Multi-rate mass transfer modeling of two-phase flow in highly heterogeneous fractured and porous media

Tecklenburg, Jan; Neuweiler, Insa; Carrera, Jesús; Dentz, Marco

doi:10.1016/j.advwatres.2016.02.010

Cited by 31 publications

(22 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first‐order transfer function has been widely used as a model to represent the whole imbibition process. It is observed, however, that this model underestimates drastically the imbibed volume at the onset of the process [ Zimmerman et al ., ; Geiger et al ., ; Tecklenburg et al ., ].…”

Section: Introductionmentioning

confidence: 99%

Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

March

Doster

Geiger

2016

Water Resources Research

View full text Add to dashboard Cite

Spontaneous countercurrent imbibition into a finite porous medium is an important physical mechanism for many applications, included but not limited to irrigation, CO 2 storage, and oil recovery. Symmetry considerations that are often valid in fractured porous media allow us to study the process in a onedimensional domain. In 1-D, for incompressible fluids and homogeneous rocks, the onset of imbibition can be captured by self-similar solutions and the imbibed volume scales with ffiffi t p . At later times, the imbibition rate decreases and the finite size of the medium has to be taken into account. This requires numerical solutions. Here we present a new approach to approximate the whole imbibition process semianalytically. The onset is captured by a semianalytical solution. We also provide an a priori estimate of the time until which the imbibed volume scales with ffiffi t p . This time is significantly longer than the time it takes until the imbibition front reaches the model boundary. The remainder of the imbibition process is obtained from a selfsimilarity solution. We test our approach against numerical solutions that employ parametrizations relevant for oil recovery and CO 2 sequestration. We show that this concept improves common first-order approaches that heavily underestimate early-time behavior and note that it can be readily included into dual-porosity models. Key Points: New physically based model for spontaneous imbibition Model captures transition from earlytime to late-time imbibition Model validated for different applications Correspondence to: R. March, rafael.march@pet.hw.ac.uk Citation: March, R., F. Doster, and S. Geiger (2016), Accurate early-time and latetime modeling of countercurrent spontaneous imbibition, Water Resour.

show abstract

Section: Introductionmentioning

confidence: 99%

Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

March

Doster

Geiger

2016

Water Resources Research

View full text Add to dashboard Cite

show abstract

“…These yield transfer terms with memory functions that are non-local in time and therefore notoriously challenging to interpret or exploit in solutions and simulators. To simplify calculations these have been expanded in series of exponentials yielding a series of first order transfer terms with varying transfer rate coefficients (Tecklenburg et al, 2016). Also heterogeneous fracture spacings yield series of first order transfer terms with varying coefficients due to varying shape factors (Haggerty and Gorelick, 1995).…”

Section: Multi-continuum Modelsmentioning

confidence: 99%

Flow in Fractured Porous Media: A Review of Conceptual Models and Discretization Approaches

2018

View full text Add to dashboard Cite

The last decade has seen a strong increase of research into flows in fractured porous media, mainly related to subsurface processes, but also in materials science and biological applications. Connected fractures totally dominate flow-patterns, and their representation is therefore a critical part in model design. Due to the fracture's characteristics as approximately planar discontinuities with an extreme size to width ratio, they challenge standard macroscale mathematical and numerical modeling of flow based on averaging. Thus, over the last decades, various, and also fundamentally different, approaches have been developed. This paper reviews common conceptual models and discretization approaches for flow in fractured porous media, with an emphasis on the dominating effects the fractures have on flow processes. In this context, the paper discuss the tight connection between physical and mathematical modeling and simulation approaches. Extensions and research challenges related to transport, multi-phase flow and fluid-solid interaction are also commented on. arXiv:1805.05701v1 [physics.geo-ph]

show abstract

“…Having a pure calcium carbonate system with no chemical heterogeneity, the partitioning of the porous medium is only due to the physical heterogeneity at pore scale (fracture/matrix), and therefore, no localization of reactions is assumed. We consider one immobile zone only, to align the formulation with the time‐dependent single‐rate mass transfer model as opposed to multiple rate mass transfer model where multiple mass transfer processes occur simultaneously in a porous medium (see, e.g., Fernandez‐Garcia & Sanchez‐Vila, ; Geiger et al, ; Maier et al, ; Soler‐Sagarra et al, ; Tecklenburg et al, ). As such equation (3) can be rewritten as

ϕ_{m} r_{sans-serif-italicf, sans-serif-italicm} \frac{\partial c_{sans-serif-italicA, sans-serif-italicm}}{\partial sans-serif-italict} + u_{x} \frac{\partial c_{sans-serif-italicA, sans-serif-italicm}}{\partial sans-serif-italicx} + u_{z} \frac{\partial c_{sans-serif-italicA, sans-serif-italicm}}{\partial sans-serif-italicz} = ϕ_{m} sans-serif-italicD ((), \frac{\partial^{2} c_{sans-serif-italicA, sans-serif-italicm}}{\partial x^{2}} + \frac{\partial^{2} c_{sans-serif-italicA, sans-serif-italicm}}{\partial z^{2}}) - α ((), c_{sans-serif-italicA, sans-serif-italicm} - c_{sans-serif-italicA, sans-serif-italicim, sans-serif-italicj}) + r_{sans-serif-italicchem, sans-serif-italicA, sans-serif-italicm},

ϕ_{im} r_{sans-serif-italicf, sans-serif-italicim} \frac{\partial c_{sans-serif-italicA, sans-serif-italicim}}{}

…”

Section: Simplified Co2 Reaction With Calcium Carbonatementioning

confidence: 99%

“…Having a pure calcium carbonate system with no chemical heterogeneity, the partitioning of the porous medium is only due to the physical heterogeneity at pore scale (fracture/matrix), and therefore, no localization of reactions is assumed. We consider one immobile zone only, to align the formulation with the time-dependent singlerate mass transfer model as opposed to multiple rate mass transfer model where multiple mass transfer processes occur simultaneously in a porous medium (see, e.g., Fernandez-Garcia & Sanchez-Vila, 2015; Geiger et al, 2013;Maier et al, 2013;Soler-Sagarra et al, 2016;Tecklenburg et al, 2016). As such equation (3) can be rewritten as…”

Section: Simplified Co 2 Reaction With Calcium Carbonatementioning

confidence: 99%

Convective‐Reactive CO₂ Dissolution in Aquifers With Mass Transfer With Immobile Water

Babaei

Islam

2018

Water Resources Research

View full text Add to dashboard Cite

The objective of this paper is to study the impact of immobile water, its fraction, and its mass transfer with the flowing region on efficiency of CO2 dissolution in aquifers with an immobile water zone. A continuum scale code is developed with underlying assumptions of spatially homogeneous and temporally invariable partitioning fraction of the porous media, first‐order mass transfer between the mobile and immobile zones, and simplified reaction of CO2 aqueous solution with calcium carbonate rock. Using ranges of values for Damköhler number (Da), fraction of the total pore volume, and mass transfer coefficient rate (α), 96 simulations are conducted. It is shown that due to a lower intensity of reaction in the mobile region, intermediate values of α serve as a threshold below which the mass transfer coefficient is not affecting the overall CO2 storage and above which overall CO2 storage increases as a function of mass transfer coefficient. Additionally, we found that (i) when α is high and geochemistry is intensive (high Da), the overall CO2 storage decreases with increase in fraction of mobile water. This is because CO2 storage through consumption of rock in immobile water with higher geochemistry is reduced. (ii) When α is high but Da is low, the system is effectively a single porosity medium with no chemistry‐influenced discrimination between mobile and immobile zones, and therefore, overall CO2 storage increases with fraction of mobile water. (iii) When α is low, the magnitude of Da does not influence the overall CO2 storage.

show abstract

Multi-rate mass transfer modeling of two-phase flow in highly heterogeneous fractured and porous media

Cited by 31 publications

References 45 publications

Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

Flow in Fractured Porous Media: A Review of Conceptual Models and Discretization Approaches

Convective‐Reactive CO₂ Dissolution in Aquifers With Mass Transfer With Immobile Water

Contact Info

Product

Resources

About

Multi-rate mass transfer modeling of two-phase flow in highly heterogeneous fractured and porous media

Cited by 31 publications

References 45 publications

Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

Flow in Fractured Porous Media: A Review of Conceptual Models and Discretization Approaches

Convective‐Reactive CO2 Dissolution in Aquifers With Mass Transfer With Immobile Water

Contact Info

Product

Resources

About

Convective‐Reactive CO₂ Dissolution in Aquifers With Mass Transfer With Immobile Water