Flow of Newtonian fluids through an Oil Reservoir:
In a producing oil reservoir, in a radial coordinate system (as against unidirectional fluid flow) under non-isothermal conditions, will the viscous/shear stress tensor ‘still’ depend (a) linearly; (b) isotropically; & (c) covariantly – on the rate of strain?
Dear Suresh Kumar Govindarajan,
Greetings, I think that it is depending on the different parameters.
Regards, Saeed
in general reservoir fluids can have quite different viscous reological properties. For example when reservoir pressure decreases in an undersaturated reservoir ( pressure higher tgan bubble point), the asphaltenes can start separating from the rest of the crude. Just before this phase transition the oil becomes highly viscous and strongly non-newtonia. This can be experienced as plugging of the reservoir rock. Furthermore the typical shear stress in reservoir flow are extremely low. In typical rolling-ball viscosity measurements the shear stress is order of magnitudes higher and the non-Newtonian behaviour of the crude near (tixotropy) will escape observation. Also upon gas injection (miscible CO2 flooding) I expect such complex behaviour.
Note however that it is good common practice to start a modelling process by using the most simple model. That is assuming a Newtonian behaviour. You should only consider non-Newtonian behaviour if you are forced to do so by evidence. Introducing non-Newtonian behaviour adds empirical parameters in an already very complex model with many poorly defined reservoir properties (rock permeability, non-homogeneity, fractures…). My advice is therefore: start by using a Newtonian results, but be aware it is not always an accurate model.
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