Equilibrium Model Research Articles

Integrating different fidelity models for process optimization: A case of equilibrium and rate-based extractive distillation using ionic liquids

We integrate equilibrium and rate-based models to formulate a hybrid optimization scheme for designing an ionic liquid-based extractive distillation process for mixed-refrigerant separation. The equilibrium model assumes vapor–liquid equilibrium at each stage but challenges arise with low-volatility, high-viscosity solvents, which drive the system away from equilibrium. The rate-based approach considers mass and heat transfer rates, giving more accurate representation. We compare the two models for separating R-410A, an azeotropic mixture of R-32 and R-125, using [EMIM][SCN] ionic liquid as entrainer. Analyzing over 4300 simulations with various dimensionality reduction and topological analysis techniques, we find that predictions from the two models exhibit similar trends, but the overestimation in equilibrium-based purities sometimes leads to infeasible process designs. The proposed optimization algorithm thus combines the strengths of the two models to locate feasible and optimal designs.

Late Triassic continental eclogite in the central Tibetan Plateau reveals 2500-km-long Paleo-Tethys continental subduction

Permian−Triassic eclogites exposed on the Tibetan Plateau have traditionally been attributed to Paleo-Tethys oceanic subduction. Here we report new data that indicate a continental-subduction origin of the Pianshishan eclogites along the Longmuco-Shuanghu Paleo-Tethys suture in northern Tibet. Phase equilibrium modeling and zircon U-Pb dating constrain eclogite-facies metamorphism of ∼2.1 GPa/530 °C to have occurred ca. 235 Ma. Xenocrysts of ca. 1850 Ma metamorphic zircons and crustal trace element signatures reveal a continental protolith for the Pianshishan eclogites, demonstrating deep subduction of continental passive margins during the early Late Triassic. The Qianmai eclogites along the Changning-Menglian suture in Southwest China have the same petrogenesis, indicating that these two coeval eclogites resulted from continental subduction that extended over 2500 km along the Paleo-Tethys suture. This collision not only marks the end of the Paleo-Tethys Wilson cycle but also could have formed a high-elevation range, comparable in length to the Himalaya, that amplified Tethyan megamonsoons during the Late Triassic Carnian Pluvial Episode.

Computational multiphase mixture simulations of a two-phase R-744 ejector geometry in transcritical R-744 heat pump applications

Purpose Two-phase R-744 ejectors are critical components enabling energy recovery in R-744 heat pump and refrigeration systems, but despite their simple geometry, the flow physics involve complex multiphase mixing phenomena that need to be well-quantified for component and overall system improvement. This study aims to report on multiphase mixture simulations for a specific two-phase R-744 ejector with supercritical inlet conditions at the motive inlet side. Design/methodology/approach Four different operating conditions, which have motive inlet pressure range of 90.1 bar–101.1 bar, are selected from an existing experimental data set. A two-phase thermodynamic equilibrium (TPTE) model is used, where the fluid properties are described by a thermodynamic look-up table. Findings The results show that the TPTE model overpredicts mass flow rates at the motive inlet, resulting in a relative error ranging from 15.6% to 21.7%. For the mass flow rate at the suction inlet, the relative errors are found less than 1.5% for three cases, while the last case has an error of 12.4%. The maximum deviation of the mass entrainment ratio is found to be 8.0% between the TPTE model and the experimental data. Ejector efficiency ranges from 25.4% to 28.0%. A higher pressure difference between the ejector outlet and the diverging nozzle exit provides greater pressure lift. Research limitations/implications Based on the results, near future efforts will be to optimize estimation errors while enabling more detailed field analysis of pressure, density, temperature and enthalpy in the computational domain. Originality/value The authors have two main original contributions: 1) the presented thermodynamic look-up table is unique and provides unique computation for the real-scale ejector domain. It was created by the authors and has not been applied before as far as we know. 2) To the best of the authors’ knowledge, this study is the first study that applies the STAR-CCM+ multiphase mixture model for R-744 mixture phenomena in heat pumps and refrigeration systems.

Dynamic spatial price equilibrium, dynamic user equilibrium, and freight transportation in continuous time: A differential variational inequality perspective

In this paper we provide a statement of dynamic spatial price equilibrium (DSPE) in continuous time as a basis for modeling freight flows in a network economy. The model presented describes a spatial price equilibrium due to its reliance on the notion that freight movements occur in response to differences between the local and distant prices of goods for which there is excess demand; moreover, local and distant delivered prices are equated at equilibrium. We propose and analyze a differential variational inequality (DVI) associated with dynamic spatial price equilibrium to study the Nash-like aggregate game at the heart of DSPE using the calculus of variations and optimal control theory. Our formulation explicitly considers inventory and the time lag between shipping and demand fulfillment. We stress that such a time lag cannot be readily accommodated in a discrete-time formulation. We provide an in-depth analysis of the DVI's necessary conditions that reveals the dynamic user equilibrium nature of freight flows obtained from the DVI, alongside the role played by freight transport in maintaining equilibrium commodity prices and the delivered-price-equals-local-price property of spatial price equilibrium. By intent, our contribution is wholly theoretical in nature, focusing on a mathematical statement of the defining equations and inequalities for dynamic spatial price equilibrium (DSPE), while also showing there is an associated differential variational inequality (DVI), any solution of which is a DSPE. The model of spatial price equilibrium we present integrates the theory of spatial price equilibrium in a dynamic setting with the path delay operator notion used in the theory of dynamic user equilibrium. It should be noted that the path delay operator used herein is based on LWR theory and fully vetted in the published dynamic user equilibrium literature. This integration is new and constitutes a significant addition to the spatial price equilibrium and freight network equilibrium modeling literatures. Among other things, it points the way for researchers interested in dynamic traffic assignment to become involved in dynamic freight modeling using the technical knowledge they already possess. In particular, it suggests that algorithms developed for dynamic user equilibrium may be adapted to the study of urban freight modelled as a dynamic spatial price equilibrium. As such, our work provides direction for future DSPE algorithmic research and application. However, no computational experiments are reported herein; instead, the computing of dynamic spatial price equilibria is the subject of a separate manuscript.

Investigation of non-equilibrium phenomena in nitrogen RF inductively coupled plasma discharges: a state-to-state approach

Abstract This work presents a vibrational and electronic (vibronic) state-to-state (StS) model for nitrogen plasmas implemented within a multi-physics modular computational framework to study non-equilibrium effects in inductively coupled plasma (ICP) discharges. The vibronic master equations are solved in a tightly coupled fashion with the flow governing equations eliminating the need for invoking any simplifying assumptions when computing the state of the plasma, leading to a high-fidelity physical modeling. The model’s computational complexity is reduced via a maximum entropy coarse-graining approach, verified through zero-dimensional isochoric calculations. The coarse-grained StS model is employed to study the plasma discharge in the ICP facility at the von Karman Institute for Fluid Dynamics, Belgium. Results reveal pronounced discrepancies between StS predictions and those obtained based on local thermodynamic equilibrium (LTE) models, which are conventionally used in the simulation of such facilities. The analysis demonstrates a substantial departure of the internal state populations of atoms and molecules from the Boltzmann distribution. This has significant implications for energy coupling dynamics, affecting the discharge morphology. Further analysis reveals a quasi-steady-state population distribution in the plasma core, allowing for the construction of an efficient and ‘self-consistent’ macroscopic two-temperature (2T) formulation. Non-LTE simulations indicate significant disparities between the StS model and the commonly used Park 2T model, whereas the newly proposed 2T model aligns closely with StS simulations, capturing key features of non-equilibrium plasma formation. In particular, the current study highlights the importance of the vibrational-translational energy transfer term in shaping the plasma core morphology, suggesting a notable sensitivity to heavy-impact vibrational excitations and dissociative processes.

Asymmetrical Monetary Relations and Involuntary Unemployment in a General Equilibrium Model

Abstract This article aims to model Keynesian involuntary unemployment within the framework of Walrasian general equilibrium, incorporating an additional hypothesis: the possibility of credit restrictions by banks or financial intermediaries. Keynes’s theory of involuntary unemployment is based on the rejection of the “second classical postulate,” which leads to the idea that entrepreneurs alone decide the level of employment. This is what some Keynesians call the asymmetry of the wage relationship. The result is a restriction of Walras’ law, which no longer includes the labor market. However, the problem is that entrepreneurs themselves may find themselves constrained by financial intermediaries. If there is a second type of asymmetry, i.e., between banks/financial intermediaries and entrepreneurs, Walras’ law will be doubly restricted since it will also exclude the credit market. I set out to identify the consequences of the properties of involuntary unemployment in a general equilibrium model.

N exus: a framework for controlled simulations of idealized galaxies

ABSTRACT Motivated by the need for realistic, dynamically self-consistent, evolving galaxy models that avoid the complexity of full, and zoom-in, cosmological simulations, we have developed Nexus, an integral framework to create and evolve synthetic galaxies made of collisionless and gaseous components. Nexus leverages the power of publicly available, tried-and-tested packages: the stellar-dynamics, action-based library Action-based Galaxy Modelling Architecture (AGAMA); and the adaptive mesh refinement, N-body/hydrodynamical code Ramses, modified to meet our needs. In addition, we make use of a proprietary module to account for galaxy formation physics, including gas cooling and heating, star formation, stellar feedback, and chemical enrichment. Nexus’ basic functionality consists in the generation of bespoke initial conditions (ICs) for a diversity of galaxy models, which are advanced in time to simulate the galaxy’s evolution. The fully self-consistent ICs are generated with a distribution-function-based approach, as implemented in the galaxy modelling module of AGAMA – up to now restricted to collisionless components, extended in this work to treat two types of gaseous configurations: hot haloes and gas discs. Nexus allows constructing equilibrium models with disc gas fractions $0~\le ~f_{\rm {\rm gas}}~\le ~1$, appropriate to model both low- and high-redshift galaxies. Similarly, the framework is ideally suited to the study of galactic ecology, i.e. the dynamical interplay between stars and gas over billions of years. As a validation and illustration of our framework, we reproduce several isolated galaxy model setups reported in earlier studies, and present a new, ‘nested bar’ galaxy simulation. Future upgrades of Nexus will include magnetohydrodynamics and highly energetic particle (‘cosmic ray’) heating.

A dynamic approach for MR T2-weighted pelvic imaging

T2-weighted 2D fast spin echo sequence serves as the standard sequence in
clinical pelvic MR imaging protocols. However, motion artifacts and blurring caused
by peristalsis present significant challenges. Patient preparation such as administering
antiperistaltic agents is often required before examination to reduce artifacts, which
discomfort the patients. This work introduce a novel dynamic approach for T2
weighted pelvic imaging to address peristalsis-induced motion issue without any patient
preparation.
Approach: A rapid dynamic data acquisition strategy with complementary sampling
trajectory is designed to enable highly undersampled motion-resistant data sampling,
and an unrolling method based on deep equilibrium model is leveraged to reconstruct
images from the dynamic sampled k-space data. Moreover, the fix-point convergence of
the equilibrium model ensures the stability of the reconstruction. The high acceleration
factor in each temporal phase, which is much higher than that in traditional static
imaging, has the potential to effectively freeze pelvic motion, thereby transforming
the imaging problem from conventional motion prevention or removal to motion
reconstruction.
Main results: Experiments on both retrospective and prospective data have
demonstrated the superior performance of the proposed dynamic approach in reducing
motion artifacts and accurately depicting structural details compared to standard static
imaging.
Significance: The proposed dynamic approach effectively captures motion states
through dynamic data acquisition and deep learning-based reconstruction, addressing
motion-related challenges in pelvic imaging.

Aggregated economic damages and the role of dynamic carbon tax under climate change: A dynamic general equilibrium model

A rational assessment of the aggregated economic damages and a more effective carbon tax are crucial for climate governance. However, existing studies still under-recognize the utility damages and dynamic carbon taxes. In this study, we construct a multi-regional dynamic general equilibrium model considering both production and utility damages. Then, this paper re-estimates the regional aggregated economic damages reasonably (including utility damages) and compares in detail the role of static carbon tax, dynamic carbon tax and regionally optimal dynamic carbon tax (RCT). We found that: (1) As climate change intensifies, the world will suffer >8 % of production damage and 1 % of utility damage by the end of the 21st century. Of these, the US and China face more pronounced economic damage. (2) If the carbon tax is implemented only in some regions, other regions will have a “free rider” benefit. An environmentally friendly dynamic carbon tax (fast and then slow) would be more effective, giving economies room to adapt to the carbon tax. The risk of exacerbating global inequality needs to be guarded against when using carbon tax. (3) Based on the regional social cost of carbon (R-SCC), implementing RCT is most effective for curbing climate change and achieving warming targets. This paper contributes to improving the understanding of assessing regional economic damage from climate change and recognizing the role of dynamic carbon tax.

Economy-wide impact of targeting and repurposing fossil fuel subsidies in Malaysia

Fossil fuel subsidy reform is a critical strategy for fostering cleaner energy systems and promoting sustainable development. The Malaysian government has signalled commitments to implement a targeted fuel subsidy reform where vulnerable households would be unaffected by the direct impact of higher fuel prices even after the reform. But despite this commitment, little is known about the economy-wide impact of the reform. This study employs a dynamic Computable General Equilibrium (CGE) model to examine the economic, social, and environmental impact of a targeted fuel subsidy removal in Malaysia under a spontaneous and gradual implementation scenario. The research also explores the impact of direct cash transfers to households and reinvestment in key sectors of the economy in the aftermath of the reform. Results from the study show that subsidy removal brings positive gains to the Malaysian economy in the medium to long term. Sequencing the phaseout of subsidies, providing compensation to vulnerable households, and reinvesting in education, health, transportation, and food assistance helps to avoid short-term adverse effects on households and output. The study recommends the need for a gradual removal of fuel subsidies that is accompanied by cash transfers to vulnerable households and investment in key sectors of the economy.

Economic impacts of large dams on downstream brickmaking in developing countries

Large dams have positive and negative impacts, including disrupting brickmaking on the floodplains downstream due to flow regulation and sediment reduction, affecting the supply of essential construction material, notably in developing countries. In this study, we introduce an analytical framework to assess the economywide effects of large dams on downstream brickmaking, focusing on Traditional Fired Clay Brick (TFCB). The framework includes three steps: characterizing the impacts on river flow and sediment load using river system modeling and secondary data, understanding the role of TFCB production in the economy based on survey and economic data, and quantifying the economywide impacts of changes in TFCB production using dynamic computable general equilibrium modeling. We demonstrate the functionality of the approach by conducting a case study of the impacts of the Grand Ethiopian Renaissance Dam (GERD) on the Sudanese economy due to changes in TFCB production by comparing two scenarios: “with GERD” and “no GERD.” Results show that Sudan’s accumulated (2023–2050) discounted (at 0.5% annually) Gross Domestic Product (GDP) at factor cost would decline by US$ 6 billion (−0.38%) due to a reduction in TFCB production. Consumer flexibility regarding brick types and the ability of alternative brick sources to fill the demand gap are key determinants of the impacts.

A joint Cournot equilibrium model for the hydrogen and electricity markets

Hydrogen production through renewable energy-powered electrolysis is pivotal for fostering a sustainable future hydrogen market. In the electricity sector, hydrogen production bears an additional demand that affects electricity price, and mathematical models are needed for the joint simulation, analysis, and planning of electricity and hydrogen sectors. This study develops a Cournot and a perfect competition model to analyze the links of the electricity and hydrogen sectors. In contrast to other solving methods approaches, the Cournot model is solved by convex reformulation techniques, substantially easing the resolution. The case studies, focusing on the Iberian Peninsula, demonstrate the region's potential for competitive hydrogen production, and the advantages of perfect competition to maximize the use of renewable energies, in contrast to Cournot's oligopoly, where the exercise of market power raises electricity prices. Sensitivity analyses highlight the importance of strategic decision-making in mitigating market inefficiencies, with valuable insights for stakeholders and policymakers.

Supply chain network equilibrium with outsourcing for fresh agricultural products under stochastic demands

Abstract Accepted by: M. Zied Babai This paper examines a supply chain network focusing on the distribution of fresh agricultural products, incorporating outsourcing and stochastic demands considerations. Initially, we establish a generalized Nash equilibrium model with stochastic demands among fresh produce firms. Subsequently, we transform this model into a mixed complementarity system using the Karush–Kuhn–Tucker conditions. Utilizing the Fischer–Burmeister function, we further convert the mixed complementarity system into a set of nonlinear equations, amenable to solution via GAMS software. We conduct numerical experiments and perform sensitivity analysis on key parameters. Our findings suggest that higher subsidy rates incentivize firms towards production outsourcing, particularly benefiting low-income farmers, thereby potentially increasing profits. Moreover, market fluctuations play a pivotal role in ensuring the stability and profitability of firms, with moderate fluctuations presenting opportunities for fresh enterprises to adapt, innovate and capitalize on evolving market conditions. These results offer valuable insights for effective management of fresh produce supply chains.

Would carbon tax policy promote real estate prices?

Real estate plays a pivotal role in carbon emissions. Carbon tax policy is a crucial measure for mitigating enterprises' carbon emissions. However, imposing a carbon tax on productive enterprises in the real estate industry to reduce emissions may increase their production costs, which could easily be passed on to buyers, thus inflating real estate prices and impeding policy effectiveness. To examine the impact and negative consequences of carbon tax policy applied to the real estate industry, we develop a dynamic stochastic general equilibrium model encompassing building materials manufacturers, real estate firms, and the environmental regulatory government. Findings indicate that implementing the carbon tax policy significantly reduces carbon emissions in the real estate industry. However, the existence of a price transmission mechanism makes carbon tax policies susceptible to driving up real estate prices. Further welfare analysis shows that increasing carbon tax rates will result in social welfare losses, allowing the government to modify and refine its policy objectives.

Assessing investment priorities for inclusive agricultural transformation in Tanzania

AbstractMotivationPolicy‐makers dealing with conflicting development goals and constrained budgets must comprehend the relative cost effectiveness of agricultural and rural development initiatives.PurposeWe assess the impact of alternative interventions on development outcomes—economic growth, job creation, poverty reduction, and diet quality—to inform decision‐making and resource allocation in Tanzania's agriculture. We analyse trade‐offs among development objectives and explore budget reallocation to enhance the efficiency of public spending.Approach and methodsWe used a computable general equilibrium (CGE) model linked top‐down with microsimulation modules to simulate the impact of public investment options.FindingsNo single option emerges as the most effective across all development objectives. Investments in improved inputs and extension for horticulture and cash crops stand out for diet quality and employment creation. Livestock services show consistently high rankings across multiple objectives. Investments to boost cereals and root crops promote growth and reduce poverty but do little to increase employment and diet quality.Budget reallocation towards more cost‐effective interventions can significantly enhance the development effectiveness of Tanzania's agricultural expenditures and would substantially increase cumulative gross domestic product growth between 2019 and 2028.Policy implicationsPolicy‐makers can use the findings to design and prioritize agricultural interventions that better align with broader development objectives. Tanzania can achieve higher benefits and contribute to overall development goals by reallocating resources towards more cost‐effective expenditure options.

Household Well-Being, Environment and Health in the Peripheries of the Metropolitan Area of Oaxaca City

Objective: The economy of poor urban households is analyzed using a well-being function that also considers incomes, sociodemographic characteristics (CS), housing and the environment. Theoretical structure: The dependent variable is household well-being (BF) and the explanatory variables are all incomes obtained from the market economy, as well as government transfers (TG). The CS represent resources that facilitate obtaining income; housing provides income indicators; and the environment are the physical conditions that determine the state of health. Methodology: A probabilistic survey was applied to a sample of households in four poor peripheral neighborhoods. The equations were constructed using ordinary least squares regression and the beta coefficients measure the contribution of the variables from the four categories above to the BF. The effects of these variables on health expenditure (GS) are also measured. Discoveries: The main incomes that contribute to the BF were determined and these make a contribution equivalent to that of the set of variables of the CS, housing and family businesses. Likewise, the environment and diseases increase GS. Practical and social implications: Research shows that poor peripheral urban households participate in the market economy and that an increase in average age contracts their level of BF. Originality/value: The tested model turned out to be versatile and accurate in analyzing the economies of poor urban households and has greater explanatory power than the agricultural household models and the applied general equilibrium model.

Formation of a magnetized hybrid star with a purely toroidal field from phase-transition-induced collapse

ABSTRACT Strongly magnetized neutron stars are popular candidates for producing detectable electromagnetic and gravitational-wave signals. Gravitational collapses of neutron stars triggered by a phase transition from hadrons to deconfined quarks in the cores could also release a considerable amount of energy in the form of gravitational waves and neutrinos. Hence, the formation of a magnetized hybrid star from such a phase-transition-induced collapse is an interesting scenario for detecting all these signals. These detections may provide essential probes for the magnetic field and composition of such stars. Thus far, a dynamical study of the formation of a magnetized hybrid star from a phase-transition-induced collapse has yet to be realized. Here, we investigate the formation of a magnetized hybrid star with a purely toroidal field and its properties through dynamical simulations. We find that the maximum values of rest-mass density and magnetic field strength increase slightly and these two quantities are coupled in phase during the formation. We then demonstrate that all microscopic and macroscopic quantities of the resulting hybrid star vary drastically when the maximum magnetic field strength goes beyond a threshold of $\sim 5 \times 10^{17}$ G, but they are insensitive to the magnetic field below this threshold. Specifically, the magnetic deformation makes the rest-mass density drop significantly, suppressing the matter fraction in the mixed phase. These behaviours agree with those in the equilibrium models of previous studies. Therefore, this work provides a solid support for the magnetic effects on a hybrid star.

Regulatory Effects of the Combinations of Aggregate and Structural Monetary Policy Instruments: an application of New Keynesian DSGE model to China

This paper selects Chinese macroeconomic data from the first quarter of 2009 to the first quarter of 2020 and employs a New Keynesian dynamic stochastic general equilibrium model that incorporates the financial accelerator mechanism, price stickiness, and invisible government guarantees. The regulatory effects of different combinations of monetary policy instruments are compared from five perspectives: the shock effect of monetary policy, the magnitude of economic volatility of non-monetary policy shocks, the Central Bank loss function, the gap in the distribution of household income, and the heterogeneous firm external financing premium. Our findings indicate that the regulatory effects of the aggregate price-based and structural quantity-based monetary policy instrument combination are optimal, a conclusion that is further supported by the robustness test. It is therefore recommended that the Central Bank consider the potential benefits of a combined approach to aggregate and structural monetary policy instruments, with a view to enhancing credit availability for the real economy. This paper represents a significant contribution to the field, as it is the first to explicitly propose four distinct monetary policy instrument combinations, thereby overcoming the limitations of previous studies that have focused on a single instrument or a narrow range of instruments. The paper also contributes to the theoretical understanding of monetary policy instruments.

Valorization of Eggshell as Renewable Materials for Sustainable Biocomposite Adsorbents—An Overview

The production and buildup of eggshell waste represents a challenge and an opportunity. The challenge is that uncontrolled disposal of generated eggshell waste relates to a sustainability concern for the environment. The opportunity relates to utilization of this biomass resource via recycling for waste valorization, cleaner production, and development of a circular economy. This review explores the development of eggshell powder (ESP) from eggshell waste and a coverage of various ESP composite sorbents with an emphasis on their potential utility as adsorbent materials for model pollutants in solid–liquid systems. An overview of literature since 2014 outlines the development of eggshell powder (ESP) and ESP composite adsorbents for solid–liquid adsorption processes. The isolation and treatment of ESP in its pristine or modified forms by various thermal or chemical treatments, along with the preparation of ESP biocomposites is described. An overview of the physico-chemical characterization of ESP and its biocomposites include an assessment of the adsorption properties with various model pollutants (cations, anions, and organic dyes). A coverage of equilibrium and kinetic adsorption isotherm models is provided, along with relevant thermodynamic parameters that govern the adsorption process for ESP-based adsorbents. This review reveals that ESP biocomposite adsorbents represent an emerging class of sustainable materials with tailored properties via modular synthetic strategies. This review will serve to encourage the recycling and utilization of eggshell biomass waste and its valorization as potential adsorbent systems. The impact of such ESP biosorbents cover a diverse range of adsorption-based applications from environmental remediation to slow-release fertilizer carrier systems in agricultural production.

Adsorption of Cr(VI) and phosphate anions by amino-functionalized palm oil fibers.

This work developed a novel sustainable adsorbent (PF-Aq) prepared by the amino-functionalization of palm oil fibers (PF). XPS, SEM/EDS, TGA/DSC, and FT-IR techniques proved the successful functionalization of the PF with the amino group. The PF-Aq adsorbent presents a high adsorption capacity for phosphate and Cr(VI) ions. Adsorption kinetics of the ions onto the PF-Aq followed the general-order models, with 240- and 300-min equilibrium times for phosphate and Cr(VI), respectively. The Freundlich equilibrium model can explain the adsorption of phosphate and Cr(VI) on the PF-Aq. Besides, the maximum adsorption capacities were 151.07mgg-1 for phosphate and 206.08mgg-1 for Cr(VI). The best pH for the adsorption of both ions on PF-Aq was 4.0. Interestingly, adsorption was exothermic for phosphate and endothermic for Cr(VI). The adsorption capacities were reduced by 16% for phosphate and 10% for Cr(VI) after 5 adsorption-desorption cycles, demonstrating the good recyclability of the PF-Aq. It can be concluded that PF-Aq is a relevant adsorbent to uptake phosphate and Cr(VI) from water due to its high adsorption capacity, low cost, recyclability, availability, and fast kinetics. Finally, the excellent adsorption potential results from inserting amino groups in the PF, allowing electrostatic interactions between adsorbent and adsorbate.