Pseudo-Steady fluid flow through an oil reservoir: Feasible under special circumstances?

When multi-phase fluid (water, oil and gas) is flowing out of an under-saturated oil reservoir – towards the production well - by primary recovery; and if assume that the same amount of outgoing fluid flux is replaced by an incoming single-phase water-influx from surrounding aquifers that enters the reservoir, in the same time, whether the fluid flow through this petroleum reservoir can be assumed to be flowing under steady-state conditions 'hypothetically'?

Along the spatial length of reservoir between the production-well and the drainage radius, if we hit a point randomly in space, whether the fluid flow can remain as a constant with time – under any given special circumstances (so that the problem can be assumed to be under “simplified” steady-state conditions)?

Will it be feasible - to trace - the path of water, oil and gas particles - as it moves through the reservoir – towards the production well (at the pore-scale)?

During this process, will the instantaneous velocity of the respective water, oil and gas particle’s velocity will remain tangent to the streamline?

Also, will it be feasible to capture the number of streamlines passing through the cross sectional area of the reservoir (per unit area) in a direction – normal to the direction of fluid flow, so that the rate of flow of water, oil and gas can be deduced separately?

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