You may now already that the **equivalent circulating density** is a combination between current mud weight and frictional pressure. However, this post I would like to share more detail in regard to the bottom hole pressure when the well is in static and dynamic condition when the forward circulation is performed.

For forward circulation, we circulated from mud pump into drill pipe and the mud is returned from the annulus as you can see in the diagram below.

**Under a static condition:** The bottom hole pressure is equal to hydrostatic pressure from the drilling fluid.

BHP = Hydrostatic Pressure

**Under a dynamic condition:** Stand pipe pressure equates to summation of pressure loss of whole system.

Stand pipe pressure = Pressure loss in drill string + Pressure loss in BHA + Pressure loss across the bit + pressure loss in the annulus

The pressure loss acts opposite way while fluid is being moved; therefore, if you look at the annulus side, you will be able to determine the bottom hole pressure at the dynamic condition as per the equation below.

Bottom hole pressure = Hydrostatic Pressure + pressure loss in the annulus

Under the dynamic condition, the only effect on the bottom hole pressure is the pressure loss in the annulus. This is the reason why the ECD while forward circulation is expressed like this;

ECD = Current Mud Weight + [(pressure loss in the annulus) ÷ (0.052 x TVD of the well)]

**Ref book: ** **Formulas and Calculations for Drilling, Production and Workover, Second Edition**

I have a question, why the pressure loss across the bit does not affect the bottomhole pressure?

If I reference the BHP to tubing site, shouldn’t be like this

BHP=pump pressure+hydrostatic pressure-pressure loss across the bit- pressure loss in the drillstring+pressure loss in BHA?

It depends on which side you refer to. For example if you refer to drill pipe side, your equation is

BHP=pump pressure+hydrostatic pressure-pressure loss across the bit- pressure loss in the drillstring-pressure loss in BHA

or if you are reference to annulus side, your equitation will be

BHP = hydrostatic pressure + annular pressure loss.

Both of them are equal in terms of mathematics.

sorry i meant, minus pressure loss in BHA

Why does the annular pressure increase during the influx when gas moves upwards due to pressure release while the height of mud decreases?

The annular pressure increase due to loss of hydrostatic pressure.

BHP = Hydrostatic Pressure + Surface Pressure. Once the gas is moving up, the gas volume expand therefore the well will lose the hydrostatic pressure. In order to balance formation pressure as stated in the equation, the surface pressure will increase.

In UBD Operation

BHP in annuals side will be :

Pbh = Mud hydrostatic + Annular fractional pressure + Choke pressure

is that correct?

Thank you

Yes. This is correct.

tnx for share us this information

Considering the hole size and OD of the pipe is same throughtout the hole, would ECD in annulus be the same at TD and at say, in the middle?

It is the same ECD.