Fluid Mechanics Applied to Rehabilitation with Liner Installation

A case study of a project that substantially increases well efficiency.

By Robert M. St. Louis and Mark J. List

Proper pump performance requires attention to a number of details.

However, as wells age they can present additional challenges. This article presents a case study addressing the value of doing the work necessary to ensure water velocities in the well are proper after changes are made as a result of well rehabilitation.

The fluid mechanics employed are not as detailed as those that might be applied. Rather, the approach taken here emphasizes a practical method that can be easily applied by other practitioners.

The site in question has multiple deep, large diameter dewatering wells. Some wells are up to 3600 feet deep, and casing is generally in the 24- or 18-inch-diameter range. Pumping rates are generally in the range of 1800 to 2500 gallons per minute from each well.

Background

Dewatering well DW-23 was constructed in late 2008, with 18-inch, 0.375-inch wall mild steel ful flo louver casing to 2736 feet below grade. In 2016 during routine maintenance of the pumping equipment, a video survey indicated the well required rehabilitation. The initial rehabilitation effort involved a double surge block (swab) equipped with a brush. During brushing and airlifting, gravel pack and formation material began to circulate out of the well.

A second video survey showed extensive erosion of louvers over several intervals, necessitating the installation of a liner to prevent pumping of the remaining gravel pack. The original 18-inch casing had an inside diameter (I.D.) of 17.25 inches, and the pump that was planned for installation had an outside diameter (O.D.) of 10 inches.

Prior to liner installation, brushing and swabbing of the well continued until the well was clean. After the brushing and swabbing process was complete, the well was disinfected, and the swab was used to agitate the hypochlorite solution into the near well environment.

Crews at this site always follow the best practice of installing a shroud on electric submersible pumping equipment. Because the pumping assembly was to be installed within the liner, it was critical the design provided sufficient annular space to maintain flows of 8 feet per second or less between the liner and shroud. An additional complicating factor was the fact the original well was not perfectly plumb, in spite of being drilled using a long, rigid drilling assembly. Nevada is known for “crooked ground,” as contractors like to say.

Liner Design

Ful flo louver casing was chosen for the liner because of its robustness and efficiency. The liner had to have sufficient compressional strength to allow it to stand on the bottom of the well because there was no desire to extend it all the way to the surface. Therefore, the liner would be installed using a back-off tool and would have to support its own weight. A total of 600 feet of liner was to be installed in this instance. It should be noted the liner manufacturer does not endorse the practice of installations requiring the liner to be in compression.

The actual O.D. of ful flo louver casing is calculated as:

True O.D. = O.D. + (2 × slot opening) + (2 × wall thickness)

The decision was made to use 15-inch O.D. ful flo casing, 0.375-inch wall, with 0.125-inch slots. Therefore, the actual O.D. was 16 inches. The weld collars add another 0.75-inch, for a total O.D. of 16.75 inches. Fortunately, the casing manufacturer has the ability to build casing of non-standard diameter.

In order to ensure the liner could be installed in the somewhat crooked well, the ful flo louver liner was ordered with the louvers inverted (in other words, the shutter portion of the louvers pointed up-well when installed). This eliminated any opportunity for the shutters on the liner to snag on the bottom of the casing louvers.

Figure 1. Schematic cross section through the louvers on the casing and the liner (no scale).

Furthermore, a steel bullnose was attached to the bottom of the liner, providing a round geometry that facilitated liner installation. Figure 1 is a schematic cross section of the louvers on the casing and liner, illustrating how the shutters on the liner would essentially slide past the bottom of the casing louvers.

Shroud Design

Having selected the liner, which would have a 14.25-inch I.D., the next phase in the design involved working through the fluid mechanics to ensure proper water velocities. The motors required a minimum flow of 1 foot per second (fps) to provide adequate cooling. The maximum flow past the motors or in the annulus between the shroud and liner was to be limited to 8 fps to maintain low friction losses through decreased turbulent flow.

In order to accommodate the 10-inch O.D. pump, the upper portion of the shroud would utilize 12.75-inch O.D. schedule 40 (0.406-inch wall) pipe. The 12-inch pipe would be connected to the lower portion of the shroud by means of a concentric reducer.

Given the O.D. of the motors was 7.375 inches, the shroud I.D. had to be at least 10 inches (the shroud used prior to rehabilitation was 13.375-inch O.D., 12.415-inch I.D.). Pipe with 10.75-inch O.D. and 0.25-inch wall was selected, resulting in an I.D. of 10.25 inches. The annulus between the liner I.D. and the shroud O.D. resulting from this selection was 1.75 inches, with an annular area (Aa) of 0.477 square feet (ft2). The annulus between the O.D. of the motors (7.375 inches) and the I.D. of the shroud would be 1.4375 inches, with an Aa of 0.276 ft2.

The design pumping rate (Q) for this well was 1850 gpm, or 4.1 cubic feet per second (cfs). Dividing the volume by the annular area, the resulting velocity (V) between the motors and shroud would be 14.9 fps, and between the shroud and the liner 8.6 fps. The calculation can be written as:

V = Q(cfs)/Aa

While the velocity between the shroud and liner resulting from this arrangement was slightly high, the velocity inside the shroud was unacceptable.

It was obvious some water had to bypass the bottom of the shroud and report directly to the intake of the pump in order to achieve satisfactory velocity inside the shroud. This approach has been successfully applied in geothermal applications, but was new to the subject site.

Switching the terms around in the equation above, we could solve for the minimum Q(cfs) between the motor surface and the shroud I.D. required to maintain 8 fps or less past the motor:

Q(cfs) = Vmax × Aa

Substituting our 8 fps and 0.276 ft2 into this equation results in a maximum Q of 2.21 cfs (991 gpm) inside the shroud. The minimum flow required to bypass the shroud intake is therefore 1850 gpm minus 991 gpm, or 859 gpm.

Porting the shroud tube near the pump intake is a practical method to provide a bypass path for flow directly to the pump. To simplify hydraulic analysis, the circular orifice can be used to model the port configuration needed. The following equation can be used to approximate flow through a circular orifice under certain conditions (refer to Cameron Hydraulic Data, page 2-8):

Q(gpm) = 19.636 × C × d12 × h0.5

where:
C = 0.61
d1 = orifice diameter in inches
h = pressure drop across orifice in psi.

The orifice diameter (d1) is selected based on practical consideration of the shroud tube size and tools available (drill press vs. hand tools, etc.). In this case 0.75-inch was chosen.

Because it is known in this example all well inflow originates above the pump, pressure drop (h) is approximated as the friction loss along the flow path from the port area on the outside of the shroud to the shroud intake and inside the shroud to the pump intake. This estimate is simplified by modeling the annular areas inside and outside the shroud as a pipe with effective diameter De:

De = (4 × A/Pi) 0.5

The equation above is an algebraic manipulation of A = Pi × D0.5, where A is the cross-sectional area and Pi is a mathematical constant, generally shortened to 3.14159.

The values for De along with the rate determined for flow inside the shroud are used directly in Hazen-Williams or other pipe friction solutions such as published tables.

For the 85-foot length of 10.75-inch shroud in this case, the effective diameters are 7.11 inches for the area inside the shroud and 9.35 inches for the area outside the shroud. Friction loss (using C = 100 in the Hazen-Williams equation) for this segment is approximately 6 feet, using the inside shroud flow rate of 991 gpm.

The 2-foot length of 12.75-inch shroud from the port area to the reducer has an effective diameter of 6.37 inches and friction loss is less than 1 foot.

The deficiency in using the simplified solution methods described above is that turbulent flow is present in significant locations along the flow path. There are also velocity head losses and pump entrance losses to consider. It was decided that 11.5 feet (5 psi) would be a reasonable representation of pressure differential across the orifice port arrangement at the design conditions. Although seemingly random, this choice could not have been made without first completing approximations of friction loss.

By choosing an orifice diameter of 0.75-inch and applying the estimated pressure differential in the orifice equation, a flow rate of 23 gpm per port was determined. An arrangement of 36 ports in three rows of 12 each was selected, in part, to give a symmetrical layout on the shroud tube. This arrangement gives a total flow of 828 gpm and is reasonably close to the 859 gpm design rate selected above. Considering the total port area will increase in time due to wear, the capacity will likely increase somewhat.

Figure 2. Detail of ported shroud.

Figure 2 provides the details of how the ported shroud was constructed, and Figure 3 is a photograph of the shroud ready for installation of the pumping assembly. Note in the two figures an area of the 12-inch portion of the shroud was not ported. This aspect of the design was intended to ensure no damage would occur to the motor lead end (MLE) of the submersible power cable as a result of water jetting through the ports in the shroud.

The design assumptions were vetted using more rigorous fluid mechanical approaches, and it was found the results obtained from the simplified method described above were sufficiently accurate for this application.

After the ported shroud and pumping assembly had been installed, the pump was started. Prior to the rehabilitation effort, the well had a specific capacity of 2.03 gpm/ft of drawdown at 2100 gpm. After the rehabilitation effort, the specific capacity was 2.61 gpm/ft of drawdown at 2200 gpm, or better than 28% improvement over the well before rehabilitation. It is apparent that the design pumping rate of 1850 gpm has been exceeded due to the improved efficiency resulting from the rehabilitation.

Figure 3. Photograph of the 12-inch portion of the ported shroud (the concentric reducer is shown at the top of the elevators). The ports are visible about halfway up the shroud, and the gap designed to prevent jetting damage to the motor lead end of the power cable is apparent.

The greatly improved capacity of the well, while of considerable benefit, resulted in the design calculations being in error. At an actual pumping rate of 2200 gpm, the volume through the bottom of the shroud is 1200 gpm, and 1000 gpm through the ports. This results in an annular velocity inside the shroud of 9.7 fps, which is 21% higher than intended.

In retrospect, had we accounted for increased well efficiency resulting from the rehabilitation, which would have been an unknown, we would have chosen a conservative velocity past the motors of 5 fps, which would have provided a buffer for improved well performance.

Given this is a dewatering well, the dynamic head will increase with time, resulting in lower pumping volume, and therefore reduced annular velocity around the motors. The pump and motors have operated for three months (as of the preparation date of this article) with no issues, suggesting the ported shroud has not had adverse effects on the pumping system.

In summary, careful consideration of some simple fluid mechanics allowed the site to continue to pump this well at high volume after substantially reducing the inside diameter of the casing without incurring equipment damage. The rehabilitation effort resulted in a substantial increase in the well’s efficiency, resulting in long-term cost savings. However, the increased well yield resulted in inaccuracies in the fluid mechanics applied during design. Fortunately, the system is functioning in an acceptable manner.


Robert St. Louis, B.S., M.Sc., is a hydrogeologist who supports all of Newmont Mining Corp.’s operations around the globe. He has experience in the water well drilling industry, as well as mine hydrogeology, dewatering, and water supply. He can be reached at bob.st.louis@newmont.com.

Mark List, B.S., P.E., is a registered mining engineer with Miller Engineering/ANM Equipment. He has experience in the construction and mining industries and over the past two decades has focused on mine dewatering and pumping systems. He can be reached at mlist@mseinc.net.

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