Guideline Centrifugal Pump Selection and Piping Design For ...

The objective of this article is to provide guidelines and simplified approaches to properly size pumps and piping for mud systems. In instances where the piping runs are considerably lengthy or complex, or when heavy and viscous drilling muds are utilized, it is advisable to have these systems thoroughly analyzed by a qualified engineer for precise solutions.

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Definitions

Total Head

When discussing pumps, it is essential to employ terminology that is clear and widely recognized. On any centrifugal pump curve, the leftmost label indicates Total Head Feet. What is its significance?

The simplest method to flow water involves laying a pipeline on level ground connected to a standpipe (see Figure 1). Water will flow steadily through the pipeline from the standpipe, accelerating along with an increase in the water depth within the standpipe. The measurement of water depth from the standpipe to the centerline connection of the pipe determines the Total Head.

Total Head remains constant for a specific pump when operating at a consistent speed, irrespective of the fluid being pumped. Nevertheless, a pump’s pressure will rise as the fluid density (or mud weight) increases, following this equation:

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

For a pump that produces 200 ft-hd, the pressure encountered when pumping water is:

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: Freshwater has a weight of 8.34 lbs/gal.

The pressure developed while pumping 16 lb mud will be:

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

It should be acknowledged that the pump pressure has nearly doubled, which implies that the necessary pump horsepower has also escalated accordingly. If a pump requires 50 HP for water service, it will requisitely need the following horsepower for 16 lb/gal mud:

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

In conclusion, the Total Head of a pump remains unchanged for any fluid pumped, while only the pump pressure and horsepower will fluctuate. Therefore, sizing a pump motor must consider the heaviest mud weight to be pumped.

Pressure Head

Pressure Head signifies the vertical distance in feet that water will rise in a sight tube connected anywhere along a pipe containing liquid (refer to figure 1).

In our scenario, the required pressure head for the desilter is set at 75 ft, regardless of the mud weight. However, the required pressures would be 30.3 PSIG for water, 43.6 PSIG for 12 lb mud, and 58.1 PSIG for 16 lb mud. A practical guideline dictates that the required pressure (PSIG) equals four times the mud weight (12 LB/GAL x 4 = 48 PSIG).

Fluid

Fluid is a broad term encompassing water, brine, mud, oil, or any liquid being pumped.

Flow Rate

Flow Rate can be defined in gallons per minute, barrels per minute, or cubic feet per second.

Velocity (V)

Velocity refers to the average speed of the fluid through the pipe and is expressed in FT/SEC.

Velocity Head

Velocity Head reflects the energy required to accelerate the fluid from 0 FT/SEC in the suction tank to the velocity attained in the pipe.

VELOCITY HEAD = {(V)²}/(2G)

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

Refer to the following charts for velocity head ranges applicable to our design fluid velocities:

Velocity head, while generally a minor value, should still be factored into pump calculations.

Example Problem

Let's size a pump and piping for desilter service where the desilter is a standard 16-cone unit fitted with 4-inch diameter hydrocyclones.

STEP ONE

Identify the requisite pressure head and flow rate needed. If the pump is meant to provide service for devices like a mud mixing hopper or desilter, it is best to consult the manufacturer's guidelines or a sales representative to find out the optimal flow rate and pressure head requirements at the device. (Typically, pressure head losses downstream of devices like desilters are minimal and can be disregarded.)

Our desilter cones require 50 GPM each, with an inlet pressure head of 75 FT-HD. Consequently, the total capacity becomes:

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

STEP TWO

Choose the basic pump suitable for achieving the desired flow rate. It’s advisable to consult a manufacturer's pump curve for your chosen pump type (see example in Figure 3).

If such curves aren't available, the chart below provides reasonably accurate values for typical centrifugal pumps utilized in mud service.

The figures in Table 1 indicate the estimated maximum capacity and pressure head (FT-HD) for specified pumps at certain speeds.

The impeller of the pump can be adjusted to a smaller diameter to reduce its pressure for specific applications. Refer to the manufacturer's pump curves or representatives for determining the appropriate impeller size. Avoid exerting excessive pressure and flow for the following reasons:

• Accelerates pump wear.
• Presents unnecessary wear on equipment like hydrocyclones.
• Hydrocyclones may fail to operate effectively outside specified pressures.
• May require larger motors, cables, and starters without necessity.
• Increased operational costs for running the pump.

The pump must generate more than 75 FT-HD to ensure availability at the desilter inlet, and its capacity should meet or exceed 800 GPM. Consequently, we should contemplate using one of the following pumps from the list: 4 x 5 Pump RPM GPM at 160 FT-HD; or 5 x 6 Pump RPM GPM at 160 FT-HD.

STEP THREE

Size the piping

Typically, the suction and discharge piping of a pump shares the same diameter as the pump’s flanges. This design leads to fluid velocities that stay between the recommended ranges of 4 to 10 FT/SEC for suction lines and 4 to 12 FT/SEC for discharge lines. Other pipe diameters might be necessary based on specific conditions, but it is recommended to adhere to the established velocity guidelines. Smaller discharge pipes lead to significant pressure drops that could prevent the pump from delivering the required fluid flow. (For instance, using a 4-inch discharge pipe with a 6-inch x 8-inch pump won't yield the pump's full fluid flow.)

Consult the proposed pipe diameter and flow rate in the accompanying tables (see Figure 4) to confirm reasonable velocities.

For the desilter flow rate of 800 GPM, the following observations can be made:

For 4-inch pipe:
Velocity = 20.2 FT/SEC
Velocity Head = 6.32 FT
Friction Loss per 100 FT = 32.4 FT

For 5-inch pipe:
Velocity = 12.8 FT/SEC
Velocity Head = 2.56 FT
Friction Loss per 100 FT = 10.22 FT

For 6-inch pipe:
Velocity = 8.88 FT/SEC
Velocity Head = 1.23 FT
Friction Loss per 100 FT = 4.03 FT

For 8-inch pipe:
Velocity = 5.13 FT/SEC
Velocity Head = 0.41 FT
Friction Loss per 100 FT = 1.02 FT

From the above data, we can conclude the following:

• A 4-inch pipe is unsuitable for either suction or discharge due to excessive velocity and pressure drop.
• 6-inch pipe is appropriate for the suction pipe, considering it is generally short and straightforward, and the pump suction remains flooded. It also works well for the discharge pipe, as it likely fits the desired header.
• The 8-inch pipe can be considered for the suction line (V = 5.13 FT/SEC) as it exceeds 4 FT/SEC. The 8-inch option is advantageous for longer suction lengths or when the fluid level is low relative to the pump.

We will opt for a 6-inch pipe for both the suction and discharge piping, using the 5 x 6 Pump - RPM.

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STEP FOUR

Next, we calculate 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-inch pipe with velocity = 8.88 FT/SEC (as established in Step Three).

Vertical Head

According to Figure 2, the vertical distance from the pump to the desilter inlet is 7 FT. Thus, the vertical head requirement is 7 FT.

Pipe Losses

We will assume a length of 60 FT of pipe, augmented by four elbows and one butterfly valve within the system. Figure 3 can be referenced for a simplified answer.

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

Using the chart for 6-inch pipe, we will locate the velocity closest to 8.88 FT/SEC, which exists on the chart. The friction loss per 100 FT of pipe along with fittings is calculated to be 11.01 FT. As our pipe is merely 60 FT, friction loss is:

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

For a more precise calculation, loss from pipe fittings can be assessed utilizing 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.