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Designing a hydraulic pump installation

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An installation analysis is typically required prior to installing and operating any hydraulic pump. The equations are sufficiently complex that a computer should be used although a hand held calculator can be used if the GLR is 10 or less (a flowing gradient correlation is not required). That being said, the pumps used in a given area tend to be very similar and additional pumps will often be the same as those already in use. In such a case, then an analysis is typically done just for the initial installations. However, subsequent analyses are frequently done for the purpose of optimizing the performance of the pumps in the different wells.

Computer needs

Computer programs are available from the manufacturers for both piston and jet pumps, and are typically provided at no cost to the user. These programs are only provided in a complied format as the manufacturers consider the programing code to be confidential. A computer is always required whenever the GLR is greater than 10 (a flowing gradient correlation is required) as the solution is an iterative process when gas is present and it has been known to require almost 50 iterations to obtain a convergence. If anyone is so inclined, that person would be free to create a program for piston and/or jet pumps using the equations attached to this document. For jet pumps, loss coefficients are needed (nozzle, throat and diffuser) for the different jet pump configurations available in the industry. However, they are not part of the public domain as they are considered to be confidential information by the manufacturers. Some generic loss coefficients are available, but the user is warned against assuming that they apply to any particular jet pump.

General comments for jet pumps

Nozzle and throat combinations


The performance of a jet nozzle and throat combination is related to the size of the nozzle and the annular area between the throat and the jet stream of the nozzle.

Flow capacity

As the nozzle size and throat size increase, then the flow capacity increases. The larger nozzle flow area allows for a greater nozzle flow and a larger annular area allows for larger volumes of oil, water and gas to pass into the throat for the same differential pressure.

The ratio of the nozzle area to the throat area equals the area ratio.

As the area ratio progressively decreases, then the throat has a greater annular area for the flow of produced fluids around the nozzle. Greater production rates are possible for a constant differential pressure, but less discharge head will develop due to the reduced volume of power fluid available to interact with the greater volume of produced fluid.

The reverse is true for the larger ratio numbers. Lower production rates occur as the throat size decreases since the annular area available for fluid flow progressively decreases. A greater discharge head will develop due the greater volume of power fluid available to interact with the reduced volume of produced fluid. In many cases the user will work to select an optimum size within a horsepower constraint. The power required depends on the nozzle size, the operating pressure, the depth of the well, and especially the pump intake pressure.

In general, larger throats with a given nozzle lead to higher operating pressures because these ratios have less pressure recovery. However, when power fluid friction is significant, the use of a larger ratio may lead to lower operating pressures if the nozzle size can also be reduced.

The effect of pump discharge pressure on pump performance generally results in 1 to 5 psi extra of power fluid pressure to maintain performance for every 1 psi increase of discharge pressure. This depends on the area ratio, with the higher ratios requiring less than the smaller ratios. The discharge pressure depends to a great deal on the gas-to-liquid ratio (GLR) in the return column, which in turn depends on how much power fluid is mixed with the production.

Experience has shown that in wells deeper than about 6000 feet TVD, the use of oil as the power fluid results in a lower injection pressure. Although the use of water as a power fluid increases the pressure at the nozzle, due to its higher density, it also increases the discharge pressure. This latter effect dominates and becomes evident in deeper wells.

Analyzing piston and jet pump installations

Well Parameters

  1. Mid-Perforation Depth (TVD, ft. or m) Note: The value should be at mid-perfs as that will compensate for the contributions of the perfs both above and below that point.
  2. Pump Vertical Depth (TVD, ft. or m) This is used primarily for the hydrostatic pressure calculations for both the supply and return columns.
  3. Type of Pump Installation: Standard, Reverse or Parallel

The standard (also known as casing free) installation includes one string of tubing for the power fluid supply and the pump and BHA. The return fluids (the well fluids plus the spent power fluid) go to the surface through the casing-tubing annulus.

The reverse flow or reverse circulation installation is where the power fluid goes down the casing-tubing annulus, and the well produced fluids plus spent power fluid return up the primary tubing string. Note: This is possible only for a jet pump and not a piston pump.

The parallel installation includes one string of tubing that conducts the power fluid supply down to the pump and BHA, and a separate string of tubing that returns the produced fluids plus the spent power fluid to the surface. Technically, this can also be a reverse flow installation but the algorithm for the analysis is very nearly the same as for standard flow.

Conventional or concentric type installations are modeled using the standard or casing free type of installation. In this type of installation, there is a smaller diameter tubing string set inside and concentric to a larger diameter tubing string. The larger tubing string is considered to be the casing in order to do an analysis.

4. Casing I.D. (in. or mm): This is the actual diameter not the drift diameter. The actual diameter is the diameter through which the fluid flows, thus installations with iron sulfide, scale or paraffin deposits may have a diameter less than the original steel size diameter.

If there is a liner at the bottom of the well and the BHA is set into it, an equivalent length weighted average diameter to represent the two casing sizes is used. However, the friction losses in a casing return are generally quite low, and this correction is rarely significant. When there is gas in the return fluid, it is usually in solution or greatly compressed in the lower part of the well, and the effect of a smaller liner is usually insignificant. The return diameter when gas is present is much more critical in the upper part of the well where the gas is coming out of solution and occupying more volume. Acceleration effects can be significant here, too.

5. Tubing O.D. (in. or mm): This is the actual tubing O.D. and not the coupling O.D. The contribution of the couplings to the friction loss is insignificant except when the coupling OD is just under the casing drift diameter. In that situation, their total length should be used as a separate tubing section in the section of casing where they are that close.
6. Tubing I.D. (in. or mm): This is the actual tubing I.D. and not the drift diameter. It is the actual diameter through which the fluid flows. Thus installations with iron sulfide, scale or paraffin deposits may have a diameter less than the original steel size diameter. Whatever the ID is, it must be large enough to pass the pump.
7. Tubing Length (ft. or m): This is the actual measured depth of the power fluid supply tubing string from the surface to the pump. It must be greater than or equal to the vertical pump depth specified in Item 2.
8. Pipe Condition: new, average or old: This takes into consideration the surface condition of the tubing in the system and is used for friction loss calculations. Values used for roughness are usually 0.0018 for new tubing, 0.0033 for average and, 0.0048 for old.
9. Oil Gravity (API): This is the produced oil gravity in degrees API. The value used must be for the produced oil at stock tank conditions and corrected to 60 degrees Fahrenheit (standard conditions).
10. Water Cut (%): This is the percentage of water in the production, not the return fluids. It is normally obtained from a 24-hour well test. The test conditions may be at the pressure and temperature of the test or metering separator used to meter the oil and water or determined from the volumes reported at stock tank conditions. (Does not ned to be corrected to standard conditions.)
11. Water Specific Gravity: This is the specific gravity of the produced water relative to fresh water, which has a specific gravity of 1.00.
12. Producing GOR (scf/STB or m3/m3): This is the gas-oil-ratio (GOR) of the produced oil in cubic feet of gas per barrel of oil produced or cubic meters of gas per cubic meter of oil produced at standard conditions of 60F and 14.7 psia.

The importance of the accuracy of this input variable cannot be overemphasized. This value is a major factor in determining the friction pressure drop of the return fluids, and is used to determine all of the correlation derived fluid properties. The accuracy of the GOR determines how well a program can model the well performance.

13. Gas SP. Gravity (air=1.): This is the produced gas specific gravity relative to the specific gravity of air = 1.00. The presence of H2S or CO2 will lead to higher values. The gas gravity is a major factor used to determine correlation derived fluid properties.
14. Separator Press (psig or kpa): This is the operating pressure of the test or metering separator used to meter the oil, water, and gas volumes.

In many cases a tank battery serves one well or a limited number of wells and the stock tanks are used to gauge the production of a well. If the fluids are measured at stock tank conditions then use the operating pressure of the last treater vessel or production separator that is immediately upstream of the stock tanks. Thus, the operating pressure of the pressure vessel that dumps its oil and water into the stock tanks is considered to be the separator pressure used for the calculations.

The separator pressure variable is used to correct the GOR value from the test condition to the dead oil condition found in the stock tanks and establishes the base value for the oil and water volumes for use by multi-phase flow correlations.

15. Well Static BHP (psig or mpa): This is the static or reservoir bottomhole pressure. The static BHP is the pressure to which the oil reservoir would build and stabilize at if no further production were allowed. This is the first of three values used to construct an inflow performance relationship (IPR) curve for the well. Remember: The pressure datum is at the midpoint of the perforation interval.
17. Well Flowing BHP (psig or mpa): Use the steady state producing or flowing bottomhole pressure that corresponds to the production rate specified for the oil and water in Item 18 (Well Test Flow Rate). The IPR curve and its ability to model changes in the production rate for different producing bottom hole pressures is dependent on the accuracy of the reported rates and pressures.
16. Well Test Flow Rate (bpd or m3): This is the total liquid flow rate of the oil and water as reported by a 24-hour production test. If the actual rate is not based on a 24 hour test period, then use an estimate of what the rate would be if reported on a 24 hour basis. The multi-phase flow correlations are based on the volumes produced during a 24-hour basis. In addition, the program used should correct the oil and water rate reported at the test conditions to the oil and water volumes that would occur at stock tank conditions as the IPR relation and the multi-phase flow correlations use those values.
17. Wellhead Temp. (deg F or deg C): This is the temperature at the wellhead of the return fluid consisting of the well produced fluids plus the spent power fluid. The well temperature is used to calculate the well temperature gradient. The wellhead temperature affects the calculation of the pump discharge pressure by affecting the fluid property values calculated by the multi-phase fluid flow correlation.
18. Bottomhole Temp. (deg. F or deg C): This is the bottomhole temperature reported at the perforation depth (normally it is greater than the surface temperature).
19. Does Gas By-pass Pump: yes or no: This specifies how much, if any, free gas will go through the pump. Obviously, gas cannot be by-passed around the pump if a packer is also in the well.

The effectiveness of downhole gas separators is difficult to predict accurately. If the yes option, or vented, is used, then a program will typically calculate the amount of free gas at any given pump intake pressure (total GOR minus the dissolved GOR). It will then calculate the area ratio of the power fluid string I.D. to the casing I.D. and multiply it times the free gas volume. This amount is assumed to go through the pump, with the remainder being by-passed or vented. In a typical installation, this calculation method would allow about 80% of the free gas to be vented.

Another technique concerning vented installations is a method whereby the non-vented option is used and the GOR value is hand calculated. The GOR will vary from the minimum value equal to the solution GOR calculated at pump intake conditions to the GOR reported at test separator conditions. This capability to override the area ratio factor is especially important when modeling an existing pump installation.

20. Power Fluid: oil or water The programs will allow the user to select the type of power fluid and it is virtually always one that comes from the well being produced. It is possible to use any liquid but its characteristics must be known if it is not from the well.
21. Power Fluid API/Specific Gravity: This will be one of the liquids from the well or a third type as explained in #20.
22. Bubble Pt. Pressure (psia or kpa): If possible, use a value that has been determined from a PVT analysis, or as calculated by flash calculation procedures provided the composition of the reservoir fluid is known. If not, then a correlation must be used.
23. Wellhead Press (psig or kpa): The bubble point pressure is used in developing the well inflow performance relationship (IPR) curve. The value that is used should be the pressure of the return fluids as they exit the wellhead. The performance of a pump is dependent on the discharge pressure required to overcome the effects of fluid friction, hydrostatic pressure due to the fluid gradient, and the wellhead or back pressure acting on the system. This value can significantly change the pump discharge pressure when gas is present because it affects the density of the upper portion of the return column.

To model installations with a well site unit, use a wellhead pressure that is greater than or equal to the current flowline pressure plus 40 psig. An operating pressure at least 40 psig above the flowline pressure is required for proper hydrocyclone operation.

Equations and Algorithm for Using a Hand Held Calculator to Analyze a Piston Pump Installation (GLR < 10)

The following calculations, performed in order, will provide the information necessary to determine the proper piston pump for any well application. (The user may wish to use more sophisticated calculation techniques in place of some of the equations listed below.)


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See also

Hydraulic pumping

Downhole hydraulic pump installations

Downhole hydraulic pump types

Hydraulic pumping surface equipment

Hydraulic pumping systems for single wells


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