Porous network rheology

Rheology of the Porous Network formulates the relations between stress and strain in a fluid-filled network when the solid phase is viscoelastic. 

K. S. Sorbie, P.J. Clifford and E.R.W. Jones, The rheology of pseudoplastic fluids in porous media using network modelling. /. Colloid Interface Sci., 130 (1989) 508-533. 

A point of terminology is repeated here to remind the reader. The term apparent viscosity , pp, is used to describe the observed macroscopic rheology of the polymeric fluid in a porous medium. The quantity effective viscosity ,, refers in a rather similar way to the observed effective viscosity in a single capillary. Each quantity is defined phenomenologically—from Darcy s law (Equation 6.4) and rj ff from Poiseuille s law (Equation 3.75). This distinction should be kept clear, especially when considering porous media models based on networks of capillaries, as discussed later in this chapter. The overall viscosity of the non-Newtonian fluid in the network as a whole is whereas the viscosity in each of the capillaries may be different and is In this latter case, will be in some sense an average value of the in the individual capillaries. 

In this section, some of the approaches that have been used to analyse observations on the flow of non-Newtonian fluids in porous media will be reviewed. Some discussion on this topic has already been presented in Sections 6.3 and 6.4, and here these comments will be put into context. Later in this section, there will be further expansion on some recently proposed methods based on network modelling for studying in-situ rheology. 

Sorbie, K. S. (1989) Network modelling of xanthan rheology in porous media in the presence of depleted layer effects. SPE 19651, Proceedings of the SPE 64th Annual Fall Conference, San Antonio, TX, 8-11 October 1989. 

Sorbie, K.S. 1989. Network Modeling ofXanthan Rheology in Porous Media in the Presence of Depleted Layer Effects. Paper SPE 19651 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 8-11 Pctober. DPI 10.2118/19651-MS. 

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