Importance of poroelastic coupling in dynamically active aquifers of the Po River Basin, Italy

Abstract

Abstract. Uncoupling between the flow field and the stress field in pumped aquifers is the basis of the classical groundwater hydrology. Recently, some authors have disputed the assumption of uncoupling with regard to both fluid dynamics and porous medium deformation. The issue is very important as it could undermine the traditional approach to simulate subsurface flow, analyze pumping tests, and predict land subsidence caused by fluid withdrawal. The present paper addresses the problem of coupling versus uncoupling in the Po river plain, a normally consolidated and normally pressurized basin which has experienced in the last 50 years a pronounced pore pressure drawdown because of water and gas removal and where a large hydromechanical database is available from the ground surface down to 4000 m depth. A numerical study is performed which shows that the matrix which relates flow to stress is very similar to the capacity matrix of the uncoupled flow equation. A comparison of results obtained with the finite element integration of the coupled and uncoupled models indicates that pore pressure is rather insensitive to coupling anywhere within the pumped formation while in the adjacent aquitard-aquifer units, coupling induces a slight overpressure which quickly dissipates in time with a small initial influence on medium deformation, and specifically on land subsidence. As a major consequence the uncoupled solutions to the fluid dynamic and the structural problems appear to be fully warranted on any timescale of practical interest in a typical normally consolidated and pressurized basin. IntroductionWhen an aquifer, an oil/gas reservoir, or a confining bed experiences a change of the internal flow and stress fields (typically due to fluid withdrawal), the incremental effective stresses and the fluid dynamic gradients that develop within the porous medium are intimately connected. This complex interrelation was first mathematically described by Biot [1941]. A model of flow and stress based on the Biot equations is said to be a coupled model.Groundwater hydrologists and petroleum engineers who are mostly concerned with the fluid dynamic aspects of the coupled process have developed the uncoupled flow theory, whose most widespread and used equation, the so-called diffusion equation, was originally derived by Theis [1935] more than 60 years ago. This equation incorporates the rock structural behavior into a lumped mechanical parameter (the elastic storage coefficient) and is solved separately and independently for the pore pressure p. Once p is obtained, it may be used as an external source of strength in a poroelastic model of the porous system to provide the medium deformation, typically, land subsidence, i.e., the vertical displacement at the surface boundary. This is the uncoupled, or two-step, approach followed by many authors to simulate and predict land settlement due to

Geomechanical response to seasonal gas storage in depleted reservoirs: A case study in the Po River basin, Italy

“…The process is theoretically described by the 3-D fully coupled poroelasticity model originally developed by Biot [1941]. Gambolati et al [2000] and Settari et al [2005] have shown that in the reservoirs and aquifers of the Po River basin coupling between the flow and the stress fields is weak and uncoupling, as is usually assumed by hydrogeologists and petroleum engineers, is fully warranted on any timescale of practical interest.…”

Three dimensional numerical modeling of land subsidence in Shanghai

“…In geomechanical investigations at regional scale, uncoupled pressure -displacements solution can be safely used in predicting land subsidence in compacting sedimentary on any time scale of practical interest (Gambolati et al, 2000;Teatini et al, 2006Teatini et al, , 2010. In this study, an uncoupled approach is thus followed, with the flow field initially computed at each time step and the deformation then calculated using the pore pressure gradient as a known source of strength in the geomechanical model.…”

On the possible contribution of clayey inter-layers to delayed land subsidence above producing aquifers

“…Uncoupling the flow field from the stress field is a usual assumption in groundwater hydrology. Gambolati et al (2000) have shown that uncoupling has generally no measurable influence over any timescale of practical interest. Hence, in the present analysis a 1-way coupled approach is followed where the pore pressure variation is first simulated by a 3-D groundwater flow model, and then the land settlement is predicted by a 3-D geomechanical model with the pore pressure change used as an external distributed source of strength.…”