Modelling flow converging to a pumped borehole

How do we use boreholes?

Boreholes provide a way for us to understand groundwater systems through monitoring and aquifer testing. Pumping tests are controlled field experiments performed to understand the hydraulic characteristics of an aquifer. In these tests a borehole is pumped at a constant rate for a certain period of time and the variation in drawdown with time is recorded in the abstraction borehole and a set of observation boreholes or piezometers.

Boreholes can also be pumped to exploit groundwater as a resource. In southern England up to 70 per cent of the total public water supply comes from groundwater. In parts of the UK boreholes are also commonly used to abstract groundwater for private water supply, irrigation and industry.

Why do we want to model flow to boreholes?

Flow processes around an abstraction borehole.
  • To analyse the results from pumping tests where the drawdown curves are complicated by the hydrogeological setting of the borehole and simple analytical solutions are not valid;
  • To model the amount of drawdown under long-term abstraction and evaluate the sustainable yield of a supply borehole, particularly under drought conditions;
  • To predict how drawdown and yields might change under different patterns of abstraction and recharge.

How do we model flow to boreholes?

Numerical cylindrical grid models are powerful tools that can be used to model flow to boreholes. They include many of the near-well flow processes required to produce accurate solutions for pumping test analysis and to give accurate prediction of borehole efficiency, including:

  • the development of a seepage face
  • partial borehole penetration
  • the effect of well casing and well storage

These numerical models also represent complex conceptual ideas, such as vertical and horizontal aquifer heterogeneity or proximity of rivers, to allow conceptual models to be tested and improved.


The BGS undertakes research in collaboration with universities and other research institutes, industry, environmental regulators and government and non-government organisations to improve our modelling capabilities and assist in solving a wide range of environmental issues including:

  • Improving the representation of the free surface in numerical models;
  • Improving the simulation of flow processes near pumped boreholes through application of the Darcy-Forchheimer equation;
  • Groundwater management and the assessment of deployable output;
  • The inclusion of particle tracking for contaminant remediation and studying natural hazards.
Embedding radial flow numerical model within a Cartesian grid numerical model.
Conceptual model of radial flow converging to a pumped borehole.

Modelling services

In addition to our research activities we undertake modelling projects for a number of commercial clients. Previous work has included the analysis of pumping tests conducted in the Chalk aquifer in the Swanscombe area of Kent, South East England; tests conducted in the superficial deposits in Howden and Aviemore, Scotland; and tests conducted in Vowchurch, Wales. The team has skilled specialists that apply existing modelling tools and develop bespoke software as necessary.

Modelling software

The BGS has developed a number of groundwater modelling software tools that simulate groundwater flow to boreholes.

The Cylindrical grid Object Oriented Model for Pumping Test analysis COOMPuTe is a finite difference model designed to simulate groundwater flows converging to pumped boreholes. The model features simulating groundwater flows in confined and unconfined aquifers including a moving water table, a seepage face, well storage, and well losses. The model also has particle tracking capabilities enabling the delineation of the pathway of a contaminant under complex hydrogeological settings.

The SPIDDER Flow Model (Simulating Pumping Boreholes with a Darcy-Forchheimer Regional-Radial Flow Model) is being developed through an EPSRC-funded PhD by Imperial College London and the BGS, with support from Thames Water Utilities Ltd. It reflects the need to be able to simulate groundwater systems at both the catchment scale and borehole scale to assess the long-term, sustainable yield of supply boreholes. The SPIDERR Flow Model couples a radial model of the Darcy-Forchheimer equation with a Cartesian grid to allow easy linkage with the ZOOMQ3D groundwater modelling code through OpenMI.


Upton, K A, Butler, A, and Jackson, C.  2013.  Coupling a radial model of the Darcy-Forchheimer equation with a regional groundwater model to simulate drawdown at supply boreholes.  In: MODFLOW and More 2013: Translating Science into Practice, Colorado, 2013. Colorado, USA, Colorado School of Mines.

Mansour, M M, Hughes, A G, Spink, and A E F, Riches, J.  2011.  Pumping test analysis using a layered cylindrical grid numerical model in a complex, heterogeneous Chalk Aquifer.  Journal of Hydrology, 401 (1-2). 14-21.

Mansour, M M, Spink, A E F, and Riches, J.  2003.  Numerical investigation of flow to pumped wells in heterogeneous layered aquifers using radial flow models. In: MODFLOW and More 2003 : understanding through modeling, Colorado, 2003. Colorado, USA, Colorado School of Mines, 388-392.

Mansour, M M, Davies, J, Hughes, A G, and Robins, N S.  2006.  The Vowchurch gravel aquifer pipeline crossing : hydrogeological evaluation of impact.  British Geological Survey, 44pp. (CR/06/186N)

Mansour, M M, Hughes, A G, and Spink, A E F.  2007.  User manual for the layered R-theta numerical model.  British Geological Survey, 58pp. (OR/07/029)


Contact Dr Majdi Mansour for more information