Rossen, W.R.

Profile

The most complete and up-to-date listing of my research interests, publications, student supervisions, can be found on my CV, available here.

Academic Positions

Delft University of Technology, Department of Geoscience and Engineering, Professor of Reservoir Engineering, since 2006. Head of Reservoir Engineering Section (formerly Petroleum Engineering Section), 2007-2020. Emeritus Professor starting Nov. 2020.
The University of Texas at Austin, Department of Petroleum and Geosystems Engineering, Professor, 2001 - 2006. Associate Professor 1995-2001; Assistant Professor 1989-1995. Chairman, Department of Petroleum and Geosystems Engineering, 2005-2006.
Delft University of Technology, Delft, The Netherlands, Faculty of Applied Earth Sciences, Visiting Associate Professor, summer 1996.
Other professional experience: Chevron Oil Field Research Co., La Habra, CA
- 1982-85: Research on design of surfactant formulations for enhanced oil recovery (EOR). Conducting and supervising laboratory studies of the propagation and oil-recovery efficiency of surfactant formulations in corefloods.
- 1985-86: Long-range research group; continuing research in surfactant EOR. Additional responsibilities included mathematical modeling of flow through porous media and of surfactant process efficiency in the field.
- 1986-89: Research on foams for EOR. Conducted experimental and theoretical studies of mechanisms of foam generation and propagation. Specific studies included percolation modeling of foam mobilization in porous media and fundamental modeling of foam yield stress in porous media.

Education

Ph.D., Chemical Engineering, University of Minnesota, 1982
Dissertation under H. T. Davis and L. E. Scriven on modeling and experimental study of thermodynamics of surfactant-oil-water mixtures with application to Enhanced Oil Recovery (EOR). 3.88/4.0 GPA.
S. B., Chemical Engineering, Massachusetts Institute of Technology, 1976
Merit Scholar, 1972-76. 4.78/5.0 GPA.

Research

In 2020 I gave a lecture in the GeoScience and GeoEnergy Webinar series hosted by colleagues at TU Delft and Heriot-Watt U. One of the main themes is the surprises that come in doing research. The talk is available for viewing here.

In 2013 I wrote an article "Surface Physics Illustrated in the Operation of a Lava Lamp" for our Department student yearbook.

When one is appointed Professor at Delft University of Technology, one gives an introductory lecture (Intreerede) summarizing one's view one's field of research. I choose to give some reflections on the tension between complexity and simplicity in our modeling of complex phenomena in nature. The text should be read along with the slides; the slides are referred to by number in the text. Click to view text. Click to view slides.

In 2010 I was invited to write a short essay for the SPE publication for young professionals, The Way Ahead. I chose as a topic, "Should I Consider Graduate School?" Click to view text.

Reflections on teaching:

Link to film interview when I was a candidate for Best Teacher of TU Delft in 2011. Link to interview after I was given that award. After the award I was interviewed for TU Delft highlights.
Slides from a presentation I made in 2014 on my thoughts on University engineering education.
I wrote an article for the 2021 yearbook of the Mjnbouwkundige Vereeniging on adaptations I've made to the BSc course in Physical Transport Phenomena to incorporate applications to geothermal research.

Award for "outstanding service" as an SPE Associate Editor, 2014.
Named Improved Oil Recovery Pioneer, SPE/DOE Symposium on Improved Oil Recovery, Tulsa, OK, 2012.
Named Best Instructor, Delft University of Technology, 2011.
Distinguished Member Award, Society of Petroleum Engineers, 2006.
Distinguished Achievement Award for Petroleum Engineering Faculty, Society of Petroleum Engineers, 2002.

An extended list of publications and the CV can be downloaded here.

Pure lists my recent publications since 2006, when I came to TU Delft. In cases where the publications are available in Open Access, it provides the text of the article.

Key publications and presentations are listed below are grouped into the following research topics:

Gases such as steam, carbon dioxide (CO₂) and hydrocarbon gases are injected into oil reservoirs to increase the recovery of oil. These gases are much less dense and less viscous than the oil they attempt to displace, so they tend to finger through or migrate to the top of the reservoir, leaving most of the oil behind. Foams can help these gases to sweep oil reservoirs more efficiently. The publications below include an overview of the use of foams in these applications, experiments, and analytical and computer models of foam processes on the reservoir scale.

One particularly noteworthy product of this research was the identification of two distinct flow regimes for foam in porous media. One is controlled by foam stability at the "limiting capillary pressure." Bubble sizes change drastically in this regime. The other appears to be controlled by bubble trapping and mobilization at fixed bubble size.

W. R. Rossen, "Foams in Enhanced Oil Recovery," in R. K. Prud'homme and S. Khan, ed., Foams: Theory, Measurements and Applications, Marcel Dekker, New York, 1996.
A brief overview of CO₂ foam (that also applies to other foam processes) is in a presentation I made to an SPE Applied Technology Workshop in Oct. 2010.
Al Ayesh, A. H., Salazar, R., Farajzadeh, R., Vincent-Bonnieu, S., and Rossen, W. R., "Foam Diversion in Heterogeneous Reservoirs: Effect of Permeability and Injection Method," SPE Journal 22, 1402-1415 (2017) doi:10.2118/179650-PA
Boeije, C. S., et al., "A Methodology for Screening Surfactants for Foam Enhanced Oil Recovery in an Oil-Wet Reservoir," SPE Reservoir Evaluation and Engineering 20, 795-808 (2017). doi.org/10.2118/185182-PA
Namdar Zanganeh, M., and Rossen, W. R., "Optimization of Foam EOR: Balancing Sweep and Injectivity," SPE Reservoir Evaluation and Engineering 16, 51-59 (2013).
Alvarez, J.M., Rivas, H., and Rossen, W.R., "A Unified Model for Steady-State Foam Behavior at High and Low Foam Qualities," SPE Journal 6 (Sept. 2001), 325-333.
Kim, J. S., Dong., Y., and Rossen, W. R., "Steady-State Flow Behavior of CO₂ Foam," SPE Journal10 (Dec. 2005), 405-415.
Rossen, W.R., "Foam in Porous Media," in J. F. Sadoc and N. Rivier, ed., Foams and Emulsions, Kluwer Academic Publishers, 1999.
Shen, C., Nguyen, Q. P., Huh, C., and Rossen, W. R., "Does Polymer Stabilize Foam in Porous Media?," SPE 99796 prepared for presentation at the 2006 SPE/DOE Symposium on Improved Oil Recovery, Tulsa, OK, 22-26 April.
W. R. Rossen and Q. Lu, "Effect of Capillary Crossflow on Foam Improved Oil Recovery," paper SPE 38319, Proc. 1997 SPE Western Regional Meeting, Long Beach, CA, June 25-27.
W. R. Rossen and Z. H. Zhou, "Modeling Foam Mobility at the Limiting Capillary Pressure," SPE Adv. Technol.3, 146 (1995).

The issue of how foam is created and maintained in porous media is important not only for foam modeling and simulation, but because it is a crucial factor in long-distance foam propagation. The first publication listed below makes this link, based on population-balance modeling of foam described in a separate section.

At the 2020 EuFoam conference I made a presentation on the link between foam generation and propagation. Link to slides for that presentation. A 2017 presentation discusses the situation before the recent experiments of Yu et al. confirmed the predictions of theory relating foam generation to propagation.
Yu, G., et al., "Foam Propagation at Low Superficial Velocity: Implications for Long-Distance Foam Propagation," accepted for publication by SPE Journal. doi:10.2118/201251-PA (available on Open Access)
Ashoori, E., et al., "Multiple Foam States and Long-Distance Foam Propagation in Porous Media," SPE Journal 17, 1231-45 (2012).
Yu, G., et al., "Coreflood Study of Effect of Surfactant Concentration on Foam Generation in Porous Media," Industrial and Engineering Chemistry Research 58, 420-427 (2019).
Rossen, W. R.: "Comment on 'Verification of Roof Snap-Off at a Foam-Generation Mechanism in Porous Media at Steady State,'" Colloids and Surfaces A: Phyiscochemical and Engineering Aspects322, 261–269 (2008).
Gauglitz, P.A., et al., “Foam Generation in Homogeneous Porous Media,” Chem. Eng. Sci. 57, 4037-4052 (2002).
Chen, M, et al., "Pore-network study of the mechanisms of foam generation in porous media," Phys. Rev. E73 036304 (2006).
Chen, M., et al.: "Insights on Foam Generation in Porous Media from Pore-Network Studies," Colloids Surfaces A: Physicochem Eng. Aspects 256 (2-3), 181-189 (2005).
Rossen, W. R., "A Critical Review of Roof Snap-Off as a Mechanism of Steady-State Foam Generation in Homogeneous Porous Media," Colloids Surfaces A: Physicochem Eng. Aspects, 225 (1-3) 1-24 (2003).
W. R. Rossen, et al., "Percolation Modeling of Foam Generation in Porous Media," AIChE J.40, 1082 (1994).
W. R. Rossen and P. A. Gauglitz, "Percolation Theory of Creation and Mobilization of Foams in Porous Media," AIChE J.36, 1176 (1990).

If direct foam propagation from an injection well is not feasible, it may be possible to place foam far from the injection well taking advantage of the mechanism of foam generation as gas flows upward across sharp permeability changes.

Shah, S. Y., et al. "Foam Generation in Flow Across a Sharp Permeability Transition: Effect of Velocity and Fractional Flow," SPE Journal 25, 451-464 (2020, February). doi:10.2118/195517-PA
Shah, S. Y., et al., "Foam generation by capillary snap-off in flow across a sharp permeability transition," SPE Journal 24, 116-128 (2019).
Rossen, W.R., "Foam Generation at Layer Boundaries in Porous Media," SPE Journal 4, 409-412 (Dec. 1999).
Li, Q., and Rossen, W. R., "Injection Strategies for Foam Generation in Homogeneous and Layered Porous Media," SPE 96116 presented at the 2005 SPE Annual Technical Conference and Exhibition, Dallas, TX, 9-12 October.

Foam is usually injected in alternating slugs of gas and liquid ("Surfactant Alternating Gas," or SAG; this is also called FAWAG). Simplified analytical models for foam suggest that SAG foam processes have superior injectivity and should be able to overcome gravity override with minimal rise in injection-well pressure. Simulation studies support this conclusion, and experimental work seeks to determine the parameters crucial to this process. Most recently, we discovered that injectivity is enhanced by a variety of complex near-well phenomena: dry-out and collapse of foam in a very small region around the injection well; liquid fingering through trapped gas; and dissolution of gas into these liquid fingers. Studies continue to the best way to take laboratory data for scale-up to field-scale SAG processes.

J. Gong, et al. (2020), "Effect of Superficial Velocity on Liquid Injectivity in SAG Foam EOR. accepted for publication by Fuel. Part 1: Experimental Study," . Part 2: Modeling.
Gong, J., et al., (2020). "Injectivity of Multiple Slugs in Surfactant Alternating Gas Foam EOR: A CT Scan Study" SPE Journal.
Gong, J., et al. (2020), "Laboratory Investigation of Liquid Injectivity in Surfactant-Alternating-Gas Foam Enhanced Oil Recovery," accepted for publication by Transport in Porous Media 131, 85–99 (2020).
Salazar-Castillo, R. and Rossen, W. R., "Scale-up of Laboratory Data for Surfactant-Alternating-Gas Foam EOR," SPE Journal (June, 2020). doi:10.2118/201204-PA
Salazar-Castillo, et al., "Fractional-Flow Theory for Non-Newtonian Surfactant-Alternating-Gas Foam Processes," Transport in Porous Media 131, 399–426 (2019).
Boeije, C. S., and Rossen, W. R., "SAG foam flooding in carbonate rocks," J. Petroleum Science and Engineering 171, 843-853 11 (2018).
Gong, J., et al., "Modelling of Liquid Injectivity in Surfactant-Alternating-Gas Foam Enhanced Oil Recovery," SPE Journal, 2019. 24(3); p. 1123-1128.
Shan, D. and Rossen, W.R., "Optimal Injection Strategies for Foam IOR," SPE Journal 9 (June 2004), 132-150.
Kloet, M. B., et al., "Optimal Design Criteria for SAG Foam Processes in Heterogeneous Reservoirs," SPE 121581 presented at the 2009 SPE EUROPEC/EAGE Annual Conference and Exhibition, Amsterdam, The Netherlands, 8–11 June 2009.
Xu, Q., and Rossen, W. R., "Experimental Study of Gas Injection in Surfactant-Alternating-Gas Foam Process," SPE Reservoir Evaluation and Engineering 7 (Dec. 2004), 438-448.
Rossen, W. R., and Bruining, J., "Foam Displacements With Multiple Steady States," SPE Journal 12 (March 2007), 5-18.

The best model is the simplest one that represents the mechanisms that are key in a given situation. For most purposes simpler ("implicit texture") models, where foam properties are represented as a function of local conditions, do as good a job as any. For cases where foam is not at local equilibrium between processes of creation and destruction, more-complicated Population-Balance modeling is required: for the entrance region of a porous medium, at a shock front, and in cases where foam generation is in doubt. I have employed both population-balance modeling and the simpler models. A minimum of mechanisms necessary to describe observed behavior are implemented in the model. In particular, with the two flow regimes identified by experimental studies (see above), the a model must include parameters for the collapse of foam at high capillary pressure and for foam behavior at lower capillary pressure. Extensions of the model with more-sophisticated algorithms for foam generation are described in the section on population-balance modeling below.

Rossen, W. R., "Numerical Challenges in Foam Simulation: A Review," SPE 166244 presented at the SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 30 September–2 October 2013. Summarized and highlighted in Feb. 2014 issue of J. Petr. Technol. doi:10.2118/166232-MS
Boeije, C. S., and Rossen, W. R., "Fitting foam-simulation-model parameters to data: I. co-injection of gas and liquid," SPE Reservoir Evaluation and Engineering, 18(2), 264-272 (2015).
Rossen, W.R. and Boeije, C. S., "Fitting foam-simulation-model parameters to data: II. surfactant-alternating-gas foam applications," SPE Reservoir Evaluation and Engineering, 18(2), 273-283 (2015).
Kapetas, L., et al., "Effect of permeability on foam-model parameters: an integrated approach from core-flood experiments through to foam diversion calculations," Colloids and Surfaces A: Physicochem. Eng. Aspects 530, 172-180 (2017).
Jones, S. A., et al., “Effect of Surfactant Concentration on Foam: From Coreflood Experiments to Implicit-Texture Foam-Model Parameters," J. Ind. & Eng. Chem. 37, 268-276 (2016).
Lotfollahi, M., et al., "Comparison of implicit-texture and population-balance foam models," J. Natural Gas Sci. Eng. 31, 184-197 (2016).
Farajzadeh, R., et al., "Effect of Permeability on Implicit-Texture Foam Model Parameters and the Limiting Capillary Pressure," Energy and Fuels, 29(5), 3011-3018 (2015).
Ashoori, E., and Rossen, W.R., "Can Formation Relative Permeabilities Rule Out a Foam EOR Process?," SPE Journal 17(2), 340-351 (2012).
Cheng, L., et al., "Simulating Foam Processes at High and Low Foam Qualities," paper SPE 59287 presented at the 2000 SPE/DOE Symposium on Improved Oil Recovery, Tulsa, OK, 3-5 April.
Rossen, W.R., et al., "Simplified Mechanistic Simulation of Foam Processes in Porous Media," SPE Journal, 4, 279-287 (Sept. 1999).
Shi, J.-X. and Rossen, W.R., "Simulation of Gravity Override in Foam Processes in Porous Media," SPE Reserv. Eval. and Eng.1, 148-154 (April 1998).

Fractional-flow modeling of foam has proved very useful, highlighting the controlling mechanisms in complex simulations, identifying numerical artifacts in simulations, and pointing toward SAG injection as a means to overcome gravity effects with little or no rise in injection-well pressure. In one case a fractional-flow model was the best way to interpret foam effectiveness in a field pilot. More-recently, we have implemented non-Newtonian rheology into fractional-flow models for foam in radial flow. Applications of method-of-characteristics modeling to gravity override are listed in the section on gravity segregation below.

A 2016 presentation summarizes some of the insights offered by fractional-flow modeling of EOR and specifically foam processes. A 2014 presentation summarizes how it helped interpret a foam field test.
Salazar-Castillo, R. O., et al., "Fractional-Flow Theory for Non-Newtonian Surfactant-Alternating-Gas Foam Processes," Transport in Porous Media 131, 399–426 (2019).
Tang, J., et al., "Three-Phase Fractional-Flow Theory of Foam-Oil Displacement in Porous Media with Multiple Steady States," Water Resources Research 55, 10319-10339 (2019)
Rossen, W. R., et al., "Long-Time Diversion in SAG Foam Enhanced Oil Recovery From A Field Test," SPE Reservoir Evaluation and Engineering 20(1) (Feb. 2017), 1-7.
Leeftink, T. N., et al., "Injectivity Errors in Simulation of Foam EOR," J. Petroleum Sci. Eng. 126, 26–34 (2015). doi:10.1016/j.petrol.2014.11.026.
de Velde Harsenhorst, R. M., et al., "Extension and Verification of a Simple Model for Vertical Sweep in Foam SAG Displacements," SPE Reservoir Evaluation and Engineering, 17(3), 373-383 (2014).
Grassia, P., et al., "Analysis of a Model for Foam Improved Oil Recovery," J. Fluid Mech. 751, 346-405 (2014).
Rossen, W. R., et al., "Fractional Flow Theory Applicable to Non-Newtonian Behavior in EOR Processes," Transport in Porous Media 89(2), 213-236 (2011).
Namdar Zanganeh, et al., "The Method of Characteristics Applied to Oil Displacement by Foam," SPE Journal 16 (March 2011), 8-23. doi:10.2118/121580-PA.
Ashoori, E., et al., "Fractional-Flow Theory of Foam Displacements with Oil," SPE Journal 15, 260-273 (2010).
Rossen, W. R., and Bruining, J., "Foam Displacements With Multiple Steady States," SPE Journal 12 (March 2007), 5-18.
Dong, Y., and Rossen, W. R., "Insights from Fractional-Flow Theory for Models for Foam IOR," 14th European Symposium on Improved Oil Recovery, Cairo, Egypt, 22-24 April, 2007.
Shan, D. and Rossen, W.R., “Optimal Injection Strategies for Foam IOR,” SPE Journal 9 (June 2004), 132-150.
Rossen, W.R., Zeilinger, S.C., Shi, J.-X., and Lim, M.T., "Simplified Mechanistic Simulation of Foam Processes in Porous Media," SPE Journal 4, 279-287 (Sept. 1999).
Z. H. Zhou and W. R. Rossen, "Applying Fractional-Flow Theory to Foam Processes at the 'Limiting Capillary Pressure'," SPE Adv. Technol. 3, 154 (1995).
Z. H. Zhou and W. R. Rossen, "Applying Fractional-Flow Theory to Foams for Diversion in Matrix Acidization," SPE Prod. Fac. 9, 29 (1994).

Fractional-flow theory has been especially helpful in the study of gravity segregation in gas flooding and with foam:

Boeije, C. S., and Rossen, W. R., "Gas Injection Rate Needed for SAG Foam Processes to Overcome Gravity Override," SPE Journal 20, 49-59 (2015).
Jamshidnezhad, M., et al., "Injection of Water above Gas for Improved Sweep in Gas IOR: Performance in 3D," SPE Reserv. Eval. Eng. 13 (4), 699-709 (Aug. 2010).
Rossen, W.R., and van Duijn, C.J., "Gravity Segregation in Steady-State Horizontal Flow in Homogeneous Reservoirs," J. Petr. Sci. Eng. 43, 99-111 (2004).
Rossen, W. R., et al., "Injection Strategies to Overcome Gravity Segregation in Simultaneous Gas and Water Injection Into Homogeneous Reservoirs," SPE Journal 15 76-90 (2010).
Jamshidnezhad, M., et al., "Well Stimulation and Gravity Segregation in Gas Improved Oil Recovery," SPE Journal 15, 91-104 (2010).

Foam properties are controlled by bubble size. Therefore, in principle, a complete model for foam should account for processes of bubble creation and destructions and the effect of bubble size on foam properties. The equation for evolving bubble size is called a "population balance." We developed the first population-balance model for foam that accounts for the multiple steady states seen in foam-generation experiments, probed its steady-state behavior and did numerical simulations. More recently, we have merged this modeling with fractional-flow methods, focusing on two regions were local steady state does not apply: the entrance region of the porous medium, and shock fronts where bubble size changes drastically. This led to a key insight: the relation between conditions for foam generation and for foam propagation far from an injection well. Experimental confirmation of that connection is described under "Foam generation and propagation" above.

Ashoori, E., et al., "Multiple Foam States and Long-Distance Foam Propagation in Porous Media," SPE Journal 17, 1231-45 (2012).
Ashoori, E., et al., "Roles of Transient and Local Equilibrium Foam Behavior in Porous Media: Traveling Wave," Colloids and Surfaces A: Physicochem. Eng. Aspects 377, 228–242 (2011).
Ashoori, E., et al., "Stability Analysis of Uniform Equilibrium Foam states for EOR Processes," Transport in Porous Media 92, 573-595 (2012).
Ashoori, E., et al., "Dynamic Foam Behavior in the Entrance Region of a Porous Medium," Colloids and Surfaces A: Physicochem. Eng. Aspects 377, 217–227 (2011).
Kam, S. I., and Rossen, W. R., "A Model for Foam Generation in Homogeneous Porous Media," SPE Journal 8 (Dec. 2003), 417-425.
Kam, S. I., Nguyen, Q. P., Li, Q., and Rossen, W. R.: "Dynamic Simulations With an Improved Model for Foam Generation," SPE Journal 12 (March 2007), 35-48.

In several experimental and modeling studies we have examined the effect of oils on foam and the best way to represent their effect in foam models.

Tang, J., et al., "CT Coreflood Study of Foam Flow for Enhanced Oil Recovery: the Effect of Oil Type and Saturation," Energy 188 (2019).
Hussain, A. A. A., et al., "The Impacts of Solubilized and Dispersed Crude Oil on Foam in a Porous Medium," Colloids and Surfaces A: Physicochemical and Engineering Aspects 579, 123671 (2019).
Tang, J., et al., "Quantitative Modeling of the Effect of Oil on Foam for Enhanced Oil Recovery," SPE Journal 24 (June 2019) 1057-1075 (SPE-194020-PA).
Tang, J., et al., "Experimental Investigation of the Effect of Oil on Steady-State Foam Flow in Porous Media," SPE Journal 24, 140-157 (2019).
A.A.A. Hussain, et al., "Impact of Crude Oil on Pre-Generated Foam in Porous Media," J. Petroleum Science Engineering 185, 106628 (2020).
Farajzadeh, R., Andrianov, A., Krastev, R., Hirasaki, G. J., and Rossen, W. R., "Foam-Oil Interaction in Porous Media: Implications for Foam Assisted Enhanced Oil Recovery," Advances in Colloid and Interface Science, 183-184 (November 2012), 1-13.

Gravity segregation is one of the principle causes of poor sweep efficiency in gas-injection EOR. A remarkably simple model for segregation proposed by Stone in 1982 applies to foam as well under certain restrictive conditions. We explore the implications of these models for gravity segregation with and without foam, as well as alternate injection methods proposed to outperform the process described originally by Stone. Gravity override in SAG foam processes is explored in the section on SAG above.

My research on gravity override, through 2009, is summarized in a presentation.
Rossen, W.R., and van Duijn, C.J., "Gravity Segregation in Steady-State Horizontal Flow in Homogeneous Reservoirs," J. Petr. Sci. Eng.43, 99-111 (2004).
Jamshidnezhad, M., van der Bol, L., and Rossen W. R.: "Injection of Water above Gas for Improved Sweep in Gas IOR: Performance in 3D," accepted for publication in SPE Reserv. Eval. Eng.
Rossen, W. R., van Duijn, C. J., Nguyen, Q. P., Shen, C., and Vikingstad, A. K., "Injection Strategies to Overcome Gravity Segregation in Simultaneous Gas and Water Injection Into Homogeneous Reservoirs," SPE Journal15 76-90 (2010).
Jamshidnezhad, M., Chen, C., Kool, P., and Rossen, W. R.: "Well Stimulation and Gravity Segregation in Gas Improved Oil Recovery," SPE Journal15, 91-104 (2010).
Shi, J.-X. and Rossen, W.R., "Simulation of Gravity Override in Foam Processes in Porous Media," SPE Reserv. Eval. and Eng. 1, 148-154 (April 1998).
Stolwijk, G. H., and Rossen, W. R., "Gravity Segregation in Gas IOR in Heterogeneous Reservoirs," presented at the 15th European Symposium on Improved Oil Recovery, Paris, France, 27 – 29 April 2009.
Faisal, A., Bisdom, K., Zhumabek, B., Mojaddam Zadeh, A., and Rossen, W. R., "Injectivity and Gravity Segregation in WAG and SWAG Enhanced Oil Recovery," SPE 124197 presented at the 2009 SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 4–7 October 2009.

The behavior of foam in porous media is controlled by the behavior of individual soap films between bubbles in the foam. These soap films resist stretching, much as the elastic surface of a balloon resists stretching; as a result, the foam itself remains trapped unless it is pushed hard enough (technically, unless a minimum pressure gradient is exceeded). Mechanisms of foam generation are addressed in a separate section above. In this section we address the difficulty in mobilizing soap foams in the porespace of the rock, and the pressure gradient required to keep a mature foam flowing through rock. This latter problem is closely related to "Plateau's problem," described in the nineteenth century by the Belgian scientist Henri Plateau: the shape of soap films stretched across wire supports. In this application, however, the soap film is stretched across a pore. If Plateau's problem is "a soap film on a wire," this represents "a soap film in a box."

In a series of papers we have explored in some detail the difficulties in measuring the extent of gas trapping by foam in porous media, using a novel method of visualizing Xe tracer in situ during a coreflood. Mass transfer between flowing and adjacent trapped gas is so rapid that it makes distinguishing the two from effluent composition extremely difficult.

Nonnekes, L. E., et al., "Effect of Gas Diffusion on Mobility of Foam for Enhanced Oil Recovery," Transp. Porous Media 106(3), 669-689 (2015). DOI 10.1007/s11242-014-0419-z.
A 2017 presentation summarizes some of the key issues involving foam mechanisms, including yield stress, measuring gas trapping, and foam generation.

Huh, C., and Rossen, W. R., "Approximate Pore-Level Modeling for Apparent Viscosity of Polymer-Enhanced Foam in Porous Media," SPE Journal 13 (March 2008), 17-25.
Cox, S.J., et al., "A Theory of the Effective Yield Stress of Foam in Porous Media: The Motion of a Soap Film Traversing a Three-Dimensional Pore," Colloids Surfaces A: Physicochem Eng. Aspects 245, 143–151 (2004).
Xu, Q., and Rossen, W. R., "Effective Viscosity of Foam in Periodically Constricted Tubes," Colloids Surfaces A: Physicochem Eng. Aspects 216 (1-3), 175-194 (2003). A video of a soap film traversing a 2D pore is in the following presentation.
Chen, M., et al.: "The Flow and Displacement in Porous Media of Fluids with Yield Stress," Chemical Engineering Science, 60 (15), August 2005, 4183-4202.
Balan, H. O., Balhoff, H. O., Nguyen, Q. P., and Rossen, W. R., "Network Modeling of Gas Trapping and Mobility in Foam EOR," Energy and Fuels 25(9), 3974-3987 (2011).
Rossen, W.R. and Wang, M.-W., "Modeling Foams for Acid Diversion," SPE Journal, 4, 92-100 (June 1999).
W. R. Rossen, "Minimum Pressure Gradient for Foam Flow in Porous Media: Effect of Interactions with Stationary Lamellae," J. Colloid Interface Sci. 139, 457 (1990).
W. R. Rossen, "Theory of Minimum Pressure Gradient of Flowing Foams in Porous Media. I. Incompressible Foam," J. Colloid Interface Sci. 136, 1 (1990).
W. R. Rossen, "Theory of Minimum Pressure Gradient of Flowing Foams in Porous Media. II. Effect of Compressibility," J. Colloid Interface Sci .136, 17 (1990).
W. R. Rossen, "Theory of Minimum Pressure Gradient of Flowing Foams in Porous Media. III. Asymmetric Lamella Shapes," ," J. Colloid Interface Sci. 136, 38 (1990).

Kil, R. A., et al., "Determining Trapped Gas in Foam From CT Images," SPE Journal 16 (March 2011), 24-34. doi:10.2118/124157-PA
Li, Z., Rossen, W. R., and Nguyen, Q. P., “Three-Dimensional Modeling of Tracer Experiments to Determine Gas Trapping in Foam in Porous Media," Energy & Fuels 24, 5, (2010).
Nguyen, Q. P., et al., "Determination of Gas Trapping With Foam Using X-Ray CT and Effluent Analysis," SPE Journal 14, 222-236 (2009).
Farajzadeh, R., et al., "Effect of Gas Type on Foam Film Permeability and Its Implications for Foam Flow in Porous Media," SPE 131297 presented at the SPE EUROPEC/EAGE Annual Conference and Exhibition held in Barcelona, Spain, 14–17 June 2010.

During drilling and operation of oil and gas or geothermal wells, debris can accumulate in the near-well region that greatly restricts the flow of gas and oil into the well. Acid is injected into wells in order to dissolve this debris, but the same debris prevents acid from entering the zones most in need of cleanup. Foam, injected either with or in separate slugs alternating with acid, can help even-out the injection of acid into various layers, making well cleanup more efficient. The publications listed below include experiments, simulation and analytical models for the foam-acid process.

Nguyen, Q. P., et al.: "CT Study of Liquid Diversion with Foam," SPE Production & Operations (Feb. 2009), 12-21.
Kam, S. I., et al., "Experimental Study of High-Temperature Foam for Acid Diversion," Journal Petroleum Sci. Eng. 58 138–160, (2007).
Xu, Q., and Rossen, W. R., "Laboratory Study of Gas Trapping in Foam-Acid Diversion," SPE Reservoir Evaluation and Engineering 7 (Dec. 2004), 438-448.
Cheng, L., et al., "Simulation of Dynamic Foam-Acid Diversion Processes," SPE Journal 7 (Sept. 2002), 316-324
Rossen, W.R. and Wang, M.-W., "Modeling Foams for Acid Diversion," SPE Journal 4, 92-100 (June 1999).
Robert, J.A. and Rossen, W.R., "Fluid Placement, Diversion and Pumping Strategy," in M. J. Economides and N. G. Nolte, ed., Reservoir Stimulation, 3rd ed., Prentice Hall, Englewood Cliffs, NJ, 2000.
S. C. Zeilinger, et al., "Improved Prediction of Foam Diversion in Matrix Acidization," paper SPE 29529, Proc. 1995 SPE Production Operations Symposium, Oklahoma City, OK, April 2-4, 1995.
Z. H. Zhou and W. R. Rossen, "Applying Fractional-Flow Theory to Foams for Diversion in Matrix Acidization," SPE Prod. Fac. 9, 29 (1994).
K. R. Kibodeaux, et al., "Sensitivity Study of Foam Diversion Processes for Matrix Acidization," paper SPE 28550, Proc. 1994 SPE Annual Technical Conference and Exhibition, New Orleans, LA, Sept. 26-28, 1994.
A. D. Hill and W. R. Rossen, "Fluid Placement in Matrix Acidizing," paper SPE 27982, Proc. Tulsa/SPE Centennial Petroleum Engineering Symposium, Tulsa, OK, Aug. 29-31, 1994.

Foam can also redirect the flow of gas or liquid in in situ cleanup of groundwater. The same trends in behavior observed in research on foam for oil recovery apply to environmental remediation, but the permeabilities are higher and the constraints on injection well pressure are more severe.

Mamun, C. K., et al., "Extending Foam Technology from Improved Oil Recovery to Environmental Remediation," paper SPE 77557, presented at the SPE 2002 Annual Technical Conference and Exhibition, San Antonio, 29 Sept. - 2 Oct.
Mamun, C. K., et al., "Simulating Use of Foam in Aquifer Remediation," Proceedings of the XIVth International Conference on Computational Methods in Water Resources (CMWR XIV), June 23-28 2002, Delft, The Netherlands, S.M. Hassanizadeh, R.J. Schotting, W.G. Gray, G.F. Pinder, eds., Volume 1, 867-874.

The interpretation of EOR field trials must deal simultaneously with two sources of uncertainty: uncertainty about the geological formation and about the effectiveness of the EOR process itself. Previous work addresses one issue or the other, but not (to our knowledge) both. We have considered how to evaluate the effectiveness of the process in the midst of geological uncertainty.

Fatemi, et al., "Discerning In-Situ Performance of an EOR Agent In the Midst of Geological Uncertainty: II. Fluvial-Deposit Reservoir," accepted for publication by SPE Journal 24 (June 2019), 1076-1091.
Fatemi , S. A., Jansen, J, D., and Rossen, W. R., "Discerning in-situ performance of an EOR agent in the midst of geological uncertainty I: Layer cake reservoir model," J. Petr. Sci. Eng. 158, 56–65 (2017).

Many oil and gas reservoirs are heavily fractured by the natural stresses developed over the life of the formation. These fractures greatly alter the flow patterns in the reservoir. A single fracture is itself a two-dimensional porous medium, and flow through it can be studied using network modeling. The publications below describe experimental methods for characterizing fractures (SPEFE paper), microscopic modeling of flow in fractures (SPE 28700 and 24915), and field-scale simulation of naturally fractured reservoirs (SPE 28700). A more recent article (SPE 59720) describes the connectivity threshold (like a percolation threshold) in networks of fractures obeying power-law statistics for fracture length.

Yet more recently, we have studied the generation and rheology of foam in models with a variety of roughness patters and mean aperture.

The work of Bander AlQuaimi on foam in fractures and on the appropriate capillary number for characterizing flow in fractures is summarized in the slides of a 2018 presentation. Sadly, the pdf of this presentation misses some really impressive videos Bander recorded.
AlQuaimi, B. I., and Rossen, W. R., "Foam Generation and Rheology in a Variety of Model Fractures," Energy & Fuels 33, 68–80 (2019).
AlQuaimi, B. I., and Rossen, W. R., "Study of foam generation and propagation in fully characterized physical-model fracture," J. Petroleum Sci. and Eng. 175, 1169-81 (2019).
AlQuaimi, B. I., and Rossen, W. R., "Characterizing Foam Flow in Fractures for Enhanced Oil Recovery," J. Petroleum Sci. and Eng. 175, 1160-68 (2019).
AlQuaimi, B. I., and Rossen, W. R., "Capillary Desaturation Curve for Residual Nonwetting Phase in Natural Fractures," SPE Journal 23, 3, 788-802 (2018).
Gong, J., and Rossen, W. R., "Characteristic Fracture Spacing in Primary and Secondary Recovery for Naturally Fractured Reservoirs," Fuel 223, 470–485 (2018).
Gong, J, and Rossen, W. R., "Modeling flow in naturally fractured reservoirs: effect of fracture aperture distribution on dominant sub-network for flow," Pet. Sci. 14, 138-154 (2017).
Gong, J, and Rossen, W. R., "Shape factor for dual-permeability fractured reservoir simulation: Effect of non-uniform flow in 2D fracture network," Fuel 184, 81-88 (2016).
Rossen, W.R., et al., "Connectivity and Permeability in Fracture Networks Obeying Power-Law Statistics," SPE 59720 presented at the 2000 SPE Permian Basin Oil and Gas Recovery Conference, Midland, TX, 21-23 March.
A. T. A. Kumar, et al., "Measurement of Aperture and Multiphase Flow in Fractures Using NMR Imaging," SPE Form. Eval. 9, 101 (1997).
W. R. Rossen and A. T. A. Kumar, "Effect of Fracture Relative Permeabilities on Performance of Naturally Fractured Reservoirs," paper SPE 28700, Proc. 1994 SPE International Petroleum Conference and Exhibition of Mexico, Veracruz, Mexico, Oct. 10-13, 1994.
W. R. Rossen and A. T. A. Kumar, "Single- and Two-Phase Flow in Natural Fractures," paper SPE 24915, Proc. 1992 SPE Annual Technical Conference and Exhibition, Washington, DC, Oct. 4-6, 1992.

The behavior of foam in the interconnected, network-like porespace of oilfield rock raises fundamental issues related to nonlinear transport processes in networks: in particular, transport in cases where flow requires exceeding some threshold potential gradient (a voltage or pressure gradient) along the entire flow path. Another fascinating application is the origin of shear-thickening behavior of polymer solutions in porous media in elastic turbulence. The publications listed below address several issues related to this topic.

Tang, J., et al., "New Capillary Number Definition for Micromodels: the Impact of Pore Microstructure," Water Resources Research 55, 1167-1178 (2019).
Kawale, D., et al., "Polymer conformation during flow in porous media " Soft Matter 46, 1-11 (2017).
Kawale, D., et al., "Elastic instabilities during flow of hydrolyzed polyacrylamide solution in porous media: Effect of pore shape and salt." Soft Matter 13, 765-775 (2017). DOI: 10.1039/C6SM02199A
Chen, M., Rossen, W. R., and Yortsos, Y. C.: "The Flow and Displacement in Porous Media of Fluids with Yield Stress," Chemical Engineering Science, 60 (15), August 2005, 4183-4202.
W. R. Rossen and C. K. Mamun, "Minimal Path for Transport in Networks," Phys. Rev. B 47, 11,815 (1993).
W. R. Rossen, "Size Distribution of Blocked Clusters on a Bethe Tree," J. Phys. A: Math Gen .24, 5155 (1991).
W. R. Rossen, "A New Percolation Statistic With Unusual Properties," J. Phys. A: Math. Gen. 21, L533 (1988).

Much of this research was motivated by concern about gas trapped in waste tanks at the Hanford Nuclear Reservation. The results extend to foamy sands used in some tunneling processes and in foam fracturing in the petroleum industry.

Kam, S.I., et al., "The Yield Stress of Foamy Sands," Colloids Surfaces A: Physicochem Eng. Aspects 202 (1), 53-62 (2002).
Kam, S.I. and Rossen, W.R., "The Compressibility of Foamy Sands," Colloids Surfaces A: Physicochem Eng. Aspects, 202 (1), 63-70 (2002).
Kam, S.I., et al., "Effective Compressibility of a Bubbly Slurry: I. Theory of Behavior of Bubbles Trapped in Porous Media," J. Colloid Interface Sci. 241, 248-259 (2001).
Kam, S.I, et al., "Effective Compressibility of a Bubbly Slurry: II. Fitting Numerical Results to Field Data and Implications," J. Colloid Interface Sci. 241, 260-268 (2001).
Ali, S.A., et al., "Stability of Solids-Coated Liquid Layers Between Bubbles," Industrial and Engineering Chemistry Research 39, 2742-2745 (2000).
Kam, S.I. and Rossen, W.R., "Diffusive Growth and Compressibility of Bubbles in Porous Media," Proc. EuroConference on Foams, Emulsions and Applications, Delft, The Netherlands, 5-8 June 2000.
Kam, S.I. and Rossen, W.R., "Anomalous Capillary Pressure, Stress and Stability of Solids-Coated Bubbles," J. Colloid Interface Sci. 213, 329-339 (1999).

Professional society and major governmental committees

Member, Organizing Committee, EAGE European Symposium on Improved Oil Recovery, Dresden,2007-present.
Recognized as "A Peer Apart" (reviewed 100 or more papers) by Society of Petroleum Engineers, 2007.
Review papers for Chemical Engineering Science, SPE Journal, Transport in Porous Media, Contaminant Hydrodynamics, Colloids and Surfaces A: Physicochemical and Engineering Aspects, and other journals

William Rossen

Emeritus Professor of Reservoir Engineering

+31 15 27 86038
W.R.Rossen@tudelft.nl
Faculty of Civil Engineering and Geosciences

Building 23

Stevinweg 1 / PO-box 5048

2628 CN Delft / 2600 GA Delft

Room number: 3.17

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Rossen, W.R.

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William Rossen

Emeritus Professor of Reservoir Engineering

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Maximising the yield of an oilfield

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