### Pressure and Friction Losses

The hydrostatic pressure is the force exerted by the column of the drilling fluids at a determined depth at a static status. It is related to the vertical depth and the density of the fluid. It is not related to the volume or the shape of the well (vertical, deviated or horizontal). At the dynamic status (while circulating) there are other friction losses which contribute in the level of the pressure in the wellbore depending on the direction of the flow. These friction losses are due to the internal friction of the fluids and the contacts between the drilling fluids wellbore walls.
When circulating, the pressure at the bottom of the well equals to the sum of the hydrostatic pressure and the annular friction losses.

Here are some exercises to illustrate the pressure concept:

**Problem 1:****Case 1:**

Phyd= 0.052 x 10 x 5000

Phyd= 2600 psi

In this case the bottom pressure is the same as the hydrostatic pressure

Pbottom=2600 psi

In this case the bottom pressure is the same as the hydrostatic pressure

Pbottom=2600 psi

**Case 2:**

Related to the case 1, the Phyd=2600 psi

In this case of circulation (Q=2000 lpm), the bottom pressure equals to the sum of the hydrostatic pressure and the annular friction losses:

Pbottom=2600 + 200

Pbottom=2800 psi

**Problem 2:**

The friction losses are related to the flow rate Q, density MW, any change of one of these parameters or both of them can affect the level of the friction losses.

In the case when the mud weight is changed, the new friction losses becomes:

In the case when the flow rate is changed, the new friction losses becomes:

In the case when both of them are changed, the new friction losses becomes:

The followed examples illustrate which parameter can affect more the losses.

**Case 1: Change of flow rate**

Q1=2000 lpm, Q2=1500 lpm

Phyd=0.052 x 10 x 5000

Phyd=2600 psi

Pbottom=2600+200

Pbottom=2800 psi

There is a change of the pressure due to the change of the flow rate:

Pannu2=200 x (1500 / 2000)²

Pannu2=112 psi

The bottom pressure becomes in the new situation:

Pbottom=2600+112

Pbottom=2712 psi

And the new stand pipe pressure becomes:

SPP2=2000 x (1500 / 2000)²

SPP2=1125 psi

Pbottom=2600+112

Pbottom=2712 psi

And the new stand pipe pressure becomes:

SPP2=2000 x (1500 / 2000)²

SPP2=1125 psi

**Case 2: Change of mud weight****MW1=10 ppg, MW2=12 ppg**

**Phyd2=0.052 x 12 x 5000**

Phyd2=3120 psi

The new friction losses is:

Pannu2=200 x (12 / 10)

Pannu2=240 psi

So the bottom pressure is:

Pbottom=3120 + 240

Pbottom= 3360 psi

And the stand pipe pressure becomes:

SPP2=2000 x (12 / 10)

SPP2= 2400 psi

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**Problem 3: Are you going to get a kick? **

In this example, the possibility of getting a kick is investigated.

Que question is: in both situations, in static or with circulation, can the formation fluids come into the wellbore?

**Case1:**

Phyd=0.052 x 12.50 x 9400

Phyd=6110 psi

In static Pbottom=Phyd

With this situation: the well will not flow in static, because the hydrostatic pressure Phyd is greater than the pore pressure (Pbottom > Ppores)

**Case2:**

Pbottom=Phyd+Pannu

Pbottom=6110+220

Pbottom=6330 psi

Obviously, the well will not flow while circulation because the bottom pressure is more than the pore pressure.

According to calculation performed previously, you can notice that in static the bottom pressure is less than the pore pressure (Phyd=6110 psi < Ppores=6200 psi). So, the well will flow, but in the dynamic mode (with circulation) the bottom pressure becomes greater than the pore pressures (Pbottom=6330 psi > Ppores=6200 psi) so the well will not flow.

###
**Exercise 4: What is your pressures after closing on a kick? **

In this example, the shut in drill pipe pressure and the casing pressure are calculated.

**1. SDPP:**

Phyd= 0.052 x 12.50 x 11600

Phyd=7540 psi

Pbottom=Phyd (Static mode)

SDPP=Ppores-Pbottom

SDPP=8100-7540

SDPP=560 psi

**2. SICP**

The annulus contains two column of two different fluids: the drilling fluids and the formation fluids, so the pressure on the bottom is the combination of these two columns.

Z=Zinflux+Zdrilling_fluids

Zinflux is the height of the kick and it is equals to Hinflux=650ft

Zdrilling_fluids is the height of the drilling fluids in the annulus

Zdrilling_fluids=Z-Hinflux

Zdrilling_fluids=11600-650 ,

Zdrilling_fluids=10950 ft

The bottom pressure in the annulus is sum of the exerted pressure by the columns of drilling fluids and the influx.

Pbottom=(0.052 x 12.50 x 10950) + (0.052 x 2.50 x 650)

Pbottom=7202 psi

ICP=Ppores-Pbottom

ICP=8100-7202

ICP=898 psi

The bottom pressure in the annulus is sum of the exerted pressure by the columns of drilling fluids and the influx.

Pbottom=(0.052 x 12.50 x 10950) + (0.052 x 2.50 x 650)

Pbottom=7202 psi

ICP=Ppores-Pbottom

ICP=8100-7202

ICP=898 psi

nice

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