# A mathematical model can calculate the lifespan of drainage pipes

2019-12-02Arthur Vromans, who recently completed a doctorate in Mathematics, has developed a model which calculates the degradation process of drainage pipes. The model can assess the lifespan of existing pipes and what materials should be used to build pipes in the future.

Through measuring for instance water flow, chemical reactions, temperature, and other factors in and outside the pipes, it is possible to use the model to monitor the status of existing drainage pipes and calculate how long they can be expected to last before they need to be replaced.

“When old drainage pipes break, they can undermine the ground and potentially cause sinkholes,” says Arthur Vromans, a doctor of Mathematics. “My model allows us to estimate the speed of degradation in the sewage system over 30 years.”

Since he completed his Degree of Licentiate in the spring of 2018, Arthur has worked to refine the model in such a way that it can include further variables and describe the actual process better.

“I have been focusing on seeing how the model changes when you average it on a small scale to obtain behaviour at a large scale. I have shown what the large scale behaviour is and how good this averaging is by quantifying the error. This is important because the small scale behaviour is almost impossible to calculate on a computer, it takes too much time and energy. With the large scale behaviour you can calculate everything very quickly and we know how much the error is.”

On 25 October, Arthur Vromans’s publicly defended his doctoral thesis. The model is described in the thesis, titled “Homogenization of pseudoparabolic reaction-diffusion-mechanics systems: Multiscale modeling, well-posedness and convergence rates".

Read the doctoral thesis here.

Listen to Arthur in the podd, Forskningspodden, episode 63.