**Environmental Contamination Remediation and Management**

Jonás García-Rincón · Evangelos Gatsios · Robert J. Lenhard · Estella A. Atekwana · Ravi Naidu Editors

Advances in the Characterisation and Remediation of Sites Contaminated with Petroleum Hydrocarbons

# **Environmental Contamination Remediation and Management**

### **Series Editors**

Erin R. Bennett, School of the Environment, Trent University, Peterborough, Canada

Iraklis Panagiotakis, Environmental Engineer & Scientist, ENYDRON – Environmental Protection Services, Athens, Greece

### **Advisory Editors**

Maria Chrysochoou, Department of Civil & Environmental Engineering, University of Connecticut, Storrs, CT, USA

Dimitris Dermatas, School of Civil Engineering, National Technical University of Athens, Zografou, Greece

Luca di Palma, Chemical Engineering Materials Environment, Sapienza University of Rome, Rome, Italy

Demetris Francis Lekkas, Environmental Engineering and Science, University of the Aegean, Mytilene, Greece

Mirta Menone, National University of Mar del Plata, Mar del Plata, Argentina

Chris Metcalfe, School of the Environment, Trent University, Peterborough, Canada

Matthew Moore, United States Department of Agriculture, National Sedimentation Laboratory, Oxford, MS, USA

There are many global environmental issues that are directly related to varying levels of contamination from both inorganic and organic contaminants. These affect the quality of drinking water, food, soil, aquatic ecosystems, urban systems, agricultural systems and natural habitats. This has led to the development of assessment methods and remediation strategies to identify, reduce, remove or contain contaminant loadings from these systems using various natural or engineered technologies. In most cases, these strategies utilize interdisciplinary approaches that rely on chemistry, ecology, toxicology, hydrology, modeling and engineering.

This book series provides an outlet to summarize environmental contamination related topics that provide a path forward in understanding the current state and mitigation, both regionally and globally.

Topic areas may include, but are not limited to, Environmental Fate and Effects, Environmental Effects Monitoring, Water Re-use, Waste Management, Food Safety, Ecological Restoration, Remediation of Contaminated Sites, Analytical Methodology, and Climate Change.

Jonás García-Rincón · Evangelos Gatsios · Robert J. Lenhard · Estella A. Atekwana · Ravi Naidu Editors

# Advances in the Characterisation and Remediation of Sites Contaminated with Petroleum Hydrocarbons

*Editors*  Jonás García-Rincón Legion Drilling & Numac Wetherill Park, NSW, Australia

Robert J. Lenhard San Antonio, TX, USA

Ravi Naidu Advanced Technology Centre The University of Newcastle Callaghan, NSW, Australia

Evangelos Gatsios INTERGEO Aspropyrgos, Greece

Estella A. Atekwana Department of Earth and Planetary Sciences University of California Davis Davis, CA, USA

ISSN 2522-5847 ISSN 2522-5855 (electronic) Environmental Contamination Remediation and Management ISBN 978-3-031-34446-6 ISBN 978-3-031-34447-3 (eBook) https://doi.org/10.1007/978-3-031-34447-3

© The Editor(s) (if applicable) and The Author(s) 2024. This book is an open access publication.

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The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

# **Preface**

Petroleum hydrocarbons (PHCs) are among the most common and widespread contaminants in urban and industrial environments. Following a release from containment facilities, these complex mixtures of organic compounds can be found as nonaqueous phase liquids (NAPLs) in the subsurface, where they may act as a persistent source of contamination for soil and groundwater systems. Common petroleum fuels such as petrol (gasoline), diesel, and kerosene-type jet fuel are lighter-than-water NAPLs (LNAPLs).

Subsurface characterisation and remediation of sites contaminated with PHCs is often challenging due to the multi-fluid, multi-component nature of the problem and the various physical, chemical, and biological processes involved in a dynamic and naturally heterogeneous hydrogeological setting. Establishing an effective and sustainable strategy to manage risks posed by PHCs must be done considering all stakeholders and existing regulatory framework.

The objective of this book is to give visibility to advances in the characterisation and remediation of PHC-impacted sites, as well as pertinent concepts and methods that may still be underutilised by the remediation industry internationally. Potential future lines of research and development as well as best practices that provide guidance to contaminated land practitioners are presented throughout the book.

The book contains three sections: Chaps. 1–6 mainly address understanding and analysing the fate and transport of PHCs in the subsurface; Chaps. 7–11 focus on site characterisation tools; and Chaps. 12–18 discuss in situ remediation technologies and site management strategies.

In the first section, Chap. 1 serves as an introduction to the rest of the book and presents an overview of the main challenges found in PHC-contaminated sites. Chapter 2 critically underpins our assessment of LNAPL distribution by examining the historical development of constitutive relationships between water, LNAPL, and air governed by fluid saturations and capillary pressures. Chapter 3 shows in more detail how these constitutive relationships enable the estimation of subsurface LNAPL volumes, in particular in unconsolidated media with multi-modal pore distributions. Chapter 4 further explores the effects of subsurface heterogeneity on LNAPL distribution by discussing the application of geological-based sequence stratigraphy to both site investigation and remediation. Chapter 5 focuses on natural source zone depletion (NSZD) mechanisms, which are essential to understand the fate and transport of petroleum NAPLs. Lastly, Chap. 6 addresses petroleum vapour intrusion and the risks linked to it.

In the second section, Chap. 7 discusses high-resolution site characterisation (HRSC) approaches for the investigation of subsurface physical properties by using direct push, nuclear magnetic resonance (NMR), and groundwater tracing technologies, and Chap. 8 focuses on high-resolution targeted NAPL delineation methods. Chapter 9 explains the influence of PHC biodegradation on geophysical measurements and how biogeophysics can contribute to optimise site investigation outcomes. Chapters 10 and 11 consider, respectively, the use of molecular biological tools (MBTs) and compound-specific isotope analysis (CSIA) to determine the presence and activity of PHC-degrading microorganisms and assess remediation performance.

In the third section, each chapter examines the application of different in situ remediation technologies. Chapter 12 evaluates the utility and challenges of estimating LNAPL transmissivity and implementing hydraulic recovery systems. Chapter 13 deliberates how NSZD can be incorporated into a site management strategy. Chapter 14 stresses the continued central role of bioremediation. Chapter 15 examines the range of in situ chemical oxidation (ISCO) possibilities. Chapter 16 explores the use of activated carbon injectates as a sorptive and treatment substrate. Chapter 17 discusses the novel application of foams as a remediation and blocking agent. Chapter 18 presents advances in low-temperature thermal remediation.

Not all topics could be covered and more could have been included regarding certain subjects (e.g. sustainability and resiliency considerations for site management, cutting-edge laboratory analytical techniques, or assessment of risks posed by PHC biodegradation by-products), but we hope this book will contribute to the increased adoption of improved theories and methods within our industry and promote further research in the fields of contaminated site characterisation and in situ remediation.

Sydney, Australia Athens, Greece San Antonio, USA Davis, USA Newcastle, Australia Jonás García-Rincón Evangelos Gatsios Robert J. Lenhard Estella A. Atekwana Ravi Naidu

# **Reviewers**

*Note*: Chapter reviews represented the reviewers' experience and opinion and were not necessarily made on behalf of their organisations

Michael Annable, University of Florida Tanya Astbury, formerly at Shell and VIVA Energy Dawit Bekele, Douglas Partners/University of Newcastle Barbara Bekins, USGS Francis H. Chapelle, Chapelle and Associates Rick Cramer, Burns and McDonnell Susan De Long, Colorado State University Eduardo de Miguel, Technical University of Madrid Everton de Oliveira, Hydroplan/Groundwater Project Kenneth D. Ehman, Chevron Mateus Knabach Evald, Finkler Sustainable Technologies Marco Falconi, ISPRA Juliana Gardenalli de Freitas, São Paulo Federal University Erin Hauber, US Army Corps of Engineers Ian Hers, Hers Environmental William Herkelrath, USGS Kelly Johanna Hidalgo Martínez, University of Campinas Parisa Jourabchi, ARIS Tissa Illangasekare, Colorado School of Mines Seung-Woo Jeong, Kunsan National University Thomas Kady, USEPA Jimmy C. M. Kao, National Sun Yat-Sen University Saeed Kiaalhosseini, Golder-WSP Steve K. Kalule, USK Consulting Ravi Kolhatkar, Chevron Mark Kram, Groundswell Technologies Poonam Kulkarni, GSI William W. Little, W. W. Little Geological Consulting

Don Lundy, GES Mark Lyverse, formerly at Chevron Deqiang Mao, Shandong University Wesley McCall, Geoprobe Systems Kevin G. Mumford, Queen's University Charles Newell, GSI Dimitrios Ntarlagiannis, Rutgers University Dan Pipp, Geoprobe Systems Colin P. Plank Burns and McDonnell Kavitha Ramadass, University of Newcastle José Luis Rodríguez Gallego, University of Oviedo Mònica Rosell, University of Barcelona Matthew Rosseau, GHD Michael R. Shultz, Burns and McDonnell Natasha Sihota, Chevron Jonathan W. Smith, Shell Kristen Thoreson, Regenesis Courtney Toth, University of Toronto Eleni Vaiopoulou, Concawe Remke van Dam, Southern Geoscience Consultants Paul Van Geel, Carleton University Carsten Vogt, Helmholtz-UFZ Dave Walsh, Vista Clara Anne Wozney, Golder-WSP Yijun Yao, Chinese Academy of Sciences William Zavora, Calgon Carbon Corporation Julio Zimbron, E-Flux

# **Contents**

#### x Contents

# **Contributors**

**David F. Alden** Tersus Environmental, Wake Forest, NC, USA

**Eliot A. Atekwana** Department of Earth and Planetary Sciences, University of California Davis, Davis, CA, USA

**Estella A. Atekwana** Department of Earth and Planetary Sciences, University of California Davis, Davis, CA, USA

**Olivier Atteia** UMR EPOC, Bordeaux-INP, Talence, France

**G. D. Beckett** AQUI-VER, Inc, Park City, UT, USA

**Henri Bertin** I2M-CNRS, University of Bordeaux, Nouvelle-Aquitaine, France

**Daniel Bouchard** GHD, Montreal, Canada

**James J. Butler Jr.** Kansas Geological Survey, University of Kansas, Lawrence, KS, USA

**Hung K. Chang** Department of Applied Geology and Centro de Estudos Ambientais, UNESP—São Paulo State University, Rio Claro, SP, Brazil

**John F. Devlin** Geology Department, University of Kansas, Lawrence, KS, USA

**Peter Dietrich** Department Monitoring and Exploration Technologies, Helmholtz Centre for Environmental Research-UFZ, Leipzig, Germany

**Craig Divine** Arcadis U.S. Inc, Highlands Ranch, CO, USA

**Sandra M. Dworatzek** SiREM, Guelph, ON, Canada

**Nicolas Fatin-Rouge** IC2MP, CNRS, University of Poitiers, Poitiers, France

**Emily Fitzhenry** INRS-ETE, Quebec, QC, Canada

**Jonás García-Rincón** Legion Drilling & Numac, Wetherill Park, NSW, Australia

**Randy St. Germain** Dakota Technologies, Inc., Fargo, ND, USA

**Ron Gestler** Geosyntec Consultants International, Inc., Guelph, ON, Canada

**Patrick Ho**¨**hener** Aix-Marseille University, Marseille, France

**Kayvan Karimi Askarani** Civil and Environmental Engineering Department, Colorado State University, Fort Collins, CO, USA; GSI Environmental Inc., Houston, TX, USA

**Trent A. Key** ExxonMobil Environmental and Property Solutions Company, Spring, TX, USA

**Robert J. Lenhard** San Antonio, TX, USA

**Gaisheng Liu** Kansas Geological Survey, University of Kansas, Lawrence, KS, USA

**Richard Martel** INRS-ETE, Quebec, QC, Canada

**Sarah M. Miles** Geosyntec Consultants International, Inc., Guelph, ON, Canada

**Jonah Munholland** Arcadis U.S. Inc, Highlands Ranch, CO, USA

**Scott Noland** Remediation Products Inc., Golden, CO, USA

**Leonard O. Ohenhen** Department of Geosciences, Virginia Tech, Blacksburg, VA, USA

**Tom Palaia** Jacobs Solutions, Greenwood Village, CO, USA

**Sid Park** Jacobs Solutions, Greenwood Village, CO, USA

**Andy Pennington** Arcadis U.S. Inc, Highlands Ranch, CO, USA

**Clément Portois** Colas Environnement, Bordeaux, France

**Davinder Randhawa** Arcadis U.S. Inc, Highlands Ranch, CO, USA

**Michael O. Rivett** GroundH2O Plus, Birmingham, United Kingdom

**Thomas Robert** INRS-ETE, Quebec, QC, Canada

**Silvia Rossbach** Department of Biological Sciences, Western Michigan University, Kalamazoo, MI, USA

**Derek Rosso** Arcadis U.S. Inc, Highlands Ranch, CO, USA

**Junaid Sadeque** AECOM, Los Angeles, CA, USA

**Tom Sale** Civil and Environmental Engineering Department, Colorado State University, Fort Collins, CO, USA

**Ryan C. Samuels** AECOM, Los Angeles, CA, USA

**Miguel A. Alfaro Soto** Department of Applied Geology and Centro de Estudos Ambientais, UNESP—São Paulo State University, Rio Claro, SP, Brazil

**Julie Sueker** Arcadis U.S., Inc., Broomfield, USA

**Dora M. Taggart** Microbial Insights, Inc, Knoxville, TN, USA

**Neil R. Thomson** Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, Canada

**Martinus Th. van Genuchten** Department of Nuclear Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil

**Iason Verginelli** Laboratory of Environmental Engineering, Department of Civil Engineering and Computer Science Engineering, University of Rome Tor Vergata, Rome, Italy

**Alexandre Vicard** UMR EPOC, Bordeaux-INP, Talence, France

**Gary P. Wealthall** Geosyntec Consultants, Atlanta, USA

**Edward Winner** Remediation Products Inc., Golden, CO, USA

# **Acronyms and Symbols**

# **Chapter 1 Complexities of Petroleum Hydrocarbon Contaminated Sites**

**David F. Alden , Jonás García-Rincón , Michael O. Rivett , Gary P. Wealthall, and Neil R. Thomson**

**Abstract** This introductory chapter provides an overview of some challenges encountered during assessment and remediation of sites contaminated by petroleum hydrocarbons (PHCs), especially due to the presence of petroleum non-aqueous phase liquid (NAPL). PHC contamination of soil and groundwater has become recognized globally as an environmental concern. NAPL releases may go unnoticed for years and can be costly, time-consuming, and challenging to cleanup. Environmental investigations are required to assess the subsurface conditions, and, when necessary, appropriate remedial strategies are implemented. Remediation success depends on the development of a living conceptual site model, evaluation, and selection of potential treatment technologies followed by technology implementation and performance monitoring. This chapter outlines various challenges commonly found at PHC-contaminated sites associated to regulatory issues, multiphase flow mechanics, NAPL partitioning and biodegradation, and hydrogeological controls.

D. F. Alden (B)

J. García-Rincón

M. O. Rivett GroundH2O Plus, 41 Wilmington Road, Quinton, Birmingham B32 1DY, United Kingdom e-mail<EMAIL_ADDRESS>
G. P. Wealthall Geosyntec Consultants, Atlanta, USA

N. R. Thomson Department of Civil and Environmental Engineering, University of Waterloo, West Waterloo, Ontario N2L 3G1, Canada e-mail<EMAIL_ADDRESS>
© The Author(s) 2024

**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1007/978-3-031-34447-3\_1.

Tersus Environmental, 1116 Colonial Club Rd., Wake Forest, NC 27587, United States e-mail<EMAIL_ADDRESS>
Legion Drilling & Numac, 11–13 Metters Place, Wetherill Park, NSW 2164, Australia e-mail<EMAIL_ADDRESS>
J. García-Rincón et al. (eds.), *Advances in the Characterisation and Remediation of Sites Contaminated with Petroleum Hydrocarbons*, Environmental Contamination Remediation and Management, https://doi.org/10.1007/978-3-031-34447-3\_1

**Keywords** Contaminated land management · Fuel hydrocarbons · LNAPL contamination · Source zone remediation · Sustainability

### **1.1 Introduction**

Petroleum hydrocarbons (PHCs) are among the most common and widespread subsurface contaminants in urban and industrial environments. PHCs are primary compounds found in crude oil and its refined products. These organic liquids contain a large number of different hydrocarbons with the most common being alkanes, cycloalkanes (naphthenes), aromatic hydrocarbons, and more complex substances like asphaltenes. Some common products and liquid wastes containing PHCs include:

Residential, industrial, or transport activities that use these petroleum products may be sources of contamination through accidental or intentional spills, releases from above ground and underground storage tanks, and leaks from associated pipelines. Petroleum releases can occur at gas stations, refineries, bulk-product terminals, manufactured gas plant facilities (gasworks), airports, homes heated with oilburning devices, pipelines, chemical manufacturing facilities, landfills, clandestine disposal sites, metal cutting facilities, automotive repair shops, oil drilling pads, and farms.

PHC products typically comprise complex mixtures of predominantly non-polar organic compounds that together form organic liquid fuels or oils. These liquids are commonly referred to as "non-aqueous phase liquids" (NAPLs), are relatively immiscible (sparingly soluble) with water, and can persist in the subsurface as sources of soil and groundwater pollution for decades. A defining property of the NAPL is its density relative to water. NAPLs are classified as either lighter than water (LNAPL) or denser than water (DNAPL). Most petroleum NAPLs are LNAPLs. As such, upon reaching the capillary fringe and the water table, LNAPL will laterally spread with limited invasion below the water table due to its buoyancy. A DNAPL such as some coal tars or creosotes, on the other hand, may penetrate vertically downward well beyond the water table through the saturated zone.

Mass transfer, natural attenuation, and natural source zone depletion (NSZD) phenomena are also critical to understanding the fate and transport of PHCs in the subsurface. Partitioning of LNAPL constituents into other phases (water, gas) result in aqueous and gas phase plumes of organic compounds that could pose risks to human health and the environment. Important classes of PHCs that are of environmental concern include the more soluble mono-aromatic hydrocarbons (i.e., benzene, ethylbenzene, toluene, and xylenes (BTEX)), polycyclic aromatic hydrocarbons (PAHs) (e.g., naphthalene, fluorene, and anthracene), and gasoline additives such as the fuel oxygenate methyl tert-butyl ether (MTBE). Microbial degradation (biodegradation) processes have been frequently found to play a pivotal role in mitigating risks derived from PHC contamination.

As conceptualized in Fig. 1.1, when LNAPL is released into an unconsolidated porous medium, it will tend to migrate downwards through the unsaturated zone under the influence of gravity with its flow path affected by variations in water content and the porous medium's properties. For instance, the presence of a finer-grained layer acting as a capillary barrier will cause lateral spreading of the LNAPL at the interface between layers. If the LNAPL pressure builds and is able to overcome the non-wetting fluid capillary entry pressure of the finer-grained layer, then it will break through the finer-grained layer. Otherwise, it will flow along the top and eventually around the finer-grained layer.

If sufficient LNAPL volume is present, the LNAPL will continue to flow downwards to the water table. Once the LNAPL reaches the water-saturated capillary fringe, downward movement of LNAPL and buoyancy forces can displace some water in the capillary fringe and in the uppermost water-saturated zone below the water table. Lateral LNAPL spreading will occur due to density contrasts with some bias of the main LNAPL body down the hydraulic gradient. This would not preclude migration in other directions in response to geological heterogeneities and preferential migration pathways in the porous or fractured geologic media and influence of local gradients induced by LNAPL pressures. The LNAPL body will eventually stabilize as the LNAPL pressure heads and gradients weaken due to LNAPL redistribution and NSZD processes.

Water-table fluctuations due to daily and seasonal variations or local groundwater pumping induce vertical migration of mobile LNAPL and the creation of an LNAPL "smear zone". As the water table falls, LNAPL mass will be transferred downward while leaving behind a trail of residual LNAPL (not occluded by water) retained in the pores. As the water table rises, part of the LNAPL will move upward, while other LNAPL mass becomes entrapped (occluded by water) due to capillary forces. Depending on the amplitude of the groundwater fluctuations, LNAPL may be trapped meters below the elevation of the mean water table in the saturated zone. In addition, residual LNAPL will be retained in pores that the LNAPL encountered as it migrated through the unsaturated zone. The amount of residual and entrapped LNAPL is a function of porous medium properties, LNAPL fluid properties, and fluid saturation history. The cross-sectional illustration of an LNAPL body in Fig. 1.1 has been shaped by one or more water-table fluctuations.

**Fig. 1.1** Conceptual LNAPL architecture in the subsurface following a point release, along with petroleum hydrocarbons fate and transport mechanisms (central figure); LNAPL mobility as a function of relative saturations of air, water, and LNAPL (left circles); factors modulating *in-situ* petroleum hydrocarbon biodegradation (top right circle) (adapted from Lundy and Gogel 1988; Rivett et al. 2011; CL:AIRE 2014; Vila et al. 2019; García-Rincón 2020)

In general, water preferentially wets the geological formation with respect to LNAPL and air (which commonly are the intermediate-wetting fluid and non-wetting fluid, respectively) except in very dry soils, where water may be the non-wetting fluid. Released LNAPL to the subsurface is hence usually non-wetting preferring to occupy the more spacious pore body rather than pore throats, thereby minimizing contact with the solid grains that may remain water coated. With repeated spills, the LNAPL may transition from a non-wetting to a wetting fluid in time. Changes in LNAPL chemical composition may also change its wettability. As a result of all these factors, LNAPL architecture varies dramatically between sites and across geological settings. This is generally illustrated in the conceptual models of CL:AIRE (2014) depicting LNAPL behavior for a number of geologic settings, including mildly to highly heterogeneous unconsolidated porous media (e.g., sands to glacio-fluvial sands and gravel) and low and high matrix porosity fractured bedrock (e.g., granite to sandstone).

As shown in Fig. 1.1, a dissolved or aqueous phase plume will develop in the capillary fringe and in the saturated groundwater zone, and a vapor or gas phase plume will develop in the unsaturated zone. Since most LNAPLs are "multicomponent" comprising complex mixtures of PHC compounds, both the aqueous and gas phase plumes will likewise be multicomponent in nature. The composition of the aqueous phase plume is controlled by the dissolution rate and the effective solubility of each LNAPL component that is LNAPL composition-dependent. The composition of the gas phase plume is controlled by the volatilization rate and the effective partial pressure of each LNAPL component which is likewise LNAPL composition dependent. As the LNAPL weathers, the more soluble and volatile components in the LNAPL will become depleted, and the remaining LNAPL will become enriched with progressively less soluble and volatile compound constituents. The change in composition may influence physical properties such as LNAPL density and viscosity.

The significance of microbial degradation (biodegradation) to PHC sites cannot be overstated. While biodegradation of individual PHC compounds varies, most hydrocarbons are relatively biodegradable across a range of aerobic and anaerobic conditions ranging from nitrate reducing to methanogenic. The contribution of biodegradation to the natural attenuation of dissolved-phase hydrocarbon plumes has long been recognized and may cause sufficient attenuation of plumes prior to their reaching receptors at risk to justify the use of monitored natural attenuation (MNA) as a viable site management strategy (Wiedemeier et al. 1999; USEPA 1999b; ASTM 2004; CL:AIRE 2014; ITRC 2018). It has only been in recent years, however, that the significance of biodegradation in LNAPL source zone areas has been recognized leading to the emergent adoption of NSZD monitoring as a management option to complement or even replace active remedial interventions (Rivett and Sweeney 2019). In particular, the role of methanogenesis and direct outgassing from the LNAPL source circumventing the assumed requirement for hydrocarbons to dissolve to be biodegraded was overlooked for many years and may lead to significant vapor-based NSZD far exceeding the aqueous-based depletion (Smith et al. 2022).

Effective LNAPL problem conceptualization within specific PHC-contaminated site scenarios underpins the management of risks and appropriate intervention remedy selection. Recognition needs to be made of the breadth of risks or drivers at sites, including nuisance impairment of beneficial use of resources or aesthetic values, societal community concerns, and business factors including reputational risk and problem persistence leading to intergenerational equity issues (CL:AIRE 2014). One possible approach to risk evaluation discussed in CL:AIRE (2014) is to categorize risks by "LNAPL saturation" (largely controlling LNAPL mobility) or composition. "Saturation" risks occur when pore-space LNAPL saturations exceed residual or entrapped saturation thresholds enabling LNAPL mobility and risks of migration of the LNAPL body to receptors resulting in, for example, seepage of LNAPL oily films into surface waters, or LNAPL contamination of supply wells. Addressing saturation risks are often an initial site priority. Composition risks, on the other hand, derive from the LNAPL chemical composition, which may include constituents that have toxicity to human health or the environment and may pose direct or indirect, chronic, or acute risks. Certain constituents may also be highly volatile and flammable and therefore drive explosive risks. Composition risks hence include the migration of toxic constituents such as BTEX or PAHs within dissolvedphase plumes to supply wells or within vapor plumes migrating toward and accumulating with PHC degradation products such as methane in buildings and posing explosive risks. It is recognized within this simple bi-classification of risks that the mobility of the LNAPL will still be influenced by its composition as composition determines physical properties such as viscosity and interfacial tensions; however, such changes are usually very gradual.

The remainder of this chapter will provide a more detailed overview of challenges associated with:

### **1.2 Problem Recognition and Regulatory Environment**

### *1.2.1 Problem recognition—The Case of Large Oil Spills*

Contaminated site assessment and management has evolved to being a multidisciplinary field dealing with hydrogeological, chemical, biological, fluid mechanics, and management topics, often requiring subject-matter experts from a variety of backgrounds including environmental, chemical, and civil engineering, geology, microbiology, toxicology, statistics, legal, and project management.

Subsurface contamination by PHCs can be a result of leaking storage tanks and pipelines, accidental releases, or intentional disposals. Without accurate wet-stock reconciliation or leak-detection systems, subsurface releases can go unnoticed for years, an "invisible problem" that can be costly, time-consuming, and difficult to treat after it is discovered. Often, PHC cleanup reminds the general public's mind of large oil spills, nevertheless, cleanup of local gasoline stations is the predominant type of events managed by the soil and groundwater PHC remediation industry.

Large oil spills galvanize significant media and public attention because they have catastrophic local environmental and human health impacts and, when on land, may create complex surface water and groundwater remediation problems that can take years of effort to manage the environmental impacts. Examples include the 1989 *Exxon Valdez* oil tanker collision into a reef offshore of Alaska, USA, that drew much media coverage and attention to the detrimental environmental impacts that occurred to 2000 km of the intertidal beaches and marshes along the shoreline of Prince William Sound (Xia and Boufadel 2010). The 2010 *Deepwater Horizon*  explosion and oil rig blowout illustrates the potential consequences of not following established safety protocols. The heavy oil spill from the tanker *Prestige* in 2002 affected 1900 km of the coast in the northwest of Spain, devastating the local economy and demonstrating the gargantuan effort required to restore conditions to a pre-spill state. One of the earliest and largest oil spills on land is the seemingly forgotten 18 month long hydrocarbon eruption in 1910 at Lakeview Gusher #1 in California, USA, where oil-soaked soils are still present. The United Nations Environment Program (UNEP) released a report in 2011 documenting the environmental degradation of the land and waters of the Niger River Delta in Ogoniland, Nigeria, associated with operations of the multinational petroleum industry in the area since the 1970s. This document set out urgent recommendations for cleanup and protection of drinking water and health of exposed populations. The cleanup effort is nevertheless far from being completed. Other examples of oil spills associated with unstable sociopolitical environments include the Kuwaiti oil fires caused by Iraqi military forces during the Gulf War in 1991 and the multiple attacks to the Caño Limón–Coveñas crude oil pipeline in the Arauca Department, Colombia.

Some large oil spills have yielded significant research opportunity, a foremost example of relevance to the soil and groundwater remediation community being the terrestrial oil pipeline rupture near Bemidji, Minnesota, in 1979 (Fig. 1.2). The release consisted of 1,700,000 L of crude oil, of which 400,000 L remained in the subsurface after the initial cleanup works in 1980. In 1983, the United States Geological Survey (USGS) established the National Crude Oil Spill Fate and Natural Attenuation Research Site, which has produced decades of data and has been paramount for the current understanding of natural processes at PHC-contaminated sites. The ongoing USGS research project has four primary objectives: (I) characterizing the nature, toxicity, and prevalence of partial transformation products emanating from the crude oil source; (ii) evaluating the secondary impacts (such as arsenic cycling) of biodegradation; (iii) understanding the timeframe of natural attenuation of PHC source zones; and (iv) developing field tools, methods, and data that support evaluations of environmental health effects of natural attenuation of crude oil (USGS 2021). The numerous research outcomes produced at Bemidji illustrate the importance of establishing experimental sites for the study of subsurface contamination phenomena.

The great proportion of PHC-contaminated sites requiring cleanup are relatively small sites in industrialized countries. In the United States alone, there are 135

**Fig. 1.2** Crude oil reached a wetland near Bemidji after the rupture of an oil pipeline. Initial efforts to remove the floating oil were conducted by the pipeline company in 1979 using pumps and other machinery (photo courtesy of Jared Trost, USGS)

reported operating refineries and over 133,000 gas stations. Between 1998 and 2021, 564,767 petroleum releases from underground storage tanks (USTs) were reported, and 85% have been addressed to meet regulatory requirements (i.e., "closed"). (UST FAQ www.epa.gov/ust, accessed on May 28, 2022 https://www.epa.gov/ust/frequentquestions-about-underground-storage-tanks#gen11).

### *1.2.2 Regulatory Frameworks*

In the context of a country's regulatory framework, oil spills on land are sources of soil and groundwater contamination often brought to light during environmental assessments driven by real estate transactions, suspicion of chemical leakage from existing tanks or historical land use, or as a precautionary action prior to future land use. The need to meet regulatory compliance and achieve cleanup standards agreed to mitigate risks is often a key remediation driver. Risks do not just relate to human health but also the environment, assets, reputation, and financial aspects.

Environmental law is often created in response to high-profile events in which the press generates public awareness (Wargo 2009). Once an issue gains societal recognition as a problem, it may get on the docket of government institutions through organized interest group pressure and eventually may receive enough attention by governing policymakers for decisional action (Kraft and Vig 2010). For example, the wide distribution of Rachel Carson's famous book *Silent Spring* in the early 1960s, warning about the compounding effect pesticides have on the environment focused public opinion sharply and likely incentivized the creation of the United States Environmental Protection Agency (USEPA) that now sets corrective action guidelines with respect to contaminated soils and groundwater in the United States. Extraordinary events, such as the Cuyahoga River in Ohio catching fire thirteen times between 1868 and 1969 due to petroleum NAPL on its surface, prompted establishment of the National Environmental Policy (NEPA), which mandates that federal agencies assess the potential environmental impacts of their actions and the Clean Water Act to reduce emissions from industrial facilities (Wargo 1998). Arguably the most pivotal has been the infamous New York State Love Canal (landfill) Incident in the 1970s soon after which groundwater contamination problems emerged throughout the United States where public interest and perception changed dramatically (Hadley and Newell 2012). The incident was an important catalyst for the cleanup of contaminated aquifers in the United States as it prompted the passing of the Superfund Act, technically known as the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), which was passed in 1980. Its notoriety raised the profile of groundwater contamination internationally.

Parallels in contaminated land and groundwater legislations to manage PHC and most contaminants are evident amongst countries in North America, Europe, and in Australia. Although PHCs and LNAPL contamination are rarely directly specified within such legislations, oil/fuel storage and transport-specific regulations enable groundwater protection and are indirectly concerned with PHCs and LNAPL. Similarly, many countries have agency–government (or related national organizations) published non-statutory guideline documents specific to PHC- and LNAPL -contaminated sites that guide the assessment, characterization, and remediation of these sites specifically. By way of example, specific regulatory acts that influence PHC remediation practices in the United States are summarized below:

of the groundwater at a particular facility [such as drinking, agriculture, discharge to adjacent groundwater or surface water bodies]" (USEPA 2004).

Similar types of legislation are mimicked internationally to varying degrees. In some countries, contaminated land regulations are based on laws approved at national level and their implementation and the manner in which they are interpreted are often left to federal agencies. In contrast, in other countries jurisdiction for legislation may be at a state or regional level rather than national. Either way, both often create differences between regions and pose much of the burden of implementing environmental protection work on state and local governments. For example, the Brownfield Act in the United States relies on state voluntary response programs, through which states create incentives to assist in the cleanup and reuse of brownfield properties and ensure resources for long-term monitoring and other needs.

Globally, numerous published (often non-statutory) guidance developed nationally or at state/regional level exist for investigating, assessing, understanding, and addressing the presence and migration of NAPL releases. Plans typically require that sites achieve a permanent mitigation solution in terms of eliminating significant risk or removing oil and hazardous material to the most feasible extent. Some jurisdictions may set LNAPL recovery goals to the highest potential or "ceiling" values as determined from site-specific estimates of LNAPL and hydrogeological properties, while others determine that NAPL is of concern when the apparent LNAPL thickness measured in a monitoring well exceeds a certain thickness. Such approaches may not always be supported by the technical literature and current multiphase flow understanding.

# *1.2.3 Toward Improved Management and Regulation of PHC-Contaminated Sites*

LNAPL treatment remedies focus on removing, destroying, or stabilizing LNAPL, particularly when this LNAPL poses risks if it is mobilized or can form dissolvedphase and vapor plumes of toxic constituents. Since removal is often technically and/or economically unfeasible, the industry seems to increasingly favor in-situ treatments addressing the LNAPL source zone or focusing on the aqueous or vapor-phase PHC plumes when the only objective is to create a barrier to protect sensitive receptors against contaminant exposure. In many cases, actively monitoring a contaminant plume suffices as a contamination management strategy, in which cases supporting evidence is typically gathered to show that risks are controlled.

Creating a regulatory framework is usually a political, long, arduous, and constantly evolving process. One of the factors influencing this evolution is the technical and economic challenges encountered by remediation practitioners. For example, the presence of NAPL in combination with unfavorable complexities has encouraged stakeholders to advocate to modify cleanup criteria or create technical impracticability waivers. In the United States, for example, there are various alternative cleanup end points, where instead of meeting a drinking water maximum contaminant levels, site-specific risks to potential receptors are evaluated and mitigated using both remediation techniques and engineering controls. Risk-based goals are sometimes a response to the economically prohibitive resources required to eliminate contamination. In other words, remediation objectives have evolved from practically complete removal to focus on interim stages that address site-specific needs that are evaluated in terms of intended land use and stakeholder requirements, which in turn requires effective stakeholder engagement. Hadley and Newell (2012) proposed *functional* remedial goals that incorporate contaminant mass discharge as a remediation metric.

The adoption of sustainability practices, including prioritizing smaller environmental footprints and integrating concepts such as environmental health, social equity, and economic vitality in the assessment of cleanup methods, has been gaining popularity in the remediation industry. In countries like Australia, Brazil, South Africa, the United Kingdom, and the United States, among others, the management and remediation of contaminated soil and groundwater is sometimes incorporating sustainability concepts into their guidelines and/or risk-based regulatory frameworks (Defra 2012; Scott and McInerney 2012 as cited in CL:AIRE 2014). The design of resilient remediation systems is also gaining traction as there is greater awareness on how climate change, extreme weather events (ITRC 2021), and unstable sociopolitical environments may negatively impact existing systems.

Along with sustainability and resiliency, environmental justice and indigenous and nature rights are philosophies that may influence contaminated site management. Values brought forward by the environmental justice movement have gained momentum since it first emerged in the United States in the late 1980s after the publication of *Toxic Waste and Race*, a study exposing disparities in the burden of environmental degradation and pollution facing minority and low-income communities (Commission for Racial Justice of the United Church of Christ 1987). The United States government begun addressing this issue by creating environmental justice offices in the EPA and the Department of Justice. Similarly, values adopted by indigenous movements that may drive changes in regulations and potentially groundwater cleanup include nature's rights and concepts such as *Sumak Kawsay*,a Quechua value embracing ancestral, communitarian knowledge and lifestyle. Based on this philosophy, the 2008 Constitution of Ecuador incorporated the concept of *the rights of nature*, as did the 2010 Law of the Rights of Mother Earth in Bolivia.

### **1.3 Multiphase Flow Mechanics**

An understanding of multiphase flow processes in water-NAPL-gas systems (see Chaps. 2, 3, and 17) is paramount for the development of sound conceptual site models (CSMs) as well as the design of effective remediation strategies. As depicted in Fig. 1.3, NAPL, water, and gas coexist in the pore space. NAPL behavior is understood through the interaction of forces in the system that are a function of each fluid's properties such as viscosity, density, surface and interfacial tension, wettability, and physical properties associated to a chemical composition. For a comprehensive introduction to multiphase flow mechanics in porous media, the reader is referred to Corey (1994).

**Fig. 1.3** Water-LNAPL-gas system in a sand tank where a fluorescent tracer was added to the LNAPL (photo and video courtesy of Julio Zimbron, E-Flux). See Electronic Supplementary Material for a video illustrating how some LNAPL mass became entrapped (occluded by water) after rising the water level in the tank (ESM\_1)

LNAPL behavior may sometimes be considered counterintuitive, and its oversimplification has historically led to costly consequences. Examples include the misconception that the LNAPL thickness in a monitoring well corresponds to a similar thickness of LNAPL uniformly saturating the vicinity of the monitoring well (as opposed to a more accurate elevation-dependent LNAPL saturation profile that penetrates below the water table). Similarly, in-well LNAPL thickness has often been assumed proportional to the NAPL mass in the subsurface without considering site-specific LNAPL-retention properties or the LNAPL distribution architecture.

The fate, migration, and stability of LNAPLs markedly vary by type of LNAPL, reflecting differences in their intrinsic fluid properties. Although a low-viscosity NAPL such as gasoline moves faster and perhaps further, it may still reach hydrostatic equilibrium relatively quickly. Viscous LNAPLs like a heavy oil or coal tar creosote, on the other hand, may not equilibrate within practical time frames as the LNAPL body continues to migrate very slowly. Weathering of the LNAPL may cause properties to change; for instance, viscosity and density can increase and borderline LNAPLs such as coal tar creosote may render them becoming borderline DNAPLs with time.

Rationalization of seasonal variations of observed LNAPL thickness in monitoring wells can be better appreciated when multiphase flow concepts are considered together with geological complexities. For instance, within unconfined aquifers the thickness of LNAPL in wells is usually observed to decrease as the water table rises. In contrast, within a confined aquifer, the thickness of LNAPL in wells increases as the potentiometric surface rises since the monitoring well provides a "pressure release" for LNAPL confined by the overlying aquitard. Predicting the volume of scattered LNAPL blobs and ganglia entrapped below the water table (discontinuous, water occluded LNAPL) represents a significant challenge, but is important as these represent long-term sources of contamination. The profile of LNAPL entrapped varies with water-table elevation and may lead to seasonal changes in the mass transfer of PHCs into the dissolved-phase and vapor-phase plumes.

It is possible to encounter LNAPL at significant depths below modern water tables. Such a scenario found in the LA Basin was ascribed to sites with older, historical releases of LNAPL and subsequent rising water tables since the 1950s (as also shown in the case study in Chap. 4). It is not unusual for many cities in developed nations to show rising water tables over recent decades, especially where groundwater was long used by industries that have since demised, for instance both London and Birmingham in the UK.

Quantifying subsurface LNAPL mass requires estimating LNAPL volumes at multiple locations. Site-specific uncertainties complicate this task, such as lack of knowledge of the LNAPL source and type, formation heterogeneity at the scale of centimeters, unknown historical water-table fluctuations, and delineating the depth intervals impacted by LNAPL. Such investigations when at depth may be expensive and challenging especially in consolidated aquifer systems (e.g., sandstone or fractured rock). Often three-dimensional spatial interpolation of data is required as characterization resources are usually limited to discern the detail of LNAPL architecture ideally sought.

A NAPL mass estimate represents a critical baseline parameter used to evaluate the efficiency of remediation technologies or, combining it with estimates of NSZD rates, the longevity of the LNAPL mass (see Chaps. 5 and 13). The scarcity of monitoring points, misinterpretation of in-well LNAPL thickness values and the sensitivity of multiphase LNAPL flow to permeability within intrinsically heterogeneous geological environments means that constraining LNAPL mass estimates can often be a rather "holy grail" challenge but nevertheless important to make efforts to constrain these estimates as far as possible and recognize associated uncertainties present.

### **1.4 Complexities Associated with PHC NAPL Composition**

Refined fuel NAPLs consist of complex mixtures of potentially hundreds of compounds blended with biofuel components such as ethanol in gasoline or fatty acid methyl ester (FAME) in diesel, octane enhancers (such as MTBE), and lowvolume additives (such as detergents and anti-foaming agents). Microbial products, metabolites, and other non-PHCs such as natural organic matter or additional organic contaminants like halogenated compounds can also be found at sites impacted by petroleum NAPL releases. This complicates the definition, analysis, and quantitation of bulk parameters such as total petroleum hydrocarbons (TPH) in environmental media and has led to the reliance on a few specific compounds like BTEX or certain PAHs and the adoption of fractionation approaches for risk assessment purposes (ITRC 2018). Analytical techniques such as silica gel cleanup, non-targeted twodimensional gas chromatography with time-of-flight mass spectrometry (GCxGC-TOFMS), or high-resolution mass spectrometry, to name a few, are being increasingly employed to investigate the fate of PHCs and better inform risk assessments (Bekins et al. 2020; Bojan et al. 2021; O'Reilly et al. 2021). As discussed in Chaps. 10 and 11, molecular biological tools (MBTs) and compound-specific isotope analysis (CSIA) are also gaining popularity to forensically investigate contaminated sites, evaluate remediation performance, and/or identify the responsible party when multiple possible contamination sources exist.

The overall LNAPL composition, along with the age of the release and weathering processes (dissolution, volatilization, and biodegradation), dictates how the bulk properties of an LNAPL, such as density, viscosity, and toxicity will vary with time. Although the majority of petroleum LNAPLs or refined individual constituents (e.g., benzene solvent) are less dense than water and, in general, cease their downward migration upon reaching the vicinity of the water table the densities of coal tar and creosotes may evolve from being marginally less dense than water to more dense than water as discussed above.

Partitioning or mass transfer of individual constituent compounds from the NAPL to adjacent gaseous (air) or aqueous phases are critical processes leading to the continual formation of vapor phase plumes in the vadose zone and dissolved-phase plumes in groundwater. Mass transfer rates from a NAPL are highly dependent upon the chemical composition of the NAPL which varies substantially across the wide range of NAPL types. Both volatilization and dissolution of the individual compounds in a multicomponent NAPL will vary with time as the composition of the NAPL changes as the effective solubility and volatility of a compound depends on its mole fraction within the NAPL. Preferential dissolution or vaporization of more soluble and volatile compounds may leave the remaining NAPL progressively enriched in less soluble and less volatile compound constituents and result in an overall declining mass transfer of hydrocarbon mass with time. The most common volatile organic compounds found in PHC NAPLs that are monitored due to their known toxicity are BTEX, some PAHs, and fuel oxygenates (e.g., MTBE). The relatively high volatility and solubility of these compounds allows them to deplete from the NAPL mass fairly rapidly, eventually reducing the composition-based risk NAPL poses with respect to these compounds.

The spatial extent of dissolved-phase PHC plumes is limited by various depletion mechanisms such as dilution by dispersion and diffusion, volatilization, biodegradation, and sorption and retention. It is thus valuable to identify site-specific limitations to natural attenuation of PHCs. Because biodegradation of dissolved-phase constituents can be the dominant contaminant mass loss process under various groundwater conditions, it is critical to review potential limitations to biodegradation. These include extreme pH levels, low temperatures, insufficient electron acceptors, and the abundance of labile carbon or the presence of inhibitory compounds. Biodegradation mechanisms and rates are a function of biogeochemical conditions which can vary in time and space. For instance, conditions can relatively quickly become anaerobic or even methanogenic at the core of a contaminant plume where PHC are used by microorganisms as a carbon and energy (electron donor) source. Aerobic respiration processes thus deplete dissolved oxygen prior to degrading all the PHC and thus need to turn to nitrates, sulfates, or other reduced compounds in groundwater for terminal electron acceptors. Between the anaerobic core and a typically aerobic fringe of the plume intermediate redox zones may be dominated by sulfate-, manganese-, iron-, or nitrate-reducing metabolic processes. Nevertheless, not all compounds are readily biodegradable under certain redox conditions and biodegradation rates can be easily inhibited by lack of electron acceptors or micronutrients, pH outside of circumneutral conditions, extreme temperatures, or in the presence of inhibitory chemicals. The natural attenuation process knowledge base will also underpin effective selection of treatment technologies. For example, biodegradability of a specific PHC can determine the suitability of bioremediation approaches such as biosparging, bioventing, bioaugmentation, or anaerobic biostimulation.

With practitioner focus on quantifying natural attenuation of dissolved plumes, it has only been recently appreciated that natural depletion of LNAPL mass can be significant (Rivett and Sweeney 2019). Of key significance, has been the comparatively recent recognition and emerging acceptance that the vapor-based mass transfer from LNAPL may have been underappreciated and may be much more relevant than aqueous phase mass transfer limited by the low solubility of most hydrocarbons (Smith et al. 2022). In particular, the importance of LNAPL losses via volatilization and methanogenesis and subsequent aerobic biodegradation of methane in the overlying unsaturated zone that mitigate contaminant breakthrough at ground surface (Lundegard and Johnson 2006). Such direct losses imply that less soluble PHC components may be degraded circumventing the need for (and commonly held previous belief) these constituents to be dissolved first in order to biodegrade in the aqueous phase. Monitoring NSZD processes may represent a source zone management strategy or be used to evaluate the effectiveness of active remediation techniques against a baseline NSZD rate. In addition, the presence of microorganisms, extracellular polymeric substances, and bubbles formed during ebullition may influence LNAPL transport. For instance, bioclogging of the pore space limits the aquifer's permeability. The evaluation of the dynamic influence on NAPL's fate due to water-table fluctuations or shallow subsurface temperature variations across climatic zones represents research opportunities.

# **1.5 Geological and Hydrogeological Concepts that Help Tackle LNAPL Management Challenges**

The heterogeneity of hydrogeological systems inevitably renders complex LNAPL distribution, and the likelihood of complex dissolved and vapor plume generation and fate. It is unsurprising then that the remediation of such NAPL architectures and the associated plumes is likewise challenging. CL:AIRE (2014) provides generic conceptual models for a variety of geological systems, ranging from porous unconsolidated sedimentary units to karst limestone and fractured bedrock of all types. While such conceptual models are illustrative of a specific (hydro)geology setting, site-specific characterization is required to develop a CSM to underpin effective remedy development. The most challenging geological settings are those with a high degree of heterogeneity, which can range in scale from centimeters (pore properties) to kilometers (type of sediment or rock body, tectonic setting, and climate).

The sensitivity of LNAPL migration to subsurface heterogeneity inevitably poses challenges to elucidating the detail of LNAPL migration and its retention. However, some general features may be predictable with preferential migration through coarser-textured materials and wider aperture fractures in fractured or dual porosity systems as shown by the various hydrogeological scenarios in CL:AIREe (2014). Pooling or confining of LNAPL by a system's more contiguous, finer-textured units is also reasonably predictable.

In unconsolidated sediment, sedimentary rocks, and some extrusive igneous flows, primary physical factors are those developed at the time of initial deposition such as grain size, grain sorting, and grain shape may be determined from core logs. Secondary physical characteristics developed post deposition or eruption in response to surface weathering, burial, and movement of fluids are important to consider. Example processes affecting porosity and permeability include compaction (intergranular space reduction), cementation (pore filling by precipitation of minerals from groundwater), burrowing (mixing by organisms), dissolution (enlargement of pores or development of new pores through groundwater dissolution and removal), and fracturing (cracks or fissures from a variety of processes).

A particular challenge for remediation practitioners to overcome is the heterogeneous nature of porous media, not just in terms of porosity and permeability but also mineralogy, geochemistry, and biological microenvironments. The depositional environment of sedimentary units frequently results in sediments that vary greatly and abruptly both in the direction of sediment transport and perpendicular to it. For instance, fluvial systems typically consist of a mixture of channel bar deposits composed of sand and/or gravel interbedded with overbank mudstones, or perhaps silt or clay-rich units that may serve as aquitards restricting groundwater flows or act as capillary barriers impeding NAPL migration. This results in geological units that can be highly partitioned with interleaved aquifer–aquitard sequences with create a complex groundwater flow behavior (see Chap. 4 for further details on depositional environments).

Of concern to both contaminant fate and remediation efforts is the identification of preferential migration pathways as well as relatively stagnant or low-flow regions in which groundwater flow and contaminant transport are limited.

### **1.6 Summary**

The ever-increasing value of groundwater as a freshwater resource, along with a better understanding of risks and sustainability issues associated to the release of PHC compounds will further justify the adoption of improved characterization and remediation approaches. By highlighting complexities encountered in this process, this chapter is not only a reminder to practitioners of the diligence required to carry out projects successfully but also invites the wider research community to continue to pursue underpinning science that helps address complexities encountered at the field scale.

Environmental policy is evolving by incorporating collaborative decision-making that involves multiple stakeholders, public–private partnerships, market-based incentives, and enhanced flexibility in rulemaking and enforcement (Kraft and Vig 2010). This complements the management and remediation of contaminated soil and groundwater increasingly being undertaken in the context of sustainable, risk-based regulatory frameworks.

Thousands of petroleum NAPL projects have successfully mitigated risk of exposure to hazardous chemicals, many sites classified as toxic have been restored to beneficial uses, and remediation has served as a profitable practice in the short and long term. The understanding of PHC contamination in the subsurface, the associated regulations protecting human health and the environment, and the associated cleanup methods and technologies have become more efficient over the years to overcome technical and economic challenges that have often delayed cleanups for significant periods of time.

Ultimately, CSMs take into account available information and the latest research about conditions and risks of contaminated sites. Because PHC remediation is complex, specialized characterization techniques are developed to locate and quantify contaminants, demonstrate degradation rates and mechanisms, forecast their persistence, and evaluate performance of remediation techniques. Management of PHC-impacted sites involves continued CSM updating, with the goal of mitigating risks by implementing site management strategies.

Still, much remains to be done. Site investigation and characterization can always be improved, risks better understood, implemented remedies more efficient, targeted, cost effective and sustainable, community awareness and education increased, and underpinning science advanced. These provide rationale for this volume and the subsequent chapters that seek to draw together a substantial part of our learning to date and identify future research required.

### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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# **Chapter 2 Historical Development of Constitutive Relations for Addressing Subsurface LNAPL Contamination**

**Robert J. Lenhard and Jonás García-Rincón**

**Abstract** An overview of the historical development of *k-S-P* relations (constitutive relations) to model potential flow of light nonaqueous phase liquids (LNAPLs) in the subsurface is presented in this chapter. The focus is advancements proposed by Parker, Lenhard, and colleagues over time. Discussion includes constitutive relations for incorporation in numerical multiphase flow models as well as constitutive relations for predicting subsurface LNAPL volumes and transmissivities from fluid levels measured in monitoring groundwater wells. LNAPL saturation distributions are given for various subsurface properties and layering sequences.

**Keywords** Capillary pressure · LNAPL saturation · LNAPL-specific volume · Multiphase modeling · Relative permeability

# **2.1 Introduction**

The potential contamination of groundwater by hydrocarbon fuels, such as gasoline (petrol), diesel, and heating oils, has existed since these products were produced. Hydrocarbon fuels, which exist as light nonaqueous phase liquids (LNAPLs), enter the subsurface by leaks in storage containers, pipes, and spills. Once in the subsurface, hydrocarbon compounds can potentially partition in water and contaminate groundwater resources. Typically, hydrocarbon fuels consist of many compounds each with different capabilities (properties) for partitioning into water, subsurface gas, and onto solid matter. Groundwater becomes contaminated by (1) dissolved fuel compounds moving downward by gravity in the vadose zone as water recharges the surface aquifer; (2) volatized fuel compounds partitioning in vadose zone water and

e-mail<EMAIL_ADDRESS>
J. García-Rincón Legion Drilling and Numac, 11–13 Metters Place, Wetherill Park, NSW 2164, Australia

© The Author(s) 2024

J. García-Rincón et al. (eds.), *Advances in the Characterisation and Remediation of Sites Contaminated with Petroleum Hydrocarbons*, Environmental Contamination Remediation and Management, https://doi.org/10.1007/978-3-031-34447-3\_2

R. J. Lenhard (B) San Antonio, TX, USA

groundwater; and (3) direct partitioning into groundwater as the fuels collect at the top of the water-saturated region or get entrapped in it. In this chapter, we briefly discuss the efforts to model subsurface LNAPL behavior including permeability (*k*)-saturation (*S*)-pressure (*P*) relations; prediction of subsurface LNAPL saturations, volumes, and transmissivities based on LNAPL and water levels in nearby groundwater wells; and conclude with suggestions for some improvements in LNAPL predictive models. A focus is on constitutive (*k-S-P*) relations developed by Parker, Lenhard, and colleagues.

# **2.2 Recognition of Health Effects from LNAPLs in the Subsurface**

Initially, there was little concern of health effects from LNAPLs in the subsurface because the health effects from exposure to some of the compounds were not well understood, except for introduced alkyl leads, e.g., tetraethyl lead in the 1920s (Lewis 1985; Oudijk 2007). Lead was known to have adverse human health effects for some time. Only after relatively high occurrences of sickness and cancer were reported, the health effects from exposure to LNAPL compounds became better understood. For example, benzene, toluene, and xylenes, which are components of LNAPLs, were eventually recognized as either toxic or carcinogenic to humans (IARC 1987; ATSDR 1995; EPA 2007). As the health effects from compounds in LNAPLs were better understood, more stringent regulations were introduced to minimize potential soil and groundwater contamination. Additionally, there were requirements to clean up contaminated sites to minimize the adverse health effects to humans, limit risks to the environment, and reduce other negative impacts from subsurface LNAPL contamination.

# **2.3 Predicting Subsurface LNAPL Behavior: Early Developments**

To plan the remediation of LNAPL-contaminated sites, cost-effective approaches and designs are needed. Practitioners need to know the volume and distribution of LNAPL in the subsurface. Initially, the thickness of LNAPL in boreholes (groundwater wells) was used to estimate the LNAPL thickness in the subsurface (de Pastrovich et al. 1979; Hall et al. 1984). The LNAPL thickness in the subsurface was then used to calculate the subsurface LNAPL-specific volume (LNAPL volume per horizontal surface area), which is an important factor for designing remediation systems. Hampton and Miller (1988) conducted laboratory investigations of the relationship between the LNAPL thickness in a borehole and that in subsurface media and concluded that the LNAPL thickness in the subsurface is not a good measurement of the LNAPL-specific volume because other factors were involved such as porous media pore-size distributions and pore-scale physics that govern LNAPL saturation distributions. The pore-scale physics of LNAPLs in the subsurface that could potentially result in groundwater contamination, however, were well-known (van Dam 1967; Schwille 1967) when these early models were proposed. Because available computers at the time were limited, remediation practitioners used relatively simple expressions to help with remediation strategies and designs.

Abriola and Pinder (1985a,b) were among the first to develop a numerical model to address subsurface LNAPL contamination, which was able to solve the governing equations for multiphase (air, LNAPL, water) flow. Relatively soon afterward, several other multiphase flow numerical models were developed (e.g., Faust 1985; Osborne and Sykes 1986; Baehr and Corapcioglu 1987; Kuppusamy et al. 1987; Kaluarachchi and Parker 1989). To predict the potential flow of air, LNAPL, and water in incompressible porous media, a set of governing equations is

$$\phi \frac{\partial}{\partial t} (\mathcal{S}\_a \rho\_a) = \nabla \left[ \frac{k k\_{ra} \rho\_a}{\eta\_a} (\nabla P\_a + \rho\_a g \nabla z) \right] \tag{2.1}$$

$$\phi \frac{\partial}{\partial t} (\mathcal{S}\_o \rho\_o) = \nabla \left[ \frac{k k\_{ro} \rho\_o}{\eta\_o} (\nabla P\_o + \rho\_o g \nabla z) \right] \tag{2.2}$$

$$\phi \frac{\partial}{\partial t} (\mathcal{S}\_{\mathbf{w}} \rho\_{\mathbf{w}}) = \nabla \left[ \frac{k k\_{\mathbf{w}} \rho\_{\mathbf{w}}}{\eta\_{\mathbf{w}}} (\nabla P\_{\mathbf{w}} + \rho\_{\mathbf{w}} \mathbf{g} \nabla z) \right] \tag{2.3}$$

where

φ is the porosity (assumed to be constant for each media type),

*Sa*, *So*, *Sw* are the air, LNAPL, and water saturations, respectively,

ρ*a*, ρ*o*, ρ*w* are the air, LNAPL, and water mass densities, respectively,

*k* is the intrinsic permeability tensor,

*kra*, *kr o*, *krw* are the air, LNAPL, and water relative permeabilities, respectively, η*a*, η*o*, η*w* are the air, LNAPL, and water dynamic viscosities, respectively, *Pa*, *Po*, *Pw* are the air, LNAPL, and water fluid pressures, respectively, *g* is the scalar gravitational constant,

*t* is time, and,

*z* is elevation.

The equations (Eqs. 2.1–2.3) need to be solved simultaneously because the dependent saturation variable in each equation is a function of the independent pressure variable of other equations as well as the relative permeabilities. Consequently, the equations are relatively difficult to solve. Hassanizadeh and Gray (1990) proposed another approach and governing equations to describe multiphase flow based on macroscale thermodynamic theory. Their equations, which were based on fundamental laws of physics, were for only two-fluid systems, but Hassanizadeh and Gray (1990) stated that it would be straightforward to extend the theory to more than two fluids.

A simplifying assumption for solving Eqs. (2.1–2.3) can be made by assuming air to be at atmospheric pressure whenever there is interconnected air (continuous air phase). Richards (1931) made such assumption when considering water movement through soils. Under this assumption, then Eq. (2.1) can be neglected. This assumption is likely realistic for soils near the interface with the atmosphere, where air can freely move from soil pores to the atmosphere and vice versa. However deeper in the subsurface, continuous air may not be atmospheric because of time-dependent atmospheric conditions. The air pressure may vary with elevation. If there are clay or cemented layers, then there may be significant differences in the air pressures on opposite sides of the layers. Air flow has been observed at breathing boreholes which means an air pressure gradient exists. Furthermore, if vacuum extraction of LNAPL vapors is employed as a remediation option, then Eq. (2.1) is needed for any computer simulations (predictions). Employing the Richards (1931) assumption may not always be valid; it would depend on subsurface conditions and what is being simulated.

Important elements for predicting multiphase flow are the physical relations, particularly the relations describing how saturations and relative permeabilities vary as a function of the fluid pressures. Typically, the relations between fluid saturations and pressures are empirically parameterized and the parameters are utilized to predict fluid relative permeabilities. For two-fluid systems (air–water or LNAPL–water), only one set of parameters is needed. For three-fluid systems (air–LNAPL–water), there can be multiple sets of parameters.

Leverett (1941) proposed that the total-liquid saturation in multiphase systems, with gas and liquid phases, is a function of the capillary pressure at gas–liquid interfaces in which gas is the nonwetting fluid. Therefore, the total-liquid saturation (sum of water and LNAPL) would be a function of the air–LNAPL capillary pressure for air–LNAPL–water systems in porous media where water is the wetting fluid and LNAPL has intermediate wettability between air and water. From the petroleum industry, the water saturation is commonly assumed to be a function of the oil– water (LNAPL–water) capillary pressure in which water is a strongly wetting fluid. For three-fluid systems, the total-liquid saturation can be predicted from the air– LNAPL capillary pressure using one set of parameters and the water saturation can be predicted from the LNAPL–water capillary pressure using another set of parameters. Both sets of parameters need to reflect the same pore-size distribution for the predictions to be accurate and avoid numerical convergence issues as the twofluid (air–water) system transitions into a three-fluid (air–LNAPL–water) system and vice versa.

To calculate the LNAPL saturation, the water saturation is subtracted from the total-liquid saturation. Commonly, water is assumed to be the wetting fluid, air is the nonwetting fluid, and LNAPL has intermediate wettability between water and air. Under this condition and neglecting fluid films, water will preferentially occupy the smallest pore spaces, air will occupy the largest continuous pore spaces, and LNAPL will occupy intermediate-sized pore spaces. However, this wettability sequence does not hold for all porous media or LNAPLs. In some cases, porous media can have LNAPL-wet, mixed-wet, or fractional-wet wettability instead of a strongly water-wet wettability (Anderson 1987). The distribution of fluids within the pore spaces will be governed by the wettability. Hence, the calculation of fluids saturations as a function of capillary pressures will depend on the wettability. In the following discussions in this chapter, we assume the porous media to be strongly water wet.

### **2.4 The Parker et al. (1987) Nonhysteretic Model**

Parker et al. (1987) proposed a parametric formulation to describe nonhysteretic *k-S-P* relations for air–LNAPL–water systems in porous media where water is the wetting fluid, LNAPL has intermediate wettability, and air is the nonwetting fluid. The formulation can be calibrated relatively easily using more readily available air–water *S-P* measurements or published parameters. The scaling approach yields closed-form expressions of *k-S-P* relations that could be employed to predict behavior in two-fluid air–water, air–LNAPL, or LNAPL–water systems, or three-fluid air–LNAPL–water systems.

For *S-P* relations, Parker et al. (1987) proposed a scaled *S*∗(*h*∗) functional as

$$S^\*(h^\*) = \overline{S}^{aw}\_w(\beta\_{aw}h\_{aw})\tag{2.4}$$

$$S^\*(h^\*) = \overline{S}^{ao}\_o(\beta\_{ao}h\_{ao})\tag{2.5}$$

$$S^\*(h^\*) = \overline{S}^{\prime \prime \prime}\_w(\beta\_{\partial \prime} h\_{\partial \prime}) \tag{2.6}$$

$$S^\*(h^\*) = \overline{S}^{aww}\_w(\beta\_{ow}h\_{ow})\tag{2.7}$$

$$S^\*(h^\*) = \overline{S}^{row}\_t(\beta\_{ao}h\_{ao})\tag{2.8}$$

where superscripts *aw*, *ao*, *ow*, and *aow* refer to air–water, air–LNAPL, LNAPL– water, and air–LNAPL–water fluid systems, respectively; β*aw*, β*ao*, and β*ow* refer to air–water, air–LNAPL, and LNAPL–water scaling factors, respectively; *haw*, *hao*, *how*  are air–water, air–LNAPL, and LNAPL–water capillary heads, respectively [*haw* = (*Pa* − *Pw*) <sup>ρ</sup>*wg*; *hao* <sup>=</sup> (*Pa* <sup>−</sup> *Po*) <sup>ρ</sup>*wg*; *how* <sup>=</sup> (*Po* <sup>−</sup> *Pw*) ρ*wg*]; and *Sw*, *So*, and *St*  are the effective water, LNAPL, and total-liquid saturations, respectively, defined by

$$
\overline{S}\_{j} = \begin{pmatrix} S\_{j} - S\_{m} \end{pmatrix} \Big/ \begin{pmatrix} 1 - S\_{m} \end{pmatrix} \tag{2.9}
$$

in which *Sj* ( *j* = *w*, *o*, *t*) are actual saturations and *Sm* is the minimum or irreducible wetting fluid saturation. To mathematically describe the relations, Parker et al. (1987) adapted the van Genuchten (1980) *S-P* equation to predict the effective saturations. However, the Brooks-Corey (1966) mathematical equation or other models for describing *S-P* relations also could be used.

The fluid pair scaling factors (β*aw*, β*ao*, and β*ow*) are obtained by regressing air–LNAPL and LNAPL–water *S-P* data, if available, against air–water *S-P* data; however, obtaining such data may not be available or too time-consuming and expensive to conduct. Lenhard and Parker (1987a) overcame this issue by showing that the scaling factors can be estimated from ratios of interfacial tensions as

$$
\beta\_{aw} = 1\tag{2.10}
$$

$$\left. \beta\_{ao} = {}^{\sigma\_{aw}} \right|\_{\sigma\_{ao}} \tag{2.11}$$

$$
\beta\_{ow} = \sigma\_{aw} \Big/\_{\sigma\_{ow}} \tag{2.12}
$$

where σ*aw*, σ*ao*, and σ*ow* are air–water, air–LNAPL, and LNAPL–water interfacial tensions, respectively. By defining β*aw* = 1, Parker et al. (1987) made the *S-P*  parameters to be based on air–water *S-P* relations. This made it considerably easier to obtain parameters to describe the *S*∗(*h*∗) relations because one could use available air–water *S-P* data or published air–water parameters and ratios of interfacial tensions, which are more easily measured than air–LNAPL and LNAPL–water *S-P*  data. Consequently, investigators can conduct numerical simulations of multiphase flow without the need and cost for *S-P* data from different fluid systems. Enforcing

$$
\beta\_{aw} = \,^1\!/\_{\beta\_{ao}} + \,^1\!/\_{\beta\_{ow}} \tag{2.13}
$$

which is the same as σ*aw* = σ*ao* + σ*ow* ensures the *S-P* relations of air–water and air–LNAPL–water systems will match as an air–water system transitions into an air–LNAPL–water system and vice versa (Lenhard et al. 2002), which is important for convergence of numerical models as fluid systems change. Lenhard and Parker (1987a) noted that when measuring interfacial tensions, all fluids need to be in equilibrium with each other, particularly water. The condition given by Eq. (2.13) indicates that LNAPL will spread on water surfaces. A similar scaling approach was advanced by Leverett (1941) when he was extrapolating *S-P* data for one rock sample to similar rock types with different intrinsic permeabilities and porosities (slightly different pore structure between rock types) in petroleum reservoirs. Parker et al. (1987) extrapolated *S-P* data for different fluid systems in a porous medium with constant rigid pore structure —not between different porous media.

For nonhysteretic *k-S* relations, Parker et al. (1987) followed van Genuchten (1980) by employing the Mualem (1976) model for air–water systems, but extended it for air–LNAPL–water fluid systems in porous media to yield closed-form equations for predicting three-fluid relative permeabilities as

$$k\_{rw} = \overline{S}\_{w}^{0.5} \left\{ 1 - \left[ 1 - \overline{S}\_{w}^{1/m} \right]^{m} \right\}^{2} \tag{2.14}$$

$$k\_{ro} = (\overline{S}\_t - \overline{S}\_w)^{0.5} \left\{ \left[ 1 - \overline{S}\_w^{1/m} \right]^m - \left[ 1 - \overline{S}\_t^{1/m} \right]^m \right\}^2 \tag{2.15}$$

$$k\_{ra} = \overline{S}\_a^{0.5} \left(1 - \overline{S}\_t^{1/m}\right)^{2m} \tag{2.16}$$

in which the *krw*, *kr o*, and *kra* are the water, LNAPL, and air relative permeabilities, respectively, and *m* is a van Genuchten (1980) *S-P* parameter *<sup>m</sup>*<sup>=</sup> <sup>1</sup><sup>−</sup> <sup>1</sup> *n* . Closed-form expressions for relative permeabilities are in Parker and Lenhard (1989) when the Brooks-Corey (1966) *S-P* model is used in Burdine's (1953) relatively permeability integral.

The approach of Parker et al. (1987) allowed investigators to model air–water and air–LNAPL–water flow in the subsurface using numerical models that can be easily calibrated. Only air–water van Genuchten parameters α, *n*; the irreducible water saturation (*Sm*); and the interfacial tensions σ*ao*, σ*ow* are needed for the *k-S-P* relations when the van Genuchten (1980) and Mualem (1976) models are used for water-wet porous media. The nonhysteretic *k-S-P* relations were initially tested against air–LNAPL–water experimental data by Lenhard et al. (1988) in a multiphase numerical model. When the Brooks-Corey (1966) and Burdine (1953) models are used for water-wet porous media, only the air–water Brooks–Corey parameters *hd*  (displacement head) and λ (pore-size index); the irreducible water saturation (*Sm*); and the interfacial tensions σ*ao*, σ*ow* are needed for the *k-S-P* relations.

### **2.5 Hysteretic Model**

Shortly after Parker et al. (1987) proposed the nonhysteretic *k-S-P* relations, Parker and Lenhard (1987) and Lenhard and Parker (1987b) proposed hysteretic *k-S-P* relations, which accounts for contact angle, pore geometry ("ink bottle"), and nonwetting fluid entrapment effects in the both vadose and liquid-saturated zones when fluids change from drying-to-wetting saturation paths and vice versa. The entrapment of LNAPL in water and entrapment of air in LNAPL and water are considered. Nonwetting fluid entrapment occupies pore space that would otherwise be occupied by a relative wetting fluid and displaces the relative wetting fluid into larger pore spaces. For example, entrapped LNAPL by water will displace water into larger pore spaces at the same actual water saturation and, thereby, increase the conductance rate of water. The effect increases the water relative permeability and decreases the LNAPL relative permeability at given actual water and LNAPL saturations for wetting fluid imbibition saturation paths than for wetting fluid drying saturation paths. To account for these effects, Parker and Lenhard (1987) and Lenhard and Parker (1987b) introduced the term "apparent" fluid saturations where the apparent two-phase (air–water) water saturation is the sum of the effective entrapped air saturation in water and the effective water saturation; and the apparent three-phase (air–LNAPL–water) water saturation is the sum of the effective entrapped air and LNAPL saturations in water and the effective water saturation. The apparent saturations better index the pore sizes in which the continuous fluids reside than effective or actual saturations for predicting relative permeabilities. The hysteretic *k-S-P* relations were initially tested against transient air–LNAPL–water experimental data by Lenhard et al. (1995) in a multiphase numerical model, which yielded good results.

# **2.6 Predicting LNAPL Saturations, Volumes, and Transmissivity from Well Levels**

To further help develop LNAPL remediation strategies and forecast threedimensional LNAPL movement, Parker and Lenhard (1989) vertically integrated *k-S-P* relations and incorporated them into a two-dimensional numerical model (ARMOS) (Kaluarachchi et al. 1990). The earlier Parker et al. (1987) nonhysteretic *k-S-P* relations provided the framework. The model, ARMOS, was later modified to include LNAPL entrapment in both the unsaturated and liquid-saturated zones (Kaluarachchi and Parker 1992). The calculation of the LNAPL entrapment volume in a vertical slice of the unsaturated zone is based on the change in the air–LNAPL level in wells from rising water tables. The LNAPL entrapment volume in a vertical slice of the liquid-saturated zone is based on the change in the LNAPL–water level in wells from rising water tables. Parker et al. (1994) used ARMOS to model LNAPL migration and direct LNAPL recovery at LNAPL spill sites from knowledge of fluid levels in wells. Waddill and Parker (1997a) later proposed semi-analytical algorithms to predict LNAPL trapping and recovery from wells in diverse soils. The algorithms were incorporated in a version of ARMOS and tested against experimental data (Waddill and Parker, 1997b). Later, the approach of Parker and Lenhard (1989) was incorporated in American Petroleum Institute's (API) LDRM model (API 2007).

Parker and Lenhard (1989) developed the vertically integrated nonhysteretic *k-S-P* relations for incorporation into multiphase numerical models to assist remediation practitioners. However, not all LNAPL remediation practitioners have access to numerical models so Lenhard and Parker (1990) published equations for determining the LNAPL volume in a vertical slice of the subsurface from fluid level elevations in wells that can be used in simple computer programs. At the same time, Farr et al. (1990) also published equations to determine LNAPL volume in a vertical slice of the subsurface. Both publications assume vertical equilibrium conditions and use the Brooks-Corey (1966) *S-P* model for developing their equations. The difference in the approaches is Lenhard and Parker (1990) utilized elevations from the fluid levels in the wells to determine LNAPL and water pressures, and Farr et al. (1990) utilized depths from the surface to determine LNAPL and water pressures. The air phase is assumed to be atmospheric in both models.

**Fig. 2.1** A cartoon showing determining of total-liquid (*St* ), water (*Sw*), and LNAPL saturations from wells adjacent to LNAPL-contaminated soils

Using the approach of Lenhard and Parker (1990) and Farr et al (1990) to determine LNAPL and water pressures, and hence air–LNAPL and LNAPL–water capillary pressures, from elevations (depths) of the air–LNAPL and LNAPL–water interfaces in the wells, the subsurface LNAPL saturations adjacent to wells can be calculated. Figure 2.1 shows an example of information that can be obtained. From the air– LNAPL and LNAPL–water capillary pressures, the total-liquid saturations (*St*) and the water saturations (*Sw*), respectively, can be calculated, which by difference yields the LNAPL saturations (*So* = *St* − *Sw*).

The shape of the Fig. 2.1 LNAPL saturation-elevation profile is similar to the "shark fin" shape description (Frollini and Petitta 2018) reported by researchers/ practitioners. However, the shape depends on porous media type. For example, Fig. 2.2 shows the predicted LNAPL saturations as a function of elevation for the scenario where the air–LNAPL interface in a well is at an elevation of 150 cm above a datum and the LNAPL–water interface is at an elevation of 100 cm above the same datum for a LNAPL thickness in the well of 50 cm. If an accompanying well is only screened in the water-saturated zone, then the air–water interface would occur at an elevation of 135.5 cm above the datum, which can be determined from Eq. 2.5 in Lenhard and Parker (1990). Hydrostatic conditions are assumed so the LNAPL and water pressures vary linearly with elevation. Furthermore, nonhysteretic *S-P* relations are assumed, i.e., entrapped and residual LNAPL saturations are not considered. The datum elevation for determining the LNAPL saturations can be arbitrarily set. The predicted *St* and *Sw*, from which the LNAPL saturations are determined in Fig. 2.2, are obtained using the van Genuchten (1980) model, but other *S-P* models could be used (e.g., Brooks and Corey 1966; Alfaro Soto et al. 2019). The left diagram in Fig. 2.2 is for a loamy sand soil and the right diagram is for a clay loam soil. The shape of the predicted LNAPL saturation-elevation distribution is noticeably different, especially the LNAPL saturation values at each elevation. The LNAPL saturations in the clay loam soil extend to higher elevations than those in the loamy sand soil, but not to a large extent. The LNAPL saturations in Fig. 2.2 become zero at an elevation of 188 cm for the loamy sand soil and become zero at an elevation of 193 cm for the clay loam soil. The LNAPL saturation predictions in Figs. 2.1 and

**Fig. 2.2** Predicted LNAPL saturation-elevation distributions of a loamy sand (left) and a clay loam (right) soil for a scenario where the air–LNAPL interface in a well is at an elevation of 150 cm and the LNAPL–water interface is at 100 cm (center)

2.2 assumed that all the LNAPL is mobile or free as originally proposed by Lenhard and Parker (1990).

# **2.7 Incorporating Free, Residual, and Entrapped LNAPL Fractions**

Later, Lenhard et al. (2004) proposed further adaptions to the *k-S-P* relations proposed by Parker et al (1987). Understanding that *kro* will be greater than 0 whenever the effective *So* (*So*) is greater than 0, unless *kro* is arbitrarily set to zero at some *So*, Lenhard et al. (2004) proposed an approach for methodically setting *kro* = 0 at variable *So* by considering a residual LNAPL saturation. When *kro* > 0 because *So*  > 0, then LNAPL will continually drain from the vadose zone until vertical *S-P*  equilibrium conditions are established. Setting *kro* = 0 arbitrarily at some fixed *So*  is not realistic because the mobility of LNAPL at different water saturations will not be the same. For example, setting *kr o*. = 0 at *So* = 0.15 might be reasonable when the effective water saturation (*Sw*) = 0.2, because the LNAPL will reside in small pores; but, not when *Sw* = 0.7, because the LNAPL will reside in larger pores. The LNAPL may be immobile when *Sw* = 0.2, but much of the LNAPL will likely be mobile at *Sw* = 0.7, so setting *kro* = 0 at some arbitrary LNAPL saturation is not reasonable for all water saturations.

Lenhard et al. (2004) considered LNAPL to exist in three forms: free, entrapped, and residual. Free LNAPL is continuous and can move freely in porous media when a LNAPL total-pressure gradient exists. Entrapped LNAPL is water-occluded LNAPL that results from water displacing LNAPL from pore spaces and can potentially exist everywhere in the subsurface (i.e., above and below the water-saturated zone). Entrapped LNAPL is discontinuous and immobile; it will not move under water and LNAPL total-pressure gradients typical in porous media. Residual LNAPL is immobile LNAPL that is not water occluded, which may exist as LNAPL wedges and films. There may be LNAPL films connecting some residual LNAPL (wedges) to free LNAPL, but the movement of LNAPL through the films is likely to be very slow and

**Fig. 2.3** A cartoon showing air (white), LNAPL (red), and water (blue) in subsurface pore spaces

cause the residual LNAPL to behave as if practically immobile under most LNAPL total-pressure gradients. Figure 2.3 shows a cartoon of air, LNAPL, and water in water-wet, subsurface, porous media as envisioned by Lenhard et al. (2004). Air is shown as white and exists when the air–LNAPL capillary pressure is greater than 0. LNAPL is shown as red with LNAPL films slightly darker red. The LNAPL films are attached to water films in pores containing air that previously were LNAPL filled and attached to water films in LNAPL-filled pores. Water-occupying pores is lighter blue. Water films wetting the solid particle grains (dark gray) is darker blue.

Figure 2.4 shows expanded sections of Fig. 2.3 which displays the Lenhard et al. (2004) concepts of free, entrapped, and residual LNAPL. Free LNAPL (Fig. 2.4a–c) is LNAPL continuous throughout the pore spaces that can move freely in response to LNAPL total-pressure gradients. It does not include LNAPL films (Fig. 2.4a,c) on water films (Fig. 2.4a,c) which theoretically will not move freely; the LNAPL films are assumed to be relatively immobile. Entrapped LNAPL (Fig. 2.4c) as explained earlier is water-occluded LNAPL which will not move in response to water and LNAPL total-pressure gradients. The water-occluded LNAPL is discontinuous and exists as blobs in pore bodies and LNAPL wedges that do not drain prior to waterfilling pores during increasing water saturations. A similar situation may occur with water in smaller pores surrounded by larger pores that fill with LNAPL before the water in the small pores drain resulting in isolated water (Fig. 2.4b). Residual LNAPL is idealized as LNAPL wedges and films in the three-phase air–LNAPL– water zones (Fig. 2.4a). It also includes the relatively immobile LNAPL wedges and films (Fig. 2.4c) in the two-phase LNAPL–water zones.

The concepts of free, entrapped, and residual LNAPL advanced by Lenhard et al. (2004) were incorporated in numerical codes by White et al. (2004) and Oostrom et al. (2005) and were shown to be important for predicting LNAPL behavior in the vadose zone. Additional models to incorporate a residual LNAPL saturation in *k-S-P*  relationships were proposed by Wipfler and van der Zee (2001) and Van Geel and Roy (2002). Oostrom et al. (2005) tested both the Van Geel and Roy (2002) and Lenhard et al. (2004) formulations against transient three-fluid column experiments.

### **2.8 Recent Developments. The Lenhard et al. (2017) Model**

Effects of entrapped and residual LNAPL (Lenhard et al. 2004) were considered by Lenhard et al. (2017) when predicting subsurface LNAPL saturations and transmissivity from LNAPL and water levels in wells. In the Lenhard et al. (2017) model, historical air–LNAPL and LNAPL–water interface levels in wells were considered. Specially, the highest air–LNAPL interface elevation and the lowest LNAPL–water interface elevation were included. The highest air–LNAPL interface elevation in an observation well reflects the highest elevations in the subsurface that may contain residual LNAPL. The lowest LNAPL–water interface elevation reflects the lowest elevations that may contain entrapped LNAPL. Both entrapped and residual LNAPL will affect the LNAPL relative permeability at a location because they reduce the amount of free or mobile LNAPL at that elevation. The LNAPL relative permeability distribution governs the LNAPL transmissivity.

For the same configuration of air–LNAPL and LNAPL–water interface elevations in a well as Fig. 2.2 (current levels) and assuming the air–LNAPL interface elevation at one time was 50 cm higher (i.e., historical elevation is 200 cm) and the LNAPL–water interface elevation was 50 cm lower (i.e., historical elevation is 50 cm), predicted free, entrapped, and residual LNAPL saturations are shown in Fig. 2.5. Again, the van Genuchten (1980) model was used to predict the *S-P* relations consistent with the Lenhard et al. (2017) model. In comparison to Fig. 2.2, the upper free LNAPL elevation for the loamy sand soil in Fig. 2.5 is predicted to be about 20 cm lower. This results because residual LNAPL occurs, which is not mobile (free), and some minor entrapped LNAPL exists as water displaced LNAPL from those pores when the water table was raised (i.e., as the LNAPL–water interface in the well was raised from the historical level). The residual LNAPL for the loamy sand soil in Fig. 2.5 is predicted to occur about 50 cm higher than the free LNAPL in Fig. 2.2, because the historical air–NAPL level is 50 cm higher. The lower free LNAPL elevation is the same for the loamy sand soil in Figs. 2.2 and 2.5 because the lower free LNAPL occurrence is a function of the current LNAPL–water level (i.e., 100-cm elevation) and not historical levels. However, the lower entrapped LNAPL elevation for the loamy sand soil in Fig. 2.5 is predicted to be about 50 cm lower than the free LNAPL in Fig. 2.2 because the historical LNAPL–water level is 50 cm lower. There is no predicted entrapped LNAPL in Fig. 2.2 because it was not considered in the nonhysteretic *S-P* relations. For Fig. 2.5, the maximum possible entrapped LNAPL was set at 0.15, and the maximum possible residual LNAPL was set at 0.15. These are additional parameters in Lenhard et al. (2004, 2017). The LNAPL distributions in Fig. 2.5 can help practitioners design remediation programs focused on free, entrapped, and residual LNAPL and not only on free LNAPL as in Fig. 2.2.

The predicted free LNAPL volume in a vertical slice of the loamy sand soil per cm<sup>2</sup> of surface area in Fig. 2.2 is predicted to be 11.7 cm3/cm2, whereas the free LNAPL volume is predicted only to be 9.9 cm3/cm2 in Fig. 2.5. The difference is because of considering residual and entrapped LNAPL in Fig. 2.5. The difference also has a significant effect on predicted LNAPL transmissivities using the methodology in Lenhard et al. (2017). When entrapped and residual LNAPL are not considered, the predicted free LNAPL transmissivity is 6200 cm2/day for the loamy sand soil with an assumed water-saturated hydraulic conductivity of 350 cm/day. When entrapped and residual LNAPL are considered, the predicted free LNAPL transmissivity is 4225 cm2/day—a difference of over 30%. If a calculation is conducted that accounts for only LNAPL under positive LNAPL pressures, then the predicted free LNAPL

**Fig. 2.5** Predicted free (red solid line), entrapped (black dotted line), and residual (green dashed line) of a loamy sand (left) and a clay loam (right) soil where the current air–LNAPL and LNAPL– water interface elevations in a well are the same as in Fig. 2.2 with the historical highest air–LNAPL level 50 cm higher than current and the historical lowest LNAPL–water level 50 cm lower than current

transmissivity is only 4830 cm2/day for the loamy sand in Fig. 2.2 and 3360 cm2/ day in Fig. 2.5. Because only LNAPL under positive pressure will enter a borehole, estimations of LNAPL transmissivity should be based on LNAPL under positive pressure for planning direct LNAPL recovery from wells.

### **2.9 Layered Porous Media**

When the contaminated subsurface can be represented as homogeneous, the subsurface LNAPL distributions can have a "shark fin" shape. For layered porous media, however, the subsurface LNAPL distribution shape can be more varied. Consider a scenario where two coarse layers are separated by a fine layer. Assume a LNAPLcontaminated subsurface with a 20-cm fine layer between two coarse layers that may be over 100 cm thick. In nearby monitoring wells, the air–LNAPL interface in one well occurs at an elevation of 160 cm above the datum and the LNAPL–water interface in the same well occurs at an elevation of 100 cm above the datum for a LNAPL thickness of 60 cm in the well. In an accompanying well screened only in the water-saturated zone, the air–water interface occurs at an elevation of 142 cm above the datum. Assuming hydrostatic conditions, nonhysteretic *S-P* relations, and the van Genuchten (1980) model to predict *St* and *Sw*, the subsurface LNAPL saturation distribution can be predicted. Figure 2.6 shows the results for the fine layer occurring between the 120- and 140-cm elevations. Because the fine layer is below the air–LNAPL interface in the well and above the elevation of the LNAPL–water interface, the fine layer will be completely saturated with LNAPL and water. The fine layer will have a higher water saturation than the coarse layers because of its smaller pore sizes. The contrast in pore sizes between the coarse and fine layers can produce significant differences in LNAPL saturations at the boundaries between the layers. The resulting shape of the subsurface LNAPL distribution will consequently be very different than a "shark fin" shape.

**Fig. 2.6** Predicted LNAPL, total-liquid (*St* ), and water (*Sw*) saturations for a scenario involving a fine layer between two coarse layers with 60 cm of LNAPL inside a nearby monitoring well

**Fig. 2.7** Predicted LNAPL, total-liquid (*St* ), and water (*Sw*) saturations for a scenario involving a coarse layer between two fine layers with 60 cm of LNAPL inside a nearby monitoring well

The shape of the subsurface LNAPL distribution curve will depend on whether there are contrasting pore sizes between potential layers, the location of the layers relative to the air–LNAPL and LNAPL–water interface elevations in nearby wells, and the thickness of LNAPL in the wells. As another example, consider a scenario where two fine layers are separated by a coarse layer. Assume a LNAPL-contaminated subsurface with a 20-cm coarse layer between two fine layers that may be over 100 cm thick. The opposite configuration as for Fig. 2.6. Further, assume the same conditions and fluid levels in wells as for Fig. 2.6. Using the same calculation protocols, Fig. 2.7 shows the results of the predicted total liquid, *St* , and water, *Sw*, saturations. For Fig. 2.7, the coarse layer is completely liquid-saturated for the same reason as the fine layer in Fig. 2.6, but the water saturation is low because of its larger pore sizes. The low water saturation yields a high LNAPL saturation for the coarse layer. The contrasting sizes of pores in the coarse and fine layers produce a significant difference in LNAPL saturations at the boundaries of the layers—just like in Fig. 2.6, but in the opposite direction. The shape of the subsurface LNAPL distribution curve can be quite complex for layered porous media and not a simple "shark fin" shape. Furthermore, an abrupt change in pore sizes at layer boundaries can result in LNAPL moving laterally versus downward similarly to a capillary break of constructed soil covers over waste pits. The subsurface LNAPL distribution depends on many factors.

### **2.10 Summary and Steps Forward**

The historical development of *k-S-P* relations described in this chapter largely follows advancements proposed by Parker, Lenhard, and colleagues. Many of their proposed concepts and equations are incorporated in today's multiphase numerical models or code developers have used some of their concepts in building their models. However, further advancements are still required to help accurately predict the subsurface behavior of LNAPL, especially the effects of microbiological action and potential changes in fluid properties over time.

A key element of *k-S-P* models is that they mimic physics of multiphase flow, even if the models may be empirical. The various forms of LNAPL in the subsurface need to be addressed. Careful estimation of model parameters is needed also to produce good predictions, but this is not routinely done by contaminated land practitioners nor typically required by regulators. Improved and more accessible measurement methods for two-fluid and three-fluid systems should be developed and adopted.

Similarly, the effects of heterogeneous subsurface conditions should be acknowledged by investigators and considered when conducting numerical simulations or using simple predictive models. This may be incorporated into models specifically developed to represent heterogeneous environments with layered systems or multimodal pore-size porous media (see Chap. 3).

Some models to predict LNAPL volumes, distribution, and transmissivity may not account for certain processes, which may have not been considered relevant enough for practical purposes in the past. Additional research may be needed to elucidate the relevance of mechanisms like those associated to natural source zone depletion (e.g., entrapment of gases caused by methanogenic outgassing or presence of microorganisms and extracellular polymeric substances) on LNAPL distribution predictions. More information on natural source; zone depletion phenomena is presented in Chap. 5. Further research is also needed for systems not exhibiting strongly water-wet characteristics.

Good understanding of multiphase flow principles is paramount to develop sound conceptual site models and, therefore, should be an essential skill of regulators and practitioners managing LNAPL-contaminated sites. Multiphase models are currently underutilized and may help to analyze LNAPL remediation options and design costeffective solutions, including mass recovery systems (see Chap. 12) and any other in-situ remediation strategies targeting the LNAPL source zone.

### **References**

Abriola LM, Pinder GF (1985a) A multiphase approach to the modeling of porous media contamination by organic compounds-part I: equation development. Water Resour Res 21(1):11–18

Abriola LM, Pinder GF (1985b) A multiphase approach to the modeling of porous media contamination by organic compounds-part 2: numerical simulation. Water Resour Res 21(1):19–26

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# **Chapter 3 Estimating LNAPL Volumes in Unimodal and Multimodal Subsurface Pore Systems**

**Miguel A. Alfaro Soto, Martinus Th. van Genuchten, Robert J. Lenhard, and Hung K. Chang**

**Abstract** In this chapter, we compare modeling approaches for determining the specific volume of light nonaqueous phase liquids (LNAPLs) in the subsurface on top of the water-saturated zone following spills or leaks at or near the soil surface. We employ both unimodal and multimodal pore-size capillary pressure–saturation functions in our predictions. Hydrologic properties, both fluid properties and pore-size distribution, are important for accurate predictions. Before presenting our results, we discuss fluid interfacial tensions, fluid wettability, and pore structures. Data from the literature are used in our calculations to show that the use of multimodal unsaturated soil hydraulic properties can lead to significantly different subsurface LNAPL-specific volume predictions compared to when unimodal formulations are used. The differences can be significant even when the capillary pressure–saturation curves appear similar over the capillary pressure range relevant to the hypothetical LNAPL contamination scenarios. Consequently, the multimodal pore structure of porous media needs to be addressed to avoid potentially erroneous estimates of the resources and time needed to remediate LNAPLs from contaminated areas.

**Keywords** Capillary pressure-saturation relations · LNAPL-specific volume · Multimodal pore-size distribution · Pore structure · Subsurface LNAPL distribution

M. A. Alfaro Soto (B) · H. K. Chang

Department of Applied Geology and Centro de Estudos Ambientais, UNESP—São Paulo State University, Rio Claro, SP, Brazil e-mail<EMAIL_ADDRESS>
H. K. Chang e-mail<EMAIL_ADDRESS>
M. Th. van Genuchten Department of Nuclear Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil e-mail<EMAIL_ADDRESS>
R. J. Lenhard San Antonio, TX, USA

© The Author(s) 2024 J. García-Rincón et al. (eds.), *Advances in the Characterisation and Remediation of Sites Contaminated with Petroleum Hydrocarbons*, Environmental Contamination Remediation and Management, https://doi.org/10.1007/978-3-031-34447-3\_3

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### **3.1 Introduction**

Soil hydraulic properties are very important for predicting the subsurface behavior of fluids, including light nonaqueous phase liquids (LNAPLs) that may accumulate above the water-saturated zone and potentially result in groundwater contamination. Accounting for pore-size distributions and fluid properties is critical. Relatively small differences in either may produce erroneous predictions. Models that predict subsurface LNAPL behavior commonly use capillary pressure–saturation (*S-P*) relations to describe fluid saturations and to estimate fluid relative permeabilities. *S-P* relationships and the size distribution of pores govern subsurface LNAPL volumes. Two of the most common *S-P* functions are those by Brooks and Corey (1964) and van Genuchten (1980), both of which were developed initially for porous media having normal or lognormal pore-size distributions.

Integrating LNAPL saturations over a vertical slice of the subsurface yields subsurface LNAPL-specific volumes, which are important for planning remedial cleanup activities (Wickramanayaque et al. 1991). Governmental regulatory agencies commonly require removing the LNAPL mass to the maximum extent practicable. Both the volume and architecture of the LNAPL body influence the performance of any remediation effort. Several authors have proposed methods to calculate subsurface LNAPL-specific volumes following accidental spills on the soil surface or by leaking underground storage tanks, mostly by utilizing fluid levels measured in monitoring wells (e.g., Charbeneau et al. 2000; Farr et al. 1990; Lenhard and Parker 1990; Lenhard et al. 2017; Sleep et al. 2000). Closed-form analytical equations are obtained when the Brooks and Corey *S-P* model is used to predict subsurface LNAPL-specific volumes (Farr et al. 1990; Lenhard and Parker 1990). Numerical integration, on the other hand, is needed when the van Genuchten *S-P* model is employed to predict subsurface LNAPL volumes (Parker and Lenhard 1989). Throughout this chapter, we will use the terms soils and porous media interchangeably, noting that pedogenesis processes may substantially influence hydraulic properties (Fogg and Zhang 2016).

An unresolved issue still is that all porous media do not necessarily have normal or lognormal pore-size distributions. Many natural porous media have multimodal poresize distributions as shown by Peters and Klavetter (1988), Durner (1994), Romano et al. (2011), Wijaya and Leong (2016), Madi et al. (2018), among many others. The focus of this chapter is comparing predictions of subsurface LNAPL distributions in porous media when unimodal and multimodal pore-size distributions are assumed. We present our results after discussing the literature and data used for our calculations.

### **3.2 Pore Structures**

Soils are made up of mostly mineral particles of different sizes (e.g., sand, silt, and clay). In their natural state, these components are often aggregated by means of a series of physical, chemical, and/or biological processes to create structures of different shapes and sizes. The aggregates commonly possess internal voids or pores of varying sizes, leading to a dual-porosity porous medium. Such a medium typically has larger (interaggregate) pores between the aggregates and smaller (intraaggregate) pores within the aggregates. Pore sizes may range from macropores (larger than 50 nm) to mesopores (between 2 and 50 nm) to micropores (smaller than 2 nm) according to the International Union of Pure and Applied Chemistry (IUPAC).

Pore sizes in soils can be measured by various techniques as described by Dane and Topp (2002), such as mercury porosimetry, thermal porosimetry, nitrogen sorption, microscopy or x-ray tomography. Soils typically have a normal or lognormal poresize distribution, generally leading to unimodal characteristics since most soils are made up of well-graded particles. However, many soils have more complex pore systems with bimodal or multimodal pore-size distributions (Peters and Klavetter 1988; Romano et al. 2011; Wijaya and Leong 2016; Madi et al. 2018).

Pore sizes govern the ability of porous media to retain fluids against fluid pressures. For example, fine-textured soils with their higher percentages of clay (> 50%) can drain water at low capillary pressures (0.01 MPa) similar as coarser-textured soils. This behavior is more related to the pore-size distribution than the grain size of the porous media. Bimodal or multimodal pore-size distributions can be found also in structured soils and fractured rocks containing large pores (fractures) interspersed with smaller and less permeable micropores of the soil or rock matrix (Peters and Klavetter 1988; Gerke and van Genuchten 1993). Multimodal pore-size distributions occur because of irregular particle-size distributions, the creation of secondary porosity as a result of genetic or other processes (such as physical or chemical aggregation, or biological processes), and/or the effects of glaciation (moraine) or solifluction. Many tropical soils (such as Ultisols and Oxisols) and volcanic soils (Andisols) frequently exhibit multimodal pore-size distributions (Spohrer et al. 2006; Alfaro Soto et al. 2008; Rudiyanto et al. 2013; Seki et al. 2021).

Pore sizes and their geometry affect *S-P* relations. Soils with unimodal and multimodal pore-size distributions often have very dissimilar *S-P* relationships. Mathematical functions used to describe unimodal pore-size distributions, hence, may be inadequate for describing multimodal pore-size distributions without adjustments. The standard Brooks and Corey (1964) and van Genuchten (1980) *S-P* models are applicable to media having normal or lognormal pore-size distributions, but may be inappropriate for predicting LNAPL distributions in porous media having multimodal pore- or particle-size distributions.

### **3.3 Water and LNAPL Saturations**

In this section, several fluid and soil properties such as interfacial tensions, wettability, and capillary pressures are described briefly since they are important for calculating subsurface fluid saturation distributions. Additional information can be found in Chap. 2. Our discussion refers to continuous fluid phases (no fluid entrapment or fluid films).

When more than one fluid phase exists in a porous medium, interfaces will develop between the immiscible fluid phases. At the interfaces, there will likely be an imbalance of attractive forces causing the interfaces to contract, thus forming an interfacial tension (commonly called surface tension when between a gas and a liquid). A difference in fluid pressure across the interfaces will cause them to have a curvature with the convex side having the greater fluid pressure. The degree of curvature depends on the magnitude of the pressure difference between the immiscible fluid phases.

Wettability is the preference of a fluid to spread or adhere to a surface. Generally, the surface is considered to be a solid (porous media grains and/or aggregates). Several different types of wettability may exist, such as fractional wettability and mixed wettability (Tiab and Donaldson 1996), but these will not be discussed in this chapter. We will focus on porous media having a singular or constant wettability. Fluids that wet solid surfaces in preference to other fluids will make a contact angle less than 90 degrees when measured from the solid surface, and are then referred to as the wetting fluid. When a fluid spreads completely on a solid surface, the contact angle is 0 degrees. Different levels of wetting have been recognized. Strong wetting is when the contact angle is less than 30 degrees, moderate wetting when the contact angle is 30°–75°, and neutral wetting when the contact angle is 75°–105°. The other fluid in a two-fluid system is then referred to as the nonwetting fluid.

In porous media containing three fluids (e.g., air, a LNAPL, and water), wettability preference can refer also to which fluid will spread on another fluid (Parker et al. 1987; Tiab and Donaldson 1996). The fluid that wets the solids is the wetting fluid. The fluid that wets the wetting fluid is typically referred to as having intermediate wettability. The fluid wetting the intermediate wetting fluid is referred to as the nonwetting fluid. Neglecting fluid films, wettability dictates which fluid will preferentially occupy what pore sizes. The wetting fluid will generally occupy the smallest pores and the nonwetting fluid the largest pores. Fluids with intermediate wettability will occupy the intermediate-sized pores.

The fluid pressure difference across the interface of immiscible fluid phases is called the capillary pressure. If the capillary pressure is 0, then the interface will not be curved (such as a LNAPL on top of water in a jar). If the capillary pressure is greater than 0, then the interfaces will be curved with the relative wetting fluid on the concave side of the curvature. For example, water will be on the concave side of a curved air–water interface in a capillary tube inserted in a pool of water. Water would be the wetting fluid at a sub-atmospheric pressure, and air would be the nonwetting fluid at atmospheric pressure. The capillary pressure across interfaces is related to the interfacial tension between the relative wetting and nonwetting fluids and the radii of curvature of the interfaces in the orthogonal directions. This relationship is called the Laplace equation of capillarity (Corey 1994):

$$P\_c = \sigma \left(\frac{1}{R\_1} + \frac{1}{R\_2}\right) \tag{3.1}$$

where σ is the interfacial tension of the fluid pair at the interface, and *R*1 and *R*2 are the radii of curvature of the interface in orthogonal directions.

The radii of curvature of the interfaces (*R*) can be related to pore radii by the contact angle the wetting fluid makes with the porous media solids such as

$$R = r/\cos\chi\tag{3.2}$$

where *r* is the pore radius and γ the contact angle. If the cross-sectional area across a fluid interface is assumed to be circular, in which case *R*1 = *R*2, the Laplace equation reduces to

$$P\_c = 2\sigma \cos \chi / r \tag{3.3}$$

which is commonly given in textbooks. The above shows that the capillary pressure can be used to index pore sizes in which fluid interfaces occur, and to determine fluid saturations.

### **3.4 Capillary Pressure–Saturation Curves**

If two immiscible fluids are present in a porous medium, fluid interfaces only occur between the two fluids. For an air–water fluid system, the fluid interfaces are between air and water. The degree of curvature of the air–water interfaces (i.e., the air–water capillary pressure) can index what pore sizes are occupied by which fluids (the Laplace equation of capillarity and wettability). The capillary pressure will then index the fluid saturations. Air–LNAPL–water fluid systems, where water is the wetting fluid and LNAPL has intermediate wettability between air and water, will have two types of fluid interfaces: one set of interfaces between the LNAPL and water and one set between air and the LNAPL. The radii of curvature of the two sets of interfaces (i.e., the capillary pressures) will be different because the fluids will occupy different pore sizes. Under this wettability (water is the wetting fluid), the LNAPL–water capillary pressure has long been known to index the water saturation. The air–LNAPL capillary pressure then indexes the total-liquid (LNAPL plus water) saturation as advanced by Leverett (1941). The difference between total-liquid saturation and water saturation is the LNAPL saturation.

The relationships between capillary pressure and saturation can be measured by either increasing or decreasing the capillary pressure or the fluid saturation and measuring the changes in fluid saturation or capillary pressure. When the air–water (for a two-fluid system) or LNAPL–water (for a three-fluid system) capillary pressure in water-wet porous media is increased from the completely water-saturated state, the resulting saturation path is called a drying (or drainage) process with regard to the wetting fluid. When the air–water (two-fluid system) or LNAPL–water (three-fluid system) capillary pressure is decreased, it is a wetting (or imbibition) process with regard to the wetting fluid. An example of an *S-P* curve for an air–water system is shown in Fig. 3.1 for a unimodal pore-size distribution when water is the wetting fluid. For the water drainage curve beginning at *Sw* = 1, the water saturation, at which there is no further water drainage when the air–water capillary pressure is increased, is shown as *S*wr. Commonly, *S*wr is called the residual (or irreducible) water saturation. For the water wetting (imbibition) curve beginning at *S*wr, air can be occluded by water during water imbibition (i.e., air can become discontinuous by being surrounded by water). The maximum occluded nonwetting fluid saturation (i.e., air) at a capillary pressure of 0 is shown as *S*nr. In the petroleum industry, the occluded nonwetting fluid is also called residual saturation, but its use generally is restricted to two-fluid systems (i.e., brine oil reservoirs). In the hydrology literature, *S*nr is also called a residual saturation. In air–LNAPL–water systems, however, LNAPL can become occluded by water and, also, can become essentially irreducible in pore wedges and bypassed pores following LNAPL drainage in the vadose zone. To distinguish between these two processes, Parker and Lenhard (1987) called discontinuous LNAPL occluded by water as entrapped LNAPL, and referred to essentially irreducible LNAPL in the vadose zone as residual LNAPL, which is similar to water residual saturation (i.e., irreducible saturations as the capillary pressures are increased). One can have be entrapped LNAPL in both the vadose and the water-saturated zones.

The water drainage curve beginning at *Sw* = 1 in Fig. 3.1 and the water wetting curve beginning at *Sw* = *S*wr have been called main curves. Any wetting fluid drainage curve initiated from *Sw* < 1 or wetting process initiated from *Sw* > *S*wr is called a scanning curve. We note here also that *S-P* relationships are not unique. They are usually subject to hysteresis, which means that different *S-P* relations will occur depending on whether the fluids are draining or wetting. Nonwetting fluid entrapment, contact angle changes, and pore-size contrasts (the "ink-bottle effect" as described by Hillel 1980) are some reasons for hysteresis in *S-P* relations.

**Fig. 3.1** Hypothetical capillary pressure–saturation (S-*P*) curve when water is the wetting fluid

Mathematical models are often used to describe the *S-P* relationships. Common models are those by Brooks and Corey (1964), van Genuchten (1980), and Kosugi (1996). Here, we limit ourselves to van Genuchten's formulation given by

$$\overline{S} = \left[1 + (\alpha h\_c)^n\right]^{-m} \tag{3.4}$$

in which α, *n,* and *m* are quasi-empirical shape parameters, *hc* is the capillary pressure head, and *S* is the effective wetting-fluid saturation given by:

$$\overline{S} = (S - S\_r)/(1 - S\_r) \tag{3.5}$$

where *S* is the actual wetting-fluid saturation and *Sr* the residual (or irreducible) wetting-fluid saturation. Equation (3.5) is generic for any fluid system and assumes that no entrapped (residual) nonwetting fluid is present (e.g., entrapped air in an air–water system).

For air–LNAPL–water fluid systems where water is the wetting fluid and LNAPL has intermediate wettability between air and water, two *S-P* relations are needed. One is the LNAPL–water *S-P* relationship, which relates the LNAPL–water capillary pressure to the water saturation. The second is the air–LNAPL *S-P* relationship, which relates the air–LNAPL capillary pressure to the total-liquid saturation. Both are needed to determine LNAPL saturations. When not considering entrapment of air and LNAPL, the effective water and effective total-liquid saturations in three-fluid air–LNAPL–water systems can be determined similarly to Eq. (3.5). The effective water saturation (*S*w) can be determined by replacing *S* and *Sr* in Eq. (3.5) by water saturation (*Sw*) and the residual water saturation (*S*wr), respectively, as

$$\overline{S}\_{\rm w} = (S\_{\rm w} - S\_{\rm wr})/(1 - S\_{\rm wr}) \tag{3.6}$$

The effective total-liquid saturation (*St*) can be determined by replacing *S* and *Sr* in Eq. (3.5) by the total-liquid saturation (*St*), which is the sum of the water and LNAPL saturations, and the residual water saturation (*S*wr), respectively, as

$$\overline{S}\_1 = (S\_t - S\_{\text{wr}})/(1 - S\_{\text{wr}}) \tag{3.7}$$

Figure 3.1 is typical for porous media having unimodal pore-size distributions. Alfaro Soto et al. (2008) measured the air–water capillary pressure–water content relations of soils from the state of São Paulo, Brazil that showed characteristics of bimodal or trimodal pore-size distributions (Fig. 3.2a). The curves are different from the unimodal curve shown in Fig. 3.1. Many formulations for multimodal *S-P* curves have been proposed over the years (Ragab et al. 1981; Smettem and Kirkby 1990; Othmer et al. 1991; Mallants et al. 1997; Alfaro Soto et al. 2008; Rudiyanto et al. 2013; Li et al. 2014). One of the best-known models was formulated by Durner (1994), based on van Genuchten's (1980) unimodal *S-P* model:

$$\overline{S} = \sum\_{i=1}^{j} w\_i \left[ 1 + (\alpha\_i h\_c)^{n\_i} \right]^{-m\_i} \tag{3.8}$$

where *j* represents the number of subsystems composing the total pore distribution; *wi* are subcurve weight factors varying between 0 and 1, which sum to unity; and α*<sup>i</sup>* , *ni*, and *mi* are the van Genuchten parameters of each subsystem. Similar combinations can be constructed using Brooks and Corey (1964) type subfunctions, including a mixture of different types of subfunctions (e.g., Zhang and Chen 2005; Dexter et al. 2008; Li 2014; Seki 2021). The fitted curves in Fig. 3.2a were obtained using multiple van Genuchten (1980) subcurves as expressed by Eq. (3.8).

**Fig. 3.2** Multimodal characteristics of soils from the state of São Paul, Brazil: **a** Capillary pressure– saturation curves, **b** pore-size distribution curves

The differences between the various curves in Fig. 3.2a are more clearly shown by their equivalent lognormal pore-size distributions given by *P*(*hc*) = d*S*(*hc*)/ dlog(*h*) (Fig. 3.2b). The plots reflect the bimodal and trimodal structures of the soils. Figure 3.2a highlights the limitations of standard unimodal models (Fig. 3.1) when describing *S-P* relationships of aggregated soils or fractured rocks.

To investigate how the predictions of subsurface LNAPL distributions may differ using unimodal and multimodal *S-P* formulations, we considered two lateritic soils with multimodal pore structures. Alfaro Soto et al. (2019) extracted data for these two soils (Soils A and F) from Mallants et al. (1997). Figure 3.3 shows the air–water capillary pressure data and best-fit unimodal and multimodal *S-P* curves for both soils. The unimodal *S-P* curves are based on Eq. (3.4), and the multimodal curves (bi- and trimodal) are based on Eq. (3.8). Figure 3.4 further shows the lognormal pore-size distributions, obtained again using *P*(*S*) = d*S*(*h*)/dlog(*h*), for the soils in Fig. 3.3 as a function of pF = log (*hc*) with *hc* in cm. The two figures exhibit clear differences between the unimodal and multimodal curves.

Figure 3.3a shows that the unimodal and multimodal *S-P* curves of the sandy loam soil are very similar (Fig. 3.3a) for capillary heads less than about 0.55 m (pF = 1.75). Between capillary heads of about 0.55–1.6 m (pF = 1.75–2.2), the multimodal *S-P*

**Fig. 3.3** Measured capillary pressure head–saturation data and optimized (best-fit) curves assuming unimodal, bimodal, and trimodal pore-size distributions for **a** A sandy loam soil from Rio Claro, Brazil, and **b** a silty clay soil from São Carlos, Brazil (Alfaro Soto et al. 2019)

**Fig. 3.4** Relative pore-size distributions assuming unimodal, bimodal, and trimodal pore systems for (**a**) A sandy loam from Rio Claro, Brazil and (**b**) a silty clay from São Carlos, Brazil (Alfaro Soto et al. 2019)