02 - 1a total dynamic head

Artificial Lift

REDA Pumps: Total Dynamic Head - TDH

Upon completion of this section, you should be able to:

Explain the concept of Total Dynamic Head.

List the components of TDH.Calculate the TDH given a set of parameters.

Explain the effect on TDH when using different tubing sizes.Explain the effect of fluid composition on TDH (i.e. water cut, oil density, etc)

Total Dynamic HeadTotal Dynamic HeadTotal Dynamic HeadTotal Dynamic Head


TDH is the sum of three basic components:

1) The Net Vertical Lift or net distance which the fluid must be lifted.

2) The friction loss in the tubing string

3) The wellhead pressure which the unit must pump against.

Flow

FlowFlow

Ground Level

Producing Fluid Level

Pump Set Depth

Wellhead

Net Vertical Lift1

2Total Friction Loss

Wellhead Pressure

3

Components of the TDH


Net vertical lift is the vertical distance through which the

fluid must be lifted to get to the surface.

The energy required to lift the fluid can be determined by the

equation:

Work (energy) = mghWhere: m is the mass of the fluid,

g is the acceleration due to gravity, and h is the height the fluid is lifted.

Flow

FlowFlow

Ground Level


Pump Set Depth

Wellhead

Net Vertical Lift

Note that the vertical lift only

depends on where the fluid level

is.

From the Net Lift stand point, it

makes no difference where the

pump is set.

1

Net Vertical LiftNet Vertical LiftNet Vertical LiftNet Vertical Lift

FlowFlow

Ground Level


Pump Set Depth

Wellhead

Net Vertical Lift

Note that even

though the pump is much

lower, the net lift does not

change.

Pump Set Depth

Net Vertical LiftNet Vertical LiftNet Vertical LiftNet Vertical Lift

Total Dynamic Head Total Dynamic Head Total Dynamic Head Total Dynamic Head ---- Net Vertical LiftNet Vertical LiftNet Vertical LiftNet Vertical Lift

Why is the vertical lift independent

of where the pump is set?

What if, instead of lifting the fluid vertically, we move it

sideways? How much work did we do?

None!

If Work (energy) = mgh,The h is zero if we move sideways so the work must be zero.


What about deviated wells?


Net LiftNet Lift

PFL

Regardless of

where the pump is

set, or the angle,

the vertical lift will

not change.

For the purposes of this example, we will assume we are given

a fluid level of 4000 feet from surface (vertical distance).

Net Vertical Lift = 4000 ft

Remember if the well is deviated, the total measured distance

from surface could be much greater but, since the work done

in moving the fluid sideways is zero, only the vertical distance

matters.

1


What is friction?

Total Dynamic Head Total Dynamic Head Total Dynamic Head Total Dynamic Head ---- Friction LossFriction LossFriction LossFriction Loss

Friction is an energy loss (we actually measure it as a

pressure loss) due to viscous shear of the flowing fluid.

In a fluid, molecules are free to move past each other but

there may be a little resistance. This resistance is due to

shear forces which must be overcome.


In a single phase fluid, most of the liquid is moving along

together so there is not much shear in the liquid itself and this

friction can usually be ignored.

Excuse me

Certainly

Sorry

No

Worries


The walls of the pipe, however, will tend to "stick" to the fluid so

shear forces between the pipe and the fluid can be quite large

and increase as the velocity of the fluid increases.

Hey!

Ouch!

I want out

of here!

Velocity

Profile

(Laminar Flow)


The amount of friction present can be represented by a "friction

factor" - f . Given f we can calculate the pressure loss from

the following:

Where P = pressure loss = fluid densityv = fluid velocity

gc = gravity constant

d = pipe diameter

P f vg d

c

= 2

2


Assume the flow rate is not zero but is some constant value. What happens

to the friction as the pipe diameter increases?

P f vg d

c

= 2

2


As the pipe diameter increases, the P decreases as can be seen in the equation. But something else also happens. What is it?

P f vg d

c

= 2

2


As the pipe diameter increases, the velocity, v, decreases by

the square of the diameter change so it is reduced drastically.

These two factors make an increase in pipe diameter have a

large impact on decreasing the frictional pressure losses.


So how do we calculate friction loss?

Total Dynamic Head Total Dynamic Head Total Dynamic Head Total Dynamic Head ----

Friction LossesFriction LossesFriction LossesFriction Losses

P f vg d

c

= 2

2

Fortunately, there are many charts available for determining

friction as we do not need to use these equations. A very useful

chart for our purposes follows:

Total Dynamic Head Total Dynamic Head Total Dynamic Head Total Dynamic Head ----

Friction LossesFriction LossesFriction LossesFriction Losses

Friction Loss

This is how to use the chart:

Say, for example, we have a total tubing length of 6500 feet and

we want to produce 5000 bpd. We have both 2 7/8" tubing and

3.5" tubing in stock. What will the friction be?

Total Dynamic Head Total Dynamic Head Total Dynamic Head Total Dynamic Head ---- Friction LossesFriction LossesFriction LossesFriction Losses

Friction Loss

200

5000

First, find the flow rate

on the X axis and move

up to the correct tubing

2-7/82-3/8

73

5000

3-1/2

Friction Loss

Since we have 6500' of tubing:

For 3 1/2", Friction = 73*6.5 = 475 feet of loss

If we can use 3 1/2" tubing, this will allow us to use a smaller

pump and motor which will reduce cost.

2


Is bigger tubing always better?

No

potential problems due to solids in suspension (sand).

Unfortunately the best teacher here is experience.


Wellhead pressure is sometimes called "Surface Pressure",

"Back Pressure" or even "Flowline Pressure". Actually the most

accurate term is "Tubing Discharge Pressure" since this is the

pressure at the discharge of the tubing from the well.

The Tubing Discharge Pressure is the resistance at the surface

the pump must overcome. Some components could be;

separator, heater treater, long flow lines etc.

Total Dynamic Head Total Dynamic Head Total Dynamic Head Total Dynamic Head ---- Wellhead PressureWellhead PressureWellhead PressureWellhead Pressure

"Back Pressure" is also a good term since it implies the correct

location in the discharge of the tubing string. "Flowline

Pressure" can actually be a much lower pressure if a surface

choke is being used to cut back the flow rate from the well.

"Surface Pressure" is just ambiguous.

All these terms are used interchangeably in the industry.


Up to this point, we have been calculating everything in terms of

"feet". This is very convenient when sizing a pump.

WHY?


For example, given:

Well head pressure = 200 psi

Water Cut (1.07 sp. Gr.)= 60%

Oil Cut = ?


This is the equation to convert from psi to feet but we still need to know the

specific gravity.

Wellhead Pressure*2.31

Wellhead "Feet" = ----------------------------------

sp.gr.


Petroleum Engineers prefer to use the API gravity because it is a larger

number and easier to "get a feel for". The equations for converting from one

unit to the other are:

Sp.Gr. =141.5

131.5 + API

API = 141.5

131.5Sp.Gr.


What is the specific gravity of an oil with API=30?

What is the API of fresh water (sp.gr.=1.0)?


For our example, use an oil with an API gravity of 30. This means that we are assuming the oil specific gravity is 0.876.

Sp.Gr. =141.5

131.5 + 30= 0.876


Next, find the composite specific gravity of the fluid in the well?

The best way to do this is simply to take an "arithmetic average".


is the water fraction

is the oil fraction

is the water specific gravity

is the oil specific gravity

Where :

Sp. Gr. = w f o

w

o

+

( )

)(

o

w

f

f

of w


For our example, the composite specific gravity is 0.992

Sp. Gr. = (0.60 x 1.07) + (0.40 x 0.876) = 0.992

Sp. Gr. = (fw x w) + (fo x o)


You are now ready to convert the wellhead pressure from [psi] to feet.

Wellhead Pressure*2.31

Wellhead "Feet" = ----------------------------------

sp.gr.


Using the numbers in our example:

200 psi *2.31 ft/psi

Wellhead "Feet" = ----------------------------- = 465 ft

0.992

3


The TDH will be the sum of:

Net Lift,Friction Loss, andWellhead pressure.

We will assume 2 7/8" tubing since it was in inventory:


Flow

FlowFlow

Ground Level


Pump Set Depth

Wellhead

Wellhead Pressure = 465 feet

2Total Friction Loss = 1300'

Net Vertical Lift1

4000

+1300

+ 465

5,765 ft of TDH

Total Dynamic Head

3

So we would need to design a pump with enough stages to

produce 5765 feet of head.

What happens if the composite specific gravity was lower

than we calculated?

(i.e. 0.82 instead of 0.992)


If this were the case, the wellhead "feet" would have been 563 feet instead of

465 which means we were 92 feet short in our calculations.

The pumps rate would therefore be less than expected.

We would need a pump to deliver 5857 feet of TDH rather than one for 5765

feet.


A word of caution when using fluid levels from "Sonic Logs"

to determine net lift...

Sonic Logs estimate the fluid level by making a loud noise

in the annulus (usually a compressed air) and measuring

the amount of time it takes for the sound wave to reflect

back to the wellhead after it hits the fluid level.

Total Dynamic Head Total Dynamic Head Total Dynamic Head Total Dynamic Head ---- determining fluid level

The Sonic level determination only looks at where the fluid level

is and not what the fluid is.

There will be significant variations for:

Gassy wells (foam not solid fluid)

High water cut wells


Oil

Produced Fluid

Example:

Top of Perforations = 8,350 ftPump Setting Depth = 6,900 ftFluid Level (Sonic) = 5,600 ftWater Cut = 70%Spec. Grav. (Water) = 1.04Oil API Gravity = 32

What is the Pwf and PIP?


0.30 0.865

The crude oil specific gravity is 0.865 and the fluid composite gravity is 0.988.

Sp.Gr. = +0.70 1.04 = 0.988

Oil Sp.Gr. =_141.5__

131.5 + 32= 0.865


For the portion above the intake, we assume due to natural separation, that the

fluid is all oil with a specific gravity of 0.865 and this is a reasonable assumption.

PIP = (6900 - 5600)ft x 0.433 psi/ft x 0.865

= 487 psi


For the portion below the intake, we assume that the fluid is the same as

produced from the well. That is to say that it is 70% water and the average

specific gravity is 0.988.

P = (8350 - 6900) ft x 0.433 psi/ft x 0.988= 620 psi


The perforation pressure will be the sum of the pressure at the pump intake

(PIP) and the pressure differential between the pump setting depth and the

perforation depth.

P = 487 + 620 = 1,107psiperfs


If we had assumed that the total fluid column in the well were a crude/water

mixture, we would have calculated a perforation pressure of 1,176 psi instead of

1,107 psi. Although this seems like a small difference, this could cause large

errors in the determination of the PI for the well which, in turn, could easily

cause us to oversize a pump.

Pperfs = (8350 - 5600) ft x 0.433 psi/ft x 0.988

= 1176 psi


Questions?Questions?Questions?Questions?

02 - 1a total dynamic head

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