The purpose of this article is to present some guidelines and simplified techniques to size pumps and piping typically used in mud systems. If unusual circumstances exist such as unusually long or complicated pipe runs or if very heavy or viscous drilling muds are used, a qualified engineer should analyze the system in detail and calculate an exact solution.

## Definitions

### Total Head

To write about pumps, one must use words that are known and well understood. For example, the label on the lefthand side of any centrifugal pump curve is Total Head Feet. What does this mean?

The simplest way to flow water is to lay a length of pipe on the level ground and connect it to a standpipe (Figure 1). Water from the standpipe will flow steadily through the pipe. It flows faster when there is greater depth of water in the standpipe. The depth of water measured down the standpipe to the pipe connection centerline is the Total Head.

Total Head remains constant for a particular pump operated at a constant speed regardless of the fluid being pumped. However, a pump’s pressure will increase as the fluid density (mud weight) increases according to the following relationship:

PMUD(PSIG) = PWATER(PSIG) x {FLUID DENSITY(LBS/GAL)}/8.34

If a pump produces 200 ft-hd, then it follows that the pressure developed when pumping water will be:

PWATER = 200 FT-HD x 0.433 (PSIG/FT) x {FLUID DENSITY(LBS/GAL)}/8.34

PWATER = 200 FT-HD x 0.433 X 8.34/8.34 = 86.6 PSIG

NOTE: *Fresh water weighs 8.34 lbs/gal.*

The pressure developed when pumping 16 lb mud will be:

PMUD = 200 FT-HD x 0.433(PSIG/FT) x (16/8.34)LBS/GAL = 166.1 PSIG

Note that the pump pressure almost doubled. It follows that the required pump horsepower has increased by the same percentage. If the pump required 50 HP for water service, it will require the following horsepower for 16 lb/gal mud:

HP2 = HPWATER x (16/8.34) LBS/GAL = 50 x 1.92 = 95.9 HP

To summarize, a pump’s Total Head remains constant for any fluid pumped, only the pump pressure and pump horsepower will change. Therefore, a pump motor must be sized according to the heaviest weight mud to be pumped.

### Pressure Head

Pressure Head is simply the distance in feet that water will rise up a sight tube connected anywhere to a pipe with liquid in it. (see figure 1)

In our example problem, the required desilter pressure head is 75 ft. for any mud weight. However, the pressure would be 30.3 PSIG for water or 43.6 PSIG for 12 lb mud or 58.1 PSIG for 16 lb mud. A good rule of thumb is that the required pressure (PSIG) equals 4 times the mud weight (12 LB/GAL x 4 = 48 PSIG).

### Fluid

Fluid is a general term meaning water, brine, mud, oil or any other liquid being pumped.

### Flow Rate

Flow Rate will be expressed in gallons per minute, barrels per minute or cubic feet per second.

### Velocity (V)

Velocity of the fluid down the pipe is the average velocity across the inside diameter and is expressed in FT/SEC.

### Velocity head

Velocity Head is an expression of the energy required to accelerate the fluid from 0 FT/SEC in the suction tank up to the velocity of the fluid in the pipe.

VELOCITY HEAD = {(V)2}/(2G)

G = (GRAVITATIONAL CONSTANT) = 32.2 FT/SEC/SEC

The following charts may be used for velocity head ranges of our design fluid velocities.

Velocity (V) | Velocity Head | (VH) |

5 FT/SEC | 0.39 | FT-HD |

10 FT/SEC | 1.55 | FT-HD |

15 FT/SEC | 3.49 | FT-HD |

20 FT/SEC | 6.21 | FT-HD |

Velocity head is generally not a large number but should be included in pump calculations.

## Example Problem

We will size a pump and piping for desilter service. the desilter is a typical 16 cone unit equipped with 4″ diameter hydrocyclones.

### STEP ONE

Determine the required pressure head and flow rate. If the pump is to supply a device such as a mud mixing hopper or a desilter, consult the manufacturer’s information or sales representative to determine the optimum flow rate and pressure head required at the device. (On devices like desilters the pressure head losses downstream of the device are considered negligible and are usually disregarded.)

Our desilter cones require 50 GPM each at an inlet pressure head of 75 FT-HD. therefore, the total capacity will become:

16 CONES x 50 GPM = 800 GPM AT 75 FT-HD

### STEP TWO

Select the basic pump to pump the desired flow rate. Its best to refer to a manufacturer’s pump curve for your particular pump. (See example – Figure 3).

If a curve is not available, this chart below gives reasonably accurate values for typical centrifugal pumps used for mud service.

The values in Table 1 represent the approximate maximum capacity and pressure head (FT-HD) for a given pump and speed.

Table 1. Capacity and Pressure for Various Pump Sizes

Pump Size | Maximum Nominal Capacity Pressure In Mud Service |

2*3 1150RPM | 200GPM at 80 FT-HD |

2*3 1750RPM | 400GPM at 175 FT-HD |

3*4 1150RPM | 450GPM at 80 FT-HD |

3*4 1750RPM | 750GPM at 175 FT-HD |

4*5 1150RPM | 800GPM at 70 FT-HD |

4*5 1750RPM | 1000GPM at160 FT-HD |

5*6 1150RPM | 1100GPM at 60 FT-HD |

5*6 1750RPM | 1200GPM at 160 FT-HD |

6*8 1150RPM | 1300GPM at 80 FT-HD |

6*8 1750RPM | 1600GPM at 175 FT-HD |

The pump’s impeller may be machined to a smaller diameter to reduce its pressure for a given application. Refer to the manufacturer’s pump curves or manufacturer’s representative to determine the proper impeller diameter. Excessive pressure and flow should be avoided for the following reasons:

- Pump wears at a faster rate.
- Equipment such as hydrocyclones wear at a faster rate.
- Hydrocyclones do not operate effectively at a higher or lower pressure than specified.
- A larger electric motor, electric cable, and starter may be required unnecessarily.
- Energy cost to operate the pump will be greater.

The pump must produce more than 75 FT-HD at the pump if 75 FT-HD is to be available at the desilter inlet and the pump’s capacity must be at least 800 GPM. Therefore, we should consider using one of the following pumps from the above list: 4″ x 5″ Pump 1750 RPM – 1000 GPM at 160 FT-HD; or 5″ x 6″ Pump 1750 RPM – 1200 GPM at 160 FT-HD.

### STEP THREE

#### Size the piping

The pump suction and discharge piping is generally the same diameter as the pump flange diameters. The resulting fluid velocities will then be within the recommended ranges of 4 to 10 FT/SEC for suction lines and 4 to 12 FT/

SEC for discharge lines. Circumstances may dictate that other pipe diameters be used, but remember to try to stay within the above velocity guidelines. Smaller pump discharge piping will create larger pressure drops in the piping

and the pump may not be able to pump the required amount of fluid. (For example, don’t use a 4″ discharge pipe on a 6″ x 8″ pump and expect the pump’s full fluid flow.)

Find the proposed pipe diameter and flow rate in the attached tables (Figure 4 ) and confirm that the velocities are reasonable.

For our desilter flow of 800 GPM, note from the attached tables:

**For 4″ pipe –**

**Velocity = 20.2 FT/SEC**

**Velocity Head = 6.32 FT**

**Friction Loss per 100 FT Pipe = 32.4 FT**

**For 5″ pipe –**

**Velocity = 12.8 FT/SEC**

**Velocity Head = 2.56 FT**

**Friction Loss per 100 FT Pipe = 10.22 FT**

**For 6″ pipe –**

**Velocity = 8.88 FT/SEC**

**Velocity Head = 1.23 FT**

**Friction Loss per 100 FT Pipe = 4.03 FT**

**For 8″ pipe –**

**Velocity = 5.13 FT/SEC**

**Velocity Head = 0.41 FT**

**Friction Loss per 100 FT Pipe = 1.02**

We may conclude from the above data that:

- 4″ pipe should not be used for either suction or discharge piping. The velocity and pressure drop are too high.
- 6″ pipe may be used for the suction pipe since it is relatively short and straight and the pump suction is always flooded. 6″ pipe is fully acceptable for the discharge pipe and is a good choice since the desired header is probably 6″ pipe.
- 8″ pipe may be used for the suction pipe (V = 5.13 FT/SEC) since V is still greater than 4 FT/SEC. 8″ pipe would be preferred if the suction is long or the suction pit fluid level is low with respect to the pump.

We will use 6″ pipe for both the suction and discharge piping and will use the 5″ x 6″ Pump -1750 RPM.

### STEP FOUR

We now determine the total pressure head requirement of our piping system:

Total Pressure Head = Velocity Head + Pipe Losses + Vertical Head + Head Requirement of Desilter

#### Velocity Head

VEL-HD = 1.23 FT for 6″ pipe and velocity = 8.88 FT/SEC (Step Three)

#### Vertical Head

From Figure 2 we see that the vertical distance from the pump to the desilter inlet is 7 FT.

Therefore, the vertical head requirement = 7 FT.

#### Pipe Losses

We will assume that we have 60 FT of pipe, four elbows and one butterfly valve in the system. You may use Figure 3 alone for a simplified solution.

FIGURE 3. Friction loss for water or mud in feet head per 100 feet of pipe (f = 0.03) with or without pipe fittings.

Find the chart for 6″ pipe and look up the velocity closest to 8.88 FT/SEC. 8.88 does appear on the chart. The friction loss per 100 FT of pipe with fittings is 11.01 FT. Since we only have 60 ft of pipe, our friction loss is:

11.01 FT x (60/100) = 6.6 FT-HD

If a more exact solution is required, the loss from pipe fittings can be determined from Figure 4.

FIGURE 4. Friction loss for water or mud in feet head per 100 feet of pipe (f = 0.03) with or without pipe fittings