Shaobin Hu

Local heat transfer characteristics of water flowing through a single fracture within a cylindrical granite specimen

The local heat transfer coefficient (LHTC) can be an effective indicator to describe the local heat transfer characteristics of fractures but has rarely been employed to investigate the local heat exchange properties of a hot dry rock fracture compared to the overall heat transfer coefficient (OHTC). The aim of this paper is to investigate the LHTC of water flowing through a single fracture within a cylindrical granite specimen under confining pressure by combining the numerical modeling approach and the experimental results. A numerical model was successfully developed and verified by the test data. It is found that the local heat transfer coefficient is obviously closely related to the fluctuation of the fracture morphology. Within a certain range of aperture, narrower fracture has higher local heat transfer ability. Increasing the flow rate did not significantly improve the local heat transfer ability in the flat area of the fracture for a fixed fracture aperture. However, at the rougher areas, the flow rate has a higher effect, and the sunken positions at the fracture surface have much larger LHTC. A correlated model was developed to describe the relationship between waviness and LHTC. In addition, a comparison between the LHTCs and the OHTCs shows that the definition-based method presents the smallest values of the OHTCs, which are the closest to the arithmetic mean values of the corresponding LHTCs.

Experimental and Numerical Study on Scale Effects of Gas Emission from Coal Particles

In order to study the scale effects and formation mechanism of gas emission from coal particles, we conducted gas desorption and diffusion experiments, investigated the variation of particle size and its effect on gas flow, analyzed and discussed the control mechanism and gas diffusion model of coal. Based on the above, we found that the bidisperse diffusion model was suitable to study the size effects of gas emission and further established a simplified numerical method of bidisperse diffusion model and compared it with the experiment results. The results showed that the accumulated gas emission volume and the initial gas emission speed have scale characteristics. The scale effects of gas emission from coal are determined by the multi-scale pore structure of coal. The diffusion coefficient and path of coal particle determined the gas flow process. Through the gas desorption and diffusion experiments, we can find a way to determine the critical diffusion parameters. On the basis of experiments and theoretical analyses performed, the processes of gas emission from coal particles are studied and their mathematical models are put forward. These models can describe the experimental phenomena fairly.

An Analytical Model for Assessing Stability of Pre-Existing Faults in Caprock Caused by Fluid Injection and Extraction in a Reservoir

Induced seismicity and fault reactivation associated with fluid injection and depletion were reported in hydrocarbon, geothermal, and waste fluid injection fields worldwide. Here, we establish an analytical model to assess fault reactivation surrounding a reservoir during fluid injection and extraction that considers the stress concentrations at the fault tips and the effects of fault length. In this model, induced stress analysis in a full-space under the plane strain condition is implemented based on Eshelby’s theory of inclusions in terms of a homogeneous, isotropic, and poroelastic medium. The stress intensity factor concept in linear elastic fracture mechanics is adopted as an instability criterion for pre-existing faults in surrounding rocks. To characterize the fault reactivation caused by fluid injection and extraction, we define a new index, the “fault reactivation factor” η, which can be interpreted as an index of fault stability in response to fluid pressure changes per unit within a reservoir resulting from injection or extraction. The critical fluid pressure change within a reservoir is also determined by the superposition principle using the in situ stress surrounding a fault. Our parameter sensitivity analyses show that the fault reactivation tendency is strongly sensitive to fault location, fault length, fault dip angle, and Poisson’s ratio of the surrounding rock. Our case study demonstrates that the proposed model focuses on the mechanical behavior of the whole fault, unlike the conventional methodologies. The proposed method can be applied to engineering cases related to injection and depletion within a reservoir owing to its efficient computational codes implementation.

An Analytical Method for Determining the Convection Heat Transfer Coefficient Between Flowing Fluid and Rock Fracture Walls

The convective heat transfer coefficient (HTC) is a useful indicator that characterizes the convective heat transfer properties between flowing fluid and hot dry rock. An analytical method is developed to explore a more realistic formula for the HTC. First, a heat transfer model is described that can be used to determine the general expression of the HTC. As one of the novel elements, the new model can consider an arbitrary function of temperature distribution on the fracture wall along the direction of the rock radius. The resulting Dirichlet problem of the Laplace equation on a semi-disk is successfully solved with the Green’s function method. Four specific formulas for the HTC are derived and compared by assuming the temperature distributions along the radius of the fracture wall to be zeroth-, first-, second-, and third-order polynomials. Comparative verification of the four specific formulas based on the test data shows that the formula A corresponding to the zeroth-order polynomial always predicts stable HTC values. At low flow rates, the four formulas predict similar values of HTC, but at higher flow rates, formulas B and D, respectively, corresponding to the first- and third-order polynomials, predict either too large or too small values of the HTC, while formula C, corresponding to the second-order polynomial, predicts relatively acceptable HTC values. However, we cannot tell which one is the more rational formula between formulas A and C due to the limited information measured. One of the clear advantages of formula C is that it can avoid the drawbacks of the discontinuity of temperature and the singular integral of HTC at the points (±R, 0). Further experimental work to measure the actual temperature distribution of water in the fracture will be of great value. It is also found that the absorbed heat of the fluid, Q, has a significant impact on the prediction results of the HTC. The temperatures at the inlet and the outlet used for Q should be consistent with the assumptions adopted in the derivation of its corresponding HTC formula. A mismatched value of Q might be the reason that some existing HTC formulas predict negative or extremely large HTCs at high flow rates.