Gypsum Scaling Research Articles

Insights into iron-accelerated gypsum scaling mitigation strategies in nanofiltration membrane process

In this study, the impact of ferric ions on gypsum crystallization and NF membrane performance was investigated to mitigate iron-accelerated gypsum scaling. Gypsum scaling in the presence of ferric ions led to a significant decline in the water flux, but a relatively higher reversible fouling ratio was observed compared to that under individual gypsum and iron-oxide scaling. Ferric ions influenced the crystallization of gypsum on NF membranes by serving as additional nucleation sites, leading to accelerated gypsum scaling. Various mitigation methods (e.g., feed spacers and cleaning processes) were evaluated to effectively control iron-accelerated gypsum scaling. The introduction of spacers exhibited a high mitigation efficiency by enhancing the mass transfer of scalant ions due to changes in the water channel hydrodynamics, but the overall efficiency decreased over time. To enhance the mitigation efficiency, different cleaning methods (e.g., CO2 oversaturated solution, HCl, and NaCl flushing) were conducted with feed spacers. A CO2 saturated solution demonstrated high cleaning efficiency owing to the high turbulence induced by CO2 bubbles, whereas HCl flushing showed negligible efficiency. NaCl flushing exhibited the highest cleaning efficiency through mono/divalent ion-exchange effects on iron-gypsum scaling. This study provides comprehensive insights into iron-accelerated gypsum scaling mitigation strategies for nanofiltration membranes, highlighting the impact of coexisting ferric compounds on gypsum scaling.

Protein-Decorated Reverse Osmosis Membranes with High Gypsum Scaling Resistance

Protein-Decorated Reverse Osmosis Membranes with High Gypsum Scaling Resistance

High-Performance Nanofiltration Membrane with Dual Resistance to Gypsum Scaling and Biofouling for Enhanced Water Purification.

Nanofiltration (NF) technology is pivotal for ensuring a sustainable and reliable supply of clean water. To address the critical need for advanced thin-film composite (TFC) polyamide (PA) membranes with exceptional permselectivity and fouling resistance for emerging contaminant purification, we introduce a novel high-performance NF membrane. This membrane features a selective polypiperazine (PIP) layer functionalized with amino-containing quaternary ammonium compounds (QACs) through an in situ interfacial polycondensation reaction. Our investigation demonstrated that precise QAC functionalization enabled the construction of the selective PA layer with increased surface area, enhanced microporosity, stronger electronegativity, and reduced thickness compared to the control PIP membrane. As a result, the QAC NF membrane exhibited an approximately 51% increase in water permeance compared to the control PIP membrane, while achieving superior retention capabilities for divalent salts (>99%) and emerging organic contaminants (>90%). Furthermore, the incorporation of QACs into the PIP selective layer was proved to be effective in mitigating mineral scaling by allowing selective passage of scale-forming cations, while simultaneously exhibiting strong antimicrobial properties to combat biofouling. The in situ QAC incorporation strategy presented in this study provides valuable guidelines for the fit-for-purpose design of the selective PA layer, which is crucial for the development of high-performance NF membranes for efficient water purification.

In-line granular filtration for mitigating gypsum scaling in membrane distillation

Mineral scaling and scaling-induced wetting are major challenges for the widespread application of membrane distillation (MD) in saline wastewater treatment. For the first time, an in-line modified activated alumina (AA) granular filtration coupled with MD process was proposed to achieve effective control of gypsum scaling. Firstly, the AA modified by NaOH impregnation with tuned pore structure and surface characteristics were supplied as the filter media. The optimized MD performance was obtained using in-line filtration with modified AA (MAA) with 20 g/L NaOH and the ratio of AA and NaOH solution of 1:3 for the duration of 24 h. Compared with severe scaling without granular filter, the optimized performance with a final normalized flux higher than 0.7 and a permeate conductivity less than 5 μS/cm at 70 % water recovery was observed. The MAA with rich pore, scale-like structures and high Na loading showed a superior ability in capturing gypsum scaling due to the enhanced heterogeneous scaling and the retention of scaling. In-line granular filtration-MD was also effective in mitigating gypsum scaling and scaling-induced wetting in saline solutions (e.g., 7–12 g/L NaCl). Our findings provide guidance for surface design of granular filter media and scaling control in membrane desalination technology.

Sacrificial MoS2-Polyelectrolyte membranes for fouling control in nanofiltration and reverse osmosis

Sacrificial membranes have emerged as a promising solution to mitigate membrane fouling through their ability to be removed and regenerated while preserving membrane integrity and performance. In this study, we synthesized sacrificial trilayers on a commercial polyamide nanofiltration membrane using layer-by-layer (LbL) assembly of two-dimensional molybdenum disulfide (MoS2) nanosheets and polyelectrolytes. Quartz crystal microbalance with dissipation (QCM-D) studies showed the trilayers to be MoS2-dominant by mass and have a total areal density of 2.37 μg/cm2 after the deposition of two trilayers. The trilayer membrane showed a slight decrease in water permeability and an increase in calcium chloride rejection compared to the pristine nanofiltration membrane. The trilayer membrane demonstrated improved organic fouling resistance over the pristine nanofiltration membrane, maintaining permeability throughout six consecutive cycles. Interestingly, the trilayer membrane after gypsum scaling exhibited sacrificial layer removal and permeability recovery with simple hydraulic cleaning. This suggests the potential for membrane regeneration and sustained fouling resistance that may be achieved by utilizing disruptive interactions with the trilayer materials. In conclusion, sacrificial membranes made of MoS2 nanosheets and polyelectrolytes exhibited excellent organic and inorganic fouling resistance and promising potential for layer removal and regeneration.

Impacts of distinct residual aluminum on gypsum scaling in nanofiltration: Identification of key species

Membrane scaling severely hinders practical application of nanofiltration (NF) for brackish water treatment. However, the contributions of residual aluminum (Al), especially various species with differing polymerization degrees and sizes, to gypsum scaling remain unclear. Herein, the complex interactions between three Al species (AlCl3, Al13 and Al30) and gypsum scaling were investigated, including surface and bulk crystallization processes. Results demonstrated that Al species adhering to the membrane surface promoted surface crystallization and altered crystal morphology. Notably, the Al13 species induced the formation of dense, complete rosette crystals causing the most severe flux decline. For bulk crystallization, Al30 was the primary species to promote nucleation. This promotion resulted from two factors: a lower nucleation energy barrier and the promoted aggregation of small crystals. Furthermore, molecular dynamics (MD) simulations revealed that the inhibition of nucleation due to the competition between Al species and calcium ions at nucleation sites was negligible compared to the strong promotion effect. These findings demonstrated that PACl exhibit higher scaling potential during NF than monomeric Al coagulants. Ultimately, the competition between surface and bulk crystallization determined the final membrane flux decline. This study offers valuable insights into the mechanisms of NF scaling caused by residual Al and guides mitigation strategies.

Functional of thin-film composite Janus membrane with sacrificial layer for inorganic scaling control in membrane distillation

Membrane distillation technology, utilized for treating hypersaline wastewater from seawater desalination, often encounters challenges related to inorganic scaling, adversely affecting membrane performance. Herein, we introduce a innovative approach employing a sacrificial layer on the surface of Thin Film Composite (TFC) membranes to concurrently enhance inorganic scaling resistance and facilitate membrane reusability. The sacrificial layer (Fe3+-TA) consisted of tannic acid (TA) complexed with iron ions (Fe3+) and could be removed and regenerated in situ. The results demonstrated that the Fe3+-TA layer significantly improved the membrane's surface smoothness and densification, maintaining superior anti-scaling performance. The modified membrane exhibited remarkable durability, sustaining six reuse cycles with a flux recovery exceeding 97 % in gypsum scaling tests. Furthermore, the formation of new complexes during gypsum scaling tests confirmed the membrane's augmented scaling retardation capabilities. Thus, integrating of a sacrificial layer into TFC membranes presents a promising strategy for advancing membrane distillation processes in hypersaline wastewater treatment.

Mechanisms of Alleviating Gypsum Scaling by Antiscalants during Membrane Desalination: Implications on Agricultural Drainage Water Reuse

Mechanisms of Alleviating Gypsum Scaling by Antiscalants during Membrane Desalination: Implications on Agricultural Drainage Water Reuse

Mineral scaling and organic fouling in electrodialytic crystallization

The management of hypersaline brine is a critical challenge to achieving a circular water economy. Traditional brine treatment technologies mainly rely on thermal evaporation, which requires intensive energy, cost, and/or areal footprint. Electrodialytic crystallization (EDC) has been recently developed as a novel process that enables brine crystallization without evaporation. However, the potential effects of mineral scaling and organic fouling on the performance of EDC have not been revealed. In this study, we systematically investigated mineral scaling and organic fouling in EDC. We demonstrate that the ion transport and crystallization efficiencies of EDC are generally unaffected by a variety of mineral scalants and organic foulants, despite an increase of energy consumption in the presence of humic acid. Further, EDC is shown to be less susceptible to gypsum scaling than RO, mainly due to the difference in concentration polarization between these two membrane processes. To mitigate gypsum scaling in an assumptive EDC-RO treatment train towards zero liquid discharge (ZLD), polyacrylic acid (PAA) is employed as an antiscalant that prevents gypsum scaling in RO while not adversely affecting EDC performance at relatively low concentration. Our study unravels the behaviors of EDC when treating feedwater with high scaling and fouling potentials, providing valuable insights for understanding mineral scaling and organic fouling when applying an ED-based technology for hypersaline brine treatment towards ZLD.

Fouling behavior of nanofiltration membrane during the refining treatment of morphlines-dominant reverse osmosis concentrate

Nanofiltration (NF) has been proven to be with great potential for the separation of morpholines with molecular weight less than 200 Da in refining reverse osmosis concentrate (ROC), but its application is significantly restricted by the membrane fouling, which can reduce the rejection and service time. To enable the long-term operation stability of nanofiltration, this work focuses on the fouling behavior of each substance in the hydrosaline organic solution on nanofiltration membrane, aiming to give insight into the fouling mechanism. To this end, in this work, the effects of salts (i.e NaCl and Na2SO4), organic substances (including N-(2-hydroxypropyl)morpholine(NMH) and 4-morpholineacetate(MHA)) and representative divalent ions (Ca2+ and Mg2+) on the performance and physicochemical properties of DK membrane were systematically investigated. The results show that both salts and organics can induce DK membrane swelling, leading to an increase of the mean effective pore size. After the filtration of Na2SO4–NaCl–H2O, the mean pore size increased by 0.002 nm, resulting in the decrease of the removal ratio of NMH and MHA for 3.82% and 13.10%, respectively. With static adsorption of NMH and MHA, the mean pore size of DK membrane increased by 0.005 and 0.003 nm. The swelling slowed the entrance of more organic molecules into membrane pores. Among them, MHA led to the terrible irreversible pore blocking. As the concentration of Ca2+ increased, gypsum scaling was formed on the membrane surface. During this process, NMH and MHA played different roles, i.e. NMH accelerated the CaSO4 crystallization while MHA inhibited. As a conclusion, the fouling behavior of substances in the high saline organic wastewater on DK membrane were systematically revealed with the fouling mechanisms proposed, which could provide an insightful guidance for membrane fouling control and cleaning in the treatment of high salinity and organic wastewater.

Pseudo-bottle-brush decorated thin-film composite desalination membranes with ultrahigh mineral scale resistance.

High water recovery is crucial to inland desalination but is impeded by mineral scaling of the membrane. This work presents a two-step modification approach for grafting high-density zwitterionic pseudo-bottle-brushes to polyamide reverse osmosis membranes to prevent scaling during high-recovery desalination of brackish water. Increasing brush density, induced by increasing reaction time, correlated with reduced scaling. High-density grafting eliminated gypsum scaling and almost completely prevented silica scaling during desalination of synthetic brackish water at a recovery ratio of 80%. Moreover, scaling was effectively mitigated during long-term desalination of real brackish water at a recovery ratio of 90% without pretreatment or antiscalants. Molecular dynamics simulations reveal the critical dependence of the membrane's silica antiscaling ability on the degree to which the coating screens the membrane surface from readily forming silica aggregates. This finding highlights the importance of maximizing grafting density for optimal performance and advanced antiscaling properties to allow high-recovery desalination of complex salt solutions.

Nano-Engineered Polyaspartate-Coated Magnetite Scale Inhibitor: A Sustainable Solution for Efficient Gypsum Scale Control in Oilfield Operations

Nano-Engineered Polyaspartate-Coated Magnetite Scale Inhibitor: A Sustainable Solution for Efficient Gypsum Scale Control in Oilfield Operations

Selective ion permeation enables reduced combined gypsum-organic fouling of loose nanofiltration membranes

During the long-term operation of NF membranes, the occurrence of combined gypsum-organic fouling is a significant challenge. While numerous studies have focused on enhancing the fouling resistance of NF through various methods (e.g., antiscalants, pretreatment), there has been limited exploration into the correlation between its structural looseness and fouling resistance. Herein, we conducted an experimental study to evaluate the correlation by employing three NF membranes with different looseness degrees: a custom-developed loosely structured NF membrane (CLNF), the moderately loose NF270, and the tightly structured NF90. Our findings indicated that NF membranes with loose polyamide structure exhibited superior fouling resistance to gypsum scaling and combined gypsum-organic fouling, induced by model organic matters like bovine serum albumin (BSA), humic acid (HA), and sodium alginate (SA). After applying SA-coating to calibrate the surface properties of the membranes to exclude the influence of surface roughness, hydrophilicity, and functional groups, our study attributed the difference in fouling resistance to variations in ionic selectivity stemming from membrane looseness. Specifically, the primary advantage of looser polyamide NF membranes lies in enhanced Ca2+ permeation, which not only reduces the “egg-box” effect and surface foulant accumulation but also diminishes cake-enhanced concentration polarization, effectively mitigating gypsum-organic fouling. In real water testing scenarios, the enhanced fouling resistance of loose NF membranes was further affirmed. This research underscored the unexpected benefit of loose NF membranes in terms of fouling resistance, providing a novel insight for future application.

Ultrasound based technology for removal of scale from downhole production tubing, an experimental verification

Deposition and blockages due to scale formation inside the production tubing are the most common problems experienced during the production of oil and gas, and this significantly leads to a decline in the production rate. Progressive scale formation limits production which subsequently leads to abandonment of the well. There is a great cost attached to preventing the occurrence and remediation of scales. Chemical and mechanical techniques for scale removal in production tubing have drawbacks like environmental concerns, equipment damage, and incomplete removal of stubborn scale. In contrast, ultrasound-based methods offer potential benefits such as non-destructiveness, enhanced efficiency, reduced chemical usage, and increased safety for workers. Despite the extensive research about the application of ultrasound to improve oil recovery, there remains a significant gap in the comprehensive exploration of optimum ultrasound parameters (frequency, power, radiation time, interval time, and location) for the removal of in-situ built scales in a simulated production tubing under different flow rates. This study addresses this gap by investigating the impact of ultrasound parameters on its performance for removal of calcium carbonate (CaCO3) and gypsum scales in a simulated production tubing system under different flow rate (100% and 50%). The ultrasound parameters include frequency (in the range of 20 kHz–120 kHz), power (50 W and 100 W), operation time, and location (externally attached and inserted into the production tubing).Initial tests revealed that adjusting the operating frequency improves the impedance matching, resulting in enhanced scale removal. The experiments also explored the influence of flow rate on scale removal, showing a general increase in removal with higher flow rates, specially at operating frequencies 20 kHz and 28 kHz. It was also demonstrated that the higher frequencies of 40 kHz, 68 kHz, and 120 kHz exhibit limited removal efficiency. The effectiveness of scale removal exhibited nonlinear variation over time, with the 28 kHz, 100 W transducer demonstrating the most significant improvement.In-pipe ultrasonic rod, operating at a constant frequency of 26 kHz, was employed to assess its performance for scale removal. Pulsed treatment was introduced to manage rod heating issues. Results demonstrated that both interval times and flow rates influenced CaCO3 removal, with shorter intervals yielding better results. The ultrasonic rod's efficacy was also observed in removing gypsum scale layers, suggesting potential applications in treating scales with various strengths. The results of this study can contribute to a better understanding of how the frequency, power, operating time and interval, and flow rate influence ultrasonic scale removal. The experimental findings provide valuable insights in optimizing practical applications for removal of scales from production tubing.

Scaling behavior in membrane distillation: Effect of Biopolymers and Antiscalants

Fouling and scaling are inherent characteristics of membrane-based separation. They lead to a reduced membrane throughput. In the case of membrane distillation (MD), they can possibly result in pore wetting and irreversible failure to sustain the mass transfer interface. Most prior research on understanding fouling and scaling uses indirect measurements (flux) or ex-situ analyses methods (such as SEM and EDX), which limit the outcomes to indirect qualitative conclusions. Particularly, studying scaling tends to be more challenging due to the complexity of the experiments and the method of investigation; it is imperative to distinguish the contributions from the bulk phase and heterogeneous nucleation. In this work, we established a non-invasive, in-situ, real-time imaging experimental apparatus to study the scaling mechanism. Our experimental setup assisted us in distinguishing distinct phases of scaling during the filtration tests. We studied the scaling mechanism of various single-component systems (sodium chloride, strontium sulfate, calcium sulfate, and calcium carbonate) in vacuum MD filtration. The effect of natural organic matter and antiscalants on gypsum scaling were systematically investigated. Overall, organic fouling on the membrane surface expedited heterogeneous crystallization while decelerating crystal growth in the bulk phase. For instance, deposited humic acid (HA) on the membrane surface promoted gypsum heterogeneous nucleation on the membrane surface due to the interactions between HA carboxylic functional groups and calcium ions. The adsorption of HA on the salt crystal also decelerated crystal growth in the bulk phase. Antiscalants delayed and decelerated both crystal nucleation and crystal growth. PAA, a polycarboxylate antiscalant at 5 ppm, was found to effectively delay the onset of nucleation and crystal growth in the bulk phase, while phosphorous antiscalants at 5 ppm only delayed the onset of nucleation in the bulk phase with a negligible influence on crystal growth. Real-time, in-situ, and non-invasive monitoring shed light on the scaling mechanism and can further be used to identify mitigation strategies.

Superhydrophobic composite membranes for membrane distillation based on CNTs networks: Overcoming the trade-off between water vapor permeability and wetting resistance

Enhancing the wetting resistance of the membrane is crucial for consolidating the stability of the membrane distillation (MD) process, but this generally leads to the decline of water vapor flux. Herein, we developed a superhydrophobic composite membrane composed of a highly hydrophobic polyvinylidene fluoride (PVDF) porous support layer and a functional superhydrophobic carbon nanotubes (CNTs) network. The CNTs network with high thermal conductivity not only reduces the temperature polarization effect, but also increases the effective evaporation area, thereby enhancing the mass transfer driving force of the MD process. Additionally, the CNTs network significantly reduces the maximum pore radius of the composite membrane, and the perfluorination treatment also reduces the surface energy of the CNTs network, thereby synergistically increasing the liquid entry pressure. The results showed that when treating high salinity water containing 3.5 wt% NaCl, the water vapor flux of the composite membrane increased from 20.0 LMH of the original PVDF membrane to 24.4 LMH, an increase of 22 %. Furthermore, the performance of the original PVDF membrane deteriorates rapidly when the concentration of surfactant in the feed exceeds 1.0 mM, while the composite membrane still maintains a stable water vapor permeability and salt rejection. More importantly, the composite membrane exhibits excellent resistance to wetting induced by gypsum scaling when using gypsum solution as the feed, which is attributed to its small surface pore size and high hydrophobicity. This research supplies new insights into the design of membrane structures used in MD processes to overcome the trade-off between water vapor permeability and wetting resistance.

Crossflow-induced membrane vibration and its effects on fouling and scaling in direct contact membrane distillation

Membrane distillation (MD) is driven by vapor pressures rather than hydraulic pressures. Consequently, certain regions of the membrane may be in an unrestrained state, which potentially lead to membrane vibrations due to the turbulence caused by crossflow. However, this crossflow-induced membrane vibration has been largely overlooked in the previous studies. Here, we made the first attempt to investigate the crossflow-induced membrane vibration through the observation using optical coherence tomography (OCT), and explore the effect of this vibration on membrane fouling and scaling. The experimental results revealed that the vibration exhibited a self-excited vibration mode, with amplitudes reaching tens of micrometers. Moreover, the amplitude could be readily adjusted through changing crossflow velocity, transmembrane pressure, and the mesh size of spacer. For humic acid (HA) fouling, the membrane vibration could effectively reduce the thickness of HA cake layer, thereby stabilizing the specific flux at a constant level of 0.85, in contrast to the continuous decline of the flux under non-vibration condition. For gypsum scaling, the membrane vibration allowed the MD under low crossflow velocity (5 cm/s) to achieve comparable scaling occurrence concentration and scaling layer thickness as those under high crossflow velocity (10 cm/s). Our findings emphasized the potential of crossflow-induced membrane vibration as an effective strategy to mitigate membrane fouling and scaling in MD and other non-pressure driven membrane systems.

A comprehensive study on combined organic fouling and gypsum scaling in reverse osmosis: Decoupling surface and bulk phenomena

Reverse osmosis (RO), as an energy efficient desalination technology that is critical to mitigate water scarcity, encounters feedwater containing both organic foulants and inorganic scalants. However, comparing with extensive studies on individual fouling or scaling, our knowledge of the behavior and mechanisms associated with combined organic fouling and mineral scaling is still lacking. Due to the potential occurrence of mineral formation in both bulk solution and on the membrane surface, a complete, mechanistic understanding of combined fouling and scaling requires decoupling of surface and bulk phenomena. Herein, our study employed a comprehensive investigation to delve into the intricate interplay of gypsum scaling and organic fouling in RO process. Our systematic approach is accomplished through three sets of experiments that include static experiments and two types of dynamic experiments (i.e., (1) combined fouling and scaling, and (2) gypsum scaling on foulant-conditioned membranes). A variety of model foulants including humic acid, alginate, bovine serum albumin (BSA), and lysozyme were used to investigate the effects of foulant type. Our results demonstrate that the behavior of combined organic fouling and gypsum scaling aligns more with that of gypsum scaling on foulant-conditioned membranes rather than static experiments where bulk nucleation occurs, indicating the predominance of surface nucleation in RO. BSA exhibited a remarkable hindering effect on gypsum scaling, whereas other foulants displayed an additive effect. The lack of scaling mitigation by lysozyme suggests that molecular properties of protein must play a role in regulating the behavior of combined fouling and scaling. Results from multiple characterization techniques reveal the foulant-scalant interactions by delineating the morphological and chemical features of the fouling/scaling layers. Our study not only elucidates the mechanisms of combined organic fouling and gypsum scaling but also sheds light on potential strategies for membrane scaling control in RO desalination.

Reverse osmosis desalination combining feed flow reversal with permeate flush for mitigation of mineral scaling

The performance of a spiral-wound reverse osmosis (RO) membrane system, operating in a cyclic mode of normal feed flow (NFF)-feed flow reversal (FFR), was evaluated for desalting feed water of high gypsum mineral scaling potential. The membrane system, with six membrane elements in series, was operated without antiscalant dosing at the condition of gypsum supersaturation at the membrane surface of the tail RO element. Automated NFF/FFR switching was triggered by an optical membrane monitoring system (MMS) installed at the last membrane element. This element alternated from being the tail to lead element at NFF and FFR modes, respectively. Multicycle NFF/FFR operation demonstrated partial cycle-to-cycle restoration of the permeate flux. However, progressive flux decline was noticeable with increased NFF/FFR cycles. Complete restoration of element productivity (in terms of permeate flux) was attained via permeate flushing (at the early membrane scaling stage) owing to gypsum scale dissolution. The study results suggest that NFF/FFR RO operation under conditions of high mineral scaling potential can be effectively combined with periodic permeate flushing. However, establishing the long-term approach feasibility will require a strategy for optimizing the frequency of NFF/FFR switching and permeate flushing in relation to the feed water quality and desalting operating conditions.

Modelling the flux decline induced by gypsum scaling in direct contact membrane distillation

Scaling has been a major technical challenge in the membrane distillation (MD) process, hindering the broader application of MD processes. Despite the increasing number of studies on MD scaling, there are limited prediction tools to describe the scaling process and help make informed decisions about the experimental conditions to prevent scaling and its irreversible damage. In this paper, a semi-analytical model was developed based on the classical nucleation theory and crystal growth to model the membrane area reduction caused by the deposition of inorganic salt crystals on the membrane surface, which is equivalent to the decrease in permeate flux resulting from scaling. The model was developed using calcium sulphate, a model scalant. The model was validated and verified with available literature data, and it has been proved that the model has the capability to produce reasonable predictions on the onset of flux decline and the declining rate with respect to the experimental data with the coefficient of determination (R2) ranging from 0.74 to 0.96. The sensitivity analysis was applied on the model, which revealed that flux decline would happen earlier in the case of higher feed temperature, higher feed velocity, and higher initial feed concentration.