It is well-known that the oil/gas flow rate increases when it flows towards a producing well in a reservoir. This can lead to alteration of flow regime when it approaches towards the well. I'd like to know the following:
1) best Reynolds number correlation that includes all possible reservoir, fluid and flow parameters
2) acceptable value of critical Reynolds number where the flow can be considered turbulent beyond that
I think that re=1 is the best number has been introduced for turbulence flow indication.
If you are working experimentally you have to define some ranges between 8-25 depending upon the setup that you have. If you are studying computational you have to choose at least 1 and maximum 1.5 for accuracy.
Re for turbulence fluid is related to mainly 2 parameters: kinetic energy or forces to viscous forces, thus we have to consider both parameters at a given stage to make the threshold values between laminar and turbulent. When it consists on gas-fluid circulation we have to consider the flow patter bubbly, or slug or annular
In reality in porous media and rocks for single phase flow there is a slow transition from laminar to Inertial flow and for that reason you will find a range of Re cr.
For fractures it was between 1 and 20 (depending on the roughness to aperture ratio) among other factors) . for more details look at:
NON-LINEAR REGIMES OF FLUID FLOW IN ROCK (2004). Int. J Rock Mech. Sci. vol 41 No 3
Reynolds number of more than 4000 signifies that the flow is turbulent and the value less than 2000 signifies that the flow is laminar. The value between 2000-4000 can be considered to be transient.
Dybbs and Edwards [1] have studied experimentally
the characteristics of turbulent ow through
porous medium using laser anemometry and ow
visualization techniques. They reported that four
ow regimes may occur through porous media. Following
[1], the rst type of ow is the Darcy or
creeping ow regime, when the ow is dominated by
viscous forces and which occurs at Rep < 1 (based on
the average particle dimension and the average pore
velocity). At Rep = O(1), boundary layers begin to develop near the solid boundaries of the pores. The
inertial ow regime is the second type of ow, which
is initiated at Rep = 1 10, when the boundary
layers become more pronounced and an \inertial core"
appears. The developing of the \core" ows outside
the boundary layers is the reason for the non-linear
relationship between the pressure drop and ow rate.
As the Rep increases, the \core" ows enlarge in size
and their in uence becomes more and more signicant
to the overall ow picture. This steady non-linear
laminar ow regime persists up to Rep 150. The
third ow regime detected by [1] is an unsteady laminar
ow eld in the Reynolds number ranges of 150 to 300.
At Rep 250, the rst evidence of unsteady ow is
observed in the form of laminar wake oscillations in
the pores. These oscillations take the form of traveling
waves characterized by distinct periods, amplitudes
and growth rates. In this ow regime, these oscillations
exhibit preferred frequencies that seem to correspond
to growth rates. Vortices form at Rep = 250 and persist
up to Rep = 300. Finally, based on ow visualization
techniques, a highly unsteady and chaotic ow regime,
which occurs for Rep > 300 and which qualitatively
resembles turbulent ow, is categorized as a fourth ow
regime by [1].
ref.: Dybbs and Edwards, R.V. \A new look at porous
media fluid mechanism - Darcy to turbulent", in Fundamentals
of Transport Phenomena in Porous Media
(Book), J. Bear and V. Corapcioglu, M. Nijho, Eds.,
the Netherlands, pp. 199-254 (1984).
http://www.springer.com/gp/book/9789400961777
after Bear (1972), Hassainzadah 1987 suggested Re > 10 for turbulent flow. SPE-180920 (2018) page-2.
Dr. Reza can you e-mail me [email protected]
i need to plot Re versus reservoir radius (rw to re)
thank you
Tarek
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