Fluid Meniscus Algorithms for Dynamic Pore-Network Modeling of Immiscible Two-Phase Flow in Porous Media

Sinha, Santanu; Gjennestad, Magnus Aa.; Vassvik, Morten; Hansen, Alex

doi:10.3389/fphy.2020.548497

Cited by 16 publications

(33 citation statements)

References 66 publications

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“…In this case, the volumetric flow rate scales nonlinearly with the pressure drop due to the fact that increasing the pressure drop by a small amount creates new connecting paths in addition to increase the flow in the previously connected paths. Earlier works (Roy et al 2019;Sinha et al 2021;Tallakstad et al 2009a;Rassi et al 2011;Tallakstad et al 2009b;Aursjø et al 2014;Gao et al 2020a;Zhang et al 2021) have provided experimental, theoretical and numerical evidences for this phenomena in porous media under uniform wetting conditions. Instead of assuming uniform wetting conditions, we here investigate the same phenomena using non-uniform wetting conditions, theoretically and numerically.…”

Section: Introductionmentioning

confidence: 92%

“…The second model that is used for the investigations in this work is a dynamic pore network (DPN) model, a complex numerical model which is not analytically solvable (Sinha et al 2021;Aker et al 1998;Knudsen et al 2002;Tørå et al 2012;Gjennestad et al 2018). A sketch of the network used in the model is given in Fig.…”

Section: The Dynamic Pore Network Model Descriptionmentioning

confidence: 99%

“…Total effective pressure is the difference between p and the total capillary pressure ∑ k p c (x k ) due to all the interfaces with positions x k ∈ [0, l � ] . Assuming that the radius does not deviate too much from its average value r i , the volumetric flow rate q i in SCU i is given by (Sinha et al 2021;Washburn 1921) where i is the saturation weighted viscosity of the fluids given by Here, s A,i = l � A,i ∕l � and s B,i = l � B,i ∕l � are saturations of the two fluids A and B with viscosities A and B and lengths l ′ A,i and l ′ B,i . In the DPN model, l ′ is the same as l from Eq.…”

Section: Commonalitiesmentioning

confidence: 99%

“…Thereafter, case studies with various specific wetting angle distribution have been performed through numerical calculations which confirmed the analytical results in addition to providing a holistic picture. Secondly, mixed wetting conditions have been implemented into a dynamic network model (Sinha et al 2021) where the motion of the fluid interfaces are followed through the porous medium. The results confirm that the volumetric flow rate Q indeed depends on the applied pressure drop P as where P t is the minimum pressure drop necessary for flow.…”

Section: Introductionmentioning

confidence: 99%

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Rheology of Immiscible Two-phase Flow in Mixed Wet Porous Media: Dynamic Pore Network Model and Capillary Fiber Bundle Model Results

et al. 2021

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Immiscible two-phase flow in porous media with mixed wet conditions was examined using a capillary fiber bundle model, which is analytically solvable, and a dynamic pore network model. The mixed wettability was implemented in the models by allowing each tube or link to have a different wetting angle chosen randomly from a given distribution. Both models showed that mixed wettability can have significant influence on the rheology in terms of the dependence of the global volumetric flow rate on the global pressure drop. In the capillary fiber bundle model, for small pressure drops when only a small fraction of the tubes were open, it was found that the volumetric flow rate depended on the excess pressure drop as a power law with an exponent equal to 3/2 or 2 depending on the minimum pressure drop necessary for flow. When all the tubes were open due to a high pressure drop, the volumetric flow rate depended linearly on the pressure drop, independent of the wettability. In the transition region in between where most of the tubes opened, the volumetric flow depended more sensitively on the wetting angle distribution function and was in general not a simple power law. The dynamic pore network model results also showed a linear dependence of the flow rate on the pressure drop when the pressure drop is large. However, out of this limit the dynamic pore network model demonstrated a more complicated behavior that depended on the mixed wettability condition and the saturation. In particular, the exponent relating volumetric flow rate to the excess pressure drop could take on values anywhere between 1.0 and 1.8. The values of the exponent were highest for saturations approaching 0.5, also, the exponent generally increased when the difference in wettability of the two fluids were larger and when this difference was present for a larger fraction of the porous network.

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Section: Introductionmentioning

confidence: 92%

Section: The Dynamic Pore Network Model Descriptionmentioning

confidence: 99%

Section: Commonalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rheology of Immiscible Two-phase Flow in Mixed Wet Porous Media: Dynamic Pore Network Model and Capillary Fiber Bundle Model Results

et al. 2021

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“…In this model, one pore is the smallest computational unit and the fluid displacements inside the pores are governed by equations for fully developed flow. We use a dynamic pore-network model where the menisci positions between the fluids track the flow (Aker et al, 1998;Sinha et al, 2021). The network in this model is defined in such a way that total pore space related to both the pore-throat and pore-bodies are represented by composite links of varying radii.…”

Section: Dynamic Pore Network Model (Dpnm)mentioning

confidence: 99%

Role of Pore-Size Distribution on Effective Rheology of Two-Phase Flow in Porous Media

Roy¹,

Sinha²,

Hansen³

2021

Front. Water

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Immiscible two-phase flow of Newtonian fluids in porous media exhibits a power law relationship between flow rate and pressure drop when the pressure drop is such that the viscous forces compete with the capillary forces. When the pressure drop is large enough for the viscous forces to dominate, there is a crossover to a linear relation between flow rate and pressure drop. Different values for the exponent relating the flow rate and pressure drop in the regime where the two forces compete have been reported in different experimental and numerical studies. We investigate the power law and its exponent in immiscible steady-state two-phase flow for different pore size distributions. We measure the values of the exponent and the crossover pressure drop for different fluid saturations while changing the shape and the span of the distribution. We consider two approaches, analytical calculations using a capillary bundle model and numerical simulations using dynamic pore-network modeling. In case of the capillary bundle when the pores do not interact to each other, we find that the exponent is always equal to 3/2 irrespective of the distribution type. For the dynamical pore network model on the other hand, the exponent varies continuously within a range when changing the shape of the distribution whereas the width of the distribution controls the crossover point.

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The Co-Moving Velocity in Immiscible Two-Phase Flow in Porous Media

et al. 2022

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We present a continuum (i.e., an effective) description of immiscible two-phase flow in porous media characterized by two fields, the pressure and the saturation. Gradients in these two fields are the driving forces that move the immiscible fluids around. The fluids are characterized by two seepage velocity fields, one for each fluid. Following Hansen et al. (Transport in Porous Media, 125, 565 (2018)), we construct a two-way transformation between the velocity couple consisting of the seepage velocity of each fluid, to a velocity couple consisting of the average seepage velocity of both fluids and a new velocity parameter, the co-moving velocity. The co-moving velocity is related but not equal to velocity difference between the two immiscible fluids. The two-way mapping, the mass conservation equation and the constitutive equations for the average seepage velocity and the co-moving velocity form a closed set of equations that determine the flow. There is growing experimental, computational and theoretical evidence that constitutive equation for the average seepage velocity has the form of a power law in the pressure gradient over a wide range of capillary numbers. Through the transformation between the two velocity couples, this constitutive equation may be taken directly into account in the equations describing the flow of each fluid. This is, e.g., not possible using relative permeability theory. By reverse engineering relative permeability data from the literature, we construct the constitutive equation for the co-moving velocity. We also calculate the co-moving constitutive equation using a dynamic pore network model over a wide range of parameters, from where the flow is viscosity dominated to where the capillary and viscous forces compete. Both the relative permeability data from the literature and the dynamic pore network model give the same very simple functional form for the constitutive equation over the whole range of parameters.

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Fluid Meniscus Algorithms for Dynamic Pore-Network Modeling of Immiscible Two-Phase Flow in Porous Media

Cited by 16 publications

References 66 publications

Rheology of Immiscible Two-phase Flow in Mixed Wet Porous Media: Dynamic Pore Network Model and Capillary Fiber Bundle Model Results

Rheology of Immiscible Two-phase Flow in Mixed Wet Porous Media: Dynamic Pore Network Model and Capillary Fiber Bundle Model Results

Role of Pore-Size Distribution on Effective Rheology of Two-Phase Flow in Porous Media

The Co-Moving Velocity in Immiscible Two-Phase Flow in Porous Media

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