Critical flow rate is the flow rate at the transition point between laminar and turbulent flow. The first step of the critical flow rate determination is to figure out the critical velocity and then substitute it into the annular flow rate.
To get the point at the transition period, the critical Reynold Number for laminar flow must be around 3470 – 1370na. With this relationship, we can determine the critical velocity by rearranging the Reynold Number and Effective Viscosity equation.
The effective viscosity equation for critical velocity is listed below:
The Reynolds number equation for critical velocity is listed below:
The critical annular velocity equation is listed below:
Flow of drilling fluids can be classified into one of three phases which are laminar, transition and turbulent flow.
Laminar Flow
Laminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow the motion of the particles of fluid is very orderly with all particles moving in straight lines parallel to the pipe walls.
Transition Flow
Transitional flow exhibits characteristics of both laminar and turbulent flow. The edges of the fluid flow in a laminar state, while the center of the flow remains turbulent. Like turbulent flows, transitional flows are difficult, if not impossible, to accurately measure.
Drilling fluid has three flow regimes which are laminar, transition or turbulent flow. The following illustrations demonstrate three types of flow
In 1883 when Mr Osborne Reynolds did the fluid study, he discovered Reynolds number describing flow of water in a circular pipe. From his experiment, the turbulent flow starts at the Reynolds Number of 2,000 and the complete turbulent flow occurs at the Reynolds Number of 4,000. Therefore, when the calculated Reynolds number of fluid is between 2,000 and 4,000, the transition flow is called.
Reynold number is the important figure because it demonstrates the flow regimes of drilling mud as laminar, transition or turbulent flow in annulus of the wellbore. In order to correctly calculate the Reynolds number, you need to use the effective viscosity, µea, which we already discuss about it from the previous topic.
The following equation is for Reynolds number in the annulus.
Where:
Rea = Reynold Number in the annulus
Va = Annular velocity, ft/min
Dh = Diameter of wellbore, inch
Do = Outside Diameter of tubular, inch
W = mud weight, ppg
µea = effective viscosity in the annulus, centi-poise
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Cutting Settling in a Vertical or Near Vertical Wellbore Causes Stuck Pipe
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Shale Instability Causes Stuck Pipe
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How To Free Stuck Pipe Caused By Differential Sticking
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Key Seat Causes Stuck Pipe
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Geo-Pressured Shale Causes Stuck Pipe
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Tectonic Stress Causes Stuck Pipe
Unconsolidated Formation Causes Stuck Pipe
How To Free Stuck Pipe Caused By Wellbore Geometry
The viscosity of drilling mud will change with a change in the shear rate because in some degree drilling fluids are shear-thinning. Because of its nature of drilling mud, people create the new term of viscosity called “Effective Viscosity” to compensate the change in shear rate of viscosity. By definition, the effective viscosity means the viscosity of Newtonian fluid that gives the same shear stress at the same shear rate.
The following equation is the effective viscosity equation.
Many types of drilling mud are classified as non-Newtonian fluid which is the behavior between Newtonian fluid model and Bingham Plastic model. The relationship between shear rate and shear stress is defined by the power law model shown below:
Today, we would like to distribute the new update drilling formula version 1.3.
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What new drilling formulas are added into the drilling formula version 1.3?
Effective Viscosity
Hydraulic Horse Power (HPP)
Optimum Flow Rate for basic system
Power Law Constant
Pressure Loss Annulus
Pressure Loss Annulus With Tool Joint Correction
Pressure Loss Drillstring
Pressure Loss Drillstring With Tool Joint Correction
Pressure Loss in Surface Equipment
Reynold Number
How many total useful drilling formulas in this version?
There are a total of 87 formulas which are divided into 7 categories (Applied Drilling Formulas, Basic Drilling Formulas, Directional Drilling Calculation, Drilling Fluid Formulas, Engineering Formulas, Hydraulic Formulas and Well Control Formulas).
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Annular velocity is the speed of fluid moving up the annulus and it must be high enough to transport cuttings generated while drilling from the wellbore. However, if the annular velocity is too high, it can create hole wash out and excessive equivalent circulating density.
When the drilling mud is circulated through a system, the moving speed is lower at location where the cross section area is bigger. Conversely, when the fluid flows through the small cross section area, the annular velocity at that point is higher.
The cross section area around drill collar and BHA has the smallest area so the annular velocity is the highest.
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= shear rate
= shear rate
The old rules for resumes that are no longer true. See which old techniques have been thrown in the trash bin. You’ll want to make sure you stop using them before you turn in your next resume.
