![CCTV-image of a transversal crack-type pipe defect with groundwater infiltration. Reprinted from Davies et al. [2001].](https://www.researchgate.net/profile/Aaron-Peche/publication/332902209/figure/fig2/AS:984544161316867@1611745028322/CCTV-image-of-a-transversal-crack-type-pipe-defect-with-groundwater-infiltration_Q320.jpg)
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Numerical modeling of pipe leakage in variably saturated soil
Abstract and Figures
Pipe leakage related to defect urban sewer and stormwater pipe networks may lead to
subsurface contamination, reduction of groundwater recharge or a significant decrease of
the groundwater table. The quantification of pipe leakage is challenging, mostly due to the
uncertain forming of a colmation layer in the defect vicinity and inaccessibility of both,
pipe defects and the surrounding soil. Numerical models can be used to quantify leakage.
At present times, only few physically-based pipe leakage models exist, all of which either
neglect or simplify variably-saturated flow.
In the present dissertation, a novel and unique three-dimensional physically-based pipe
leakage model for variably saturated soil is presented. The model consists of the newly
implemented coupling between the pipe flow simulator HYSTEM-EXTRAN and the
unsaturated-saturated flow simulator OpenGeoSys. The coupling is based on updating
of boundary conditions and source terms. The interprocess data transfer is realized using
a shared-memory. The pipe leakage model is successfully validated and verified using a
newly generated benchmark library for pipe leakage models. Benchmarks are based on two physical experiments described in literature and two newly derived analytical solutions.
A novel method for upscaling pipe leakage is presented. The method enables to significantly reduce the local refinement of spatial discretization in the pipe vicinity, which
leads to a substantial reduction of computational costs. The method is based on leakage
functions. Two leakage functions representing both, sewer and stormwater pipe leakage
are presented. Accuracy and time efficiency of the upscaling method is demonstrated by
comparing results from a fully discretized model and an upscaled model.
In the present dissertation, the pipe leakage model is applied to several case studies to
investigate the pipe leakage process. Model setups represent (i) a single defect, (ii) a leaky sewer pipe of 30 m length, and (iii) a 53 km long defect stormwater pipe network in an urban catchment.
Results of the single defect and leaky sewer pipe model (models i,ii) show that leaky pipes can hydraulically disconnect from groundwater. It is found that, for a given pipe water level, pipe water exfiltration converges as the groundwater table is lowered. Further, it is found that pipe water exfiltration increases as the intensity and duration of pipe flow events increase. The temporal distribution of pipe flow has a negligible effect on pipe
water exfiltration.
Results of the model representing a defect stormwater pipe network in an urban catchment (model iii) show the impact of pipe leakage on urban groundwater. It is shown that groundwater infiltration into a largely defect pipe network may be in the order of annual groundwater recharge. Further, it is shown that groundwater infiltration may reduce the groundwater table by several meters and that the groundwater table may be lowered to the elevation of the pipe network.
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... Integrated 1D-3D models were developed to simulate sewer exfiltration dynamics but are hard to validate due to the large number of data required for model parametrization (Rutsch et al., 2008;Peche et al., 2017;Tscheikner-Gratl et al., 2020). Karpf (2012) and Peche (2019) proposed simplified approaches for modeling sewer exfiltration, but the methods have been tested only to site-specific and pipe scales. Wolf et al. (2012) considered the temporal and spatial variation of sewer exfiltration to groundwater by conducting sampling for the period from 2002 to 2008 in the city of Rastatt. ...
... Lee et al. (2015) and Roehrdanz et al. (2017) developed a spatial model of sewer exfiltration, which allows predicting the occurrence of exfiltration in shallow groundwater and incorporates various wastewater indicators, but the outputs of the model are subjected to the groundwater shortterm observations in a small region of a city. Besides, the uncertainty of upscalling approaches in sewer exfiltration modelling remains significant issue due to a lack of understanding of core parameters and processes of sewer exfiltration (Wolf and Hötztl, 2007;Karpf, 2012;Peche, 2019). So far, the studies by Rutsch et al. (2005) and Rutsch et al. (2008) remain the only reviews that incorporate modelling aspects of sewer exfiltration (Table 1), though many changes have occurred since then. ...
... At large hydraulic gradients (between the pipe and the soil in the pipe vicinity) and soil moisture, increased sewer exfiltration leads to downwards propagation of a wetting front and sewer outflow may recharge groundwater. Sewer exfiltration is governed by the presence of a colmation layer forming in the pipe defect vicinity (Karpf, 2012;Peche, 2019). After the occurrence of a pipe defect, high sewer exfiltration rates continue until an equilibrium pressure height between insewer and soil conditions is reached. ...
Increasing evidence from studies in urban wastewater systems proves that sewer exfiltration may present a profound threat for rising levels of toxic substances and microbial pollution in groundwater. New and innovative methods for monitoring sewage exfiltration are continuously developed, which provide a solicit ground for a better understanding of key processes and influencing characteristics of sewer exfiltration to support the development of mathematical equations and models worldwide. However, modelling of sewer exfiltration and its associated impacts on groundwater are still constrained and not fully understood in large urban systems. This paper reviews the knowledge advancements and challenges of sewer exfiltration modelling. Based on the present review, we define five key research domains for developing more generic framework of large-scale models. These domains inquire to advance the representation of hydraulic modelling (e.g. testing exfiltration models coupled with biofilm growth models), modelling of solutes originating from sewer leakages (e.g. heavy metals), define the practical values of key model parameters of main model components and sub-processes for calibration and uncertainty evaluations, develop upscaling approaches for integrated multi-dimensional sewer exfiltration models, and incorporation of sewer exfiltration from private sewers.
... 2). This factor incorporates the two parameters hydraulic conductivity and thickness of the colmation layer, which are difficult to determine and often unknown in practice (Karpf et al. 2009;Peche 2019). This leads to the reformulation of Eq. 1 for calculation of exfiltration rates under the swf condition (which is the case of CSs in this study): ...
... Studies on sewer exfiltration at pipe scales indicate that the leakage process is ruled by a number of key parameters, including leakage area, depth of wastewater in the pipe, clogging layer, hydraulic permeability and soil characteristics, and hydraulic gradient from pipe surface to the groundwater (Wolf and Hötzl 2007;Karpf et al. 2009;Peche et al. 2017). These parameters describe structural and dynamic components of sewer exfiltration processes, which data demand at the catchment scale is often not available or subject to large uncertainties (Rutsch et al. 2008;Karpf and Krebs 2011;Peche 2019). The common approach for large-scale studies is so far based on mapping analysis of sewer network deteriorations (structural condition, distribution of pipes), surveying and indirectly correlating with population-based sewer discharge, or simplified assumptions of nationwide fixed rates of water loss from defective sewer pipes (e.g. ...
... Besides, incorporating process-based approaches for important model parameters (such as wastewater level or the properties of the colmation layer) in the sewer exfiltration model to replace simplified assumptions of constant parameters, or test the timevariant leakage function instead of using the equation of a fixed sewer exfiltration rate might help to better represent the exfiltration dynamics and its spatial distribution (e.g. Peche et al. 2017;Peche 2019). This will require a more detailed identification and inventory of exfiltration susceptible areas in major cities under real sewer conditions. ...
A growing literature indicates that untreated wastewater from leaky sewers stands among major sources of pollution to water resources of urban systems. Despite that, the quantification and allocation of sewer exfiltration are often restricted to major pipe areas where inspection data are available. In large scale urban models, the emission from sewer exfiltration is either neglected (particularly from private sewers) or represented by simplified fixed values, and as such its contribution to the overall urban emission remains questionable. This study proposes an extended model framework which incorporates sewer exfiltration pathway in the catchment model for a better justified pollution control and management of urban systems at a nationwide scale. Nutrient emission from urban areas is quantified by means of the Modelling of Nutrient Emissions in River Systems (MONERIS) model. Exfiltration is estimated for public and private sewers of different age groups in Germany using the verified methods at local to city scales, upscaling techniques, and expert knowledge. Results of this study suggest that the average exfiltration rate is likely to be less than 0.01 L/s per km, corresponding to approximately 1 mm/m/year of wastewater discharge to groundwater. Considering the source and age factors, the highest rate of exfiltration is defined in regions with significant proportions of public sewers older than 40 years. In regions where public sewers are mostly built after 1981, the leakage from private sewers can be up two times higher than such from public sewers. Overall, sewer exfiltration accounts for 9.8% and 17.2% of nitrate and phosphate loads from urban systems emitted to the environment, which increases to 11.2% and 19.5% in the case of no remediation scenario of projected defective sewer increases due to ageing effects. Our results provide a first harmonized quantification of potential leakage losses in urban wastewater systems at the nationwide scale and reveal the importance of rehabilitation planning of ageing sewer pipes in public and private sewer systems. The proposed model framework, which incorporates important factors for urban sewer managers, will allow further targeting the important data need for validating the approach at the regional and local scales in order to support better strategies for the long-term nutrient pollution control of large urban wastewater systems.
(Open source access at: https://link.springer.com/article/10.1007/s11356-021-12440-9)
... A coupled simulation is not required, because the time steps of surface flow are much smaller than those in the soil layer. The leakage of water from the pipe system to the soil is negligible for single events, because the leakage rate is tiny [Peche, 2019]. However, for continuous injection spill problems, the coupling of surface, pipe and soil flow would be a way to forecast the plume of pollutants in the soil and groundwater domain before it reaches surface waters or drinking water wells. ...
... A coupling of the pollution tracking and the runoff routing must be established in both directions. This can be done via an iteration of both models, like described in Peche [2019]: A master model (volume runoff routing) calculates one time step and calls the client (pollution transport) model to process the same amount of time. The result of the transport time step is analysed by the master model to adapt volume fluxes before the next time step is processed. ...
The quality of drainage water in urban areas affects the health of humans and nature.
Accumulated pollutants on surfaces and accidentally emitted hazardous substances are
washed off to the drainage system during rain events. In case of very strong rain event, the capacity of the pipe system can be exceeded and complex flow paths between the surface and the drainage system distribute the hazardous substances in the urban catchment. A prediction of potential transport paths is necessary to take actions before and during a pollution spill. Current models are not sufficiently capable of combining the pipe and surface domain for transport of pollutants.
This thesis introduces a transport model for solutes in urban drainage for the bi-directional coupled pipe system and the surface, built for use in urban heavy rainfall conditions. The applied Lagrangean particle approach diminishes the effect of numerical dissipation. The so called Random-Walk motion of particles allows to define physical dispersion in the transport. An explicit Euler scheme with an iterative design to allow for large time steps is introduced for the 1D and 2D calculation domain. The particle routing and tracking is aware of boundary collision and sinks. The particle based transport model allows for an easy balancing between fast and accurate calculation. At the same time it is well suited for exact tracking of transport paths, calculation of mass and concentration.
The model is implemented in the created software framework “GULLI”. It is designed
for very fast calculation of transport paths on large scale domains with low processor
and memory usage. Flow fields can be imported from commercial and free hydrodynamic
software models. The use is easy due to a graphical user interface. No specialised hardware is required. A forecast of a spill takes less than one minute for a forecast of three hours with 100 000 particles on a standard desktop PC.
The design is intended for use of point source spill events during heavy rainfall events. An application for the use of diffusive spread pollutants is also demonstrated. The influence of rain intensity on the wash-off and transport to the outlets of different catchments is analysed. The model can forecast concentration peaks at the outlets that can be used to optimize actively controlled wastewater treatment facilities.
For the use in pollution forecast systems during pluvial floods, the selection of precalculated flow fields is required to serve as a basis of the particle transport model. A
Nearest-Neighbour selection approach is introduced, which takes the precipitation pattern into account. A database of 944 events is used to search for flow fields that fit to an upcoming rain event. Good results could be achieved with the selection, if the response time of the pipe system is taken into account.
The workflow of the methods for flow field prediction and pollutant spread forecast is
combined and analysed regarding the total processing time to generate real-time warnings.
... Additionally to the conductive heat transport, leakage of wastewater yields a noticeable heat input (Benz et al., 2015;Ford & Tellam, 1994). Leakages of sewer pipes are challenging to detect and quantify and are strongly varying regionally (Peche, 2019). While the temperature of wastewater depends on several factors (Kretschmer et al., 2016), for Central European cities it is generally around 12-22 C (Benz et al., 2015;Cipolla & Maglionico, 2014;Schmid, 2008;Tissen et al., 2021). ...
Anthropogenic warming of the atmosphere is one if not the most pressing challenge we face in the 21st century. While our state of knowledge on human drivers of atmospheric warming is advancing rapidly, little so can be said if we turn our view toward the Earth’s interior. Intensifying land use and atmospheric climate change condition the changing thermal state of the subsurface at different scales and intensities. Temperature is proven to be a driving factor for the quality of our largest freshwater resource: groundwater. But there is only insufficient knowledge on which sources of heat exist underground, how they relate in their intensity of subsurface warming, and which consequences this warming implies on associated environments, ecosystems and resources. In this review, we propose a differentiated classification based on (1) the geometry of the heat source, (2) the scale at which the subsurface is heated, (3) the process that generates the heat, and (4) the intention of heat release. Furthermore, we discuss the intensities of subsurface warming, the density of induced heat fluxes, as well as their abundance, and draw implications for depending processes and ecosystems in the subsurface and the potential of recycling this waste heat with geothermal installations.
Pipe leakage from defect subsurface gravity sewer pipe networks potentially contaminates soil and groundwater. In recent times, an increasing number of numerical pipe leakage models incorporating pipe flow, saturated-unsaturated flow in the subsurface, and exchange fluxes from and to leaky pipes have been developed. Numerical benchmarks are required in order to demonstrate result accuracy of these models. The present technical note represents a novel numerical benchmark of the pipe leakage problem describing pipe water exfiltration into horizontal unsaturated-saturated soil. The present benchmark enables to test the accurate calculation of the spatial potential distribution in the soil, which is affected by the water level in the leaky pipe. The derivation of an analytical solution for stationary pipe water exfiltration into a horizontal aquifer and a conceptual model for the setup of a corresponding numerical model is shown. Results of the analytical model are reproduced using the numerical leakage model OGS-HE.
Mechanical and/or chemical removal of material from the
subsurface may generate large subsurface cavities, the destabilisation of
which can lead to ground collapse and the formation of sinkholes. Numerical
simulation of the interaction of cavity growth, host material deformation
and overburden collapse is desirable to better understand the sinkhole
hazard but is a challenging task due to the involved high strains and
material discontinuities. Here, we present 2-D distinct element method
numerical simulations of cavity growth and sinkhole development. Firstly, we
simulate cavity formation by quasi-static, stepwise removal of material in
a single growing zone of an arbitrary geometry and depth. We benchmark this
approach against analytical and boundary element method models of a deep
void space in a linear elastic material. Secondly, we explore the effects of
properties of different uniform materials on cavity stability and sinkhole
development. We perform simulated biaxial tests to calibrate macroscopic
geotechnical parameters of three model materials representative of those in
which sinkholes develop at the Dead Sea shoreline: mud, alluvium and salt.
We show that weak materials do not support large cavities, leading to
gradual sagging or suffusion-style subsidence. Strong materials support
quasi-stable to stable cavities, the overburdens of which may fail suddenly
in a caprock or bedrock collapse style. Thirdly, we examine the consequences
of layered arrangements of weak and strong materials. We find that these are
more susceptible to sinkhole collapse than uniform materials not only due to
a lower integrated strength of the overburden but also due to an inhibition
of stabilising stress arching. Finally, we compare our model sinkhole
geometries to observations at the Ghor Al-Haditha sinkhole site in Jordan.
Sinkhole depth ∕ diameter ratios of 0.15 in mud, 0.37 in alluvium and 0.33
in salt are reproduced successfully in the calibrated model materials. The
model results suggest that the observed distribution of sinkhole
depth ∕ diameter values in each material type may partly reflect sinkhole
growth trends.
A Lagrangean particle based transport model is introduced to calculate the potential contamination paths of solutes in drainage water in an urban area during a pluvial flood event. The necessity to capture the complexity of a surface runoff model and the coupling of pipe and surface are investigated. Results show that fully coupled hydrodynamic models are needed for a good representation of transport paths and breakthrough curves of contaminant concentration in drainage water. An analysis for time variation of a single location spill event is performed that shows a high variability in solute spreading depending on the spill relative to the rainfall characteristics.
Für Fragestellungen der Grundwasserdynamik in Zusammenhang mit Hochwasserereignissen wurde das Grundwasserströmungsprogramm FEFLOW um eine Leakage-Randbedingung erweitert, der ein nichtlinearer Zusammenhang zwischen Wasserstandsdifferenz und Leakage-Rate zugrunde liegt. Da die Austauschrate von dem gesuchten Grundwasserstand selbst abhängt, wird eine zusätzliche Iterationsschleife zur Berechnung der Wasserstandsdifferenz implementiert.
In urban stormwater pipe networks, pipe leakage may lead to reduction of groundwater recharge, to significant reduction of groundwater levels, and to subsurface contamination. In the present study, stormwater pipe leakage is simulated in a case study representing an urban catchment using the coupled groundwater-pipe network flow model OGS-HE. This model includes pipe flow, variably saturated subsurface flow and exchange fluxes to and from leaky pipes. The study area is a typical northern German urban catchment with a stormwater pipe network which is located partly below and above groundwater. The successful calibration of a groundwater model is shown. Based on the calibrated groundwater model, stormwater pipe leakage for pipe networks of different ages and different pipe defect sizes is investigated for dry-weather flow conditions and rainfall conditions. It is shown that standard defects with a size of m^2 per m pipe can result in a groundwater infiltration into the leaky pipe network, which is in the order of annual groundwater recharge. The same standard defect size leads to a reduction of local groundwater levels by several meters. Rain events of increasing return period reduce groundwater infiltration into leaky pipes and increase stormwater exfiltration from leaky pipes, while the temporal distribution of a rain event has no effect on stormwater leakage.
Watershed modeling is at the heart of modern hydrology, supplying rich information that is vital to addressing resource planning, environmental, and social problems. Even in light of this important role, many books relegate the subject to a single chapter while books devoted to modeling focus only on a specific area of application. Recognizing the need for a broad, comprehensive overview of the various types of watershed models, renowned experts Singh and Frevert carefully selected several highly popular and useful models to produce this groundbreaking reference. Watershed Models comprises seven sections that encompass 24 models chosen for a variety of characteristics, such as physical bases, mathematical sophistication, comprehensiveness, broad-based applicability, and use of modern tools. After a concise introduction, the book examines the history and evolution of watershed modeling derived from the Stanford Watershed Model along with regional calibration of models. The following six sections explore large watershed, streamflow, water quality, urban watershed, agricultural watershed, and planning and management models. Each chapter contains a wealth of information on model parameters, the strengths of each model for particular purposes, and examples of applications. Offering an up-to-date review of models used worldwide, Watershed Models supplies broad, integrated knowledge necessary for solving the complex and ongoing problems involved in resource and environmental water management.
This book presents the main hydrological methods and techniques used in the design and operation of hydraulic projects and the management of water resources and associated natural risks. It covers the key topics of water resources engineering, from the estimation of runoff volumes and unit hydrographs to the routing of flows along a river and through lakes, reservoirs, and hydraulic structures. It deals with questions regarding basic hydrological data, hydrological modeling and the prediction and forecasting of low flows and flood discharges.
This paper describes the use of the sewer model HYSTEM-EXTRAN in combination with a rule based control device using fuzzy-logic to simulate the real-time control of a sewer system. The rules for the control of the system were set up with the help of optimization procedures. The advantage of the procedure is proved by comparing the uncontrolled versus the controlled state in a simulated mode for an existing sewer system. The final system was installed and tested within the sewer system.
This paper examines the performance of infiltration of wastewater into the groundwater due to leaks in sewer systems. Experiments were carried out under a variety of conditions using domestic sewage and uniform bedding material ranging in grain-size from 0 to 40 mm. The results indicate that the infiltration is determined solely by the physical process of the colmation of the bedding sand zone. Due to the accumulation of particles in the porous media the permeability of this zone and therefore the amount of infiltrated sewage is decreased rapidly with time. This effect is commonly known as colmation. A strong influence of both solids concentration of the sewage and grain-size of the bedding material can be seen on the temporal development of the colmation. Still a steady state flow was reached under all experimental conditions in less than an hour of infiltration. The characterisation of the colmated zone by the leakage factor presents the possibility to calculate the infiltrated sewage according to Darcy's law. The infiltration of sewage into the groundwater is therefore linear dependent on the area of the leak and the pressure head. The observed values for the steady state leakage factor range between 0.001 and 0.01 1/s depending mainly on solids concentration and grain-size.
Thermochemical gas-solid reactions, as well as adsorption processes, are currently of significant interest for the design of heat storage systems. This book provides detailed models of these reactions and processes that account for heat and mass transport, chemical and physical reactions, and possible local thermal non-equilibrium. The underlying scientific theory behind the models is explained, laboratory tests are simulated, and methods for high-performance computing are discussed. Applications ranging from seasonal domestic heat storage to diurnally operating systems in concentrating solar power facilities are considered in these models, which are not available through any other sources. Finally, an outlook on future developments highlights emerging technologies.