The friction pressure is pressure loss when fluid flowing through flowing paths and it acts **in the opposite direction **of fluid flow.

**The following factors affect the friction pressure:**

• Drilling string geometry both inside diameter and outside diameter

• Fluid Properties: Rheology and density

• Geometry of wellbore: hole length, wellbore area and flow area

• Wellbore condition such as packing off, bridging, etc

• Flow Rate

• Pipe movement and pipe rotation

## Let’s illustrate friction pressure

- Pump fluid with pressure upstream of 2,000 psi and discharge at atmosphere (0 psi)
- Pressure gauge in the middle reads 1,000 psi
- The diagram is shown in Figure 1.
- Pressure acts in the opposite direction of flow.

- Friction pressure between A and B is equal to P at A – P at B. Therefore, friction pressure between A and B is 1000 psi as shown in Figure 2.

- Friction pressure between B and C is equal to P at B – P at C. Therefore, friction pressure between B and C is 1000 psi as shown in Figure 3.

- Total pressure loss of this system (Friction Pressure) is 2000 psi (Figure 4).

## Friction in a wellbore

We will apply this concept to our wellbore. This is a well with a normal forward circulation from drillstring and come out on surface from the annulus. These are some information.

- Constant Fluid both sides
- Hydrostatic Pressure = 2,500 psi
- Friction P in Drillpipe = 1,500 psi
- Friction P in Annulus = 500 psi

The well diagram is show in Figure 5.

We can draw a simple diagram by applying U-tube concept as shown in Figure 6.

Figure 7 shows the relationship in the drill pipe side.

DP – FrPdp + HPdp = BHP

Where;

DP = Drillpipe Pressure

FrPdp = Friction pressure at drillpipe side

HPdp = Hydrostatic pressure at drillpipe side

BHP = Bottom hole pressure

Figure 8 shows the relationship in the casing side.

BHP =CP + FrPann +HPann

Where;

CP = Casing Pressure

FrPann = Friction pressure in annulus

HHPann = Hydrostatic pressure in annulus

BHP = Bottom hole pressure

** You will see that in the annulus friction pressure will act to the bottom hole since the flow moves upward direction so the sign is +.

Figure 9 demonstrates the whole relationship of the whole system.

**Let’s do some calculation to get more understanding about this topic based on this example.**

Starting from the drillpipe side (Figure 10),

DP – FrPdp + HPdp = BHP

2,000 – 1,500 + 2,500 = BHP

BHP = 3,000 psi

Calculation from annulus side (Figure 11)

BHP =CP + FrPann +HPann

BHP =0 + 500 +2,500

BHP = 3,000 psi

Figure 11 demonstrates the whole system. As you can see that we can calculate the BHP from any side and we will get the same result as per U-Tube principle.

With this example, we wish that would make you get more understanding about friction pressure in a wellbore.

Please leave any comments or questions below if you have any questions.

**References**

Cormack, D. (2007). An introduction to well control calculations for drilling operations. 1st ed. Texas: Springer.

Crumpton, H. (2010). Well Control for Completions and Interventions. 1st ed. Texas: Gulf Publishing.

Grace, R. (2003). Blowout and well control handbook [recurso electrónico]. 1st ed. Paises Bajos: Gulf Professional Pub.

Grace, R. and Cudd, B. (1994). Advanced blowout & well control. 1st ed. Houston: Gulf Publishing Company.

Watson, D., Brittenham, T. and Moore, P. (2003). Advanced well control. 1st ed. Richardson, Tex.: Society of Petroleum Engineers.

How do you calculate friction pressure?

You can use the computer to model it. I’ve seen some fluid models using to calculate the friction pressure.