The approximation of geophysical parameters within a multi-layered unconfined aquifer.

Abstract

In this thesis, we address two practical problems associated with groundwater flow. Firstly, when given basic geological information is it possible to predict with reasonable accuracy the rate of flow into a well or borehole? Addressing this question can frequently be time consuming and expensive as typically tests are conducted after initial drilling operations at likely sites. Mathematical modelling
can contribute towards a more informed decision of where to site the well and by doing so help to reduce time and cost. The second problem considers the inverse situation, namely if we have prior data on the flow characteristics is it possible to infer the hydraulic properties of the component soil layers? Hydraulic conductivity is very difficult to measure accurately, particularly given the inherent heterogeneity and irregularity of soil layers. Measurements can involve lengthy electrical surveys that use soil
conductivity to estimate hydraulic characteristics. Using the data from working wells to infer likely values for hydraulic conductivity provides a useful additional source of information for local engineering teams. To address these problems we develop a mixed finite element (FE) model for the outflow from a multi-layered unconfined aquifer, which is referred to as the ’forward model’. The performance is optimised using a carefully selected h-adaptivity mesh refinement algorithm, enabling us to compute flow regimes for large-scale physical problems efficiently. This model is validated against data from three working wells used to supply water to cities in the São Paulo region of Brazil. In a multi-layered scenario, the inverse problem yields an under-determined system. The ’forward model’ is used as a component of an inversion algorithm that uses a Monte Carlo (MC) method, a fixed point iteration or a Tikhonov regularisation. In such circumstances, we are able to predict optimal values for hydraulic parameters in proximity to the well. This approach is validated using the data from the three working well examples. Finally, we consider a stochastic approach to the two problems. This helps address the uncertainty in outflow characteristics resulting from the heterogeneous nature of the soil layers. We achieve this through the application of a Monte Carlo (MC) method, made possible by the computational efficiency of the ’forward model’. It is shown, by using the 3 working well examples, that the outflow characteristics can be approximated to a good degree of accuracy, knowing only very basic information about the local geology and configuration of the well. We also show how these estimates can be improved by using additional data or perhaps used in the inverse sense to infer the hydraulic characteristics of the component soil layers within the aquifer. To this end, a Markov Chain Monte Carlo (MCMC) method is used to condition a prior distribution and quantify uncertainty in the hydraulic conductivity when data on the stabilisation flow is known.

Date of Award	13 Sept 2023
Original language	English
Awarding Institution	University of Bath
Supervisor	Tristan Pryer (Supervisor) & Chris Budd (Supervisor)