To better define the flow field around the well, the basic hydraulic flow equation is:
Q = A v
[Equation 2]
where the fluid flow in any system is a product of a velocity, times a cross sectional area applied to a well. Thus, if the cross sectional area is the cylindrical area of the bore hole wall, defined by the length of screen in the vertical dimension and the circumference expressed in terms of the diameter of the well bore in inches, then the flow to that well would be the product of permeability, times the length of the screen, times the diameter of the well corrected for the proper units of measurement as shown in equation three.
Qnfl = Kg Ls Dw/5500
[Equation 3]
|
Qnfl | = | Flow rate in gallons per minute (gpm), |
| Kg | = | Field coefficient of permeability in gpd/ft2, | |
| Ls | = | Length or column height of screen or formation (feet) | |
| Dw | = | Well bore diameter in inches |
From field experience, it has been determined that turbulent flow in a well bore begins at 2.35 times the laminar flow limit defined by equation three.
Qbtf = 2.35 Qnfl
[Equation 4]
|
Qbtf | = | Rate at beginning of turbulent flow, gpm |
The normal limit of turbulent flow available through a formation is approximately 12 times the laminar flow rate as shown in equation five.
Qbtf = 12 Qnfl
[Equation 5]
|
Qbtf | = | Maximum turbulent flow rate, gpm |
The above equations assume uniform vertical distribution of flow through the cylindrical wall area for the entire depth or thickness of the formation of uniform permeability.
The following figures illustrate the basic flow distribution that occurs normally in a large capacity well.
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