FLUID MECHANICS ASPECTS OF A BURIED NATURAL GAS PIPELINE AT A RIVER CROSSING

Transcription

1 FLUID MECHANICS ASPECTS OF A BURIED NATURAL GAS PIPELINE AT A RIVER CROSSING Gyan S. Shrivastava (Gyan.Shrivastava@sta.uwi.edu) Department of Civil and Environmental Engineering, University of the West Indies, Trinidad, West Indies Abstract. Design of a buried pipeline river crossing is a case of soil/fluid/structure interaction, and fluid mechanics plays an important role therein. Specifically, sediment-transport, buoyancy, hydrodynamic drag and lift, and flow induced vibration influence the stability of a pipeline buried beneath a river bed. Further, it may be noted that a river crossing of a high pressure buried natural gas pipeline has important health and safety concerns, since natural gas is odourless, colourless, tasteless, flammable, and less dense than air at atmospheric pressure, and exposure and rupture of a buried pipeline can send a catastrophic buoyant gas plume into the surrounding populated areas. This paper presents a brief account of the design of river crossing of a 1.52 m diameter buried natural gas pipeline in the Caribbean island of Trinidad (10 0 N, 61 0 W), and points out the shortcomings of the current design methodology which due to the inherent complexity of soil/fluid/structure interaction is essentially empirical. The paper concludes by highlighting areas for further research on the fluid mechanics aspects of a buried pipeline at river crossings. Keywords: Caribbean, Pipeline, River, Scour 1. INTRODUCTION A buried pipeline at a river crossing can become exposed, due to the scour of the underlying river bed during flood flows, to hydrostatic buoyancy force, hydrodynamic forces of drag and lift as well as flow-induced vibration. The abovementioned hydrostatic and hydrodynamic forces can rupture a buried pipeline at a river crossing during flood flows, and such a rupture has - in the case of a natural gas pipeline - grave social, economic and environmental consequences (NTSB, 1996, Thompson, 2002). Natural gas is a hazardous material, and is colourless, odourless, tasteless and inflammable. Moreover, it is less dense than the atmospheric air, and therefore a ruptured pipeline creates a buoyant plume. Further, leaking gas from a high pressure pipeline emits noise at a level which is hazardous to human hearing. Understandably, therefore, a ruptured natural gas pipeline has the potential to quickly turn into a public emergency (NTSB, 2000).This paper briefly describes, as an example and against the foregoing background, the estimation of maximum river bed scour depth, and hydraulic forces on a 1.52 m diameter buried natural gas pipeline during a 100 year flood across the Matura River in the Caribbean island of Trinidad (Fig. 1). Specifically, it seeks to highlight a gap between the state of the art (in terms of the modern numerical methods and laboratory techniques) and the state of the engineering practice in Fluid Mechanics, where engineers have to design complex field scale works amidst uncertainties of analytical methods, laboratory scale studies, limited filed data and time constraint km Point Fortin GULF OF PARIA CARIBBEAN SEA Port of Spain Arima Caroni Swamp Chaguanas Point Lisas San Fernando New Grant Matura Mayaro Moruga Sangre Grande Matura River Crossing ATLANTIC OCEAN COLUMBUS CHANNEL 2. FLUID MECHANICS ASPECTS Figure 1. Approximate location of a pipeline river crossing in Trinidad (10 0 N, 61 0 W) The estimation of river-bed scour depth and estimation of hydraulic forces and hydrodynamic stability on a buried pipeline, in case it is exposed, has three distinct fluid mechanics aspects: river-bed scour, hydraulic forces and

2 hydrodynamic stability. It should be noted that the field estimation of river-bed scour depth, in spite of considerable research in river mechanics and sediment transport (e.g. Graham, 1980, Chiew, 1991, Dey and Singh, 2007), remains empirical. As stated earlier, this is one of the areas where a practicing engineer faces a gulf between the state of the art and the state of the practice (Prakash, 1999). Against the foregoing background, the estimation of the aforementioned scour depth and hydraulic forces at the river crossing of a 1.52 m diameter pipeline across the Matura River in Trinidad is now briefly described in the following sections, and further details of the work presented in this paper may be found elsewhere (Shrivastava, 2004) Estimation of riverbed scour depth In view of the earlier mentioned consequences of rupture of a buried natural gas pipeline, an accurate estimation of the potential riverbed scour at a pipeline river crossing is essential. However, this is a difficult task for the following three reasons: First, for the estimation of a 100 year flood, the hydrologic data especially on stream flow is sparse, discontinuous and inaccurate (Shrivastava, 1999). Second, there is a need to anticipate, and include the impact of global climate change as well as land use changes in a river catchment. This is because such changes, in the course of the design life of United States a pipeline, would affect the spatial and temporal distribution of runoff as well as the sediment generation and transport, and in turn would gradually alter a river s geometry in terms of its cross section, slope and meandering. Nevertheless, 100 year peak flood flow, Q p, for the Matura River was estimated to be approximately 278 m 3 s -1 for the year 2050 by the National Resource Conservation Service (NRCS) Runoff Model (Shrivastava, 2004). Finally, there is yet no theoretical framework available for a rigorous analysis of the river bed scour phenomenon. It follows from the foregoing that on one hand there is a need to accurately estimate the potential riverbed scour, and on the other hand the required analyses have to be carried out amidst considerable uncertainty (Vincent-Genod, 1984). This uncertainty is reflected in the technical literature by the recommended scour depths ranging between 2 m to 16 m, and by the fact that the United States Department of Transportation prescribes only a minimum cover of 1.2 m. Consequently, the estimation of potential riverbed scour depth is normally based on site specific empirical approaches and heuristic reasoning (ASCE 1996, Bonn et al. 1996; Sakhalin Energy, 2003). It is recognized that rivers are authors of their own geometry and are constantly seeking a dynamic equilibrium in a changing environment. Specifically, as flood wave passes a cross section, an alluvial riverbed scours during the rising stage and recovers during the falling stage. It is this transient, and event specific, phenomenon that is of primary interest in this case. Further, the magnitude of scour is a function of the hydraulic mean depth, D m, at peak discharge. In this context it should be noted that an alluvial river, such as the Matura River, is seldom straight for a distance greater than 10 channel widths, and its meander amplitude and wave length are based on a spring analogy- expressions of erosive energy (Leopold, 2003). Further, this erosive energy is quantified by a stream factor, Z, which is the ratio of the thalweg length, L, to the corresponding Euclidean distance, λ, between two nodes as shown in Fig. 2. Accordingly, the riverbed scour depth, D s, can be expressed as: D s = Z x D m (1) Thalweg length, L A Pipeline Crossing λ A Z=L/λ =Stream Factor Figure 2. Schematic plan view of a river showing the thalweg and meander wave lengths

3 D m in Eq. (1) was estimated by an iterative solution of the Manning s equation for a compound channel to take into account flow in the flood plain (Shrivastava, 2004). Further, the value of D m in was also obtained by Lacey s Regime Equation (Sellin, 1970) as follows: D m = 0.47 (Q p /f) 1/3 (2) Where Q p is the 100 year peak flood flow and f is Lacey s silt factor given as: f = 1.76 (d 50 ) 0.5 (3) where d 50 is the mean bed material particle diameter in mm. The Manning s equation gave a higher value of D m, and was used for estimating D s. Further, bed shear stress was estimated and was found to be approximately 15 times larger than the critical bed shear stress, thereby confirming that significant river bed scour is likely to occur (Shrivastava, 2004). A maximum scour depth of 4.8 m was estimated for the Matura River crossing and Fig. 3 shows a schematic of the scour depth for buried pipeline for the estimated case as well as the worst case scenario when the scour depth may exceed the estimated scour depth. 100 Year Peak Flood Flow X L 1.52 M. Dia. Pipeline Estimated Scour Depth Worst Case Scenario (Exposed pipeline) Figure 3. Schematic of river cross section A-A, scour depths and pipeline situations 2.2 Estimation of hydraulic forces It is relevant to estimate the hydraulic forces on an exposed pipeline at a river crossing. This situation may arise due to either an insufficient scour depth provision or a peak flow exceeding the estimated value. The hydraulic forces that act under such condition can be divided into two groups: hydrostatic and hydrodynamic, and the latter can be subdivided into steady and unsteady components. The steady hydrodynamic forces refer to forces of drag and lift, and the unsteady hydrodynamic force refers to the vortex-induced vibration. Considering the complexity of soil/fluid/structure interaction, a simple methodology is used for the estimation of the aforementioned hydraulic forces. It is acknowledged that these forces can be estimated in a more accurate manner by using a physical scale model but laboratory facilities do not exist in Trinidad, and perhaps in many small island developing states for carrying out such tests. Accordingly, the hydraulic forces were estimated on the following two assumptions: (a) the flow field is two dimensional i.e. the end effects are not considered, and (b) the pipeline crossing is horizontal and in a plane perpendicular to the approaching flow. The buoyancy force per meter length, F B, was estimated as follows: Where D is the pipe diameter, ρ is the density of water and g is acceleration due to gravity. F B was estimated to be kn/m. The drag force per unit length, F D, and lift force per unit length, F L, were estimated as follows: (4)

4 (5) Where C D is the coefficient of Drag, and U is the mainstream velocity of flow in the river cross section. C D was estimated from the published experimental results (Schlichting, 1979). (6) Where C L is the coefficient of lift C D and C L = f (R e ) (7) Where R e is the Reynolds Number, and for the given R e, C L was estimated to be 0.5 (Sorensen, 1978). 2.3 Assessment of hydrodynamic stability For assessing the hydrodynamic stability of an exposed pipeline it was necessary to estimate its natural and vortex frequencies. The vortex frequency, f v, was estimated from Eq. 8 and Eq. 9. (8) S = f (R e ) (9) Where S is the Strouhal Number, and for the given R e it was estimated to be 0.25 (Schlichting, 1979). The natural frequency was estimated on the assumption, as a first approximation, that the natural vibration an exposed pipeline as shown in Fig. 3 - is similar to the transverse vibration of a simply supported beam with symmetric arbitrary overhang (Murphy, 1997). (10) Where E = Elastic Modulas of the pipeline (207x10 9 N/m 2 ), I = second moment of area = 0.1 m 4, L = is the horizontal length of the pipeline, X = length of the exposed pipeline (Fig. 3) and M = M pipeline + M hydrodynamic (added) = 1,470 kg/m. It should be noted that the added mass was considered equal to half of the mass of the fluid displaced by the pipeline (Sarpkaya and Isaacson, 1981). The condition for hydrodynamic stability can be stated as follows: The estimated values of hydraulic forces and natural and vortex frequencies are shown in Tab. 1. It can be seen that Eq. (11) is satisfied assuring the hydrodynamic stability of the exposed pipeline. Table 1. Estimated values of hydrodynamic forces, and natural and vortex frequencies at the Matura river crossing (11) River [Latitude, Longitude] Matura [ N, W] L (m) X (m) U x (m/s) R e C D F D (kn/m) F L (kn/m) f v (H z ) x f n (H z ) 3. CONCLUSIONS The estimation of scour depth at a pipeline river crossing was estimated essentially by empirical methods, and should be considered only a first approximation. This is because laboratory based studies in reported in the scientific literature are not yet applicable to field situations. Given the importance of pipelines for energy security, this should be an area of active research. In this regard, the work of Graham (1980) shows much promise, and should be further

5 developed. On the other hand, the estimation of hydraulic forces on an exposed pipeline, and hydrodynamic stability of the same, was carried out by analytical methods, albeit under simplifying assuptions. Specifically, the natural frequency of the exposed pipeline should be estimated using the actual geometry of the pipleine and more realistic boundary conditions. 4. ACKNOWLEDGEMENTS The author is grateful to TRINTOPLAN Consultants Limited for the opportunity to work on a related study in 2003 which led to further interest, and to David Hardwick for his review of some of the work reported in this paper during the author s British Petroleum Research Fellowship at Imperial College, London in REFERENCES ASCE (American Society of Civil Engineers), 1996, Pipeline Crossings, Manuals and Reports on Engineering Practice, Number 89. Bonn, B., 1996, Modelling Riverbed Erosion Hazard for Pipelines, September 5, 2003, Dey, S., and Singh, N. P., 2007, Clear-water scour depth below underwater pipelines, Journal of Hydro-environment Research, Vol. 1, No. 2, pp Chiew, Y. M, 1991, Prediction of maximum scour depth at submarine pipelines, Journal of Hydraulic Engineering, Vol. 117, No. 4, pp Graham, D. S., 1980, Pipeline river crossings: a design method, Journal of Transportation Engineering, Vol. 106, No. 2, pp Leopold, L. B., 2003, A view of the river, Harvard University Press Murphy, J., 1997, Transverse vibration of a simply supported beam with symmetric arbitrary overhang ASTM Journal of Testing and Evaluation, Vol. 25, No. 5, pp NTSB (National Transportation Safety Board), 1996, Pipeline Special Investigation Report: Evaluation of pipeline failures during flooding, Jacinto River, October 22, 2003, NTSB (National Transportation Safety Board), 2000, Investigation of the Pipeline Accident, November 13, 2003, Prakash, A., 1999, Guest Editorial, Journal of Hydrologic Engineering, Vol. 4, No. 1, Sakhalin Energy, 2003, The Trans Alaska Pipeline System, September 15, 2003, Sarpkaya, T., and Isaacson, M., 1981, Mechanics of Wave Forces on Offshore Structures, Von Nostrand, pp Schlichting, H., 1979, Boundary Layer Theory, McGraw Hill, pp Sellin, R. H. J., 1970, Flow in Channels, Gordon and Breach. London Shrivastava, 1999, Some aspects of water resources management in Trinidad, Journal of Water & Maritime Engineering, Institution of Civil Engineers (UK), 136(4): Shrivastava, G. S., 2004, Estimation of scour depth and fluid dynamic forces at buried pipeline river crossings, Unpublished Research Report, Department of Civil and Environmental Engineering, University of the West Indies. Sorensen, R. M., 1978, Basic Coastal Engineering, pp Thompson, L., 2002, When water and land meet, Pipeline and Gas Journal, Vol. 37, pp Vincent-Genod, J, 1984, Fundamentals of Pipeline Engineering, Institut Francais du Petrole Publications. 6. RESPONSIBILITY NOTICE The author is solely responsible for the printed material included in this paper.