02 - 1a Total Dynamic Head [PDF]

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Artificial Lift REDA Pumps: Total Dynamic Head - TDH



Total Dynamic Head



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 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.



Components of the TDH Wellhead Pressure Wellhead



3 Flow



Ground Level



1 2



Net Vertical Lift



Total Friction Loss Producing Fluid Level



Pump Set Depth



Flow



Flow



Total Dynamic Head ”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) = mg∆h Where: m is the mass of the fluid, g is the acceleration due to gravity, and ∆h is the height the fluid is lifted.



Net Vertical Lift Wellhead



Flow



Ground Level



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 Lift



Producing Fluid Level



Pump Set Depth



Flow



Flow



Net Vertical Lift Wellhead



Ground Level



Note that even though the pump is much lower, the net lift does not change. Producing Fluid Level



Net Vertical Lift



Pump Set Depth



Pump Set Depth



Flow



Flow



Total Dynamic Head - Net Vertical Lift



Why is the vertical lift independent of where the pump is set?



Total Dynamic Head - Net Vertical Lift What if, instead of lifting the fluid vertically, we move it sideways? How much work did we do?



None! If Work (energy) = mg∆h, The ∆h is zero if we move sideways so the work must be zero.



Total Dynamic Head - Net Vertical Lift



What about deviated wells?



Net Lift



PFL



Regardless of where the pump is set, or the angle, the vertical lift will not change.



Net Lift



Total Dynamic Head - Net Vertical Lift



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 1



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.



Total Dynamic Head - Friction Loss



What is friction?



Total Dynamic Head - Friction 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.



Total Dynamic Head - Friction Loss



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. No Worries Excuse me Sorry Certainly



Total Dynamic Head - Friction Loss 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. I want out of here!



Hey!



Velocity Profile (Laminar Flow)



Ouch!



Total Dynamic Head - Friction Loss



The amount of friction present can be represented by a "friction factor" - f . Given “f” we can calculate the pressure loss from the following:



2



f ρv ∆P = 2 gcd



Where ∆P = pressure loss ρ = fluid density v = fluid velocity gc = gravity constant d = pipe diameter



Total Dynamic Head - Friction Loss



Assume the flow rate is not zero but is some constant value. What happens to the friction as the pipe diameter increases?



2



f ρv ∆P = 2 gcd



Total Dynamic Head - Friction Loss



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



2



f ρv ∆P = 2 gcd



Total Dynamic Head - Friction Loss



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.



Total Dynamic Head Friction Losses



So how do we calculate friction loss?



2



f ρv ∆P = 2 gcd



Total Dynamic Head Friction Losses



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:



Friction Loss



Total Dynamic Head - Friction Losses



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?



Friction Loss



200



First, find the flow rate on the X axis and move up to the correct tubing



5000



Friction Loss



2-3/8”



2-7/8”



73



5000



3-1/2”



Total Dynamic Head - Friction Losses



Since we have 6500' of tubing: For 3 1/2", Friction = 73*6.5 = 475 feet of loss



2



If we can use 3 1/2" tubing, this will allow us to use a smaller pump and motor which will reduce cost.



Total Dynamic Head - Friction Losses



Is bigger tubing always better? No



…potential problems due to solids in suspension (sand). Unfortunately the best teacher here is experience.



Total Dynamic Head - Wellhead Pressure



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 - Wellhead 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.



Total Dynamic Head - Wellhead Pressure



Up to this point, we have been calculating everything in terms of "feet". This is very convenient when sizing a pump. WHY?



Total Dynamic Head - Wellhead Pressure



For example, given: Well head pressure = Water Cut (1.07 sp. Gr.)= Oil Cut =



200 psi 60% ?



Total Dynamic Head - Wellhead Pressure



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.



Total Dynamic Head - Wellhead Pressure



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 Sp.Gr.



− 131.5



Total Dynamic Head - Wellhead Pressure



What is the specific gravity of an oil with API=30? What is the API of fresh water (sp.gr.=1.0)?



Total Dynamic Head - Wellhead Pressure



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



Total Dynamic Head - Wellhead Pressure



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".



Total Dynamic Head - Wellhead Pressure



S p. Gr. =



( fw



× γ w



Where :



f



w



is the water fraction



γ



w



is the water specific gravity



f



o



is the oil fraction



γ o is the oil specific gravity



)+ ( fo



× γ o



)



Total Dynamic Head - Wellhead Pressure



For our example, the “composite” specific gravity is 0.992 Sp. Gr. = (fw x γw) + (fo x γo) Sp. Gr. = (0.60 x 1.07) + (0.40 x 0.876) = 0.992



Total Dynamic Head - Wellhead Pressure



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



Wellhead Pressure*2.31 Wellhead "Feet" = ---------------------------------sp.gr.



Total Dynamic Head - Wellhead Pressure



Using the numbers in our example:



200 psi *2.31 ft/psi Wellhead "Feet" = ----------------------------- = 465 ft 0.992



3



Total Dynamic Head



The TDH will be the sum of: Net Lift, Friction Loss, and Wellhead pressure. We will assume 2 7/8" tubing since it was in inventory:



Total Dynamic Head Wellhead Pressure = 465 feet



3



Wellhead



Flow



Ground Level



1 2



Net Vertical Lift



Total Friction Loss = 1300'



Producing Fluid Level



Pump Set Depth



Flow



4000 +1300 + 465 5,765 ft of TDH



Flow



Total Dynamic Head



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)



Total Dynamic Head



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 pump’s rate would therefore be less than expected. We would need a pump to deliver 5857 feet of TDH rather than one for 5765 feet.



Total Dynamic Head - determining fluid level



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



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



Total Dynamic Head Example: Top of Perforations = Pump Setting Depth = Fluid Level (Sonic) = Water Cut = Spec. Grav. (Water) = Oil API Gravity =



8,350 ft 6,900 ft 5,600 ft 70% 1.04 32



What is the Pwf and PIP?



Total Dynamic Head



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



Oil Sp.Gr. =



Sp.Gr. =



_141.5__ 131.5 + 32



0.70 ×1.04



= 0.865



+ 0.30 × 0.865



= 0.988



Total Dynamic Head



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



Total Dynamic Head



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



Total Dynamic Head



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.



Pperfs = 487 + 620 = 1,107psi



Total Dynamic Head



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?