A new alternative approach for investigating acidization dissolution front propagation in fluid-saturated carbonate rocks

Zhao, Chong Bin; Hobbs, B. E.; Ord, Alison

doi:10.1007/s11431-016-0666-1

Cited by 35 publications

(38 citation statements)

References 21 publications

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“…The dissolution surface that is commonly represented by the dissolution front can exist in either a stable state or an unstable state, depending on the coupled behavior among the solute diffusion, pore-fluid flow, and chemical reaction type in the whole dissolution system [34]. This indicates that this study still has certain limitations, which should be improved in the future research.…”

Section: Resultsmentioning

confidence: 98%

A Study of Analytical Solution for the Special Dissolution Rate Model of Rock Salt

Yang

Liu

Zang

et al. 2017

Advances in Materials Science and Engineering

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By calculating the concentration distributions of rock salt solutions at the boundary layer, an ordinary differential equation for describing a special dissolution rate model of rock salt under the assumption of an instantaneous diffusion process was established to investigate the dissolution mechanism of rock salt under transient but stable conditions. The ordinary differential equation was then solved mathematically to give an analytical solution and related expressions for the dissolved radius and solution concentration. Thereafter, the analytical solution was fitted with transient dissolution test data of rock salt to provide the dissolution parameters at different flow rates, and the physical meaning of the analytical formula was also discussed. Finally, the influential factors of the analytical formula were investigated. There was approximately a linear relationship between the dissolution parameters and the flow rate. The effects of the dissolution area and initial volume of the solution on the dissolution rate equation of rock salt were computationally investigated. The results showed that the present analytical solution gives a good description of the dissolution mechanism of rock salt under some special conditions, which may provide a primary theoretical basis and an analytical way to investigate the dissolution characteristics of rock salt.

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Section: Resultsmentioning

confidence: 98%

A Study of Analytical Solution for the Special Dissolution Rate Model of Rock Salt

Yang

Liu

Zang

et al. 2017

Advances in Materials Science and Engineering

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“…However, in a special case, where both the mineral dissolution ratio and the variation of the rock porosity are small, it is possible to mathematically derive the base solution of the reactive infiltration problem on the dissolution timescale, as demonstrated from a previous study . This means that two assumptions need to be used in the process of deriving the base solution, which is a theoretical solution when the dissolution‐timescale reactive infiltration system is in a stable state, from the linear stability theory point of view . The use of these two assumptions has been justified in the previous studies .…”

Section: Derivation Of Base Solutions For the Reactive Infiltration Imentioning

confidence: 97%

“…To facilitate the theoretical study of a reactive infiltration instability problem, the same theoretical problem as described in the seminal paper was commonly used to conduct the linear stability analysis of a planar chemical dissolution front in the fluid‐saturated porous rocks . In this theoretical problem, the planar chemical dissolution front (located at x = 0) is assumed to propagate in an infinite space, so that both the upstream region (ie, − ∞ ≤ x ≤ 0) and the downstream region (ie, 0 ≤ x ≤ + ∞) relative to the planar chemical dissolution front at x = 0 can be treated as two semi‐infinite domains.…”

Section: Introductionmentioning

confidence: 99%

“…This can further ensure that as the mineral dissolution ratio (or the acid dissolution capacity number) in the reactive infiltration system is very small, the theoretical problem, which is studied on a much larger timescale than the dissolution timescale , can be mathematically treated as a boundary value problem with a sharp dissolution front of zero thickness . Thus, the linear stability theory can be used to derive the first‐order perturbation equations of the problem …”

Section: Introductionmentioning

confidence: 99%

“…On the dissolution timescale, as will be considered in this study, the chemical dissolution front undergoes the following two stages: a formation stage and a propagation stage . To consider the detailed process of the formation stage, the un‐deformable porous rock should be modeled as a half space, instead of an infinite space in the previous studies . At the beginning of the formation stage, the continuously injected acid at the entrance of the dissolution‐timescale reactive infiltration system starts to dissolve the dissolvable minerals in the porous rock until the porosity of the porous rock at the entrance of the dissolution‐timescale reactive infiltration system increases from the initial porosity to the final porosity .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An interface‐condition substitution strategy for theoretical study of dissolution‐timescale reactive infiltration instability in fluid‐saturated porous rocks

Zhao

Hobbs

Ord

2019

Num Anal Meth Geomechanics

Self Cite

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Summary A theoretical study of reactive infiltration instability is conducted on the dissolution timescale. In the present theoretical study, the transient behavior of a dissolution‐timescale reactive infiltration system needs to be considered, so that the upstream region of the chemical dissolution front should be finite. In addition, the chemical dissolution front of finite thickness should be considered on the dissolution timescale. Owing to these different considerations, it is very difficult, even in some special cases, to derive the first‐order perturbation solutions of the reactive infiltration system on the dissolution timescale. To overcome this difficulty, an interface‐condition substitution strategy is proposed in this paper. The basic idea behind the proposed strategy is that although the first‐order perturbation equations in the downstream region cannot be directly solved in a purely mathematical manner, they should hold at the planar reference front, which is the interface between the upstream region and the downstream region. This can lead to two new equations at the interface. The main advantage of using the proposed interface‐condition substitution strategy is that through using the original interface conditions as a bridge, the perturbation solutions for the dimensionless acid concentration, dimensionless Darcy velocity, and their derivatives involved in the two new equations at the interface can be evaluated just by using the obtained analytical solutions in the upstream region. The proposed strategy has been successfully used to derive the dimensionless growth rate, which is the key issue associated with the theoretical study of dissolution‐timescale reactive infiltration instability in fluid‐saturated porous rocks.

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An analytical model for chemical diffusion in layered contaminated sediment systems with bioreactive caps

Yan

Xie

et al. 2019

Num Anal Meth Geomechanics

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Summary An analytical model for contaminant transport in multilayered capped contaminated sediments including the degradation of organic contaminant is presented. The effect of benthic boundary layer was treated as a Robin‐type boundary condition. The results of the proposed analytical model agree well with experimental data. The biodegradation of contaminant in bioturbation layer shows a significant influence on the flux at the surface of system. The maximum flux for the case with t1/2,bio = 0.07 year can be 4.5 times less than that of the case without considering the effect of biodegradation. The thickness of bioturbation layer has a significant effect on the performance of the capped contaminated sediment. The maximum flux for the case with lbio = 15 cm can be 17 times larger than that of the case without bioturbation layer. This may be because the effective diffusion coefficient of sand cap can be 28 times lower than Dbio. The mass transfer coefficient should be considered for the design of the capping system as the contaminant concentration at the top of system for the case with kbl = 2.5 × 10−5 cm/s can be 13 times greater than that of the case with kbl = 10−4 cm/s. The proposed analytical model can be used for verification of complicated numerical methods, evaluation of experimental data, and design of the capping contaminated sediment systems with reactive cap layers.

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A new alternative approach for investigating acidization dissolution front propagation in fluid-saturated carbonate rocks

Cited by 35 publications

References 21 publications

A Study of Analytical Solution for the Special Dissolution Rate Model of Rock Salt

A Study of Analytical Solution for the Special Dissolution Rate Model of Rock Salt

An interface‐condition substitution strategy for theoretical study of dissolution‐timescale reactive infiltration instability in fluid‐saturated porous rocks

An analytical model for chemical diffusion in layered contaminated sediment systems with bioreactive caps

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