In the context of Reservoir Engineering,
we use "Intrinsic Permeability"
(as against Hydraulic Conductivity); and
we also use "mobility" or "hydraulic diffusivity".
But, no where, "fluid density" comes into picture.
Then, How do we account for the "Variations in Density"
resulting from
(a) Dissolved-mineral content of the reservoir fluid; &
(b) temperature changes
in a typical Petroleum Reservoir - under normal circumstances?
I will say that, normally, you do all calculations about Volume, with little care about how much dense (heavy) is the fluid.
Also, in the flow through porous rock, we use Darcy law; and it uses only the viscosity, not the density of the fluid, since the flow happens at very low Reynolds numbers.
However, your dissolved minerals and temperature change will affect the viscosity.
Thermal expansion and mineral pickup are usually small, compared to the uncertainty we have on reservoir volumes.
But you can include them! Density is important eg. to calculate the hydrostatic pressure.
Under typical circumstances, we factor in variations in disolved mineral in log interpretations and ignore variations in most (all?) other reservoir aspects (static modelling and dynamic flow simulation). Occasionnaly, we factor in variations of disolved minerals all over the modelling chain (usually when there is strong variations in inital water salinity). In such cases, it is typical (but not mandatory) to limit mineral presence to the water phase. Changes in mineral content linked to variations of temperature are ignored except in peculiar circunstances such as SAGD. Above comment relate to reservoir development space and time scales not migration or digital rock physics space and time scales. Motivations are obvious considering the physics involved and the limited impact such aspects have on what matters. When to make things more complex and how to improve representation is reasonnably well understood (in my opinion).
Instead of intrinsic permeability, which provides you soil characteristics at the grain scale, the hydraulic conductivity (the capital K tensor) is the product of the intrinsic permeability and a second term addicted to fluid conditions. This term is the product between fluid density, temperature depending; gravitational acceleration constant; and fluid dynamic viscosity. Moreover, the linear (Newtonian) behaviour of dynamic viscosity tends to curve when a significative fraction of a REV is occupied by suspended solid matter. In petroleum reservoirs considering temperature effect on fluids is mandatory, because the temperature of reservoirs themselves increases by tens of degrees in respect of superficial temperature.
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