This research project is co-funded by the European Union (European Social Fund) and Greek national resources in the frameworks of the “**Archimedes III: Funding of Research Groups in TEI of Athens**” (MlS 379389), a RTD project of the “Education & Lifelong Learning” Operational Program

** Summary**

**Two-phase flow in porous media** (**2ph pm**) occupies a central position in physically important processes with practical applications in the energy and environmental sector industries.

To date, the **characterization and modeling of multiphase flows in p.m. **has delivered promising theoretical and experimental results over a **hierarchy of scales** (pore-to-production). Nevertheless, integration across those scales remains an outstanding problem. Likewise, technological progress has enabled laboratory studies to expose latent flow mechanisms; pore-scale phenomena and critical interstitial physical quantities can now be identified and assessed digitally, computationally or experimentally. At the same time, pragmatic sustainability issues on energy production/management shifted “recovery increase” trends into “process efficiency optimization” scopes and targets. As a consequence, new challenges emerge within a wide spectrum of technological problems, extending from laboratory scales, e.g. design systematic protocols for regular/special core analysis (R/SCAL) for data collection/interpretation, to industrial scales, e.g. unconventional/ enhanced oil recovery (EOR) /carbon capture & sequestration (CCS), soil & aquifer pollution & remediation or operation of trickle-bed reactors.

Without neglecting the fact that the majority of industrial applications of two-phase flow in macroscopically heterogeneous porous media are based on inherently transient processes, to understand the physics of such processes in a deeper context, we need first to understand the stationary case, **steady-state two-phase flow in p.m**.

* DeProF* is a mechanistic model for two-phase flow in p.m.; it accounts for the pore-scale mechanisms and the network wide cooperative effects, and is sufficiently simple and fast for practical purposes. It is based on the concept of decomposition into prototype flows and scaling-up pore level phenomena into the macroscopic flow.

**Scope** of the ** ImproDeProF project** is to further develop the

(1) **Disconnected flow** - A complete, rigorous and true-to-mechanism modeling of two-phase flow should incorporate the flow of disconnected non-wetting phase (NWP), a substantial and sometimes prevailing flow pattern. The flow of disconnected NWP is observed in artificial, stochastic and virtual pore network models, as well as in real p.m. and extends over regimes spanning large and small NWP ganglion dynamics, to NPW droplet flow, to emulsion type flows.

(2) **Independent variables** – The conventional approach of saturation-dependent relative permeability cannot handle a specific-enough representation of the process phenomenology across the entire spectrum of flow conditions. The set of independent variables is reappraised, considering the inherent, **flow rate dependencies** of the process.

(3) **Inherent degrees of freedom** - The process itself is a **complex hierarchical system**, strongly affected by factors residing at several different length scales and/or occurring over widely different time scales. The correlated and cross-dependent behavior of individual small-scale components (e.g. interactions between the pore scale geometry the disconnected NWP and the connected WP) induces a dynamic system behavior at the next scale (e.g. core scale) and so on (e.g. formation scales). **Ergodicity** is nested within the physics of multi-phase flows and is reflected on the incessant reconfiguration of interstitial flow structures even under steady-state flow conditions. Recent simulations suggest that inherent degrees of freedom depend strongly on the extent of the NWP disconnectedness.

Below you may find a list of recent publications produced within the framework of the *ImproDeProF* project, delineating latest advances, indicative applications and future challenges in the development of a tentative theory for two-phase flow in porous media, namely the DeProF theory.

e-mail: marval@uniwa.gr personal webpage: http://users.uniwa.gr/marval/index_en.html

**News** (updated March, 2019)

Formation of the Hellenic National InterPore Chapter --> https://www.interpore.org/news/797-formation-of-the-hellenic-national-interpore-chapter

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**ImproDeProF Project results** (updated July, 2019)

**Working Papers **

- Valavanides, M.S., Mascle, M., Youssef, S., Vizika, O. (2019) "Steady-State Two-Phase Flow in Porous Media: Laboratory Validation of Flow Dependent Relative Permeability Scaling", http://users.uniwa.gr/marval/publ/Valavanides_etal_SCA2019-005.pdf
- Valavanides, M.S. (2018) "Estimation of the number density of configurational microstates in two-phase flows in model porous media", http://users.uniwa.gr/marval/publ/Valavanides_Entropy2018.pdf

**Journal Papers **

- Valavanides, M.S. (2018) "Review of steady-state two-phase flow in porous media: independent variables, universal energy efficiency map, critical flow conditions, effective characterization of flow and pore network"
*Transp. in Porous Media***123**(1), pp. 42-99, https://doi.org/10.1007/S11242-018-1026-1, http://users.uniwa.gr/marval/publ/Valavanides_TiPM_ms918.pdf, open read-only access http://rdcu.be/IU0D - Valavanides, M.S. (2018) "Oil fragmentation, interfacial surface transport and flow structure maps for two-phase flow in model pore networks. Predictions based on extensive,
*DeProF*model simulations."*Oil & Gas Science and Technology - Rev. IFP Energies nouvelles***73**(6), pp. 1-36, https://doi.org/10.2516/ogst/2017033 also http://users.uniwa.gr/marval/publ/Valavanides_OGST_73_2018.pdf - Kamvyssas, G., Valavanides, M.S. (2017) "Analytical Solution of the Saturated Flow Problem in 7-Spot, 2D Geometries"
*Fresenius Environmental Bulletin***26**(9), pp. 5523-5528, http://users.uniwa.gr/marval/publ/Kamvyssas_Valavanides_FEB_26_2017.pdf - Valavanides, M.S., Daras, T. (2016) “Definition and Counting of Configurational Microstates in Steady-State Two-Phase Flows in Pore Networks”
*Entropy***18**(054), pp. 1-28, http://www.mdpi.com/1099-4300/18/2/54, http://dx.doi.org/10.3390/e18020054 - Valavanides, M.S., Totaj, E., Tsokopoulos, M. (2016) “Energy Efficiency Characteristics in Steady-State Relative Permeability Diagrams of Two-Phase Flow in Porous Media”
*Journal of Petroleum Science and Engineering***147**, pp. 181-201 http://dx.doi.org/10.1016/j.petrol.2016.04.039 - Tsakiroglou, C.D., Aggelopoulos, C.A., Terzi, K., Avraam, D.G., Valavanides, M.S. (2015) "Steady-state two-phase relative permeability functions of porous media: A revisit" International Journal of Multiphase Flow
**73**pp. 34–42, http://dx.doi.org/10.1016/j.ijmultiphaseflow.2015.03.001 - Valavanides, M.S., Skouras, E.D. (2014) “Rational solitary well spacing in soil remediation processes”
*Fresenius Environmental Bulletin***23**(11) pp.2847-2851, http://users.uniwa.gr/marval/publ/Valavanides_Skouras_FEB_23_11_2014.pdf - Valavanides, M.S. (2014) “Portfolios as off-equilibrium processes: similarities and affinities”
*Procedia - Social and Behavioral Sciences***119**pp.539-548, http://dx.doi.org/10.1016/j.sbspro.2014.03.060 - Valavanides, M.S. (2012) “Steady-State Two-Phase Flow in Porous Media: Review of Progress in the Development of the DeProF Theory Bridging Pore- to Statistical Thermodynamics- Scales”
*Oil & Gas Science and Technology***67**(5) pp. 787-804, http://dx.doi.org/10.2516/ogst/2012056 also http://users.uniwa.gr/marval/publ/Valavanides_OGST_67_2012.pdf

**Conference Proceedings **

- Valavanides, M.S., Mascle, M., Youssef, S., Vizika, O. (2019) "Steady-State Two-Phase Flow in Porous Media: Laboratory Validation of Flow Dependent Relative Permeability Scaling", http://users.uniwa.gr/marval/publ/Valavanides_etal_SCA2019-005.pdf
- Valavanides, M.S. (2018) "True to mechanism, flow dependent relative permeability scaling functional form for steady-state 2-phase flows in p.m.",
*International Symposium of the Society of Core Analysts*,*SCA2018-066,*Trondheim, Norway, August 27-30, http://users.uniwa.gr/marval/publ/Valavanides_SCA2018_066.pdf - Valavanides, M.S. (2018) "The taxonomy of steady-state two-phase flows in porous media",
*International Symposium of the Society of Core Analysts*,*SCA2018-123,*Trondheim, Norway, August 27-30, http://users.uniwa.gr/marval/publ/Valavanides_SCA2018_123.pdf - Valavanides, M.S. (2015) "ImproDeProF Project: Recent Advances and New Challenges in the development of the DeProF tentative theory for steady-state two-phase flow in porous media" SCinTE 2015, Athens, Nov. 5-7
- Valavanides, M.S., Skouras, E.D., Kalarakis, A.N., Burganos, V.N. (2015) "Integration of Flow Dependent Relative Permeability Maps for Two-Phase Flow in Porous Media into the COMSOL Multiphysics
^{TM}Earth Science Module"*COMSOL 2015 Conference*, Grenoble, Oct. 14-16 - Skouras, E.D., Kalarakis, A.N., Valavanides, M.S., Burganos, V.N. (2015) "Two-Phase Flow Calculations in Pore Unit-Cells Implementing Mixed FEM/Lattice-Boltzmann Simulators"
*COMSOL 2015 Conference*, Grenoble, Oct. 14-16 - Daras, T., Valavanides, M.S. (2015) "Number of Microstates and Configurational Entropy for Steady-State Two-Phase Flows in Pore Networks" AIP Conf. Proc.
**1641**pp. 147-154, http://dx.doi.org/10.1063/1.4905973 - Valavanides, M.S., Totaj, E., Tsokopoulos, M. (2015) “Retrospective examination of relative permeability data on steady-state two-phase flow in porous media” in N.E. Mastorakis
*et al.*(Editors) "*Proceedings of the International Conference on Mechanics, Materials, Mechanical & Chemical Engineering (MMCE 2015)"*ISBN 978-1-61804-295-8, pp.156-165 - Valavanides, M.S. (2014) "Operational Efficiency Map and Flow Characterization for Steady-State Two-Phase Flows in Porous Media", paper SCA2014-047,
*International Symposium of the Society of Core Analysts,*Avignon, France, September 8-1, http://users.uniwa.gr/marval/publ/Valavanides_SCA2014-047.pdf - Tsakiroglou, C.D., Aggelopoulos, C.A., Terzi, K., Avraam, D.G., Valavanides, M.S. (2014) "Explicit correlation of the steady-state two-phase relative permeability functions of porous media with the local flow rates"
*Society of Core Analysts Symposium - SCA2014,*Avignon, France, September 8-14

**Conference extnd abstracts / posters **

- Valavanides, M.S. (2017) "Steady-state two-phase flow in porous media: independent variables, critical flow conditions, universal energy efficiency map and effective, flow and system characterization."
*PoreLab Group Kick-off Meeting*, Oslo, Norway, Sept. 2017 - Valavanides, M.S. (2016) "A new methodology for effective, two-phase flow characterization of pore network structures"
*InterPore2016, 8*, Cincinnati, OH USA, May 9-12^{th}International Conference on Porous Media - Valavanides, M.S., Daras, T. (2015) "Configurational Entropy Maps for Steady-State Two-Phase Flows in Pore

Networks implementing the DeProF model algorithm"*InterPore2013, 7*, Padova, Italy, May 18-21^{th}International Conference on Porous Media - Valavanides, M.S. (2013) "Capillary vs Viscous Flow: Introduction of a Normative Methodology for the Characterization of 2-Ph Flow in P.M."
*6*, Kavala, Greece, September 9-10^{th}Panhellenic Symposium on Porous Media - Valavanides, M.S., Kamvyssas, G., Totaj, E. (2013) "Retrospective Examination of Relative Permeability Data and Operational Efficiency Aspects for Steady-State 2-Phase Fow in Porous Media"
*6*, Kavala, Greece, September 9-10^{th}Panhellenic Symposium on Porous Media - Tsakiroglou, C., Aggelopoulos, C.A., Terzi, K., Avraam, D.G., Valavanides, M.S. (2013) “Dependence of the Steady-State Relative Permeability Functions of Porous Media on Flow Rates: A Revisit”
*PSPM-6, 6*, Kavala, Greece, September 9-10^{th}Panhellenic Symposium on Porous Media - Valavanides, M.S., Kamvyssas, G. (2013) “Operational Efficiency Map of Steady-State Two-Phase Flow in Porous Media Processes”
*InterPore2013, 5*, Prague, Czech Rep., May 21-24^{th}International Conference on Porous Media

**Other **

- Valavanides, M.S. (2013) "Transformer for steady-state relative permeability data" - You may download the hyperlinked excel file in your PC, input your steady-state relperm data and discover what are the local optimum operation conditions in your process, what is the character of flow (capillary/viscous) for each condition and what is the maximum attainable process operational efficiency in your system. In case you need help just send an email to marval@uniwa.gr
- Valavanides, M.S., Totaj, E., Tsokopoulos, M. (2015) "Retrospective Examination of Relative Permeability Data on Steady-State 2-Ph Flow in Porous Media Transformation of Rel-Perm Data (k
_{ro}, k_{rw}) into Operational Efficiency Data (f_{EU})" ImproDeProF /Archimedes III, project internal report http://users.uniwa.gr/marval/ArchIII/retrorelperm.pdf. - Valavanides, M.S. (2013) “Comments on [Analysis of Fundamentals of Two-Phase Flow in Porous Media Using Dynamic Pore-Network Models: A Review by V. Joekar-Niasar and S. M. Hassanizadeh (2012)
*Crit. Rev. Env. Sci. Tech**.*42:18 pp. 1895–1976]” manuscript submitted to*Crit. Rev. Env. Sci. Tech.,*unsolicited - Valavanides, M.S. (2012) “From Pore to Network to DeProF TO aSaPP: Development of a Complete Theory for Steady-State Two Phase Flow in Porous Media, Spanning Pore- to Statistical Thermodynamics- Scales”,
*Gordon Research Conference on ‘Flow and Transport in Porous Media’*, Les Diablerets, Switzerland, June 24-29

**Past Events**

Minisymposium MS 1.12:** "Simulation (Lab, Virtual) As a Source of New Knowledge"**

held within the 8^{th} International Conference on Porous Media, May 9-12, Cincinnati, Ohio, USA

Co-organizers: M.S. Valavanides (TEI Athens), A. Hansen (NTNU), V.N. Burganos (FORTH/ICE-HT)

The mini-symposium focused on simulations within a virtual or real model domain under pre-selected or controlled conditions, in order to observe and retrieve data and measurable information within flow in porous media phenomena. The purpose is to grasp a representative image and give a better understanding of the physics of the process at the REV scale, provide insight into the pertinent mechanisms and then integrate this knowledge (not just information) into sound theoretical inferences on the macroscopic description of the processes.

Topics addressed:

(a) Implementation of current simulation technologies into providing a better understanding of the phenomenology of multi-phase flow in porous medium (understanding by simulating),

(b) Design of efficient experimental protocols that will bridge modelling with data interpretation and application into improved functional description and characterization of flow and porous media (synthesis),

(c) Other ideas/approaches integrating simulation into new knowledge, for improving tentative theories on multi-phase flows in porous media.

Minisymposium MS 1.3:** "Unconventional Modelling of Multi-Phase Flows in Porous Media"**

was held in parallel to the 7th International Conference on Porous Media

The mini-symposium focused on unconventional modelling of multi-phase flows, with special consideration on disconnected flow regimes, process’ inherent degrees of freedom, reappraisal of true-to-mechanism independent variables, etc. New approaches integrating current knowledge into a unified theory for multi-phase flow in p.m. have been communicated and emerging research perspectives have been addressed.

**Mini-symposium 1.03 hosted the following presentations** (in a/b order of first author):

"Statistical Mechanics Approach to Steady-State Two-Phase Flow in Porous Media" - I. Savani, S. Sinha, M. Vassvik, D. Bedeaux, S. Kjelstrup, K-J. Maloy & A.Hansen (Invited speaker)

"Stationary flow of non-wetting liquid through layer of unsaturated porous material" by M. Cieszko, T. Bednarek

"Configurational Entropy Maps for Steady-State Two-Phase Flows in Pore Networks implementing the DeProF model algorithm" by M. S. Valavanides & T. Daras

"Integration of relative permeability maps for two-phase flow in porous media into FEM solvers to investigate complex field-scale flows" by E.D. Skouras, A.N. Kalarakis, M.S. Valavanides & V.N. Burganos

"Two-phase flow conductivity maps implementing FEM and Lattice-Boltzmann simulators in complex pore geometries" by E.D. Skouras, A.N. Kalarakis, M.S. Valavanides & V.N. Burganos (poster)

"Model for Spatiotemporary Varying Mass Transfer Problems During Two-Phase Flow Within Pore Networks, Based on the DeProF Model Description of the Flow Patterns" by E.D. Skouras, A.N. Kalarakis, M.S. Valavanides & V.N. Burganos (poster)

"Analyzing the steady-state two-phase flow relative permeability functions of porous media in the terms of their dependence on capillary numbers: An experimental study" by C.D. Tsakiroglou, C.A. Aggelopoulos, K. Terzi, D.G. Avraam, M.S. Valavanides (poster)

"Reconceptualization of SCAL, pore structure characterization and effective, operational efficiency indices" by M.S. Valavanides (poster)

**Invitation**

**to join an international effort for Retrospective Examination of Relative Permeability Data (Dec. 2013)**

Dear Colleagues and Fellow Researchers,

You are invited to join the ImproDeProF project team efforts in collecting laboratory-measured relative permeability data sets. As a follow-up of the ImproDeProF project, it is planned to establish a data base of relative permeability data sets, and to conduct a retrospective examination focusing on latent optimum operating conditions for steady-state two-phase flow in porous media. You may find an introductory description of the planned re-investigation here (as a "RESEARCH Spotlight" in the InterPore Newsletters, courtesy of InterPore^{TM} – the International Society for Porous Media).

So far, the data base comprises a total of 179 relative permeability diagrams pertaining to laboratory runs collected from 35 published works (see [3] and [2] above).

If you have such data sets available, that you are willing to share or that could be used in this re-investigation, please contact Dr. Marios Valavanides (marval@uniwa.gr).

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