Flux in Porous Media with Memory: Models and Experiments

被引:47
作者
Di Giuseppe, Erika [2 ]
Moroni, Monica [1 ]
Caputo, Michele [3 ]
机构
[1] Univ Roma La Sapienza, Dept Hydraul Transportat & Rd, I-00184 Rome, Italy
[2] Lab FAST, F-91405 Orsay, France
[3] Univ Roma La Sapienza, Dept Phys G Marconi, I-00185 Rome, Italy
关键词
Porous media; Memory's formalism; Fractional derivatives; Mechanical compaction; FRACTIONAL CALCULUS; DIFFUSION; TRANSPORT; RELAXATION; FORMALISM; RESERVOIR; PRESSURE; WATER;
D O I
10.1007/s11242-009-9456-4
中图分类号
TQ [化学工业];
学科分类号
0817 ;
摘要
The classic constitutive equation relating fluid flux to a gradient in potential (pressure head plus gravitational energy) through a porous medium was discovered by Darcy in the mid 1800s. This law states that the flux is proportional to the pressure gradient. However, the passage of the fluid through the porous matrix may cause a local variation of the permeability. For example, the flow may perturb the porous formation by causing particle migration resulting in pore clogging or chemically reacting with the medium to enlarge the pores or diminish the size of the pores. In order to adequately represent these phenomena, we modify the constitutive equations by introducing a memory formalism operating on both the pressure gradient-flux and the pressure-density variations. The memory formalism is then represented with fractional order derivatives. We perform a number of laboratory experiments in uniformly packed columns where a constant pressure is applied on the lower boundary. Both homogeneous and heterogeneous media of different characteristic particle size dimension were employed. The low value assumed by the memory parameters, and in particular by the fractional order, demonstrates that memory is largely influencing the experiments. The data and theory show how mechanical compaction can decrease permeability, and consequently flux.
引用
收藏
页码:479 / 500
页数:22
相关论文
共 40 条
[1]   On the fractional order model of viscoelasticity [J].
Adolfsson, K ;
Enelund, M ;
Olsson, P .
MECHANICS OF TIME-DEPENDENT MATERIALS, 2005, 9 (01) :15-34
[2]  
[Anonymous], 1995, PRINCIPLES HEAT TRAN
[3]  
[Anonymous], 2003, THEORY VISCOELASTICI
[4]  
[Anonymous], 1997, The Physics of Fluids in Hierarchical Porous Media: Angstroms to Miles
[5]  
[Anonymous], 1999, FRACTIONAL DIFFERENT
[6]  
AVSEHT P, 2005, QUANTITATIVE SEISMIC
[7]   ON THE FRACTIONAL CALCULUS MODEL OF VISCOELASTIC BEHAVIOR [J].
BAGLEY, RL ;
TORVIK, PJ .
JOURNAL OF RHEOLOGY, 1986, 30 (01) :133-155
[8]  
Bear J., 1972, Dynamics of Fluids in Porous Media
[9]   STRENGTH CHANGES DUE TO RESERVOIR-INDUCED PORE PRESSURE AND STRESSES AND APPLICATION TO LAKE OROVILLE [J].
BELL, ML ;
NUR, A .
JOURNAL OF GEOPHYSICAL RESEARCH, 1978, 83 (NB9) :4469-4483
[10]  
Caputo M, 1998, ANN GEOFIS, V41, P399