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):
- Oilfield cementing fluid mechanics and well integrity
- Bubbles and particles in yield stress fluids
- Hydrodynamic instabilities in visco-plastic fluids
- Displacement flows, dispersion and mixing with generalised Newtonian fluids
- Mathematical Modelling of Industrial Processes
- Visco-plastic lubrication flows
- Restarting waxy crude oil pipelines
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
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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
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
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
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
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