## Chapter II

## Stand Pipe Pressure Or Pressure Loss (Friction Pressure) Calculations

**PP = PDS + PB + PA**

**Where:****PP**: pump pressure, psi

**PDS**:

**drill string**friction pressure, psi

**PB**:

**drilling bit**pressure drop, psi

**PA**: annulus pressure, psi

**flow regimes**, such as laminar and turbulent. In addition,

**Bingham Plastic and Power Law models**differ in form. Since these models are frequently used in drilling applications, they will be presented in the following sections. Newtonian-based equations will not be presented.

### Surface Lines Pressure Loss (Friction Pressures).

Calculating the pressure drop in surface equipment such as the standpipe and kelly is normally accomplished by equating it to an equivalent length of drill pipe. The surface equipment is separated into four groups (below Fig.) to determine an equivalent length. For example, if a rig has group three surface equipment and 4Y2-in. **drill pipe** was used, an additional 479 ft of pipe would be used to calculate pressure losses in the surface equipment.

### Pressure Loss ( Friction Pressure) In Annulus And Drill String

### A) Bingham Plastic Friction Pressures

#### A – Friction Pressure Calculations in Drill String

**1) The velocity of the fluid in the drill string is described as following:**

**Where:****V**= fluid velocity, ft/sec

**Q**= flow rate, gal/min

**d**= pipe diameter, in.

**2) The critical velocity (Vc) for laminar and turbulence determination is computed from below Eq.:**

**Where:****Vc**= critical velocity, ft/sec

**PV**= plastic velocity, cp

**YP**= yield point, Ib/l 00 fe (check also Yield Point In Drilling Mud Formula)

**p**= mud weight, Ib/gal

**3) Drill string pressure loss (Friction pressures) for laminar flow can be calculated as follows:**

**Where:****L**= section length, ft

**4)**

**Drill string pressure loss (**

**Friction pressures) for tu**

**rbulent flow is calculated according to below Eq.:**

#### B – Friction Pressure Calculations in The Annulus

**1) The velocity of the fluid in the annulus is described as following:**

**Where:****2) The critical velocity (Vc) for laminar and turbulence determination is computed from below Eq.:**

**3) Annulus pressure loss (Friction pressures) for laminar flow can be calculated as follows:**

**4) Annulus pressure loss (**

**Friction pressures) for tu**

**rbulent flow is calculated according to below Eq.:**

### Example For Using Bingham Model In Friction Pressure Calculations

**Last Example**and the following data to calculate friction pressures for flow rates of 100 and 200 gpm. Use the Bingham model.

**Solution:****1. Calculate the velocities for flow rates of 100and 200 gal/min:**

**2. Determine the critical velocity at which laminar flow will convert to turbulent flow:**

**(**1.08 x 29 + 1.08 x ( 29^2 + 12.34 x 3.5^2 x 6 x 12.9)^(1/2)

**)**/

**(**12.9 x 3.5

**) =**3.37 ft/s

**3. Calculating Friction Pressure For 100 gal/min**

For the flow rate of 100 gal/min, the actual velocity (Va) is slightly less than the critical velocity (Vc)of 3.37 ft/sec. Use the laminar flow equation. (Note that the difference between Va and Vc is small. Therefore, it might be advisable in some cases to consider calculating pressure losses

**4. Calculating Friction Pressure For 200 gal/min**

At a flow rate of 200 gal/min, the actual velocity of 6.66 ft/sec is significantly greater than the critical velocity of 3.37 ft/sec. Therefore, use the turbulent flow equation:

#### The Difference Between Friction Pressure Calculations In Both Laminar & Turbulent Flow

The **laminar and turbulence** equations can be used to illustrate the basic difference between these two flow systems. In the laminar equations, a value for the yield point (YP) is a significant part of the pressure loss, particularly when it is observed that the PV value is divided by a squared diameter. The

### B) Power Law Friction Pressures

- If Va and Vc differ significantly, choose the appropriate flow equation.
- When Va = Vc make both pressure loss computations and choose the larger.

#### A – Friction Pressure Calculations in Drill String

For computation simplicity, NR = 3,000 is assumed for turbulence criteria. Basic assumptions for friction factor correlations result in the **critical velocity equation**:

Calculating pressure loss (friction pressures) in the **drill string** using the Power Law equations for **laminar flow: **

Calculating Pressure loss (friction pressures) in the **drill string** using the Power Law equations for** turbulent flow:**

#### B – Friction Pressure Calculations in The Annulus

**Calculating critical velocity equation**

**Calculating pressure loss (friction pressures) in the annulus using the Power Law equations for laminar flow:**

**Calculating Pressure loss (friction pressures) in the annulus using the Power Law equations for turbulent flow:**

**μ**related to PV, as shown below:

#### Example Of Using Power Law To Calculate Friction Pressure

**Examples**and compute the friction pressures for the system in above Example. Use the Power Law model and a flow rate of 125 gal/min. If Va nearly equal Vc, compute the pressure drop for laminar and turbulent flow and choose the larger value.

**Solution:****l) Referring to above Examples , the data to be used are:**

**3) Use Below Equation to compute the critical velocity, Vc:**

**For purposes of illustration in this example, assume that Va of 250 ft/min nearly equal Vc**

**of 183 ft/min.****4. Calculating Laminar flow pressure losses (friction pressure)**

**5) Calculating Turbulent flow pressure losses (friction pressure)**

7) Some groups within the industry bypass Step 3 altogether and compute the pressure drops from both laminar and turbulent equations