Presentation of the model - arnaud-reveillere/SAMBA GitHub Wiki

The injection of brine, waste fluid or CO2 into deep saline aquifers will create a pressure increase that will tend to displace brine upwards if a connection (e.g., a passive abandoned well) exists.

When injection starts in the bottom storage aquifer, pressure builds up and drives an upward flow through the leak, as illustrated below.

This problem of leakage between connected aquifers has an approximate analytical solution, as described in Nordbotten et al. (2004).

However, this upward displacement of brine is countered by progressive increase in the weight of the fluid filling the leak that occurs when the dense lifting brine from the deep saline aquifer replaces the less saline brine initially filling the leak. SAMBA is the implementation of Réveillère (2013) who proposes a semi-analytical solution that enables this effect to be taken into account. It is based on:

• the linearization of brine density against depth
• the approximate evaluation of convolution products for calculating the pressurization induced by transient flows in open aquifers

The model uses time discretization but no spatial grid, and therefore shares advantages and drawbacks of analytical or semi-analytical models. It requires few clear parameters, and makes it possible to understand which physical mechanisms are dominant over time. It provides results in less than a minute on a standard workstation (computation time is reduced by 3–4 orders of magnitude compared to numerical resolution; similar gains are achieved in terms of memory use), and can therefore be used for Monte-Carlo type uncertainty analyses. It is, however, restricted by important assumptions which are difficult to overcome, such as homogeneous horizontal aquifers of constant thickness and uniform properties.