is believed that a novel and efficient oil removal method, especially including of emulsified oil removal was provided, which also shows great potential and value for the green treatment of industrial oily wastewater.

Bed expansion at backwashing in pressurised porous media filters for drip irrigation: Numerical simulations and analytical equations

Actions for improving the energy efficiency of pressurised porous media filters used in drip micro-irrigation require methods to properly determine the behaviour of both filtration and backwashing modes. The latter is essentially a fluidisation process. Though many authors have analysed fluidised bed columns, very few studies have dealt with the backwashing of granular media filters used in agriculture. The purpose of the present work was 1) to validate a computational fluid dynamics (CFD) model to simulate the backwashing regime, and 2) to assess the extent of analytical expressions for determining the expanded bed height. Experimental data were obtained using a laboratory filter for two types of porous media at superficial velocities <150 m h −1 . The CFD model used the Eulerian–Eulerian approach, and its sensitivity was investigated in a simplified two-dimensional domain. A modified three-dimensional model effectively reproduced the bed expansion for most of the experimental conditions using large time steps (0.025 s) and few internal iterations (20). Well-known analytical equations overestimated the expanded bed height at superficial velocities <150 m h −1 , but the recent RIO 1 model proposed by Kramer et al. (2020) showed very good predictive capacities. Two analytical expressions based on basic principles were developed, providing a trend which was also close to observations and a lower bound for the expanded bed height value. These conclusions were confirmed by analysing external data obtained using commercial pressurised sand filters. • The backwashing mode of a pressurised granular media filter was investigated. • The CFD model reproduced the fluidised bed behavior for superficial velocities <150 m h −1 . • The set-up of the CFD model required a case-by-case analysis. • A new analytical equation to determine the expanded bed height was obtained. • An equation to estimate the minimum expanded bed height was developed.

Environmental Assessment of Underdrain Designs for Granular Media Filters in Drip Irrigation Systems

Irrigation is very important for global food production and, therefore, it is key to moving towards increasingly sustainable irrigation systems. However, the adoption of more efficient water-use techniques, such as drip irrigation, increases energy consumption. A large part of the efficiency of drip irrigation systems depends on the equipment used, such as filters. The environmental impact of three media filters (a prototype with a porous media underdrain and two commercial filters, with inserted domes and collector arms underdrains, respectively) with different bed heights, filtration rates, and medium materials was studied using the life cycle analysis (LCA). Under the operating conditions that minimize the impact, the inserted domes design has the lowest overall impact, achieving reductions of up to 432% and 18% in some impacts regarding the porous media and the collector arm, respectively. A porous media filter has a better energy performance, but its prototype status hinders it in the raw material, building, and end-of-life phases. Conversely, the arm collector has the worst environmental performance. This work shows that filter designs should prioritize solutions that allow for minimizing the energy consumption during their operation to increase its sustainability.

Microbial community characterization in advanced water reclamation for potable reuse.

This study investigated the microbial community structure and composition across two treatment steps used in advanced water reclamation for potable reuse applications, namely Coagulation/Flocculation/Clarification/Granular Media Filtration (CFCGMF) and Ozone-Biological Activated Carbon filtration (O3/BAC). The study examined the richness, variations, and similarities of the microorganisms involved at each treatment step to better understand the role of ecology and the dynamics on unit process performance and the microbial community developed within it. The bacterial microbiomes at each treatment step were independently characterized using 16S metagenomic sequencing. Combining both treatment steps, a total of 3801 species were detected. From the total species detected, 38% and 98% were identified at CFCGMF and O3/BAC, respectively. The most abundant phyla were Proteobacteria, Bacteroidetes, Actinobacteria, and Firmicutes in both treatment steps. The identified species were classified based on their preferences to free-living style (59%) vs attached-living style (22%) showing a relatively low richness in the BAC media, but higher diversities. At the taxonomic class level, Betaproteobacteria was the predominant in both system processes. Additionally, a list of eight genera were identified as potential bacterial pathogens present in both process effluents. They are Aeromonas, Clostridium, Enterobacter, Escherichia, Flavobacterium, Legionella, Mycobacterium, and Pseudomonas. CFCGMF effluent yielded less pathogenic bacteria than both the ozone and BAC filter effluent from the O3/BAC process unit; their relative abundance accounted for about 2% and 8% for CFCGMF and O3/BAC, respectively. Detailed studies to characterize the microbial communities are crucial in interpreting the mechanisms and synergies between processes performance and microorganisms by identifying the needs and best practices to ensure public health protection. Key points • Microbial communities of two treatment processes are characterized using 16S rRNA sequencing. • Organisms that can tolerate ozone and form biofilms define microbial community in subsequent biofilters. • In relatively low abundances, potential pathogenic bacteria are detected in the treated water.

Cryptosporidium surrogate removal in pilot-scale rapid sand filters comprising anthracite, pumice or engineered ceramic granular media, and its correlation with turbidity

Removal of Cryptosporidium protozoa by granular media filtration is a critical step in conventional multi-barrier drinking-water treatment, and turbidity is commonly used to monitor system performance. We assessed the efficiencies of 3 different filter media at removing a Cryptosporidium parvum surrogate comprising glycoprotein-coated 4.5 μm polystyrene microspheres, and evaluated the responses of turbidity levels to surrogate concentrations. Field trials were performed using pilot-scale rapid sand filters comprising anthracite, pumice or engineered ceramic sand, while simulating a typical water treatment plant's operational conditions. Data from 44 trials indicated that the surrogate's log10 reduction values (LRVs) based on the peak concentrations were >3 in 100%, 70% and 41% of the trials with the ceramic sand, pumice sand and anthracite filters, respectively. The LRVs achieved in the ceramic sand filter trials (4.44 ± 0.38) were significantly greater than those in the pumice sand (3.21 ± 0.30) and anthracite (3.01 ± 0.70) filter trials (P < 0.00001).Correlations (P < 0.05) between turbidity levels and surrogate concentrations were observed in 17%, 44% and 29% of 51 trials involving the ceramic sand, pumice sand and anthracite filters, respectively. At peak surrogate breakthrough, the filtered water contained hundreds to thousands of surrogate particles/L, but the turbidity levels were <0.1 NTU in 63% and 71% of the trials with pumice and anthracite filters, respectively. In contrast, despite the ceramic sand filter achieving LRVs >3 consistently, the peak turbidity levels exceeded 0.30 NTU in 17% of the trials. Our findings highlight the need to introduce supplementary tools alongside turbidity to monitor filter performance more sensitively.

Modeling of the Suspended Solid Removal of a Granular Media Layer in an Upflow Stormwater Runoff Filtration System

Upflow granular media filtration devices are widely used for stormwater runoff treatment. However, the system performance is not well characterized due to the irregular removal of suspended solid (SS) in the pretreatment (sedimentation) chamber and, hence, its irregular input to the media layer. In this regard, the performance of the granular media layer of an upflow filtration system is investigated herein by the use of various models. Due to the significant variation in the SS concentration of the influent and effluent to and from the media layer, the deep bed filtration model, the k-C* model, and the porous media capture model provide limited descriptions of the system performance. By contrast, the performance is well described using the kinetic model, the modified k-C* model using a specific deposit, and the modified porous media capture model using a specific deposit. The parameters of the latter models are shown to be in good correlation with the filtration velocity, SS removal, and specific deposit. The results suggest that modeling using a specific SS deposit can provide an accurate description of the granular media layer performance under a highly variable influent SS concentration.

고율하수처리를 위한 생물막여과와 분리막 연계시스템 구성

Compared with the conventional MBR, granular sludge MBR due to the reactor compact design, outstanding settleability, and the ability of granules to withstand high organic loading rate has emerged with strong potential to overcome membrane fouling. The objective of this study is to configure an high-rate system using granular sludge sequencing batch reactor (GSSBR) and granular media filter (GMF) using sand and granular activated carbon (GAC)) coupled with membrane for enhancing membrane filtration performance and reducing membrane fouling in treating wastewater. As a result, GSSBR/GMF/MF configured system achieved higher efficiency than GSSBR-MBR and GSSBR/MF systems in reducing total organic carbon (TOC), total nitrogen (T-N) and total phosphorus (T-P), respectively. For transmembrane pressure (TMP), the GSSBR/GMP/MF developed much lower than that of GSSBR-MBR. In particular, the GSSBR/sand filter/MF system achieved lower TMP build-up than that of the GSSBR/GAC filter/MF system The above results indicate the GSSBR-MF coupled with GMF is more effective than conventional MBR using activated sludge in mitigating membrane fouling. The food/microorganism (F/M) ratio in the GSSBR and the biofilm growth in the GMF play an important role to reduce contaminants and TMP build-up.

Substituting polyacrylamide with an activated starch polymer during ballasted flocculation

Synthetic polymers, mostly polyacrylamides (PAMs), are frequently used in the water industry to improve the performance of clarification. However, synthetic polymers may increase headloss in granular media filters, biodegrade slowly, and are potentially toxic. Alternatively, bio-sourced starch-based polymers may eliminate the drawbacks of synthetic flocculants. Similarly to poly(acrylamide‐co‐acrylic acid), carboxymethylated starch is expected to adsorb on metal hydroxides via hydrogen bonding on carboxyl groups. However, it is already known that starch, like many other polysaccharide flocculants, is required in higher dosages for its performance to be comparable to PAM. This study identified the conditions favorable to the use of an activated starch polymer as an alternative to PAM during ballasted flocculation: mixing intensity and time, coagulation pH, ballast size and chemical composition, and polymer charge density. Ultimately, under optimal conditions, only 0.66 mg of activated starch/L was required to reach the settled water turbidity objective of 1 NTU.

On the backwash expansion of graded filter media

Granular media filtration is one of the most important and commonly used operations in water treatment and is also widely used for advanced wastewater treatment. Successful filter design requires a correct specification of backwash rates for filter cleaning. Significant progress has been made in recent years towards a capability of accurate predictions of backwash expansion of uniform (sieved) fractions of nonporous and porous nonspherical media. Graded filter media, however, have not been studied in a systematic and satisfactory way so far. Current design calculations consider a bed with a size gradation to consist of several layers of approximately uniform size according to the sieve analysis data, and the expansion of each layer is separately calculated. The total expansion is calculated by adding the expansions of all the layers. The present work evaluates the accuracy of this approach and a number of alternative calculation methods by carrying out fluidization experiments with actual filter media including silica sand, garnet sand, perlite, crushed recycled glass, activated carbon, anthracite coal, and zeolite.

Characterization and Laboratory-Scale Treatment of Municipal Drainage Wastewater of Khulna, Bangladesh

The study was conducted to characterize and perform laboratory-scale treatment of municipal drainage wastewater of Khulna, Bangladesh. Wastewater samples were collected from three different points of existing urban drain outlets into the Mayur River around Khulna. Laboratory testing shows the BOD5 and COD concentration of wastewater samples varied from 57 - 226 mg/l and 320 - 435 mg/l, respectively, and the total dissolved solids ranged from 1800 - 2525 mg/l. Therefore, a laboratory-scale treatment technology was developed to treat this wastewater. Treatment technologies adopted were primary sedimentation, followed by aeration, chemical precipitation and filtration. In treated wastewater, BOD5, COD and TDS were found to be in the range of 40 - 115 mg/l, 160 - 256 mg/l and 1356 - 1500 mg/l, respectively. These test results suggest that the performance of laboratory-scale treatment plant was not adequate to fulfil the acceptable limit (ECR’97) for safe disposal into surface water bodies. Due to poor quality of effluents, modification of laboratory-scale treatment plant was made by an activated sludge process followed by granular media filtration. The final BOD5, COD TDS and TSS concentration of effluents was found to be 1.38 - 9.8 mg/l, 32 - 192 mg/l, 590 - 1667 mg/l, and 35 - 95 mg/l respectively, which satisfy ECR’97 standard limits for safe disposal into inland water bodies.

Remediation of incomplete nitrification and capacity increase of biofilters at different drinking water treatment plants through copper dosing.

Drinking water treatment plants based on groundwater may suffer from incomplete ammonium removal, which deteriorates drinking water quality and constrains water utilities in the operation of their plants. Ammonium is normally removed through nitrification in biological granular media filters, and recent studies have demonstrated that dosing of copper can stimulate the removal of ammonium. Here, we investigated if copper dosing could generically improve ammonium removal of biofilters, at treatment plants with different characteristics. Copper was dosed at ≤1.5 μg Cu/L to biofilters at 10 groundwater treatment plants, all of which had displayed several years of incomplete nitrification. Plants exceeded the Danish national water quality standard of 0.05 mg NH4+/L by a factor of 2-12. Within only 2-3 weeks of dosing, ammonium removal rates increased significantly (up to 150%). Nitrification was fully established, with ammonium effluent concentrations of <0.01 mg NH4+-N/L at most plants, regardless of the differences in raw water chemistry, ammonium loading rates, filter design and operation, or treatment plant configuration. However, for filters without primary filtration, it took longer time to reach complete ammonium removal than for filters receiving prefiltered water, likely due to sorption of copper to iron oxides, at plants without prefiltration. With complete ammonium removal, we subjected two plants to short-term loading rate upshifts, to examine the filters' ability to cope with loading rate variations. After 2 months of dosing and an average loading rate of 1.0 g NH4+-N/m3 filter material/h, the loading rate was upshifted by 50%. Yet, a filter managed to completely remove all the influent ammonium, showing that with copper dosing the filter had extra capacity to remove ammonium even beyond its normal loading rates. Depth sampling revealed that the ammonium removal rate of the filter's upper 10 cm increased more than 7-fold from 0.67 to 4.90 g NH4+-N/m3/h, and that nitrite produced from increased ammonium oxidation was completely oxidized further to nitrate. Hence, no problems with nitrite accumulation or breakthrough occurred. Overall, copper dosing generically enhanced nitrification efficiency and allowed a range of quite different plants to meet water quality standards, even at increased loading rates. The capacity increase is highly relevant in practice, as it makes filters more robust towards sudden ammonium loading rate variations.