Research Overview

My research interests are in non-Newtonian fluid mechanics and understanding industrial processes that exploit the non-Newtonian properties of fluids. In particular I am interested in the mechanics of visco-plastic (yield stress) fluids.

Most of my projects have an environmental focus although also coming from operations arising in the petroleum industry and other natural resource industries. Significant interest and activity here centers on effective cementing of wells. These processes are important in preventing leakage of gas and other hydrocarbons from the well: during the well lifetime and at end of life (plug and abandonment). Similar techniques are used for example in CO2 storage. We also work on understanding the dynamics of methane release and entrapment from oil sands tailings ponds

Methodologically, my group conducts research that combines mathematical, experimental and computational approaches. Many of the results of our research are described in the publications of my group and our research collaborators. Research is carried out in the Complex Fluids Lab at UBC, in a strongly interdisciplinary environment. My group typically consists of 10-15 graduate students and postdocs, some internships are typically available in Summer.

Areas of interest have included the following (many of which overlap with one another):

I am always interested to hear of new applications for yield stress fluids, whether of industrial, biological, geophysical, or other origin. Industrial problems that are not suitable for academic research may be dealt with via consultancy.

Review-type articles on yield stress fluids:

  • I.A. Frigaard, “Simple Yield Stress Fluids.” Invited paper for Current Opinions on Colloidal and Interface Science, 43, 80-93, (2019)
  • I.A. Frigaard K.G. Paso, P.R. de Souza Mendes. “Bingham’s model in the oil and gas industry.” Invited review article for Rheologica Acta, 56(3), pp 259-282, (2017).
  • N. Balmforth, I. Frigaard, G. Ovarlez, “Yielding to stress: Recent developments in viscoplastic fluid mechanics”, Annual Review of Fluid Mechanics, 46, 121-146 (2014)
  • I.A. Frigaard and C. Nouar, “On the usage of viscosity regularisation methods for visco-plastic fluid flow computation” J. Non-Newtonian Fluid Mech., 127(1), pp. 1-26, (2005).

Oilfield Cementing Fluid Mechanics and Well Integrity

This has been a major activity area for my group over the past many years.

  • In primary cementing we have extensively studied laminar displacement flows in annuli, looking at the effects of standoff (eccentricity), inclination, casing movement flow rate and fluid rheology on the ability to remove drilling mud and steadily displace annular sections.
  • We have developed analogous models of annular cementing displacements for turbulent flow regimes.
  • For laminar flows we are currently supplementing the above 2D gap-averaged models with detailed 3D studies
  • We have developed simplified models for foamed cementing in annuli
  • We have 2 lab-scale annuli suitable for experimental displacements flows. One horizontal and one inclinable to any angle. We run experiments using clear lab fluids (typically weighted Carbopol, xanthan or glycerin solutions) with dimensionally similar rheological properties to wellbore fluids.
  • We are exploring methods to track the interfaces between fluid stages as displacement proceeds and then in post-placement
  • We have looked closely at displacement flows in simplified sections of the annulus (plane channels), to study the formation of residual mud layers (i.e. micro-annulus).
  • We are investigating the effects of washouts on annular cementing flows: mud conditioning and removal.
  • We are developing models for cement hydration post-placement, targeted at early stage gas-migration.
  • We are studying the mechanisms for gas invasion and how this might be influenced by cement rheology.
  • We have looked at the possibility of using chemically reactive spacer systems to improve displacement efficiency through the instigation of local instability and mixing.
  • In plug cementing, we have studied the stability of plugs that are set off-bottom addressing the question of what physical properties are needed in order for viscous pills and cement slurries to remain stationary after placement with a less dense fluid beneath.
  • In near horizontal wells we have estimated the distance that a plug may slump. We have performed similar estimates for horizontal annuli, e.g. a chemical packer
  • In pumping down the casing we extensively studied whether two given fluids displace effectively or destabilize and mix. We have developed estimates for the speed of the displacement front and the displacement efficiency, in various situations.
  • We have studied pipe flows where a fluid with large yield stress is displaced by a much less viscous Newtonian fluid, e.g. water though gelled drilling mud. This leads to residual layers on the walls and various instabilities.
  • We are currently looking at squeeze cementing fundamentals with the aim of developing a range of predictive models for the process
  • We are looking at the incidence of SCVF in Western Canada
  • We are developing well leakage models
  • We are looking at fluid mechanics aspects of P&A

Research Sponsors:

  • Schlumberger
  • NSERC
  • BC Oil & Gas Commission
  • BC OGRIS
  • PTAC
  • CFI/BCKDF
  • CNRL
  • Norwegian Research Council

Relevant Work:

    • E. Trudel, M. Bizhani, M. Zare, I.A. Frigaard, “Plug and abandonment practices and trends: a British Columbia perspective” submitted to J. Petrol. Sci. Engng., (2019).
    • O. Oladosu, A. Hasnain, P. Brown, I. Frigaard, K. Alba, “Density-Stable Displacement Flow of Immiscible Fluids in Inclined Pipes.” Physical Review Fluids, 4, 044007 (2019)
    • A. Maleki, I.A. Frigaard, “Comparing Laminar and Turbulent Primary Cementing Flows” J. Petrol. Sci. Engng., 177, 808-821, (2019).
    • A. Renteria, A. Maleki, I.A. Frigaard, B. Lund, A. Taghipour, J.D. Ytrehus. “Effects of irregularity on displacement flows in primary cementing of highly deviated wells.” J. Petrol. Sci. Engng., 172, pp. 662-680, (2019)
    • A. Etrati, I.A. Frigaard “Viscosity effects in density-stable miscible displacement flows: Experiments and simulations.” Physics of Fluids, 30, 123104 (2018).
    • A. Maleki, I.A. Frigaard “Turbulent displacement flows in primary cementing of oil and gas wells.” Physics of Fluids, 30, 123101 (2018)
    • N. Hanachi, A. Maleki, I.A. Frigaard, “A model for foamed cementing of oil and gas wells” J. Engng Math., 113(1), pp. 93–121, (2018)
    • A. Maleki, I.A. Frigaard, “Tracking fluid interfaces in primary cementing of surface casing” Phys. Fluids, 30, 093104, (2018)
    • M. Zare, I.A. Frigaard, “Buoyancy effects on micro-annulus formation: Density unstable Newtonian–Bingham fluid displacements in vertical channels.” J. non-Newt. Fluid Mech. 260, pp 145-162, (2018).
    • A. Etrati, K. Alba, I.A. Frigaard, “Two-Layer Displacement Flow of Miscible Fluids with Viscosity Ratio: Experiments.” Physics of Fluids 30, 052103 (2018).
    • M. Zare, I.A. Frigaard, “Onset of Miscible and Immiscible Fluids invasion into a Viscoplasic Fluid” Physics of Fluids 30, 063101 (2018).
    • A. Etrati, I.A. Frigaard. “A Two-Layer Model for Buoyant Inertial Displacement Flows in Inclined Pipes.” Physics of Fluids, 30(2), 022107 (2018)
    • A. Eslami, I.A. Frigaard, S.M. Taghavi, “Viscoplastic fluid displacement flows in horizontal channels: Numerical simulations.” J. non-Newt. Fluid Mech. 249, pp 79-96, (2017).
    • A. Maleki, I.A. Frigaard “Primary cementing of oil & gas wells in turbulent & mixed regimes.” J. Engng. Math., 107, pp. 201-230, (2017).
    • M. Zare, A. Roustaei, I.A. Frigaard, “Buoyancy effects on micro-annulus formation: Newtonian-Bingham fluid displacements in vertical channels.” J. non-Newt. Fluid Mech. 247, pp 22-40, (2017).
    • G.V.L. Moises, M.F. Naccache, K. Alba, I. Frigaard. "Isodense displacement flow of viscoplastic fluids along a pipe." Journal of Non-Newtonian Fluid Mechanics. 236: pp 91-103 (2016).
    • M. Zare, A. Roustaei, K. Alba, I.A. Frigaard, “Invasion of fluids into a gelled fluid column: yield stress effects.” J. non-Newt. Fluid Mech. 238, pp 212-223, (2016).
    • K. Alba, I.A. Frigaard, “Dynamics of the removal of viscoplastic fluids from inclined pipes.” J. non-Newt. Fluid Mech., 229, pp. 43-58, (2016).
    • A. Maleki, I.A. Frigaard, “Axial dispersion in weakly turbulent flows of yield stress fluids.” J. non-Newt. Fluid Mech. 235, pp 1-19, (2016).
    • A. Roustaei, I.A. Frigaard, “Residual drilling mud during conditioning of uneven boreholes in primary cementing. Part 2: Steady laminar inertial flows.” J. non-Newt. Fluid Mech., 226, pp. 1-15, (2015).
    • A. Roustaei, A. Gosselin, I.A. Frigaard, "Residual drilling mud during conditioning of uneven boreholes in primary cementing. Part 1: Rheology and geometry effects in non-inertial flows,” J. non-Newt. Fluid Mech. 220, pp. 87-98, (2015).
    • K. Alba, S.M. Taghavi, I.A. Frigaard, "Miscible density-unstable displacement flows in an inclined channel." Phys. Fluids, 26, 122104 (2014).
    • K. Alba, S.M. Taghavi, J. de Bruyn, I.A. Frigaard, "Incomplete fluid—fluid displacement of yield-stress fluids. Part 2: Highly inclined pipes", J. non-Newt. Fluid Mech. 201, 80-93 (2013)
    • K. Alba, S.M. Taghavi, I.A. Frigaard, "A weighted residual method for two-layer non-Newtonian channel flows: steady-state results and their stability", J. Fluid Mech. 731, pp. 509—544, (2013)
    • A. Roustaei, I.A. Frigaard, "The occurrence of fouling layers in the flow of a yield stress fluid along a wavy-walled channel", J. non-Newt. Fluid Mech., 198, pp. 109-124 (2013)
    • K. Alba, S.M. Taghavi, I.A. Frigaard, "Miscible density-unstable displacement flows in inclined tube", Physics of Fluids, 25(6), 067101, (2013)
    • S.M. Taghavi, I.A. Frigaard, “Estimation of mixing volumes in buoyant miscible displacement flows along near-horizontal pipes.” Can. J. Chem. Eng., accepted for publication, 91(3), pp. 399-412, (2013).
    • M. Moyers-Gonzalez, K. Alba, S.M. Taghavi, I.A. Frigaard, “A semi-analytical closure approximation for pipe flows of two Herschel--Bulkley fluids with a stratified interface.” J. non-Newt. Fluid Mech., 193, 49-67 (2013).
    • S.M. Taghavi, K. Alba, I.A. Frigaard, “Buoyant miscible displacement flows at moderate viscosity ratios and low Atwood numbers in near-horizontal ducts.” Chem. Eng. Sci., 69(1), pp. 404-418, (2012).
    • S.M. Taghavi, K. Alba, T. Seon, K. Wielage-Burchard, D.M. Martinez, I.A. Frigaard, “Miscible displacement flows in near-horizontal ducts at low Atwood number.” J. Fluid Mech., doi:10.1017/jfm.2012.26, (2012).
    • S.M. Taghavi, K. Alba, M. Moyers-Gonzalez, I.A. Frigaard, “Incomplete fluid–fluid displacement of yield stress fluids in near-horizontal pipes: Experiments and theory.” J. non-Newt. Fluid Mech., 167–168, pp. 59-74, (2012).
    • S.M. Taghavi, T. Seon, D.M. Martinez, K. Wielage-Burchard and I.A. Frigaard, “Stationary residual layers in buoyant Newtonian displacement flows.” Phys. Fluid., 23, 044105 (2011).
    • T. Burghelea and I.A. Frigaard, “Unstable parallel flows triggered by a fast chemical reaction.” J. non-Newt. Fluid Mech., 166, (9-10), pp. 500-514 (2011)
    • K. Wielage-Burchard and I.A. Frigaard, “Static wall layers in plane channel displacement flows.” J. non-Newt. Fluid Mech., 166 (5-6), pp. 245-261 (2011).
    • S.M. Taghavi, T. Seon, D.M. Martinez and I.A. Frigaard, “Influence of an imposed flow on the stability of a gravity current in a near horizontal duct.” Phys. Fluid., 22, 031702, (2010).
    • S. Malekmohammadi, M.F. Naccache, I.A. Frigaard and D.M. Martinez, “Buoyancy driven slump flows of non-Newtonian fluids in pipes.” J. of Petr. Sci. Engng., 72(3-4), PP. 236-243, (2010).
    • M. Carrasco-Teja and I.A. Frigaard, “Non-Newtonian fluid displacements in horizontal narrow eccentric annuli: Effects of motion of the inner cylinder.” J. Fluid Mech., 653, pp. 137-173 (2010).
    • S. Malekmohammadi, M. Carrasco-Teja, S. Storey, I.A. Frigaard and D.M. Martinez, “An experimental study of displacement flow phenomena in narrow vertical eccentric annuli.” J. Fluid Mech., 649, pp. 371-398 (2010).
    • I.A. Frigaard & G.A. Ngwa, “Slumping flows in annuli: design of chemical packers & cementing of subsurface pipes.” Invited paper, Trans. Por. Media, doi:10.1007/s11242-009-9467-1, (2009).
    • S.M. Taghavi, T. Seon, D.M. Martinez and I.A. Frigaard, “Buoyancy-dominated displacement flows in near-horizontal channels: the viscous limit.” J. Fluid Mech., 639, pp. 1-35, (2009).
    • M. Moyers-Gonzalez and I.A. Frigaard, “Kinematic instabilities in two-layer eccentric annular flows, part 2: shear thinning and yield stress effects, J. of Engng. Math., 65(1), pp. 25-52, (2009)
    • M. Carrasco-Teja and I.A. Frigaard, “Displacement flows in horizontal, narrow, eccentric annuli with a moving inner cylinder.” Phys. Fluids, 21 073102 (2009).
    • M. Carrasco-Teja, I. Frigaard, B. Seymour and S. Storey, “Visco-plastic fluid displacements in horizontal narrow eccentric annuli” J. Fluid Mech. 605, pp. 293-327 (2008).
    • M. Moyers-Gonzalez and I.A. Frigaard, “Kinematic instabilities in two-layer eccentric annular flows, part 1: Newtonian fluids”, J. of Engng. Math., 62(2), pp. 103-131, (2008).
    • T. Burghelea, K. Wielage-Burchard, I. Frigaard, D.M. Martinez and J, Feng. “A novel low inertia shear flow instability triggered by a chemical reaction” Phys. Fluids, 19, 083102 (2007).
    • M.A. Moyers-Gonzalez, I.A. Frigaard, O. Scherzer & T.-P. Tsai, “Transient effects in oilfield cementing flows, part 1: qualitative behaviour”, Euro. Jnl. Appl. Math. 18, pp. 477-512, (2007)
    • S. Pelipenko and I.A.Frigaard, “Two-dimensional computational simulation of eccentric annular cementing displacements.” IMA Journal of Applied Mathematics, 69: pp. 557-583, (2004).
    • S. Pelipenko and I.A.Frigaard, “Visco-plastic fluid displacements in near-vertical eccentric annuli: lubrication modelling.” J. Fluid Mech., 520, pp.343-377, (2004).
    • I.A. Frigaard and G. Ngwa, “Upper bounds on the slump length in plug cementing of near-horizontal wells” J. of Non-Newtonian Fluid Mech., 117(2-3), pp. 147-162, (2004).
    • S. Pelipenko and I.A.Frigaard, “On steady state displacements in primary cementing of an oil well.” J. of Engng. Math., 48(1), pp. 1-26, (2004).
    • S. Bittleston, J. Ferguson & I.A. Frigaard, “Mud removal and cement placement in primary cementing of an oil well.” Invited paper, J. Engineering Mathematics, 43, pp. 229-253 (2002).
    • I.A. Frigaard, M. Allouche & C. Gabard, “Setting rheological targets for chemical solutions in mud removal & cement slurry design.” Journal of Petroleum Technology, 53(8), pp. 65-66 (2001).
    • I.A. Frigaard, O. Scherzer & G. Sona, “Uniqueness & non-uniqueness in the steady displacement of two visco-plastic fluids.” ZAMM, 81(2), pp. 99-118, (2001).
    • M. Allouche, I.A. Frigaard & G. Sona, “Static wall layers in the displacement of two visco-plastic fluids in a plane slot.”, J. Fluid Mech. 424, pp. 243-277, (2000).
    • I.A. Frigaard & O. Scherzer, “The effects of yield stress variation on uniaxial exchange flows of two Bingham fluids in a cylindrical duct.” SIAM J. Appl. Math., 60(6), pp. 1950-1976, (2000).
    • H. Fenie & I.A. Frigaard, “Transient fluid motions in a simplified model for oilfield plug cementing.” Mathematical and Computer Modelling, 30(7-8), pp. 71-91, (1999).
    • I.A. Frigaard & J.P. Crawshaw, “Preventing buoyancy driven flows of two Bingham fluids in a closed pipe: fluid rheology design for oilfield plug.” J. Engng. Math., 36(4), pp. 327-348, (1999).
    • I.A. Frigaard & O. Scherzer, “Uniaxial flows of two Bingham fluids in a cylindrical duct.”
      IMA J. Appl. Math., 61, pp. 237-266, (1998).
    • I.A. Frigaard, “Stratified exchange flows of two Bingham fluids in an inclined slot.”
      J. Non-Newtonian Fluid Mech., 78, pp. 61-87, (1998).
    • S.M. Taghavi, K. Alba, I. Frigaard “Weakly-inertial Buoyant Displacement Flows In Near-horizontal Channels”, in proc. 23rd Canadian Congress of Applied Mechanics, 2011, Vancouver.
    • M. Carrasco-Teja, I.A. Frigaard & B. Seymour, “Cementing Horizontal Wells: Complete Zonal Isolation Without Casing Rotation” Society of Petroleum Engineers paper: SPE 114955, (2008).
    • D.J. Guillot, J. Desroches and I. Frigaard, “Are preflushes really contributing to mud displacement during primary cementing?” Society of Petroleum Engineers paper: SPE/IADC 105903, (2007).
    • S. Pelipenko and I.A.Frigaard, “Effective and Ineffective Strategies for Mud Removal and Cement Slurry Design.” Society of Petroleum Engineers paper number: SPE 80999, (2003).
    • I.A. Frigaard, M. Allouche & C. Gabard, “Incomplete Displacement of Viscoplastic Fluids in Slots and Pipes-Implications for Zonal Isolation.” Society of Petroleum Engineers paper number: SPE 64998, February (2001).
    • S.W. Fosso, M. Tina, I.A. Frigaard & J.P. Crawshaw, “Viscous-pill Design Methodology leads to Increased Cement Plugs Success Rates: Application and Case Studies from Southern Algeria.” Society of Petroleum Engineers paper number: SPE 62752, September 2000.
    • J.P. Crawshaw & I.A. Frigaard, “Cement Plugs; Stability and Failure by a Buoyancy-driven Mechanism.” Society of Petroleum Engineers paper number: SPE 56959, (1999).

‘

Bubbles, drops and particles in yield stress fluids:

There are different facets to this research.

  • We have carried out sedimentation experiments for particles and bubble rise experiments
  • We have made variational estimates of the critical yield stresses necessary to prevent bubbles from rising
  • We have made analytical estimates and computations for the critical yield stresses required to prevent particles from sedimenting
  • The static stability computations lead to novel methods for fractionation of particles, applied to the pulp and paper industry and elsewhere
  • We have produced analytical results relating to existence, uniqueness, symmetry of solutions, etc.
  • I have ideas I’d like to exploit further on computing suspension flows in yield stress fluids
  • We have studied the deposition of thick mined tailings in laminar flows
  • We have studied dispersion of proppant along pipe and channel geometries, as well as within a facture
  • We have studied macro-size droplet encapsulation techniques, as a means of transport
  • We have ongoing work to understand the relationship of perfect plasticity to the yield limit, when particles are held static
  • We have shown how the unyielded envelope around a particle makes the critical yield number unique and developed a heuristic rule for calculating the envelope for symmetric particles.
  • We have produced analytical results, backed up with numerical computation, that illustrate that yield limits also define energy stability limits for single particles
  • We have produced new analytical results pertaining to an anti-plane shear flow version of settling particles – essentially this is an extension of the Mosolov & Myasnikov theory.
  • We are looking at the yield limit around bubbles
  • We are looking at bubble migration across interfaces and starting to look at bubble coalescence
  • We are looking at the release of methane from oilsands tailings ponds

Research Sponsors:

  • Schlumberger
  • NSERC
  • IOSI
  • COSIA

Relevant Work:

  • E. Chaparian, A. Wachs, I.A. Frigaard, “Inline motion and hydrodynamic interaction of 2D particles in a viscoplastic fluid.” Physics of Fluids. 30(3), 033101 (2018).
  • M. Zare, I.A. Frigaard, “Onset of Miscible and Immiscible Fluids invasion into a Viscoplasic Fluid” Physics of Fluids 30, 063101 (2018)
  • E. Chaparian, I.A. Frigaard. "Cloaking: particles in a yield stress fluid." J. non-Newt. Fluid Mech. 243, pp. 47-55, (2017).
  • S. Hormozi, I. Frigaard, “Dispersion of solids in fracturing flows of yield stress fluids.” J. Fluid Mech. 830, pp. 93-137, (2017).
  • I. Frigaard, J. Iglesias, G. Mercier, C. Poschl, O. Scherzer. Critical yield numbers of rigid particles settling in Bingham Fluids and Cheeger Sets. SIAM J. Appl. Math. 77(2), pp. 638-663, (2017).
  • E. Chaparian, I.A. Frigaard, "Yield limit analysis of particle motion in a yield-stress fluid." Journal of Fluid Mechanics, 819, pp. 311-351 (2017).
  • A. Wachs, I.A. Frigaard, “Particle settling in yield stress fluids: limiting time, distance and applications.” J. non-Newt. Fluid Mech. 238, pp 189-204, (2016).
  • A. Maleki, S. Hormozi, A. Roustaei, I.A. Frigaard, "Macro-size drop encapsulation", Journal of Fluid Mechanics. (2015), vol. 769, pp. 482_521
  • A. Madani, S. Storey, J.A. Olson, I.A. Frigaard, J. Salmela and D.M. Martinez, “Fractionation of rod-like particle suspensions in a viscoplastic fluid.” Chem. Eng. Sci. 65(5), pp. 1762-1772 (2010).
  • A. Putz and I.A. Frigaard, “Creeping flow around particles in a Bingham fluid” J. non-Newt. Fluid Mech., 165(5-6), pp. 263-280 (2009).
  • A. Putz, T. Burghelea, D.M. Martinez and I.A. Frigaard, “Settling of an isolated spherical particle in a yield stress shear thinning fluid”, Physics of Fluids, 20, 033102 (2008)
  • N. Dubash and I. Frigaard, “Propagation and stopping of air bubbles in Carbopol”, J. Non-Newtonian Fluid Mech., 142, pp. 123–134, (2007)
  • N. Dubash, and I.A. Frigaard, “Conditions for static bubbles in visco-plastic fluids.” Physics of Fluids, 16(12), pp. 4319-4330, (2004).

 

Hydrodynamic instabilities in visco-plastic fluids:

This has been an area of interest for more than 25 years. It all started with my masters thesis: a long time ago, in a galaxy far, far away…

  • Methodology for linear stability in yield stress fluids, treating the yield surface perturbation correctly.
  • Energy stability methods for nonlinear stability
  • Various approximation method to derive bounds for stability
  • Plane Poiseuille flow, Hagen-Poiseuille flow
  • Taylor-Couette flow
  • Rayleigh-Bénard flow and natural convection flows
  • Rayleigh-Taylor configurations (see plug cementing and exchange flows)
  • Experimental studies of Hagen-Poiseuille flow and empirical rules for transition
  • Numerous studies of multi-layer flow stability.
  • Exposing the relationship between the yield limit and energy stability for internal flows
  • Use of energy stability for thermal switching
  • Pulsed plumes in natural convection with localized heating
  • Energy stability for the stopping of a settling particle

Research Sponsors:

  • Schlumberger
  • NSERC

Relevant Work:

  • I.A. Frigaard, A. Renteria, “Stability of flows with the BMP model in the yield stress limit” submitted to the Korea and Australia Rheology Journal, (2019).
  • I.A. Frigaard, C. Nouar, “Onset of flow in a vibrated thin viscoplastic layer.” J. non-Newtonian Fluid Mech., 266, 95-101, (2019)
  • I. Karimfazli, I.A. Frigaard, “Flow, onset and stability: qualitative analysis of yield stress fluid flow in enclosures.” J. non-Newt. Fluid Mech. 238, pp. 224-232, (2016).
  • A. Wachs, I.A. Frigaard, “Particle settling in yield stress fluids: limiting time, distance and applications.” J. non-Newt. Fluid Mech. 238, pp 189-204, (2016).
  • I. Karimfazli, I. Frigaard, A. Wachs, “Thermal plumes in viscoplastic fluids: flow onset and development.” J. Fluid Mech. 787, pp 474 – 507, (2016).
  • I. Karimfazli, I. Frigaard, A. Wachs, “A novel heat transfer switch using the yield stress.” Journal of Fluid Mechanics, 783, pp 526 - 566 (2015).
  • I. Karimfazli I.A. Frigaard, "Natural convection flows of a Bingham fluid in a long vertical channel", J. non-Newt. Fluid Mech., 201, pp. 39-55, (2013).
  • K. Alba, S.M. Taghavi, I.A. Frigaard, "A weighted residual method for two-layer non-Newtonian channel flows: steady-state results and their stability", J. Fluid Mech. 731, pp. 509—544, (2013)
  • S. Hormozi and I.A. Frigaard, “Nonlinear stability of a visco-plastically lubricated viscoelastic fluid flow.” J. non-Newt. Fluid Mech., 169–170, pp. 61-73, (2012).
  • A. Madani, D.M. Martinez, J.A. Olson, I.A. Frigaard, “The stability of spiral Poiseuille flows of Newtonian and Bingham fluids in an annular gap.” J. non-Newt. Fluid Mech., doi.org/10.1016/j.jnnfm.2012.02.007, (2012).
  • M. Moyers-Gonzalez, I.A. Frigaard and C. Nouar, “Stable two-layer flows at all Re; visco-plastic lubrication of shear-thinning and viscoelastic fluids.” J. non-Newt. Fluid Mech., 165, (23-24), pp. 1578-1587, (2010).
  • M. Moyers-Gonzalez and I.A. Frigaard, “Kinematic instabilities in two-layer eccentric annular flows, part 2: shear thinning and yield stress effects, J. of Engng. Math., 65(1), pp. 25-52, (2009)
  • B. Güzel, I. Frigaard, D.M. Martinez “Predicting laminar–turbulent transition in Poiseuille pipe flow for non-Newtonian fluids”, Chem. Eng. Sci. 64(2), pp. 254-264, (2009).
  • C. Metivier, I.A. Frigaard and C. Nouar, “Non-linear stability of the Bingham Rayleigh-Benard flow”, J. non-Newtonian Fluid Mech., 158(1-3), pp. 127-131, (2009).
  • B. Guzel, T. Burghelea, I. A. Frigaard and D. M. Martinez, “Observation of laminar-turbulent transition of yield stress fluid in Hagen-Poiseuille flow”, J. Fluid Mech., 627, pp. 97- 128 (2009).
  • M. Moyers-Gonzalez and I.A. Frigaard, “Kinematic instabilities in two-layer eccentric annular flows, part 1: Newtonian fluids”, J. of Engng. Math., 62(2), pp. 103-131, (2008).
  • T. Burghelea, K. Wielage-Burchard, I. Frigaard, D.M. Martinez and J, Feng. “A novel low inertia shear flow instability triggered by a chemical reaction” Phys. Fluids, 19, 083102 (2007).
  • J.Y. Zhang, I. Frigaard and D. Vola, “ Yield stress effects on Rayleigh-Benard convection” J. Fluid Mech. 566, pp. 389-419, (2006).
  • M.P. Landry, I.A. Frigaard & D.M. Martinez, “Stability and instability of Taylor-Couette flows of a Bingham fluid” J. Fluid Mechanics, 560, pp. 321-353, (2006).
  • I.A. Frigaard and C. Nouar, “On the usage of viscosity regularisation methods for visco-plastic fluid flow computation” J. Non-Newtonian Fluid Mech., 127(1), pp. 1-26, (2005).
  • M. Moyers-Gonzalez, I.A. Frigaard and C. Nouar, “Nonlinear stability of a visco-plastically lubricated shear flow.” Journal of Fluid Mechanics, 506, pp.117-146, (2004).
  • I.A. Frigaard and C. Nouar, “On three-dimensional linear stability of Poiseuille flow of Bingham fluids.” Physics of Fluids, 15(10), pp. 2843-2851, (2003).
  • I.A. Frigaard and C. Nouar, “Predicting Transition to Turbulence in Well Construction Flows.” Society of Petroleum Engineers paper number: SPE 81150, (2003).
  • C. Nouar & I.A. Frigaard, “Nonlinear stability of Poiseuille flow of a Bingham fluid.” J. Non-Newtonian Fluid Mech., 100, pp. 127-149, (2001).
  • I.A. Frigaard, “Super-stable parallel flows of multiple visco-plastic fluids.” J. Non-Newtonian Fluid Mech., 100, pp. 49-76, (2001).
  • I.A. Frigaard, S.D. Howison & I.J. Sobey, “On the stability of Poiseuille flow of a Bingham fluid.” J. Fluid Mech., 263, pp. 133-150, (1994).

 

Displacement flows, dispersion and mixing with generalised Newtonian fluids:

The majority of this work has been in conjunction with the study of oilfield cementing displacements and waxy crude oil restarts.

Research Sponsors:

  • Schlumberger
  • NSERC

See also:

  • J.Y. Zhang and I.A. Frigaard, “Dispersion effects in the miscible displacement of two fluids in a duct of large aspect ratio”, Journal of Fluid Mechanics, 549, pp. 225–251, (2006)
  • A. Maleki, I.A. Frigaard, “Axial dispersion in weakly turbulent flows of yield stress fluids.” J. non-Newt. Fluid Mech. 235, pp 1-19, (2016).

Mathematical Modelling of Industrial Processes:

Various processes have attracted my attention over the years. Some of this work is undertaken as consulting.

  • Spray-forming of Aluminium billets
  • Well control
  • Czrochalski crystal growth
  • Image processing using nonlinear diffusion filters
  • Injection molding
  • Oilfield cementing
  • Waxy crude oil pipelining
  • Pile grouting
  • Sand control/gravel packing
  • Fracturing flows
  • Fouling
  • Solidification of alloys
  • Fiber flows in pulp and paper processing
  • Different process-related hydrodynamic stabilities

Research Sponsors:

  • NSERC
  • Firebird
  • Schlumberger
  • MITACS

Relevant Work: (please also consult the other specific sections)

  • P. Sarmadi, I.A. Frigaard, “Stable core-annular flows in inaccessible domains via a triple-layer configuration.” Chem. Eng. Sci. X, 3, 100028, (2019)
  • A. Sarraf-Shirazi, I.A. Frigaard, “A Three Layer Model for Solids Transport in Pipes”, Chem. Eng. Sci., 205, 374-390, (2019)
  • P. Sarmadi, S. Hormozi, I.A. Frigaard. “Flow development and interface sculpting in stable lubricated pipeline transport.” J. non-Newt. Fluid Mech. 261, pp 60-80, (2018).
  • S. Hormozi, I. Frigaard, “Dispersion of solids in fracturing flows of yield stress fluids.” J. Fluid Mech. 830, pp. 93-137, (2017).
  • P. Sarmadi, S. Hormozi, I.A. Frigaard. “Triple-layer configuration for stable high-speed lubricated pipeline transport.” Physical Review Fluids, 2, 044302, (2017).
  • G. Goyal, G. Elfring, I. Frigaard, Rheology and flow studies of drag reducing gravel packing fluids. Rheologica Acta 56(11), pp. 905-914 (2017)
  • I.A. Frigaard K.G. Paso, P.R. de Souza Mendes. “Bingham's model in the oil and gas industry.” Invited review article for Rheologica Acta, 56(3), pp 259-282, (2017).
  • A. Maleki, S. Hormozi, A. Roustaei, I.A. Frigaard, "Macro-size drop encapsulation", Journal of Fluid Mechanics. (2015), vol. 769, pp. 482_521
  • K. Pougatch and I.A. Frigaard, “Thin film flow on the inside surface of a horizontally rotating cylinder: steady state solutions and their stability.” Phys. Fluids., 23, 022102 (2011)
  • N. Dubash, I.A. Frigaard and B. Stoeber, “An oscillatory flow phenomenon in microtube flows of thermally responsive fluids”, J. Engng. Math., DOI: 10.1007/s10665-010-9404-x
  • A. Guha and I.A. Frigaard, “On the stability of plane Couette-Poiseuille flow with uniform crossflow.” J. Fluid Mech., 656, pp. 417-447 (2010).
  • A. Wachs, G. Vinay & I. Frigaard, “1.5D model for start up of weakly compressible viscoplastic and thixotropic fluid in pipelines”, J. non-Newt. Fluid Mech., 159(1-3), pp. 81-94, (2009).
  • C.S. Bohun, I. Frigaard, H. Huang & S. Liang, “A Semi-Analytical Model for InSb Crystal Growth.” SIAM J. Appl. Math., SIAM J. Appl. Math. 66(5), pp. 1533-1562, (2006).
  • I.A.Frigaard & O. Scherzer, “Herschel-Bulkley diffusion filtering: non-Newtonian fluid mechanics in image processing” ZAMM, 86(6), pp. 474-494, (2006).
  • G. Lewis, I. Frigaard, H. Huang, T. Myers, R. Westbrook & M. Carrasco-Teja, “Simple models for an injection molding system”, Can. Appl. Math. Quart., 12(4), pp. 491, (2004).
  • J. Olson, I.A. Frigaard, C. Chan and J.P. Hämäläinen, “Modelling a turbulent fibre suspension flowing in a planar contraction: the 1D” Int. J. Multi-phase Flows, 30(1), pp. 51-66, (2004).
  • I.A.Frigaard, G. Ngwa and O. Scherzer, “On effective stopping time selection for visco-plastic nonlinear BV diffusion filters.” SIAM J. Appl. Math., 63(6), pp. 1911-1934, (2003).
  • I.A. Frigaard & O. Scherzer, “Spraying the perfect billet.” SIAM J. Appl. Math., 57(3), pp. 649-682, (1997).
  • I.A. Frigaard, “Solidification of Spray-formed Aluminium billets; heat flow in the bulk deposit.” J. Engng. Math. 31, pp. 411-437, (1997).
  • I.A. Frigaard, “Solidification of spray-formed Aluminium Billets; an Analysis of Thin layering Effects.” J. Engng. Math. 30, pp. 417-443, (1996).
  • I.A. Frigaard, “Growth dynamics of spray-formed Aluminium billets, part 2; transient billet growth.” J. Materials Processing and Manufacturing Science, 3(3), pp. 257-275, (1995).
  • I.A. Frigaard, “The dynamics of spray-formed billets.” SIAM J. Appl. Math., 55(5), pp. 1161-1203, (1995).
  • I.A. Frigaard, “Growth dynamics of spray-formed Aluminium billets, part 1; steady state crown shapes.” J. Materials Processing and Manufacturing Science, 3(2), pp. 173-192, (1994).
  • A.C Fowler, I.A. Frigaard & S.D. Howison, “Temperature Surges in Current-limiting Circuit Devices.” SIAM J. Appl. Math., 52(4), pp. 998-1011, (1992).
  • A. Guha and I.A. Frigaard, “Stability analysis of plane Couette-Poiseuille flow in presence of cross-flow”, proceedings of the Canadian Society for Mechanical Engineering, Forum, held in Victoria, June 7 – 9, 2010.
  • G. Vinay, A. Wachs and I. Frigaard, “Start-up of gelled waxy crude oil pipelines: a new analytical relation to predict the restart pressure.” Soc. Petrol. Eng. paper number: SPE 122443, (2009).
  • C.S. Bohun, I.A. Frigaard, H.X. Huang “A perturbation model for the growth of type III-V compound crystals” proceedings of Conference on Differential Equations and Asymptotic Theory in Mathematical Physics, OCT 20-29, 2003 Wuhan Univ, Wuhan, Peoples Republic China. Appeared in Differential Equations & Asymptotic Theory Mathematical Physics Book Series: Series In Analysis, Vol. 2 Pages: 263-279 Published: 2004
  • I.A. Frigaard, N.L. Humphries, I.M. Rezmer-Cooper and J.P. James, “High Penetration Rates: Hazards and Well Control.” Society of Petroleum Engineers paper number: SPE 37593, (1997).
  • I.A. Frigaard, “Controlling the Growth of Aluminium Spray-formed Billets.” in Sprayforming, eds. K. Bauckhage and V. Uhlenwinkel, Universität Bremen, ISBN 3-88722-388-8, pp. 29-43, (1997).
  • I.M. Rezmer-Cooper, J. James, P. Fitzgerald, A.B. Johnson, D.H. Davies, I.A. Frigaard, S. Cooper, Y. Luo and P. Bern, “Complex Well Control Events Accurately Represented by an Advanced Kick Simulator.” Society of Petroleum Engineers paper number: SPE 36829, (1996).
  • I.A. Frigaard, “Growing Spray-formed Aluminium Billets.” Proceedings, ECMI94 conference, ed. H. Neunzert, Wiley/Teubner, pp. 389-396, (1996).

 

Visco-plastic lubrication flows:

This has been a major activity area for my group over the past many years.

  • With inelastic fluids we can achieve stable multi-layer shear flows at high Re by placing an unyielded layer at the interface
  • We have had a lab-scale multi-layer flow loop dedicated to this research. In this we have run experiments using clear lab fluids (typically weighted Carbopol, xanthan or glycerin solutions) with dimensionally similar rheological properties to industrial fluids, to establish proof of concept.
  • For core-annular flows we have a wide range of experimental flows showing this stability, including visco-elastic core fluids
  • We have proven linear and nonlinear stability
  • We have studied start-up and development lengths
  • With special configurations we can achieve linearly stable flows at infinite Re!
  • We are developing our ideas for how to engineer hydrodynamically stable core-annular oil-water flows
  • We worked on controlling shape of core fluids, stably frozen in after controlled oscillation.
  • The same methodology leads to droplet encapsulation, but with the novelty of no capillary length-scale!
  • We are looking at applications in food industry, polymer processing, paper coating, oil and gas.

Research Sponsors:

  • NSERC

Relevant Work:

  • P. Sarmadi, I.A. Frigaard, “Stable core-annular flows in inaccessible domains via a triple-layer configuration.” Chem. Eng. Sci. X, 3, 100028, (2019)
  • P. Sarmadi, S. Hormozi, I.A. Frigaard. “Flow development and interface sculpting in stable lubricated pipeline transport.” J. non-Newt. Fluid Mech. 261, pp 60-80, (2018).
  • P. Sarmadi, S. Hormozi, I.A. Frigaard. “Triple-layer configuration for stable high-speed lubricated pipeline transport.” Physical Review Fluids, 2, 044302, (2017).
  • A. Maleki, S. Hormozi, A. Roustaei, I.A. Frigaard, "Macro-size drop encapsulation", Journal of Fluid Mechanics. (2015), vol. 769, pp. 482_521
  • S. Hormozi, G. Dunbrack, I. Frigaard, "Transient behaviour and shaped interface formation in non-equilibrium multilayer flows", Phys. Fluids, 26 pp. 093101 (2014).
  • S. Hormozi and I.A. Frigaard, “Nonlinear stability of a visco-plastically lubricated viscoelastic fluid flow.” J. non-Newt. Fluid Mech., 169–170, pp. 61-73, (2012).
  • S. Hormozi, D.M. Martinez, I.A. Frigaard, “Stable core-annular flows of viscoelastic fluids using the visco-plastic lubrication technique.” J. non-Newt. Fluid Mech., 166 (23–24), pp. 1356-1368 (2011).
  • S. Hormozi, K. Wielage-Burchard and I.A. Frigaard, “Entry, start up and stability effects in visco-plastically lubricated pipe flows.” J. Fluid Mech., 166 (5-6), pp. 262-278 (2011).
  • S. Hormozi, K. Wielage-Burchard and I.A. Frigaard, “Multi-layer channel flows with yield stress fluids.” J. non-Newt. Fluid Mech. 166, (5-6), pp. 262-278 (2011).
  • M. Moyers-Gonzalez, I.A. Frigaard and C. Nouar, “Stable two-layer flows at all Re; visco-plastic lubrication of shear-thinning and viscoelastic fluids.” J. non-Newt. Fluid Mech., 165, (23-24), pp. 1578-1587, (2010).
  • C.K. Huen, I.A. Frigaard and D.M. Martinez, “Experimental studies of multi-layer flows using a visco-plastic lubricant”, J. Non-Newtonian Fluid Mech., 142, pp. 150–161, (2007).
  • M. Moyers-Gonzalez, I.A. Frigaard and C. Nouar, “Nonlinear stability of a visco-plastically lubricated shear flow.” Journal of Fluid Mechanics, 506, pp.117-146, (2004).
  • M. Moyers-Gonzalez and I.A. Frigaard, “Numerical solution of duct flows of multiple visco-plastic fluids” J. Non-Newtonian Fluid Mech., 127, pp. 227-241, (2004).
  • I.A. Frigaard, “Super-stable parallel flows of multiple visco-plastic fluids.” J. Non-Newtonian Fluid Mech., 100, pp. 49-76, (2001).

 

Restarting waxy crude oil pipelines:

This has been an active collaboration with colleagues from IFP and from PUC-Rio.

  • We have identified 3 regimes for start-up, dominated by friction, compressibility and/or acoustic propagation. Most of these timescales for start-up are anyway fast compared with the actual displacement times
  • We have also computed compressible displacement flows, using axisymmetric (2D) and reduced models.
  • The effects of thixotropy have been explored
  • Sometimes it is possible to restart pipelines below the incompressible pressure limit, combining thixotropic and compressible effects
  • We are studying this in a reduced model, to try to derive semi-analytical predictions of start-up
  • We are investigating different models for compressibility, due to different bubble distributions in the oil phase, and seeing how this affects the yield stress

Research Sponsors:

  • NSERC

Relevant Work:

  • G. Moises, L. Alencar, M. Naccache, I.A. Frigaard. “The influence of thixotropy in start-up flow of yield stress fluids in a pipe.” J. Petrol. Sci. Engng. 171, pp 794-807, (2018)
  • G.V.L. Moises, M.F. Naccache, K. Alba, I. Frigaard. "Isodense displacement flow of viscoplastic fluids along a pipe." Journal of Non-Newtonian Fluid Mechanics. 236: pp 91-103 (2016).
  • A. Wachs, G. Vinay & I. Frigaard, “1.5D model for start up of weakly compressible viscoplastic and thixotropic fluid in pipelines”, J. non-Newt. Fluid Mech., 159(1-3), pp. 81-94, (2009).
  • I. Frigaard, G. Vinay and A. Wachs “Compressible displacements flows of waxy crude oils in long pipeline startup flows”, J. non-Newtonian Fluid Mech., 147, (1-2), pp. 45-64 (2007).
  • G. Vinay, A. Wachs and I. Frigaard, “Start-up transients and efficient computation of isothermal waxy crude oil flows” J. non-Newtonian Fluid Mech., 143, pp. 141-156, (2007).
  • G. Vinay, A. Wachs and I. Frigaard, “Start-up of gelled waxy crude oil pipelines: a new analytical relation to predict the restart pressure.” Soc. Petrol. Eng. paper number: SPE 122443, (2009).