Steady-State Two-Phase Flow in Porous Media: Review of Progress in the Development of the<i>DeProF</i>Theory Bridging Pore to Statistical Thermodynamics Scales

Valavanides, Marios S.

doi:10.2516/ogst/2012056

Cited by 18 publications

(21 citation statements)

References 23 publications

(39 reference statements)

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“…The flow structure-comprising a mixture of connected and disconnected fluidic elements moving at different velocities-incessantly rearranges itself within a phase space of physically admissible flow configurations [10,11]. Considering the flow to be ergodic, its time average is equal to its phase space average over all physically admissible configurations [12].…”

Section: Introduction and Scope Of Workmentioning

confidence: 99%

“…This feature was first revealed after extensive simulations of steady-state two-phase flows in model pore networks using the DeProF mechanistic model, developed by Valavanides and Payatakes [12,15]. DeProF implements hierarchical mechanistic modelling, spanning pore-to core-to field scales, to predict the pressure gradient given the flowrate of each fluid [12].…”

Section: Introduction and Scope Of Workmentioning

confidence: 99%

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Definition and Counting of Configurational Microstates in Steady-State Two-Phase Flows in Pore Networks

Valavanides

Daras

2016

Entropy

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Steady-state two-phase flow in porous media is a process whereby a wetting phase displaces a non-wetting phase within a pore network. It is an off-equilibrium stationary process-in the sense that it is maintained in dynamic equilibrium at the expense of energy supplied to the system. The efficiency of the process depends on its spontaneity, measurable by the rate of global entropy production. The latter has been proposed to comprise two components: the rate of mechanical energy dissipation at constant temperature (a thermal entropy component, Q/T, in the continuum mechanics scale) and the configurational entropy (a Boltzmann-Gibbs entropy component, klnW), due to the existence of a canonical ensemble of flow configurations, physically admissible to the externally imposed macrostate conditions. Here, we propose an analytical model to account the number of microstates, lnW, in two-phase flows in pore networks. Combinatorial analysis is implemented to evaluate the number of identified microstates per physically admissible internal flow arrangement, compatible with the imposed steady-state flow conditions. Then, Stirling's approximation is applied to downscale the large factorial numbers. Finally, the number of microstates is estimated by contriving an appropriate mixing scheme over the canonical ensemble of the physically admissible flow configurations. Indicative computations are furnished.

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Section: Introduction and Scope Of Workmentioning

confidence: 99%

Section: Introduction and Scope Of Workmentioning

confidence: 99%

Definition and Counting of Configurational Microstates in Steady-State Two-Phase Flows in Pore Networks

Valavanides

Daras

2016

Entropy

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“…The efficiency of any steady-state two-phase flow in porous media process, with respect to the maximization of the oil transport per kW of mechanical power supplied to it (or 'oil output per unit energy cost'), may be assessed by the values of the energy utilization coefficient, f EU , a macroscopic quantity originally defined by Valavanides and Payatakes (2003); [see also Valavanides, 2012; Simulations implementing the DeProF model, suggest that a set of flow conditions exist for which the sought process attains locally maximum energy efficiency, see Figure 19. Such conditions, define a locus of optimum operating conditions or critical flow conditions, r*(Ca), for each oilwater-p.m. system (Valavanides, 2014 andValavanides, 2018).…”

Section: Energy Efficiency Of Steady-state Two-phase Flow In Porous Mmentioning

confidence: 99%

“…The mechanistic model DeProF developed by Valavanides and Payatakes (2000, 2001, 2012, can be used to obtain the solution to the problem of steady-state two-phase flow in pore networks, by predicting the reduced macroscopic pressure gradient, x, given the values of physical quantities defining the flow conditions and the oil-water-p.m. system properties.…”

Section: The Deprof Hierarchical Mechanistic Model For Steady-state Tmentioning

confidence: 99%

“…To elucidate the actual, inherent flow mechanisms that form the structure of flow regimes and regulate the overall (macroscopic) behavior of immiscible steady-state twophase flows in pore networks, 2001;also Valavanides, 1998 and2012) developed the DeProF mechanistic model. The model is based on the concept of decomposition in prototype flows (see next section).…”

Section: Introductionmentioning

confidence: 99%

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Oil Fragmentation, Interfacial Surface Transport and Flow Structure Maps for Two-Phase Flow in Model Pore Networks. Predictions Based on Extensive, DeProF Model Simulations

Valavanides

2018

Oil & Gas Science and Technology - Rev. IFP Energies nouvel

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-In general, macroscopic two-phase flows in porous media form mixtures of connectedand disconnected-oil flows. The latter are classified as oil ganglion dynamics and drop traffic flow, depending on the characteristic size of the constituent fluidic elements of the non-wetting phase, namely, ganglia and droplets. These flow modes have been systematically observed during flow within model pore networks as well as real porous media. Depending on the flow conditions and on the physicochemical, size and network configuration of the system (fluids and porous medium), these flow modes occupy different volume fractions of the pore network. Extensive simulations implementing the DeProF mechanistic model for steady-state, one-dimensional, immiscible twophase flow in typical 3D model pore networks have been carried out to derive maps describing the dependence of the flow structure on capillary number, Ca, and flow rate ratio, r. The model is based on the concept of decomposition into prototype flows. Implementation of the DeProF algorithm, predicts key bulk and interfacial physical quantities, fully describing the interstitial flow structure: ganglion size and ganglion velocity distributions, fractions of mobilized/stranded oil, specific surface area of oil/water interfaces, velocity and volume fractions of mobilized and stranded interfaces, oil fragmentation, etc. The simulations span 5 orders of magnitude in Ca and r. Systems with various viscosity ratios and intermediate wettability have been examined. Flow of the nonwetting phase in disconnected form is significant and in certain cases of flow conditions the dominant flow mode. Systematic flow structure mutations with changing flow conditions have been identified. Some of them surface-up on the macroscopic scale and can be measured e.g. the reduced pressure gradient. Other remain in latency within the interstitial flow structure e.g. the volume fractions of À or fractional flows of oil through À connected-disconnected flows. Deeper within the disconnected-oil flow, the mutations between ganglion dynamics and drop traffic flow prevail. Mutations shift and/or become pronounced with viscosity disparity. They are more evident over variables describing the interstitial transport properties of process than variables describing volume fractions. This characteristic behavior is attributed to the interstitial balance between capillarity and bulk viscosity. Mean mobilization probability of i-class ganglia S 2.3 IFP Energies nouvelles International Conference Rencontres Scientifiques d'IFP Energies nouvellesNumber density of i-class ganglia S (15)Number of pore unit cells occupied by each i-class ganglion P

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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

Valavanides

2018

Transp Porous Med

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Steady-State Two-Phase Flow in Porous Media: Review of Progress in the Development of theDeProFTheory Bridging Pore to Statistical Thermodynamics Scales

Cited by 18 publications

References 23 publications

Definition and Counting of Configurational Microstates in Steady-State Two-Phase Flows in Pore Networks

Definition and Counting of Configurational Microstates in Steady-State Two-Phase Flows in Pore Networks

Oil Fragmentation, Interfacial Surface Transport and Flow Structure Maps for Two-Phase Flow in Model Pore Networks. Predictions Based on Extensive, DeProF Model Simulations

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

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