Numerical modeling and analysis of the matrix acidizing process in fractured sandstone rocks with the Extended–FEM

Xie, Yang; Luo, Zhifeng; Cheng, Long; Zhao, Liqiang; Chen, Xiang; Zhang, NanLin; Ren, Dengfeng; Cao, Yunxia

doi:10.1016/j.petrol.2022.111215

Cited by 6 publications

(8 citation statements)

References 33 publications

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“…

{v}_{f}=-\frac{{k}_{f}^{\tau }}{\mu }\frac{\partial {p}_{f}}{\partial {x}^{\tau }},

-\nabla (\rho \cdot {v}_{f})=\frac{\partial }{\partial t}(\rho {\phi }_{f})-\rho {Q}_{f}.

The fracture tangential permeability can be calculated by applying the fracture width according to the cubic law as follows.

{k}_{f}^{\tau }=\frac{{w}_{f}^{2}}{12}.

Bringing Equation () into Equation (), the acid pressure distribution in the main body of the fracture is

{w}_{f}{c}_{f}\frac{\partial {p}_{f}}{\partial t}-{w}_{f}\nabla \cdot \left(\frac{{k}_{f}^{\tau }}{\mu }\frac{\partial {p}_{f}}{\partial {x}^{\tau }}\right)={w}_{f}{Q}_{f}.

The acid concentration transport equation in the fracture consists of HF and H 2 SiF 6 concentration transport equation, which is as follows 22

w_{f} \frac{\partial C_{f, italicAi}}{\partial t} + w_{f} v_{f} \frac{\partial C_{f, italicAi}}{\partial x^{τ}} - \frac{\partial C_{f, italicAi}}{\partial x^{τ}} (w_{f} D_{Ai}^{})

…”

Section: Results and Discussionmentioning

confidence: 99%

“…The acid concentration transport equation in the fracture consists of HF and H 2 SiF 6 concentration transport equation, which is as follows 22

{w}_{f}\frac{\partial {C}_{f,{Ai}}}{\partial t}+{w}_{f}{v}_{f}\frac{\partial {C}_{f,{Ai}}}{\partial {x}^{\tau }}-\frac{\partial {C}_{f,{Ai}}}{\partial {x}^{\tau }}\left({w}_{f}{D}_{{Ai}}^{{fr}}\frac{\partial {C}_{f,{Ai}}}{\partial {x}^{\tau }}\right)=0,\unicode{x02007}\unicode{x02007}i=\mathrm{2,3}.

…”

Section: Results and Discussionmentioning

confidence: 99%

“…The acid concentration transport equation in the fracture consists of HF and H 2 SiF 6 concentration transport equation, which is as follows. 22 w C…”

Section: Evaluation Of Acid Retardation Performancementioning

confidence: 99%

“…(2) Mathematical model of the acid transport reaction of the subject within the matrix In the case of considering fluid and rock microcompressibility, similar to the form of the acid pressure equation for the antecedent within the matrix, the acid pressure equation for the main body within the matrix is 22,30…”

Section: Evaluation Of Acid Retardation Performancementioning

confidence: 99%

“…In 2003, Rodoplu et al developed a mathematical model of "two acids and three minerals" to reflect the change of permeability, and the experimental results verified the validity of the model and the good agreement with the experimental results. 21 In 2005, Xie et al 22 further applied the small-scale model developed by Li et al 23 to study the conditions for earthworm pore formation during sandstone acidification, and the results showed that sandstone reservoirs with strong inhomogeneity are favorable for earthworm pore formation at low injection rates. A similar study was done by Morgenthaler et al Similar studies on the effect of inhomogeneity showed that the effect of inhomogeneity on permeability in small-scale lithology is greater than the effect of petrographic mineralogy on permeability.…”

Section: Introductionmentioning

confidence: 99%

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Research on high efficiency and retarded autogenous mud acid for plugging removal in a sandstone reservoir—Example of Bai 823 well area

Li,

Yang,

et al. 2023

Energy Science & Engineering

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Acidification, as an effective measure to remove blockages and restore oil well productivity, has received widespread concern. However, conventional acid systems can only be used to unblock near‐wellbore zones and are difficult to act on far‐wellbore reservoirs. In this article, scanning electron microscope, energy‐dispersive X‐ray spectroscope, and X‐ray diffractometer were used to analyze the blockages in the Bai 823 well area, and it was determined that their main components were CaCO3 and FeCO3, which provided the basis for the construction of the unblocking formula. Then, the acid dissolution experiments on the plugging materials showed that the dissolution rate of 10% HCl can reach more than 85% for the scale sample; the acid dissolution experiments on the rock sample showed that the autogenous mud acid has better dissolution performance and better retardation performance for the rock sample, and the effective action time is longer, so it can be used for deeper unplugging of the reservoir. Finally, the process parameters such as the optimal acid concentration, acid dosage, and discharge volume were optimized by establishing the fracture‐matrix acid flow reaction model. Research results indicate that the autogenous mud acid can act on the blockage in the far‐wellbore area to improve the acidification effect.

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“…

{v}_{f}=-\frac{{k}_{f}^{\tau }}{\mu }\frac{\partial {p}_{f}}{\partial {x}^{\tau }},

-\nabla (\rho \cdot {v}_{f})=\frac{\partial }{\partial t}(\rho {\phi }_{f})-\rho {Q}_{f}.

The fracture tangential permeability can be calculated by applying the fracture width according to the cubic law as follows.

{k}_{f}^{\tau }=\frac{{w}_{f}^{2}}{12}.

Bringing Equation () into Equation (), the acid pressure distribution in the main body of the fracture is

{w}_{f}{c}_{f}\frac{\partial {p}_{f}}{\partial t}-{w}_{f}\nabla \cdot \left(\frac{{k}_{f}^{\tau }}{\mu }\frac{\partial {p}_{f}}{\partial {x}^{\tau }}\right)={w}_{f}{Q}_{f}.

The acid concentration transport equation in the fracture consists of HF and H 2 SiF 6 concentration transport equation, which is as follows 22

w_{f} \frac{\partial C_{f, italicAi}}{\partial t} + w_{f} v_{f} \frac{\partial C_{f, italicAi}}{\partial x^{τ}} - \frac{\partial C_{f, italicAi}}{\partial x^{τ}} (w_{f} D_{Ai}^{})

…”

Section: Results and Discussionmentioning

confidence: 99%

“…The acid concentration transport equation in the fracture consists of HF and H 2 SiF 6 concentration transport equation, which is as follows 22

{w}_{f}\frac{\partial {C}_{f,{Ai}}}{\partial t}+{w}_{f}{v}_{f}\frac{\partial {C}_{f,{Ai}}}{\partial {x}^{\tau }}-\frac{\partial {C}_{f,{Ai}}}{\partial {x}^{\tau }}\left({w}_{f}{D}_{{Ai}}^{{fr}}\frac{\partial {C}_{f,{Ai}}}{\partial {x}^{\tau }}\right)=0,\unicode{x02007}\unicode{x02007}i=\mathrm{2,3}.

…”

Section: Results and Discussionmentioning

confidence: 99%

“…The acid concentration transport equation in the fracture consists of HF and H 2 SiF 6 concentration transport equation, which is as follows. 22 w C…”

Section: Evaluation Of Acid Retardation Performancementioning

confidence: 99%

Section: Evaluation Of Acid Retardation Performancementioning

confidence: 99%