New model of Single-Well Push-Pull thermal test in a Fracture-Matrix system

Wang, Quanrong; Shi, Wenguang; Zhan, Hongbin; Xiao, X. Yan H.

doi:10.1016/j.jhydrol.2020.124807

Cited by 12 publications

(3 citation statements)

References 36 publications

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“…In the case of the inverse Goldstein‐Weber transformation, a numerical integration formula based on the Bessel function was used, which is simple to implement and has a high degree of accuracy. Regarding the inverse Laplace transform, the Stehfest method (Wang et al 2020a; Wang et al 2020b) was used to perform the inversion of the semi‐analytical solution as presented in Equations 25 through 30. To facilitate the computation, we developed a MATLAB program, which is available from the authors upon request.…”

Section: Methodsmentioning

confidence: 99%

A Novel Semi‐Analytical Solution of Over‐Damped Slug Test in a Three‐Layered Aquifer System

Cao,

Wen,

Chen

et al. 2023

Groundwater

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The slug test has been commonly used to estimate aquifer parameters. Previous studies on the slug test mainly focused on a single‐layer aquifer. However, understanding the interaction between layers is particularly important when assessing aquifer parameters under certain circumstances. In this study, a new semi‐analytical model on transient flow in a three‐layered aquifer system with a partially penetrating well was developed for the slug test. The proposed model was solved using the Laplace transform method and the Goldstein‐Weber transform method, where the semi‐analytical solution for the model was obtained. The drawdowns of the proposed model were analyzed to understand the impacts of the different parameters on the drawdowns in a three‐layered aquifer system. The results indicated that groundwater interactions between the layers have a significant impact on the slug test. In addition, a shorter and deeper well screen as well as a greater permeability ratio between the layers creates a greater interface flow between them, leading to a higher drawdown in the slug test. Finally, a slug test in a three‐layered aquifer system was conducted in our laboratory to validate the new model, which indicated that the proposed model performed better in the interpretation of the experimental data than a previous model proposed by Hyder et al. (1994). We also proposed an empirical relationship to qualitatively identify the errors in the application of single‐layer model for the analysis of response data in a three‐layered aquifer system.

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Section: Methodsmentioning

confidence: 99%

A Novel Semi‐Analytical Solution of Over‐Damped Slug Test in a Three‐Layered Aquifer System

Cao,

Wen,

Chen

et al. 2023

Groundwater

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“…There are several numerical inverse Laplace transform methods available, such as the Stehfest method (Stehfest and Harald, 1970a;Stehfest and Harald, 1970b), the Schapery method (Schapery, 1962), the Fourier series method (Dubner and Abate, 1968), and so on. The Stehfest method was demonstrated to perform well in solving the problems related to solute transport (Wang et al, 2020a;Wang et al, 2020b), and will be employed to conduct the inverse Laplace transform on Eqs. ( 8) -( 9) in this study.…”

Section: Solutions In Real-time Domainmentioning

confidence: 99%

A Novel Analytical Model of Solute Transport in an Aquifer-Aquitard System with Mixing Processes in the Reservoirs

Shi

Wang

2022

Preprint

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Analytical models have been widely used to aid understanding the physical and chemical processes of tracer (or chemicals) in an aquifer-aquitard system in the laboratory-controlled experiment, when the observation data is few or not available during the experiment. When injecting tracer into (or extracting them from) the aquifer-aquitard system during experiments, the pre-inlet and after-outlet reservoirs are indispensable. However, the concentration variation in the reservoirs was not treated properly in previous analytical models, resulting in poor performance in interpreting experimental data. In this study, new mathematical models describing the concentration variation in the pre-inlet and the after-outlet reservoirs are proposed, and they are integrated into the novel analytical model. The novel analytical model is developed under the mobile-immobile (MIM) framework in the aquifer-aquitard system, considering the longitudinal and vertical dispersion, the advection, and the first-order chemical reaction in both aquifer and aquitard. A finite-difference solution is developed and the experimental data are employed to test the new analytical model. Results indicate that the concentration variation in the reservoirs is important to solute transport in the aquifer-aquitard system in the laboratory-controlled experiment, and the new analytical model outperforms the previous models in interpreting experimental data. The global sensitivity analysis demonstrates that the output concentration of solute transport in the aquifer-aquitard system is most sensitive to the volume of water in the pre-inlet reservoir. The contribution of the diffusion effect to the total mass flux of tracer crossing the aquifer-aquitard interface is much smaller than the contribution of the dispersive and advective effects.

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“…It has the potential to be a major supplier of primary energy for U.S. based‐load generation capacity by 2050 (Tester et al 2006). To extract the thermal energy stored in EGS, fluid will be injected into the reservoirs to improve the formation permeability and connectivity by re‐lubricating the pre‐existing fractures and creating new artificial fractures (Lu 2018; Wang et al 2020). The study of heat transfer in the discrete fractures is important to understand thermal energy transfer in the fractured porous media and enhance thermal energy recovery in the EGS.…”

Section: Introductionmentioning

confidence: 99%

Analytical Model for Heat Transfer in a Discrete Parallel Fracture–Rock Matrix System

Zhou

Wang

2022

Groundwater

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Mass transport and heat transfer in the single fracture situated in the rock matrix have been investigated extensively in the past decades. Extended from the single fracture, the model of parallel fractures in the rock matrix considers the interactions of multiple fractures and the ambient rock matrix. Heat transfer in such discrete fractures is important to understand thermal energy transfer in the fractured porous media. In this study, an analytical solution is developed for transient heat transfer in discrete parallel fractures in the rock matrix. The newly proposed model accounts for thermal convection, conduction, and dispersion in the fractures, transverse thermal conduction in the rock matrix, and the interactions between parallel fractures. The analytical solutions of the spatiotemporal temperature distributions in the fractures and rock matrix are derived in the Laplace domain and verified with the previous study. The results illustrate that: (1) the fracture aperture and spacing are important to the temperature evolutions in the system. Heat transfers faster when discrete parallel fractures are wide and closely spaced; (2) different roles of longitudinal thermal conduction are observed at high and low flow velocities in the fractures; (3) thermal dispersivity in the fractures is important for temperature evolution and should not be ignored; (4) when the fractures are closely spaced, transverse thermal conduction in the rock matrix has minor influence on fracture temperature. It becomes important when the fractures are sparsely distributed; and (5) the sensitivity analysis indicates that the parallel fracture-rock matrix is most sensitive to fracture thermal dispersivity.

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New model of Single-Well Push-Pull thermal test in a Fracture-Matrix system

Cited by 12 publications

References 36 publications

A Novel Semi‐Analytical Solution of Over‐Damped Slug Test in a Three‐Layered Aquifer System

A Novel Semi‐Analytical Solution of Over‐Damped Slug Test in a Three‐Layered Aquifer System

A Novel Analytical Model of Solute Transport in an Aquifer-Aquitard System with Mixing Processes in the Reservoirs

Analytical Model for Heat Transfer in a Discrete Parallel Fracture–Rock Matrix System

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