## Pressure Drop through Surface Equipment

Pressure drop through surface equipment is one of the components in drilling hydraulics that must be considered. When we talk about surface equipment, we usually refer to those following equipment as a stand pipe, surface hoses, a swivel, a gooseneck and a Kelly.

Surface equipment on the rig – more detail here http://en.wikipedia.org/wiki/List_of_components_of_oil_drilling_rigs Continue reading

## Pressure Drop Across a Bit

Pressure across a bit occurs when the drilling mud passing through the jet nozzles. This pressure drop is important for drilling hydraulic optimization (maximum hydraulic horse power or impact force) and hole cleaning. The pressure drop at the nozzle area is a function of total flow area of the bit, flow rate and mud density.

Pressure drop across the bit can be determined by the following equation:

## Oilfield Unit

Pb = (Q²×W) ÷ (12031 × A²)

Where:

Pb = pressure drop across a bit, psi

Q = flow rate, gpm

W = mud weight, ppg

A = total flow area, square inch

Please use the following information to determine pressure drop across a bit

Flow rate = 800 gpm

Mud weight = 9.0 ppg

Total Flow Area = 0.3728 square inch

Pb = (800²×9.0) ÷ (12031 × 0.3728²)

Pb = 3,446 psi

## Metric Unit

Pb = (Q²×W) ÷ (7.191 × A²)

Where:

Pb = pressure drop across a bit, KPa

Q = flow rate, lpm

W = mud weight, kg/m³

A = total flow area, mm²

Please use the following information to determine pressure drop across a bit

Flow rate = 3,000 l/m

Mud weight = 1,100 kg/m³

Total Flow Area = 240 mm²

Pb = (3,000²×1,100) ÷ (7.191 × 240²)

Pb = 23,901  KPa

Ref books:

Lapeyrouse, N.J., 2002. Formulas and calculations for drilling, production and workover, Boston: Gulf Professional publishing.

Bourgoyne, A.J.T., Chenevert , M.E. & Millheim, K.K., 1986. SPE Textbook Series, Volume 2: Applied Drilling Engineering, Society of Petroleum Engineers.

Mitchell, R.F., Miska, S. & Aadny, B.S., 2011. Fundamentals of drilling engineering, Richardson, TX: Society of Petroleum Engineers.

## Critical Flow Rate – Drilling Hydraulics

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:

## Type of Flow in Drilling Hydraulics

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.