An empirical theory for gravitationally unstable flow in porous media

Farajzadeh, R.; Meulenbroek, Bernard; Daniel, Don; Riaz, Amir; Bruining, J.

doi:10.1007/s10596-012-9336-9

Cited by 35 publications

(22 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While all the above studies replicate the classical scaling, only two numerical studies have reported a sublinear scaling: Farajzadeh et al [32] obtained Sh ≈ 0.0794Ra 0.832 , though for a relatively limited range of Ra (10 3 -8 × 10 3 ) using a constant-concentration boundary and a linear density-concentration profile; Neufeld et al [28] numerically determined Sh ≈ 0.12Ra 0.84 (also supported by experiments) for 2 × 10 3 Ra 6 × 10 5 but using a mixture of two miscible fluids involving in-terface movement and a non-monotonic density-concentration profile. Emami-Meybodi et al [36] concluded that the method of measuring the convective flux cannot be the source of different reported scaling behaviors.…”

Section: B Numerical Studiesmentioning

confidence: 82%

“…Emami-Meybodi et al [36] concluded that the method of measuring the convective flux cannot be the source of different reported scaling behaviors. One could argue that the sublinear result of Farajzadeh et al [32] is due to the small parameter range of experiments, which includes less than one decade of Ra. Perhaps the combination of boundary set-up and densityconcentration profile shape determines the Sh-Ra scaling behavior, such that a constant-concentration BC with linear density-concentration profile results in linear scaling while an analogue two-layer fluid system with a nonmonotonic density profile results in sublinear scaling.…”

Section: B Numerical Studiesmentioning

confidence: 97%

“…The primary objective in studying dissolution trapping via natural convection is to predict the rate of CO 2 mixing over time. Previous experimental [17,[28][29][30] and numerical [18,20,[31][32][33][34][35] studies using analogue systems and constant-concentration BC have observed a quasisteady-state regime for both the convective flux and a mean dissipation rate. Scaling laws have been proposed for the long-term mass transport behavior in terms of Sherwood number (Sh) and Rayleigh number (Ra) (to be discussed in section VI).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

2018

View full text Add to dashboard Cite

We numerically examine solutal convection in porous media, driven by the dissolution of carbon dioxide (CO2) into water-an effective mechanism for CO2 storage in saline aquifers. Dissolution is associated with slow diffusion of free-phase CO2 into the underlying aqueous phase followed by density-driven convective mixing of CO2 throughout the water-saturated layer. We study the fluid dynamics of CO2 convection in the single aqueous-phase region. A comparison is made between two different boundary conditions in the top of the formation: (i) a constant, maximum aqueous-phase concentration of CO2, and (ii) a constant, low injection-rate of CO2, such that all CO2 dissolves instantly and the system remains in single phase. The latter model is found to involve a nonlinear evolution of CO2 composition and associated aqueous-phase density, which depend on the formation permeability. We model the full nonlinear phase behavior of water-CO2 mixtures in a confined domain, consider dissolution and fluid compressibility, and relax the common Boussinesq approximation. We discover new flow regimes and present quantitative scaling relations for global characteristics of spreading, mixing, and a dissolution flux in two-and three-dimensional media for both boundary conditions. We also revisit the scaling behavior of Sherwood number (Sh) with Rayleigh number (Ra), which has been under debate for porous-media convection. Our measurements from the solutal convection in the range 1, 500 Ra 135, 000 show that the classical linear scaling Sh ∼ Ra is attained asymptotically for the constant-concentration case. Similarly linear scaling is recovered for the constant-flux model problem. The results provide a new perspective into how boundary conditions may affect the predictive powers of numerical models, e.g., for both the short-term and long-term dynamics of convective mixing rate and dissolution flux in porous media at a wide range of Rayleigh numbers.

show abstract

Section: B Numerical Studiesmentioning

confidence: 82%

Section: B Numerical Studiesmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

2018

View full text Add to dashboard Cite

show abstract

“…Fully resolved nonlinear simulations [21][22][23] demonstrate that the time for the onset of nonlinear effects depends on both the amplitude of initial perturbations and Ra, and is usually much greater than t o . Our characterization of linear instability as a function of viscosity contrast and various models would facilitate the study of the onset of nonlinear convection in such systems.…”

Section: Discussionmentioning

confidence: 99%

Effect of viscosity contrast on gravitationally unstable diffusive layers in porous media

Daniel

Riaz

2014

Physics of Fluids

View full text Add to dashboard Cite

We investigate the effect of viscosity contrast on the stability of gravitationally unstable, diffusive layers in porous media. Our analysis helps evaluate experimental observations of various diffusive (boundary) layer models that are commonly used to study the sequestration of CO2 in brine aquifers. We evaluate the effect of viscosity contrast for two basic models that are characterized with respect to whether or not the interface between CO2 and brine is allowed to move. We find that diffusive layers are in general more unstable when viscosity decreases with depth within the layer compared to when viscosity increases with depth. This behavior is in contrast to the one associated with the classical displacement problem of gravitationally unstable diffusive layers that are subject to mean flow. For the classical problem, a greater instability is associated with the displacement of a more viscous, lighter fluid along the direction of gravity by a less viscous, heavier fluid. We show that the contrasting behavior highlighted in this study is a special case of the classical displacement problem that depends on the relative strength of the displacement and buoyancy velocities. We demonstrate the existence of a critical viscosity ratio that determines whether the flow is buoyancy dominated or displacement dominated. We explain the new behaviors in terms of the interaction of vorticity components related to gravitational and viscous effects.

show abstract

“…A lot of research on fingering has already been done, both on viscous fingering (SaffmanTaylor instabilities) and instabilities caused by density differences; see, for example, Diersch and Kolditz (2002), Duijn et al (2004), Farajzadeh et al (2013), and Khosrokhavar et al (2014). There are several approaches.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Front Instabilities in Density-Driven Flow, Using a Reactive Transport Model for Biogrout Combined with a Randomly Distributed Permeability Field

et al. 2016

View full text Add to dashboard Cite

Biogrout is a method to strengthen granular soil, which is based on microbialinduced carbonate precipitation. To model the Biogrout process, a reactive transport model is used. Since high flow rates are undesirable for the Biogrout process, the model equations can be solved with a standard Galerkin finite element method. The Biogrout process involves the injection of dense fluids in the subsurface. In this paper, we present our reactive transport model for Biogrout and use it to simulate an experiment in which a pulse of a dense fluid is injected in a porous medium filled with water. In this experiment, front instabilities were observed in the form of fingers. The numerical simulations showed that the fingering phenomenon was less pronounced than in the experiment. By reducing the dispersion length and implementing a randomly distributed permeability field, the fingering phenomenon could be induced. Furthermore, the results of a case study to a Biogrout application are reported.

show abstract

An empirical theory for gravitationally unstable flow in porous media

Cited by 35 publications

References 46 publications

Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

Effect of viscosity contrast on gravitationally unstable diffusive layers in porous media

Simulation of Front Instabilities in Density-Driven Flow, Using a Reactive Transport Model for Biogrout Combined with a Randomly Distributed Permeability Field

Contact Info

Product

Resources

About