Sealing boreholes against vertical flow

TIMED BLANK LINER INSTALLATION
How deeply must a FLUTe liner descend
into a hole to seal it for the night?
or,
How long must a blank liner be installed?

by
Carl Keller

Flexible Liner Underground Technologies

888-333-2433

Oct. 2000

How deep must a liner descend into a hole to seal it for the night?

The problem

The installation of flexible everting liners into boreholes to seal the hole against vertical flow and associated contaminant spread is becoming a popular application of FLUTe liners (sealing liners). Since the FLUTe liner is relatively easy to install and remove, it has been used to seal a borehole overnight after the drilling operation has ceased for the day or weekend. The next morning, it is removed to continue the drilling. However, in relatively tight formations, the installation rate for a flexible liner can be very slow.

The simple liner installation forces the water from the hole into the formation. The descent rate into a hole can be rapid initially, but as the liner seals the flow paths from the hole, the water in the hole flows more slowly into the formation. The last part of the hole can take days to seal due to the slow liner descent. The descent rate in a uniform medium is shown in Fig. 1. The long tail on the curve consumes a lot of time to seal a small remaining portion of the hole. The remedy for the slow installation is to pump the water from the hole beneath the liner. However, that requires the installation of a pump tube liner to seal around the pump tube. For deep water tables, the pump tube must have a pump at the bottom end. The procedure becomes cumbersome for the short time in the evening and the next morning to install and remove the liner before drilling begins.
The proposed solution

Figure 1 is a depth vs. time curve based upon a model with several important parts. The first part assumes that the conductivity in the hole is uniformly distributed and that the flow out of the hole is radial 1D cylindrical flow. The water is driven from the hole by the excess head in the interior of the liner. The liner descent is like a piston descending in the hole with a cross section equal to the hole diameter. Hence the volume displacement of the liner is equal to the flow from the hole.

The cylindrical flow equation is :

Where H is the length of the open section of the hole, K is the permeability, P is the pressure at radius r from the hole, Po is the pressure in the hole, ro is the hole radius, and is the viscosity of water.

If Q is equated to the liner volume displacement, A_h x v, where A_h is the hole cross section and v is the vertical velocity of the descending liner, the result is an equation for the vertical velocity of the liner as a function of the medium and hole parameters.

The time of the descent is obtained by assuming that the velocity of the descent is controlled by the open hole area. Therefore, it varies from the maximum value, vo, at the start, when the entire hole wall is available for flow, and drops to zero at the bottom of the hole when no flow area is left. With that velocity as v = vo(1 - D(t)/Do), where D is the distance of vertical liner travel and Do is the total depth of the hole, the time of the descent can be derived by integration to give the form:

D(t) = Do(1-e ^{-(vo/Do t)} ). This is the equation used to obtain the graph of Fig. 1.

The value of vo is obtained by dividing the expression above for Q by the hole cross sectional area. That is the initial velocity of the liner descent.

(A nice correction to this simple model was done by D. McWhorter to account for the shape of the flow field different from the 1-D cylinder. However, the effect is small for long holes.)
Noteworthy features of the above relationships

The initial velocity, Q/ A_h, where A_h is the hole cross section, contains the height of the saturated region, H, which is equal to Do in the time/depth equation. Hence, vo/Do, in the equation above, is independent of the saturated length of the hole. Setting D(t) to half the hole depth and solving for t_1/2, the time to traverse half the saturated section, gives the time as a function of the hole and medium parameters. But that time is independent of the length of the hole to be traversed by the liner. In other words, the longer saturated lengths are traversed at a greater velocity to yield the same time to half the hole depth (half the saturated depth actually).

Figure 1 was developed with the following hole and medium parameters:

length of saturated region: 250 ft.

hole diameter: 10 inches

medium conductivity: 0.0001 cm/sec

excess head in the liner (P-Po): 20 ft.

the range at which P(r) is the Water Table value: 1000 ro= 2500 inches.

The time to half depth is only 27 minutes. At one tenth the conductivity, it is 270 minutes to half depth. For a 100 ft. hole, the times are the same. This seems a little counter intuitive, but is correct with the assumption that the fill water can be supplied at the rate to match the very long hole velocities.
How long should the liner be installed?

Clearly, one does not want to wait until the last inch of hole is sealed, since the time to be sealed is only overnight. It is also important that it takes just as long to remove the liner if the same tension is applied to the tether as the force of the excess head during emplacement. In fact, the removal is best done by pumping the excess head down to the minimum needed to keep the liner inflated and pulling with a tension equal to: the excess head times half the hole cross section. That will result in the same time of removal as installation.

Assuming the above conditions, the first half of the hole is sealed in 14 min. Half of the remaining hole is also sealed in 14 min. After that, half the remaining hole is sealed in 14 min. The hole is now 7/8 sealed in a period of 42 min. Should one seal the last 1/8 of the hole?

The purpose of the liner installation is to seal the hole against vertical flow. In most cases, the concern is with the inflow of contaminated water at the upper part of the hole and the flow down and out of the bottom end of the hole. If the top 7/8 of the hole is filled, perhaps the risk has been adequately reduced. There is another consideration. That is that the water in the hole is being driven out at relatively high head. If that water is contaminated, the water forced into the formation would best be much less than if the hole were left standing open without any inflow of more contaminated water. If the natural gradient varies by 10 ft. of head, the outflow at the bottom of the hole can be estimated if the hole is left open. Applying a 40 ft. excess head will make the flow greater if the time of application is more than 1/4 of the time to be sealed before removal. Therefore, the time of the liner installation would best be short. That is also very convenient, since nightfall is soon after the end of the drilling day.

The nice feature of the timed installation is that if the seal is badly needed (that is for high conductivities), the time to install is relatively short.
Relevance to discontinuous conductivity situations (e.g., fractured rock)

For fractured rock, the uniform conductivity assumption is not correct. In fact, it is usually not correct. A few simple cases help to understand the difference:

All the fractures are at the bottom of the hole.

In this case, the vertical velocity of the liner will be maintained until the fractured region is reached. Then half of that region will be sealed in the times calculated above. With a single large fracture at the bottom, the half hole time is the time to reach the bottom fracture, since there is no decay of the velocity. The initial hole velocity (the whole hole conductivity based value) is maintained throughout the unfractured section.

Most of the fractures are at the top

In this case, the liner will descend to seal half the fractures in the "half hole time". It is as though the bottom unfractured section did not exist, since the flow out of that section is zero. If 7/8ths of that fractured region is sealed, there is not any significant flow path left out of the hole in the tight section. Again, driving the liner further will only enhance the flow out of the tight section at the bottom.
Hole diameter effect

Unfortunately, the vertical velocity is inversely proportional to the hole cross section. Simply put, the larger volume of water takes longer to force it out of the hole with a shallow radial gradient. The hole diameter may not have any significant effect on the velocity into the medium. The time to reach the half depth is about 4 times longer for a 10 in. hole than for a 5 in. hole. Fortunately, for a 5-6 inch hole, the times are relatively short.
In General

It is useful to think of the hole as not having length, but having a distribution of conductive paths. In the half hole time, half of the conductive paths will be sealed. In the 7/8ths hole time most of the flow paths will be sealed.

In a very tight hole, the sealing is not required. By selecting a significant conductivity, the time of installation can be estimated for a sealing liner installation. It is a great convenience that the time can be bounded by such logic as this. It makes it unnecessary to know the conductivity or the conductivity distribution. If the flow path is very conductive, it will be sealed. If not conductive, it might be sealed as the liner descends toward the more conductive zones. It is also convenient that as the liner is installed from the top down, the upper zones are sealed. Most contamination is due to surface sources and the highest concentrations are in the upper fractures. Hence most source zones are likely to be sealed by an everting liner.
Proposed approach

The following procedure should deal with most situations:

1. Install a liner for a selected time with a selected excess head. For deep water tables and relatively tight formations, an excess head of 40 ft. is suggested. The time of installation for 7/8 of the hole conductivity in a 10^-4 cm/sec conductivity is about 45 min.

2. After the 45 min. is reached, pump the water level down to 10 ft. of excess head.

3. Anchor the liner to prevent further descent, because any additional descent will require longer to remove. Leave the pump in the liner.

4. For removal, reduce the water level to 5 ft. of excess head. (raise the pump to 5’ above the water table. This prevents overpumping the liner).

5. Pull on the liner with a tension equal to 27*r² . r is in inches and the tension is in lbs. This is 170 lb. tension for a 5 in. hole and 430 lb. for an 8 in. hole. If the tension is too high, reduce it. The time for removal will be the same as the time of installation, unless the tension is reduced. In that case, it will take longer. These tensions are reasonable for a FLUTe 400 denier liner.

Note, equipment currently exists to control the water level at a set value in the descending liner.
Conclusion

This prescription for the installation of blank liners will seal 7/8 of the significant flow paths for the duration of a pause in the drilling without excessive installation and retrieval times. The assumption is that the water table is at least 40 ft. below the surface. More shallow water tables will take proportionally longer for the same length of seal. The seal is "good enough" without waiting for the seal of the entire hole. The seal is of the major conduction paths. The seal is from the top down. The times and tensions required are within those reasonably available with simple pumps and winches in the most common hole sizes.

Measurement of the actual liner velocity can give a good indication of the distribution of the conductivity with depth in the hole. A separate effort is in progress to measure the parameters in the above equations during a liner installation to assess the conductivity distribution.
Figure 1. Calculation of liner descent in a borehole