Technical Note Investigation of hydromechanical processes during cyclic extraction recovery testing of a deformable rock fracture Simon A. Mathias a,Ã , Chin-Fu Tsang b,c , Maarten van Reeuwijk d a Department of Earth Sciences, Durham University, Durham, UK b Lawrence Berkeley National Laboratory, Earth Sciences Division, MS 90-1116, Berkeley, CA 94720, USA c Department of Earth Science and Engineering, Imperial College London, London, UK d Department of Civil and Environmental Engineering, Imperial College London, London, UK article info Article history: Received 22 May 2009 Received in revised form 19 November 2009 Accepted 21 December 2009 Available online 18 January 2010 1. Introduction In many hydrogeological contexts, hydraulic properties of fractures and rock matrix (e.g. storage coefficient and perme- ability) are routinely assumed constant [1–3]. The underlying assumption is that pressure-induced deformations associated with the rock and fracture structures are not materially significant. In more recent decades, there has been increased interest in the high pressure injection of fluids into geological formations: waste water disposal [4], carbon geo-sequestration [5], geothermal energy extraction [6] etc. Consequently, there is an increasing need for numerical models that relax this assump- tion [e.g. [7–10]] alongside associated field investigation techni- ques to obtain relevant model parameters [6,11–15]. When seeking to obtain model parameters from field test results, a question arises as to whether the level of structural complexity in the model is supported by the information contained within the data used for calibration. Wessling et al. [6] sought to explore this problem through the use of different models with sequentially increasing complexity. A similar approach was used by Mathias et al. [16] to look at radially convergent tracer tests. The field investigation presented by Wessling et al. [6] involved a cyclic extraction recovery test (CERT) whereby 2500 m 3 of freshwater was injected into a Detfurth Sandstone formation over 36 h followed by five succes- sive 15 h extractions of between 443 and 523 m 3 of fluid, each separated by a 5 h recovery period. Wessling et al. [6] analyzed the CERT data using three different models. The first model used (hereafter referred to as W1) considered one-dimensional radial flow to a well of infinitesimal diameter; essentially the Theis [17] solution but with variable injection rate [see [18]]. W1 was unable to adequately simulate the injection cycle and required the specification of an unrealis- tically large storage coefficient. The second model (hereafter referred to as W2) considered the injection of fluid into a circular fracture (of fixed radius and aperture) and leak-off of fluid into the surrounding geological formation. All hydraulic parameters were kept constant as in conventional hydrogeological models. W2 performed well during the extraction cycles using reasonable parameter values. However, it overestimated pressure buildup during the injection cycle by a factor of two. The third model (hereafter referred to as W3) employed a fully coupled numerical flow and stress-strain analysis, of both the fracture and the surrounding porous medium, using the finite element modeling code, ROCMAS [7,8]. W3 successfully matched the peaks and troughs in pressure for both the injection and extraction cycles. The coupling of the flow model to the stress-strain analysis is needed for including poroelastic processes and defining the spatial and temporal distribution of the fracture aperture. However, an important finding from the W3 simulation was that pressure and aperture within the fracture quickly approached spatially uniform values. It is interesting to explore the necessity of full flow and stress-strain coupling when this finding is assumed from the start. In this paper flow and stress-strain coupling is avoided by assuming a constant total stress and a uniform fracture pressure and aperture (whose values, however, may change with time). The paper is structured as follows. First, the governing equations of the simplified problem are defined. An analytical solution is derived for the special case of incompressible fluid and ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijrmms International Journal of Rock Mechanics & Mining Sciences 1365-1609/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2009.12.008 Ã Corresponding author. Tel.: + 44 191 33 43491. E-mail address: s.a.mathias@durham.ac.uk (S.A. Mathias). International Journal of Rock Mechanics & Mining Sciences 47 (2010) 517–522