- Email: [email protected]
Quantification of annular flow in lined pipelines
Available online at www.sciencedirect.com
Tunnelling and Underground Space Technology incorporating Trenchless Technology Research
Tunnelling and Underground Space Technology 23 (2008) 727–733
www.elsevier.com/locate/tust
Trenchless Technology Research
Quantification of annular flow in lined pipelines Reda M. Bakeer a, V. Firat Sever b,* a
Ardaman & Associates Inc., Geotechnical, Environmental and Material Consultants, Louisiana 70002, USA b Boyle Engineering Corporation, 4415 Metro Pkwy, Suite 404 Fort Myers, Florida 33916, USA Received 3 May 2006; received in revised form 17 November 2007; accepted 21 December 2007 Available online 4 March 2008
Abstract This paper attempts to quantify the amount of flow within the annular space that could exist between a polymeric liner and a deteriorated host pipe. Inadequate fit of the liner within sewer line segments is likely to cause annular flow that will result in a higher flow rate within the wastewater collection system. The results of full-scale field tests performed by the authors on 12 pipelines lined with four different deformed/reformed or fold-and-form (DR/FF) and cured-in-place-pipe (CIPP) liner products indicated that gaps of different sizes existed in all of the tested pipelines. These gaps have resulted in variable annular flow in the tested pipelines. Based on the results of the full-scale tests, a mathematical relationship was established between the annular flow in a lined pipeline and the annular space. The relationship between the annular flow rate and the average annular gap size depends on the difference in head between the entry and exit points along the pipeline. In turn, the average annular gap size depends on many factors including tolerances and imperfections in the host pipe and liner, conditions of the host pipe and the quality of liner installation. A third-order polynomial equation was found to best describe the relationship between the annular flow and average gap size under high differential heads (up to 3.0 m or 10 ft); whereas, a logarithmic relationship fits best under low differential heads for wider range of annular gap sizes (up to 17.8 mm or 0.70 in.). Based on the results of the full-scale tests, this is believed to be more representative of typical liner installations. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Sewer line rehabilitation; Infiltration/inflow; Polymeric liners; Annular flow; Laterals
1. Introduction Infiltration can be defined as water entering into a sewer system from the surrounding medium through cracked pipes, pipe joints and connections or access-hole walls. The presence of a high groundwater table in an urban area could result in leakage into the sewers and an increase in the volume of wastewater to be treated. Inflow can be defined as the water discharged into a sewer system from sources such as roof leaders, cellars and yard drains, cooling-water discharges, access-hole covers, and cross connections from storm drains. During heavy rainfall events, the combined infiltration and inflow can exceed 47 L/d/m2
*
Corresponding author. Tel.: +1 239 278 7996; fax: +1 239 278 0913. E-mail address: [email protected] (V. Firat Sever).
0886-7798/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2007.12.008
(50,000 gpd per acre). Increased flows attributed to infiltration and inflow (I/I) translate into increased storage and treatment costs. The contribution of I/I to total wastewater flows depends on the quality of the materials and construction of the sewer system, maintenance, and depth of groundwater (Tchobanoglous, 1981). Trenchless methods are frequently used to rehabilitate or replace deteriorated sewer mains, seal leaky joints and cracks and repair service laterals, which would minimize I/I concerns in a wastewater collection system. Lining with polymeric liners comprises a major segment of trenchless sewer rehabilitation projects (McKim, 1997; Rowe et al., 2003). The most common rehabilitation methods with polymeric liners include sliplining (e.g., fold and form or deform/reform, pull through) and cured-in-place-pipe (CIPP) liners (NASTT, 2007). While present experience shows significant reduction of I/I in sewer systems due to
728
R.M. Bakeer, V. Firat Sever / Tunnelling and Underground Space Technology 23 (2008) 727–733
Nomenclature Q (mL/s, gpm) flow rate H (m) pressure head Z (m, ft) elevation head V (m/s) mean flow velocity hf (m) head loss due to friction g (m/s2) acceleration due to gravity d (mm, in.) difference between the inner radius of host pipe and outer radius of liner
the use of liners (Kurz, 1997), some annular flow was observed in some lined pipelines (Larsen et al., 1997), which would cause excess flow into wastewater collection systems. In an earlier publication by the authors (Bakeer et al., 2005), it was determined that the annular flow in a lined pipeline was due to the presence of a gap between the host pipe and liner following installation. This gap is attributed to tolerances and imperfections in the host pipe and liner, liner installation quality and lack of adherence between the liner and host pipe. If the host pipeline is located below groundwater table, fluids are likely to enter into the wastewater collection system through cracks in the host pipe, unsealed laterals and access holes (infiltration). Surface waters may also enter the system (inflow) through inlet holes. The experimental study by Bakeer et al. (2005) indicated a lower annular flow in pipelines lined with CIPP liners than in those lined with fold and form or deform/ reform liners (FF/DR). Also, different annular flows were measured among the different pipelines that were lined with the same type of liner. The present study aims at developing a mathematical relationship between the annular flow in a lined pipeline and the annular gap size between the host pipe and liner. The methodology is based on the results of the full-scale tests performed by the authors on pipelines rehabilitated with DR/FF liners and reported in their previous publication (Bakeer et al., 2005). 2. Experimental setup Only a brief description of the experimental study is given herein to provide the necessary background for the data used to develop the proposed mathematical relationship. More details of the full-scale tests can be found in Bakeer et al. (2005). The tests were performed using an experimental setup constructed at the outdoor storage yard of the Wastewater Collection Division in Baton Rouge, Louisiana (Fig. 1). The experimental setup consisted of six 9-m (30 ft) long vitrified clay pipelines (203 mm or 8 in. internal diameter) installed on concrete pedestals with cradle tops allowing tops of the pipelines to be placed approximately 0.46 m (1.5 ft) above ground surface. Each of the tested pipelines consisted of four standard diameter clay pipe segments and two projecting laterals.
f Re l (m)
friction factor Reynolds number radial length of the cross-sectional area of the annular space q (kg/m3) density l (N s/m2) dynamic viscosity
Water was supplied from two wooden towers, each equipped with two water tanks placed at two levels of 1.5 m (5 ft) and 3 m (10 ft) above ground surface to apply flows in the test pipelines under two different heads. Each water supply tower was used as a source of water for three pipelines labeled as Group A or B. The vitrified clay test pipelines were connected to the water supply tanks via clear PVC rigid tubes. The test pipelines were then lined with deformed/reformed or fold-and-form flexible (DR/FF) and cured-in-place-pipe (CIPP) liner products. In the first series of tests, two thermoplastic DR/FF liner products were tested. Triplicates of each product were installed in a given group of pipelines (A or B). In the second series of tests, two thermosetting plastic CIPP liner products were installed in six new clay pipelines similar to those used for testing the DR/FF tests. All of the liners in both series of tests were installed by the professional contractors according to their typical field installation procedures with minor modifications to accommodate above ground installations. An inlet hole was drilled on top of the upstream end of each pipeline prior to installation of the liners. Following liner installation, the inlet hole was used to apply a constant water head [1.5 m or 3.0 m (5 ft or 10 ft)] on the outside wall of the liner inside each pipeline. Accordingly, if any annular space existed between the liner and host clay pipe, water should migrate through the annular space to flow out through the unsealed laterals or ends of the pipeline. Flow rates through the annular space were measured by mechanical flow meters (Neptune Trident) installed on the water supply lines directly upstream of the inlet hole. Flow rates were verified by measuring the volume of water collected at the laterals, joints and ends of the pipelines over a specific time interval. Fig. 2 shows a typical flow through a lateral along a test pipeline lined with a DR/FF liner. Additional tests were performed under lower differential heads between the upstream and downstream ends of the pipelines lined with DR/FF liners (from 0.15 to 0.46 m or from 6 to 18 in.), which are more representative heads that would be expected in the field. Low head tests were performed by installing standpipe assemblies on both ends on one of the pipelines from each group (Fig. 3). Water flow was initiated at the upstream following the verification
R.M. Bakeer, V. Firat Sever / Tunnelling and Underground Space Technology 23 (2008) 727–733
729
Fig. 1. Schematic of the testing setup (Bakeer et al., 2005).
necessarily adhere to the host pipe throughout their contact area. Results of the CIPP tests were not included in the analyses due to the following: Annular flow in the DR/FF liner tests was more appreciable. The low-head tests were only performed on the DR/FF liners. Due to an installation error, the ends of all of the CIPP lined pipelines were immediately sealed, while the ends of the DR/FF lined pipelines were not initially sealed after installation of the liners.
Fig. 2. Annular flow through a lateral.
of static head at each standpipe. Water was collected in beakers at the downstream valve to determine the quantity of annular flow (collected water volume over a given period of time). 3. Flow characteristics in the annular space The analysis reported in this paper utilized measurements taken from the full-scale tests performed on the two DR/FF liner products. Results of the experimental tests indicated that an annular flow existed in all of the pipelines and for all liner products, but at different rates. This observation indicates that CIPP liners do not
Prior to installation of the liners in the clay pipelines, the flow meters were calibrated by measuring the flow rates at the two possible heads (1.5 or 3.0 m) in the six pipelines in Groups A and B (A1 and B1 are the closest & A3 and B3 are the furthest from the water supply towers). The flow ratios measured by the flow meters prior to installation of the liners in the pipelines ranged from 0.69 to 0.74, as shown in Table 1. Flow values in the unlined pipes can be confirmed through theoretical calculations. According to Bernoulli’s equation V 2 =2g þ H þ Z þ hf ¼ constant
ð1Þ
where H (m or ft) is the pressure head, Z (m or ft) is the elevation head, V (m/s or ft/s) is the mean velocity of flow, hf (m or ft) is the total head loss, and g (m/s2 or ft/s2) is the acceleration due to gravity. In all of the tests, the flow was
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Fig. 3. Experimental setup for the low differential head tests (Bakeer et al., 2005).
Table 1 Readings of the flow meters (Bakeer et al., 2005) Head (m)
Flow (mL/s) in flow meter for each test pipeline Product Aa
Product Ba
A1
A2
A3
Average
B1
B2
B3
Average
1.5 3.0
385 555
347 498
322 448
351 500
385 517
353 479
322 448
353 481
Ratio
0.69
0.70
0.72
0.70
0.74
0.74
0.72
0.73
a
The number following the product code (A or B) denotes the pipeline number. Line numbers 1 and 3 are the closest and furthest to the water supply towers, respectively.
attributed only to the head difference and the pressure head was assumed to be zero. At the water surface in the supply tank with 1.5 m (5-ft) head V ¼ 0;
Z ¼ 1:5 m ð5 ftÞ;
and
H ¼0
At the downstream end of the pipeline Z = 0, H = 0; thereby, V 21 =2g þ hf ¼ 1:5. Likewise, at the water surface in the supply tank with 3.0 m (10 ft) head V ¼ 0;
Z ¼ 3 m;
H ¼ 0;
4. Effect of annular gap size Thickness measurements were made of representative segments (Fig. 4) retrieved from the DR/FF lined pipelines at the completion of the full-scale tests. These segments were saw-cut from the test pipelines at random locations and the annular gap was measured at both ends of each segment. The annular gap size ranged from 0.1 to 1.4 mm (from 0.004 to 0.056 in.) for Product A and from 0.1 to 17.8 mm (0.004 to 0.701 in.) for Product B. Based on a
and V 22 =2g þ hf ¼ 3:0
If the effect of head loss on the ratio of the velocities (at 1.5 and 3.0 m heads) is neglected then V 1 =V 2 ¼ Q1 =Q2 ¼ ð3g=6gÞ
0:5
¼ 0:71
ð2Þ
The calculated flow ratio of 0.71 is within the measured range of 0.69–0.74 as indicated by the flow meter readings for the two tested groups of pipelines (or liner products); i.e., Groups A and B. Based on the flow meter readings, the ratio of the flow at 1.5-m (5-ft) head to the flow at 3.0-m (10-ft) head was approximately 0.68 in both pipeline groups after lining with DR/FF liners. This ratio is slightly lower than the minimum ratio of flow rate of 0.69 measured before the liners were installed. Therefore, the foregoing assumptions of zero pressure head and negligible head loss are reasonable.
Fig. 4. Pipe segment with the liner.
R.M. Bakeer, V. Firat Sever / Tunnelling and Underground Space Technology 23 (2008) 727–733
visual inspection of the retrieved samples and the observations made in the field during the tests, the annular gap size and location varied throughout the cross-section of the pipe segments, as shown in Fig. 4. Nevertheless, the annular gap size measurements were consistent with the measured flows, where a pipeline with a larger annular space yielded higher annular flow. It should be noted that the amount of flow depends also on the continuity of the gaps formed between the entry and exit points along a given pipeline segment where the annular flow takes place. However, this particular variable is extremely difficult to quantify as it varies from one pipeline to the next. The analyses reported in this paper are based on the assumption that the measured flow takes place along a continuous uniform ring, or average gap, forming between the outside wall of the liner and the inside wall of the host pipe. A uniform ring may not exist in liner installations, since for most cases, the space between the host pipe and liner is either local or eccentric rather than a uniform ring (Figs. 4 and 5). This simplification was necessitated by the random and irregular nature of the gap in actual field installations, which is extremely complex to model mathematically. In addition, this simplification allows for developing a practical design formula for use by practicing engineers. The annular gap size values were linearly interpolated between the measured values; then the measured flow rates were plotted versus the assumed average gap size (ring thickness). A non-linear relationship was established between the average annular gap size (mm) and the annular
Host pipe Liner d (annular gap as a uniform ring - idealized for flow equation
Localized annular gap - actual field condition
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flow rate (mL/s). For the high differential head tests (Dh = 1.5 or 3.0 m), this relationship is only valid for the results obtained for Product A pipelines, since a much larger average annular gap was observed in Product B. Fig. 6 demonstrates the annular flow rates versus the average annular gap size under high head differences (1.5 and 3 m), and low head differences (Dh 6 0.5 m or 18 in.) between the upstream and downstream ends of the tested pipelines. A third-order polynomial relationship was obtained using the least squares method, which fits well for an average annular gap of up to 1.3 mm (0.05 in.) under high head differences (1.5 and 3.0 m) QA ¼ 102:11d 3 þ 164:76d 2 þ 122:1d–9 ð1:5 m head differenceÞ 3
ð3aÞ
2
QA ¼ 173:87d þ 287:44d þ 160:88d–14 ð3:0 m head differenceÞ
ð3bÞ
For the low differential head tests, since the annular gap between the host pipe and liner is small, a second-order equation was used to describe the relationship between the average annular gap (ring) and the annular flow rate QA ¼ 16:445d 2 þ 2:3897d þ 3 ðlow head difference; Dh 6 0:5 mÞ
ð4Þ
The least square analysis yielded R2 values of 0.95, 0.97 and 0.95 for the low (Dh 6 0.5 m or 20 in.), 1.5 m and 3.0 m head differences, respectively. It was not possible to extend this relationship for larger average rings (d > 1.3 mm or 0.05 in.). An attempt was also made to develop a relationship between the annular flow and average annular gap (ring) sizes up to 17.8 mm (0.07 in.) by combining the annular flow data from Group A with small annular gaps and Group B with larger annular gaps. The maximum measured annular gap of 17.8 mm (0.07 in.) could develop when an HDPE liner is installed in a clay host pipe considering the high standard pipe tolerances encountered in both
Host pipe Liner 350
Host pipe Liner Eccentric annular gap - a field condition
Annular Flow (mL/s)
300 250 200 150 100 50 0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
Annular Gap/Ring (mm) 3m
Fig. 5. Cross-section of a clay pipe lined with DR/FF liner (not to scale, annular gap enlarged for the purpose of illustration).
1.5 m
Low Head
Fig. 6. Annular flow rate versus gap size.
1.4
1.6
732
R.M. Bakeer, V. Firat Sever / Tunnelling and Underground Space Technology 23 (2008) 727–733
products, as will be discussed. The analysis provided a logarithmic relationship (Eq. (5)) between the average annular gap size and the annular flow under low differential heads, which are more representative of actual field conditions, since a head difference of 1.5 m or 3.0 m is not likely to exist in typical sewer lines QA ¼ 8:8288 lnðdÞ þ 31
ð5Þ
Fig. 7 demonstrates the relationship between the average annular gap and annular flow for low differential heads and large annular gaps. While this relationship is also based on an empirical derivation, it is more applicable, because it is capable of calculating annular flows for larger average annular gaps up to 17.8 mm (0.07 in.) under low differential heads (Dh 6 0.5 m or 20 in.). These conditions are more general and are representative of typical field conditions. According to AASHTO (2005), a 203-mm (8-in.) clay pipe may have a tolerance in diameter of ±7.94 mm (±0.313 in.). The allowable tolerances for 203-mm (8-in.) polyethylene and PVC pipes are ±6.35 and ±9.53 mm (±0.25 and 0.375 in.), respectively. The diameter of a clay pipe may range from 195 mm (7.68 in.) to 211 mm (8.31 in.) with respect to the maximum allowable tolerance. Meanwhile, HDPE and PVC liners may have maximum allowable diameters as low as 194 and 191 mm (7.65 and 7.53 in.) and as high as 207 and 210 mm (8.15 and 8.28 in.), respectively. Based on these tolerances, the worst case scenario is for a liner/clay pipe rehabilitation would develop when a liner with the smallest tolerable diameter is installed in a clay pipe with the largest tolerable diameter, which would result in difference of up to 20 mm (0.79 in.), or an ‘‘average” gap size (ring) of 10 mm (0.39 in.). It should be noted that the average diameters of the host pipe and the resulting average gap size would also depend on other factors such as manufacturing quality (imperfections), installation quality, ovality, and conditions of the host pipe (sags, depressions, offsets, joints, flat spots, etc.). The standard allowed tolerances specified for
70
Annular Flow (mL/s)
60 50 40 30 20 10 0
0
5
10
15
20
other pipe materials (steel, cast iron, etc.) will also vary from these values. Tolerances in a pipeline diameter may not be as critical in rehabilitation with CIPP liners where a smaller annular space would typically exist as the more flexible liner adjusts to the configuration of the host pipe during installation and curing. However, the size of the annular space in pipelines lined with CIPP liners would vary depending on the foregoing parameters impacting DR/FF liner installations as well as the amount and type of CIPP resin. On the other hand, irregularities or imperfections in the pipeline cross-section would affect the size and continuity of the annular space for both DR/FF and CIPP liners. Excess resin may plug the annular space in some segments along the length of the CIPP lined pipeline, which may result in a discontinuous annular space in some segments of the pipeline. Again, plugging of a given segment of a continuous annular space would depend on its location relative to the entry and exit points of fluids along the given pipeline segment. However, this discontinuous annular space may become continuous with time due to cyclic and monotonic deformations of the liner under variable water and ground pressures as well as the effects of creep. Alternatively, the annular space in all types of lined pipelines could also be plugged over time with soil particles migration into the annular space, which would reduce annular flow. 5. Conclusions A mathematical relationship was developed between the average annular gap (ring) size and flow in the annular space of a lined sewer pipeline. The proposed relationship between the annular flow and average annular gap size was based on the results of series of full-scale tests used to simulate sewer pipelines (203-mm or 8-in.) lined with fold and form or deform/reform (FF/DR) liners. The average annular gap size between the host pipe and a liner was approximated by investigating representative pipe segments removed from the tested lines following the tests. The following conclusions could be made regarding the outcome of the analysis: An annular gap size up to 1.3 mm has more influence on the annular flow rate than an annular gap higher than this limit. A third-order polynomial equation best describes the relationship between the average annular gap (ring thickness) and flow in the annular space for high differential heads between the upstream and the downstream; i.e., 1.5 and 3.0 m (5 and 10 ft). A logarithmic relationship fits best for low differential heads and a wide range of average annular gaps (up to 17.8 mm or 0.701 in.), which is more applicable for most field installations.
Annular Gap/Ring (mm)
Fig. 7. Annular flow versus average gap size for the low differential head tests.
The third-order polynomial equation provided the best fit between the annular flow rate and the average annular
R.M. Bakeer, V. Firat Sever / Tunnelling and Underground Space Technology 23 (2008) 727–733
gap size (ring thickness) for both high differential heads; i.e., 1.5 m (5 ft) and 3.0 m (10 ft) and small annular gaps (up to 1.3 mm or 0.05 in.). It was possible to develop an equation for a wide range of annular gaps (from 0.1 to 17.8 mm or from 0.004 to 0.70 in.) under low differential heads using the logarithmic relationship. This range is relatively close to the expected range of average annular gap between the liner and host pipe regarding standard diameter tolerances for both the liner and host pipe (minimum liner size-maximum pipe size). It should be noted that field performance of a liner can be influenced by many factors, which were not accounted for in the reported tests. These include long-term performance and site-specific conditions encountered during field installation, and most importantly, the exact flow along a CIPP or DR/FF liner under actual field conditions will vary depending on the location of the defects or cracks (entry and exit points) in the underground line with respect to the location and continuity of the annular space along the line. More tests are needed to confirm or further refine the proposed relationship and to better define the formed gaps. This includes obtaining a statistically representative set of samples to be retrieved from actual field installations. The size, distribution, configuration and continuity of the gap(s) could be determined by direct measurements or non-destructive methods; e.g., X-ray tests. Acknowledgements The City of Baton Rouge, Department of Public Works, Wastewater Collection Division sponsored the study. Mr. Edmund P. Stumpf was the Project Director, Mr. David Ratcliff was Assistant Manager for Operations and Maintenance, and Dr. Fang Xia Yu was the Senior Project Engineer. All tests were performed at the outdoor storage
733
yard of the Wastewater Collection Division. The authors would like to express their gratitude to Dr. Glen Boyd and Dr. Leslie Guice for their contribution to the study. The investigators were assisted by a group of graduate research assistants, Messrs. Ahmed Hosny, Chanduru Suryanaryana, of Tulane University, and Messrs. Aziz Omara and Omesh Malik of Louisiana Tech University. Mr. Tony Phillips of Delta Testing and Inspection Inc., performed material tests and field monitoring. CSR Pipeline Systems, Boh Bros Construction Company, Insituform Technologies Inc., Insituform Gulf South and National Liner provided the tested products and installation at no cost to the project. References AASHTO, 2005. Standard Specifications for Transportation Materials and Methods of Sampling and Testing, 25th ed. Bakeer, R.M., Guice, L.K., Sever, V.F., Boyd, G.R., 2005. Fluid migration into lined piping systems. Tunnelling and Underground Space Technology 20 (5), 452–462. Kurz, G.E., 1997. Predicting I/I reduction for sewer rehabilitation. In: Proceedings of the Conference on Trenchless Pipeline Projects, Practical Applications, 1997, June 8–11, Boston, MA, US, pp. 103–110. Larsen, J.P., Struve, J.N., Bloetscher, F., McLaughlin, D., 1997. After rehabilitation, then what? Water Environment and Technology 9 (4), 45–49. McKim, R.A., 1997. Selection method for Trenchless technologies. Journal of Infrastructure Systems 3 (3), 119–125. North American Society for Trenchless Technology (NASTT), 2007
Tunnelling and Underground Space Technology incorporating Trenchless Technology Research
Tunnelling and Underground Space Technology 23 (2008) 727–733
www.elsevier.com/locate/tust
Trenchless Technology Research
Quantification of annular flow in lined pipelines Reda M. Bakeer a, V. Firat Sever b,* a
Ardaman & Associates Inc., Geotechnical, Environmental and Material Consultants, Louisiana 70002, USA b Boyle Engineering Corporation, 4415 Metro Pkwy, Suite 404 Fort Myers, Florida 33916, USA Received 3 May 2006; received in revised form 17 November 2007; accepted 21 December 2007 Available online 4 March 2008
Abstract This paper attempts to quantify the amount of flow within the annular space that could exist between a polymeric liner and a deteriorated host pipe. Inadequate fit of the liner within sewer line segments is likely to cause annular flow that will result in a higher flow rate within the wastewater collection system. The results of full-scale field tests performed by the authors on 12 pipelines lined with four different deformed/reformed or fold-and-form (DR/FF) and cured-in-place-pipe (CIPP) liner products indicated that gaps of different sizes existed in all of the tested pipelines. These gaps have resulted in variable annular flow in the tested pipelines. Based on the results of the full-scale tests, a mathematical relationship was established between the annular flow in a lined pipeline and the annular space. The relationship between the annular flow rate and the average annular gap size depends on the difference in head between the entry and exit points along the pipeline. In turn, the average annular gap size depends on many factors including tolerances and imperfections in the host pipe and liner, conditions of the host pipe and the quality of liner installation. A third-order polynomial equation was found to best describe the relationship between the annular flow and average gap size under high differential heads (up to 3.0 m or 10 ft); whereas, a logarithmic relationship fits best under low differential heads for wider range of annular gap sizes (up to 17.8 mm or 0.70 in.). Based on the results of the full-scale tests, this is believed to be more representative of typical liner installations. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Sewer line rehabilitation; Infiltration/inflow; Polymeric liners; Annular flow; Laterals
1. Introduction Infiltration can be defined as water entering into a sewer system from the surrounding medium through cracked pipes, pipe joints and connections or access-hole walls. The presence of a high groundwater table in an urban area could result in leakage into the sewers and an increase in the volume of wastewater to be treated. Inflow can be defined as the water discharged into a sewer system from sources such as roof leaders, cellars and yard drains, cooling-water discharges, access-hole covers, and cross connections from storm drains. During heavy rainfall events, the combined infiltration and inflow can exceed 47 L/d/m2
*
Corresponding author. Tel.: +1 239 278 7996; fax: +1 239 278 0913. E-mail address: [email protected] (V. Firat Sever).
0886-7798/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2007.12.008
(50,000 gpd per acre). Increased flows attributed to infiltration and inflow (I/I) translate into increased storage and treatment costs. The contribution of I/I to total wastewater flows depends on the quality of the materials and construction of the sewer system, maintenance, and depth of groundwater (Tchobanoglous, 1981). Trenchless methods are frequently used to rehabilitate or replace deteriorated sewer mains, seal leaky joints and cracks and repair service laterals, which would minimize I/I concerns in a wastewater collection system. Lining with polymeric liners comprises a major segment of trenchless sewer rehabilitation projects (McKim, 1997; Rowe et al., 2003). The most common rehabilitation methods with polymeric liners include sliplining (e.g., fold and form or deform/reform, pull through) and cured-in-place-pipe (CIPP) liners (NASTT, 2007). While present experience shows significant reduction of I/I in sewer systems due to
728
R.M. Bakeer, V. Firat Sever / Tunnelling and Underground Space Technology 23 (2008) 727–733
Nomenclature Q (mL/s, gpm) flow rate H (m) pressure head Z (m, ft) elevation head V (m/s) mean flow velocity hf (m) head loss due to friction g (m/s2) acceleration due to gravity d (mm, in.) difference between the inner radius of host pipe and outer radius of liner
the use of liners (Kurz, 1997), some annular flow was observed in some lined pipelines (Larsen et al., 1997), which would cause excess flow into wastewater collection systems. In an earlier publication by the authors (Bakeer et al., 2005), it was determined that the annular flow in a lined pipeline was due to the presence of a gap between the host pipe and liner following installation. This gap is attributed to tolerances and imperfections in the host pipe and liner, liner installation quality and lack of adherence between the liner and host pipe. If the host pipeline is located below groundwater table, fluids are likely to enter into the wastewater collection system through cracks in the host pipe, unsealed laterals and access holes (infiltration). Surface waters may also enter the system (inflow) through inlet holes. The experimental study by Bakeer et al. (2005) indicated a lower annular flow in pipelines lined with CIPP liners than in those lined with fold and form or deform/ reform liners (FF/DR). Also, different annular flows were measured among the different pipelines that were lined with the same type of liner. The present study aims at developing a mathematical relationship between the annular flow in a lined pipeline and the annular gap size between the host pipe and liner. The methodology is based on the results of the full-scale tests performed by the authors on pipelines rehabilitated with DR/FF liners and reported in their previous publication (Bakeer et al., 2005). 2. Experimental setup Only a brief description of the experimental study is given herein to provide the necessary background for the data used to develop the proposed mathematical relationship. More details of the full-scale tests can be found in Bakeer et al. (2005). The tests were performed using an experimental setup constructed at the outdoor storage yard of the Wastewater Collection Division in Baton Rouge, Louisiana (Fig. 1). The experimental setup consisted of six 9-m (30 ft) long vitrified clay pipelines (203 mm or 8 in. internal diameter) installed on concrete pedestals with cradle tops allowing tops of the pipelines to be placed approximately 0.46 m (1.5 ft) above ground surface. Each of the tested pipelines consisted of four standard diameter clay pipe segments and two projecting laterals.
f Re l (m)
friction factor Reynolds number radial length of the cross-sectional area of the annular space q (kg/m3) density l (N s/m2) dynamic viscosity
Water was supplied from two wooden towers, each equipped with two water tanks placed at two levels of 1.5 m (5 ft) and 3 m (10 ft) above ground surface to apply flows in the test pipelines under two different heads. Each water supply tower was used as a source of water for three pipelines labeled as Group A or B. The vitrified clay test pipelines were connected to the water supply tanks via clear PVC rigid tubes. The test pipelines were then lined with deformed/reformed or fold-and-form flexible (DR/FF) and cured-in-place-pipe (CIPP) liner products. In the first series of tests, two thermoplastic DR/FF liner products were tested. Triplicates of each product were installed in a given group of pipelines (A or B). In the second series of tests, two thermosetting plastic CIPP liner products were installed in six new clay pipelines similar to those used for testing the DR/FF tests. All of the liners in both series of tests were installed by the professional contractors according to their typical field installation procedures with minor modifications to accommodate above ground installations. An inlet hole was drilled on top of the upstream end of each pipeline prior to installation of the liners. Following liner installation, the inlet hole was used to apply a constant water head [1.5 m or 3.0 m (5 ft or 10 ft)] on the outside wall of the liner inside each pipeline. Accordingly, if any annular space existed between the liner and host clay pipe, water should migrate through the annular space to flow out through the unsealed laterals or ends of the pipeline. Flow rates through the annular space were measured by mechanical flow meters (Neptune Trident) installed on the water supply lines directly upstream of the inlet hole. Flow rates were verified by measuring the volume of water collected at the laterals, joints and ends of the pipelines over a specific time interval. Fig. 2 shows a typical flow through a lateral along a test pipeline lined with a DR/FF liner. Additional tests were performed under lower differential heads between the upstream and downstream ends of the pipelines lined with DR/FF liners (from 0.15 to 0.46 m or from 6 to 18 in.), which are more representative heads that would be expected in the field. Low head tests were performed by installing standpipe assemblies on both ends on one of the pipelines from each group (Fig. 3). Water flow was initiated at the upstream following the verification
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Fig. 1. Schematic of the testing setup (Bakeer et al., 2005).
necessarily adhere to the host pipe throughout their contact area. Results of the CIPP tests were not included in the analyses due to the following: Annular flow in the DR/FF liner tests was more appreciable. The low-head tests were only performed on the DR/FF liners. Due to an installation error, the ends of all of the CIPP lined pipelines were immediately sealed, while the ends of the DR/FF lined pipelines were not initially sealed after installation of the liners.
Fig. 2. Annular flow through a lateral.
of static head at each standpipe. Water was collected in beakers at the downstream valve to determine the quantity of annular flow (collected water volume over a given period of time). 3. Flow characteristics in the annular space The analysis reported in this paper utilized measurements taken from the full-scale tests performed on the two DR/FF liner products. Results of the experimental tests indicated that an annular flow existed in all of the pipelines and for all liner products, but at different rates. This observation indicates that CIPP liners do not
Prior to installation of the liners in the clay pipelines, the flow meters were calibrated by measuring the flow rates at the two possible heads (1.5 or 3.0 m) in the six pipelines in Groups A and B (A1 and B1 are the closest & A3 and B3 are the furthest from the water supply towers). The flow ratios measured by the flow meters prior to installation of the liners in the pipelines ranged from 0.69 to 0.74, as shown in Table 1. Flow values in the unlined pipes can be confirmed through theoretical calculations. According to Bernoulli’s equation V 2 =2g þ H þ Z þ hf ¼ constant
ð1Þ
where H (m or ft) is the pressure head, Z (m or ft) is the elevation head, V (m/s or ft/s) is the mean velocity of flow, hf (m or ft) is the total head loss, and g (m/s2 or ft/s2) is the acceleration due to gravity. In all of the tests, the flow was
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Fig. 3. Experimental setup for the low differential head tests (Bakeer et al., 2005).
Table 1 Readings of the flow meters (Bakeer et al., 2005) Head (m)
Flow (mL/s) in flow meter for each test pipeline Product Aa
Product Ba
A1
A2
A3
Average
B1
B2
B3
Average
1.5 3.0
385 555
347 498
322 448
351 500
385 517
353 479
322 448
353 481
Ratio
0.69
0.70
0.72
0.70
0.74
0.74
0.72
0.73
a
The number following the product code (A or B) denotes the pipeline number. Line numbers 1 and 3 are the closest and furthest to the water supply towers, respectively.
attributed only to the head difference and the pressure head was assumed to be zero. At the water surface in the supply tank with 1.5 m (5-ft) head V ¼ 0;
Z ¼ 1:5 m ð5 ftÞ;
and
H ¼0
At the downstream end of the pipeline Z = 0, H = 0; thereby, V 21 =2g þ hf ¼ 1:5. Likewise, at the water surface in the supply tank with 3.0 m (10 ft) head V ¼ 0;
Z ¼ 3 m;
H ¼ 0;
4. Effect of annular gap size Thickness measurements were made of representative segments (Fig. 4) retrieved from the DR/FF lined pipelines at the completion of the full-scale tests. These segments were saw-cut from the test pipelines at random locations and the annular gap was measured at both ends of each segment. The annular gap size ranged from 0.1 to 1.4 mm (from 0.004 to 0.056 in.) for Product A and from 0.1 to 17.8 mm (0.004 to 0.701 in.) for Product B. Based on a
and V 22 =2g þ hf ¼ 3:0
If the effect of head loss on the ratio of the velocities (at 1.5 and 3.0 m heads) is neglected then V 1 =V 2 ¼ Q1 =Q2 ¼ ð3g=6gÞ
0:5
¼ 0:71
ð2Þ
The calculated flow ratio of 0.71 is within the measured range of 0.69–0.74 as indicated by the flow meter readings for the two tested groups of pipelines (or liner products); i.e., Groups A and B. Based on the flow meter readings, the ratio of the flow at 1.5-m (5-ft) head to the flow at 3.0-m (10-ft) head was approximately 0.68 in both pipeline groups after lining with DR/FF liners. This ratio is slightly lower than the minimum ratio of flow rate of 0.69 measured before the liners were installed. Therefore, the foregoing assumptions of zero pressure head and negligible head loss are reasonable.
Fig. 4. Pipe segment with the liner.
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visual inspection of the retrieved samples and the observations made in the field during the tests, the annular gap size and location varied throughout the cross-section of the pipe segments, as shown in Fig. 4. Nevertheless, the annular gap size measurements were consistent with the measured flows, where a pipeline with a larger annular space yielded higher annular flow. It should be noted that the amount of flow depends also on the continuity of the gaps formed between the entry and exit points along a given pipeline segment where the annular flow takes place. However, this particular variable is extremely difficult to quantify as it varies from one pipeline to the next. The analyses reported in this paper are based on the assumption that the measured flow takes place along a continuous uniform ring, or average gap, forming between the outside wall of the liner and the inside wall of the host pipe. A uniform ring may not exist in liner installations, since for most cases, the space between the host pipe and liner is either local or eccentric rather than a uniform ring (Figs. 4 and 5). This simplification was necessitated by the random and irregular nature of the gap in actual field installations, which is extremely complex to model mathematically. In addition, this simplification allows for developing a practical design formula for use by practicing engineers. The annular gap size values were linearly interpolated between the measured values; then the measured flow rates were plotted versus the assumed average gap size (ring thickness). A non-linear relationship was established between the average annular gap size (mm) and the annular
Host pipe Liner d (annular gap as a uniform ring - idealized for flow equation
Localized annular gap - actual field condition
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flow rate (mL/s). For the high differential head tests (Dh = 1.5 or 3.0 m), this relationship is only valid for the results obtained for Product A pipelines, since a much larger average annular gap was observed in Product B. Fig. 6 demonstrates the annular flow rates versus the average annular gap size under high head differences (1.5 and 3 m), and low head differences (Dh 6 0.5 m or 18 in.) between the upstream and downstream ends of the tested pipelines. A third-order polynomial relationship was obtained using the least squares method, which fits well for an average annular gap of up to 1.3 mm (0.05 in.) under high head differences (1.5 and 3.0 m) QA ¼ 102:11d 3 þ 164:76d 2 þ 122:1d–9 ð1:5 m head differenceÞ 3
ð3aÞ
2
QA ¼ 173:87d þ 287:44d þ 160:88d–14 ð3:0 m head differenceÞ
ð3bÞ
For the low differential head tests, since the annular gap between the host pipe and liner is small, a second-order equation was used to describe the relationship between the average annular gap (ring) and the annular flow rate QA ¼ 16:445d 2 þ 2:3897d þ 3 ðlow head difference; Dh 6 0:5 mÞ
ð4Þ
The least square analysis yielded R2 values of 0.95, 0.97 and 0.95 for the low (Dh 6 0.5 m or 20 in.), 1.5 m and 3.0 m head differences, respectively. It was not possible to extend this relationship for larger average rings (d > 1.3 mm or 0.05 in.). An attempt was also made to develop a relationship between the annular flow and average annular gap (ring) sizes up to 17.8 mm (0.07 in.) by combining the annular flow data from Group A with small annular gaps and Group B with larger annular gaps. The maximum measured annular gap of 17.8 mm (0.07 in.) could develop when an HDPE liner is installed in a clay host pipe considering the high standard pipe tolerances encountered in both
Host pipe Liner 350
Host pipe Liner Eccentric annular gap - a field condition
Annular Flow (mL/s)
300 250 200 150 100 50 0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
Annular Gap/Ring (mm) 3m
Fig. 5. Cross-section of a clay pipe lined with DR/FF liner (not to scale, annular gap enlarged for the purpose of illustration).
1.5 m
Low Head
Fig. 6. Annular flow rate versus gap size.
1.4
1.6
732
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products, as will be discussed. The analysis provided a logarithmic relationship (Eq. (5)) between the average annular gap size and the annular flow under low differential heads, which are more representative of actual field conditions, since a head difference of 1.5 m or 3.0 m is not likely to exist in typical sewer lines QA ¼ 8:8288 lnðdÞ þ 31
ð5Þ
Fig. 7 demonstrates the relationship between the average annular gap and annular flow for low differential heads and large annular gaps. While this relationship is also based on an empirical derivation, it is more applicable, because it is capable of calculating annular flows for larger average annular gaps up to 17.8 mm (0.07 in.) under low differential heads (Dh 6 0.5 m or 20 in.). These conditions are more general and are representative of typical field conditions. According to AASHTO (2005), a 203-mm (8-in.) clay pipe may have a tolerance in diameter of ±7.94 mm (±0.313 in.). The allowable tolerances for 203-mm (8-in.) polyethylene and PVC pipes are ±6.35 and ±9.53 mm (±0.25 and 0.375 in.), respectively. The diameter of a clay pipe may range from 195 mm (7.68 in.) to 211 mm (8.31 in.) with respect to the maximum allowable tolerance. Meanwhile, HDPE and PVC liners may have maximum allowable diameters as low as 194 and 191 mm (7.65 and 7.53 in.) and as high as 207 and 210 mm (8.15 and 8.28 in.), respectively. Based on these tolerances, the worst case scenario is for a liner/clay pipe rehabilitation would develop when a liner with the smallest tolerable diameter is installed in a clay pipe with the largest tolerable diameter, which would result in difference of up to 20 mm (0.79 in.), or an ‘‘average” gap size (ring) of 10 mm (0.39 in.). It should be noted that the average diameters of the host pipe and the resulting average gap size would also depend on other factors such as manufacturing quality (imperfections), installation quality, ovality, and conditions of the host pipe (sags, depressions, offsets, joints, flat spots, etc.). The standard allowed tolerances specified for
70
Annular Flow (mL/s)
60 50 40 30 20 10 0
0
5
10
15
20
other pipe materials (steel, cast iron, etc.) will also vary from these values. Tolerances in a pipeline diameter may not be as critical in rehabilitation with CIPP liners where a smaller annular space would typically exist as the more flexible liner adjusts to the configuration of the host pipe during installation and curing. However, the size of the annular space in pipelines lined with CIPP liners would vary depending on the foregoing parameters impacting DR/FF liner installations as well as the amount and type of CIPP resin. On the other hand, irregularities or imperfections in the pipeline cross-section would affect the size and continuity of the annular space for both DR/FF and CIPP liners. Excess resin may plug the annular space in some segments along the length of the CIPP lined pipeline, which may result in a discontinuous annular space in some segments of the pipeline. Again, plugging of a given segment of a continuous annular space would depend on its location relative to the entry and exit points of fluids along the given pipeline segment. However, this discontinuous annular space may become continuous with time due to cyclic and monotonic deformations of the liner under variable water and ground pressures as well as the effects of creep. Alternatively, the annular space in all types of lined pipelines could also be plugged over time with soil particles migration into the annular space, which would reduce annular flow. 5. Conclusions A mathematical relationship was developed between the average annular gap (ring) size and flow in the annular space of a lined sewer pipeline. The proposed relationship between the annular flow and average annular gap size was based on the results of series of full-scale tests used to simulate sewer pipelines (203-mm or 8-in.) lined with fold and form or deform/reform (FF/DR) liners. The average annular gap size between the host pipe and a liner was approximated by investigating representative pipe segments removed from the tested lines following the tests. The following conclusions could be made regarding the outcome of the analysis: An annular gap size up to 1.3 mm has more influence on the annular flow rate than an annular gap higher than this limit. A third-order polynomial equation best describes the relationship between the average annular gap (ring thickness) and flow in the annular space for high differential heads between the upstream and the downstream; i.e., 1.5 and 3.0 m (5 and 10 ft). A logarithmic relationship fits best for low differential heads and a wide range of average annular gaps (up to 17.8 mm or 0.701 in.), which is more applicable for most field installations.
Annular Gap/Ring (mm)
Fig. 7. Annular flow versus average gap size for the low differential head tests.
The third-order polynomial equation provided the best fit between the annular flow rate and the average annular
R.M. Bakeer, V. Firat Sever / Tunnelling and Underground Space Technology 23 (2008) 727–733
gap size (ring thickness) for both high differential heads; i.e., 1.5 m (5 ft) and 3.0 m (10 ft) and small annular gaps (up to 1.3 mm or 0.05 in.). It was possible to develop an equation for a wide range of annular gaps (from 0.1 to 17.8 mm or from 0.004 to 0.70 in.) under low differential heads using the logarithmic relationship. This range is relatively close to the expected range of average annular gap between the liner and host pipe regarding standard diameter tolerances for both the liner and host pipe (minimum liner size-maximum pipe size). It should be noted that field performance of a liner can be influenced by many factors, which were not accounted for in the reported tests. These include long-term performance and site-specific conditions encountered during field installation, and most importantly, the exact flow along a CIPP or DR/FF liner under actual field conditions will vary depending on the location of the defects or cracks (entry and exit points) in the underground line with respect to the location and continuity of the annular space along the line. More tests are needed to confirm or further refine the proposed relationship and to better define the formed gaps. This includes obtaining a statistically representative set of samples to be retrieved from actual field installations. The size, distribution, configuration and continuity of the gap(s) could be determined by direct measurements or non-destructive methods; e.g., X-ray tests. Acknowledgements The City of Baton Rouge, Department of Public Works, Wastewater Collection Division sponsored the study. Mr. Edmund P. Stumpf was the Project Director, Mr. David Ratcliff was Assistant Manager for Operations and Maintenance, and Dr. Fang Xia Yu was the Senior Project Engineer. All tests were performed at the outdoor storage
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yard of the Wastewater Collection Division. The authors would like to express their gratitude to Dr. Glen Boyd and Dr. Leslie Guice for their contribution to the study. The investigators were assisted by a group of graduate research assistants, Messrs. Ahmed Hosny, Chanduru Suryanaryana, of Tulane University, and Messrs. Aziz Omara and Omesh Malik of Louisiana Tech University. Mr. Tony Phillips of Delta Testing and Inspection Inc., performed material tests and field monitoring. CSR Pipeline Systems, Boh Bros Construction Company, Insituform Technologies Inc., Insituform Gulf South and National Liner provided the tested products and installation at no cost to the project. References AASHTO, 2005. Standard Specifications for Transportation Materials and Methods of Sampling and Testing, 25th ed. Bakeer, R.M., Guice, L.K., Sever, V.F., Boyd, G.R., 2005. Fluid migration into lined piping systems. Tunnelling and Underground Space Technology 20 (5), 452–462. Kurz, G.E., 1997. Predicting I/I reduction for sewer rehabilitation. In: Proceedings of the Conference on Trenchless Pipeline Projects, Practical Applications, 1997, June 8–11, Boston, MA, US, pp. 103–110. Larsen, J.P., Struve, J.N., Bloetscher, F., McLaughlin, D., 1997. After rehabilitation, then what? Water Environment and Technology 9 (4), 45–49. McKim, R.A., 1997. Selection method for Trenchless technologies. Journal of Infrastructure Systems 3 (3), 119–125. North American Society for Trenchless Technology (NASTT), 2007