01/09/2021 – 31/08/2024

Call: Proyectos de I+D+i Retos Investigación (ref. PID2020-115023RB-I00)

Project Description

Tackling environmental challenges is this generations defining task (EC Green Deal 2020). One such challenge, the goal of holding global warming to well below 2°C (IPCC 2018; Paris Agreement 2015), can now only be achieved through the extraction of atmospheric greenhouse gases in tandem with emission reductions and a range of other measures. Similarly the goal of a toxic free environment requires the removal of a multitude of existing contaminants.

The primary focus of the proposed project concerns the development, analysis and application of mathematical models for the removal of contaminants by column sorption from a flowing fluid. Column sorption, is perhaps the most popular practical sorption method and is used for a wide range of processes, such as the removal of emerging contaminants, volatile organic compounds, CO2, dyes and salts. It may be applied to both liquids and gases.

The mathematical description of column sorption involves coupling advection-diffusion equations to sink (removal) equations, all applied over an evolving domain. The research topic falls within the broad category of moving boundary problems (MBPs). The Industrial Mathematics Research Group at the Centre de Recerca Matemática has a long history of studying related problems in the context of phase change driven by diffusion (both thermal and chemical). The aim of this proposal is to exploit this experience to tackle pressing environmental issues, initially within the context of contaminant removal by sorption. However since this study is predominantly mathematical, and with an eye to the future expansion of the group, it is intended to apply similar techniques to an analogous problem concerning energy absorption in green roofs.

The study is motivated by interdisciplinary collaborations as well as environmental concerns.

The goal is therefore to transfer the mathematical techniques of phase change to the more complex situations encountered in column sorption and heat transfer on green roofs and to present results which can guide practical and innovative solutions. Above all, to use mathematics to make a significant positive impact on the environment and aid in the fight against climate change.

Project Principal Investigator

Timothy G. Myers (CRM)

Industrial Mathematics Group


Despite international agreements, greenhouse gases continue to increase since the beginning of the revolution industrial. In 2019, around 43 billion tons of CO2 were emitted into the atmosphere. While great efforts are being made globally to control these emissions, certain industries cannot or do not want to drastically reduce their emissions in the short term. Classic examples of this type of policy are industries based on energy from hydrocarbons, or the automotive and cement industries. Incorporating equipment based on sorption columns in production chains it is possible to reduce emissions by around 90%. The construction of green roofs in buildings can help at a local and global level. We expect that the publication of the results from our work in appropriate journals, as well as the interaction with research groups of experimental character, contributes to our work being used to improve current sorption techniques.

Any contribution of the proposed project in terms of cost or efficiency improvement, however small, could be extremely important in the fight against climate change. Any idea that can help reduce the transfer of pollutants to water streams or fertile soils represents a great contribution to the environment. If we can use mathematical results to provide simple guidelines that motivate city councils to build green roofs or promote that these are installed at a private level, then we will be taking a step towards reducing global warming while improving the quality of life of its citizens.

The project is mathematical in nature, but the subject matter involved is interdisciplinary and the results have relevant practical applications. Specifically, in the field of sorption columns, currently the results that exist are mainly numerical and/or experimental. The introduction of carefully developed models, and the mathematical analysis of the equations that rule them, will provide a greater degree of understanding of the dominant mechanisms thus allowing improvements to be made in the processes and in future designs. It is important not to underestimate the importance of providing analytical solutions, since in these the role of each system parameter appears in a clear and precise way and therefore show how to modify them to improve efficiency in the extraction of contaminants. Using this approach also on, for example, multiple contaminants and exothermic reactions, the work is expected to impact a wide range of industrial processes. So far, the need for analysis of green roofs has arisen from private environmental initiatives and from the civil society. The improvement of the knowledge of the mathematical processes involved makes it possible to provide clear and rigorously justified guidelines that can be used to advise local governments around the world about the need to install roofs and green spaces.

Our goals and the philosophy of the research team are perfectly adapted to Challenges 3 (clean energy) and 5 (climate change), but at the same time we hope that, by improving the quality of the air, we can also have something to contribute to Challenge 1 (health and well being) due to the environmental pollution.

Project investigation Team

Maria Aguareles Carrero
Universitat de Girona


Francesc Font Martínez
Universitat Politècnica de Catalunya



Adewunmi Fareo
University of the Witwatersrand


Brian Wetton
University of British Columbia


Nilima Nigam
Simon Fraser University


Ian Griffiths
University of Oxford


Sarah Mitchell
University of Limerick


Harvey Thompson
University of Leeds


M Aguareles, M Calvo-Schwarzwalder, F Font, TG Myers. A mathematical model for the energy stored in green roofs. Applied Mathematical Modelling 115, 513-540
TG Myers, A Cabrera-Codony, A Valverde. On the development of a consistent mathematical model for adsorption in a packed column (and why standard models fail). International Journal of Heat and Mass Transfer 202, 123660
M Aguareles Carrero, E Barrabés Vera, T Myers, A Valverde. Mathematical analysis of a Sips-based model for column adsorption. © Physica D: Nonlinear phenomena, 2023, vol. 448, art. núm. 133690