Search

In order to characterize the influence of fractures, multiple fields, and the differences between organic matter and inorganic matter on the transport of shale gas, a weighted coefficient is used to couple the transition diffusion model and Knudsen diffusion model to establish a permeability model of gas diffusion that is suitable for any Knudsen number. A gas flow model is established for organic matter considering diffusion, matrix shrinkage, stress sensitivity, and adsorption layer thickness; likewise, a gas flow model is established for inorganic matter considering diffusion and stress sensitivity. On this basis, the matrix grid in the discrete fracture model is further sub-divided into an organic matter grid and an inorganic matter grid, and the Galerkin finite element method is used to solve the discrete fracture model. The reliability of the established discrete fracture model is verified by comparing the proposed model to the BACA discrete fracture model. For validation, a shale gas well in the Yanan field in the Ordos basin is simulated using the proposed model. The results show that the effect of diffusion and matrix shrinkage on production can be ignored, but stress sensitivity and adsorption layer thickness have a moderate influence on production. Furthermore, neglecting the differences between organic matter and inorganic matter leads to errors. The errors are larger when there is less organic content or when the porosity ratio or pore diameter ratio are smaller. If hydraulic fracturing generates a larger number of fractures in the shale with relatively shorter half-lengths and bigger apertures, the production stabilization effects and the ultimate recovery rate will improve. For the shale gas well in the case study, the fitting error is approximately 74% if the dual-porosity model is used, but the fitting error decreases to less than 2% if the proposed discrete fracture model is used. [ABSTRACT FROM AUTHOR]

Izbash's law, which has a simpler form and exhibits narrower variations of coefficients than Forchheimer's law, has been successfully used to describe nonlinear flow in rough fractures. However, the meaning of its coefficients and its relationship with Forchheimer's law are poorly understood. Based on mathematical derivations, we identified the relationship between the cubic law, Forchheimer's law, and Izbash's law. An improved, dimensionally consistent Izbash's law which can be treated as the modified cubic law was formulated by incorporating a correction coefficient m I. The value of this coefficient depends on fluid properties, fracture geometries, and flow rate, and can be used to estimate the nonlinear flow state at given flow rates, in a similar fashion to Forchheimer number (F 0). A critical m I value (m cri) of 1.1 was determined that indicates whether the nonlinear effect can be ignored. Because m I is flow-rate-dependent, it can serve to describe the local flow behaviors, whereas the Izbash's exponent m is generally treated as a constant. At the maximum flow rate for a given pressure gradient versus flow rate curve, the value of m is approximately equal to that of m I , indicating that m represents the maximum nonlinear deviation. To validate the improved Izbash's law and the relevant findings, results from four experimental studies were utilized, and numerical simulations were performed. The result of this validation suggests the rationality of the analysis. The multiscale roughness effects on the coefficients were also investigated by selecting two different sampling intervals to construct the fracture surface. It was demonstrated that secondary roughness can enhance the development of nonlinear flow and increase the value of m , while its effects are strongly dependent on internal geometrical properties. • Relationship between cubic law, Forchheimer's law, and Izbash's law is revealed. • An improved Izbash's law is proposed. • The critical value of m for characterizing the onset of nonlinear flow is 1.1 [ABSTRACT FROM AUTHOR]

This study numerically investigated the nonlinear flow behaviors under the combined influences of shear displacement, roughness, and pressure gradient. Two-dimensional (2D) self-affine fractures with five fractal dimensions (1.1–1.5) were generated by the Weierstrass−Mandelbrot (W−M) function. Different conditions with six shear displacements (0.5–3.0 mm) and five pressure gradients (1–100 kPa/m) were applied to each model and the nonlinear flow behaviors were investigated based on microscopic descriptions and macroscopic characterizations. The results show that shear displacement coupled with the effect of high roughness can easily lead to heterogeneous void spaces and emergence of eddies. The flow rate of unmated rough fractures is always larger than that of mated rough fractures due to the effects of geometries and eddies, while this situation may be reversed in relatively smooth fractures. Rougher fractures correspond to lower flow rates under the same conditions and many eddies still exist although the fractures are mated. Increasing the pressure gradient can accelerate the development of eddies in rough fractures, while when the pressure gradient exceeds a certain value, its effect is restrained by apertures. In general, increasing the shear displacement and roughness can enhance the proportion of the quadratic term in Forchheimer's law. However, not all fractures were satisfied with these points. Increasing the shear displacement from 2.5 mm to 3.0 mm in the fracture with fractal dimension of 1.1 and increasing the fractal dimension from 1.4 to 1.5 at the shear displacement of 1.0 mm both decreased the proportion of the quadratic term. The ratio of the mechanical aperture to the hydraulic aperture (E/e) varies between 1.0 and 2.8, and its relationship with the Reynolds number (Re) can be described by a power function for the fractures with the fractal dimension of 1.1–1.4 (or JRC = 0.3–18). The relationship of E/e versus Re is strongly dependent on the fracture roughness, and for a given roughness the relationship is almost the same under different shear displacements and pressure gradients. However, this phenomenon is no longer valid as the fracture becomes rougher. The results of this study can deeply advance the understanding of nonlinear flow in rough fractures and its dependence on shear displacement, roughness, pressure gradient, and especially their combined influences under high Re. • Shear dilation was considered in 2D fractures generated by the W−M function. • Shear displacement can enhance the evolution of eddies in rough fractures. • Increasing roughness can advance the emergence of nonlinear flow. • Relationship between E / e and Re was established. [ABSTRACT FROM AUTHOR]

Abstract Drill cuttings unavoidably enter the annulus and affect the rheology of the drilling fluid in the process of drilling. The rheological properties of drilling fluids containing varying particle size and cuttings amounts were measured by using a rotational viscometer equipped with a widened gap. An algorithm based on Tikhonov regularization was proposed to transform the viscometry data into flow curves. Validity and availability of the presented algorithm were investigated by applying the algorithm to the base drilling fluid (without cuttings). Results showed that the flow curves of the cuttings-laden KCl/Polymer drilling fluids used in this study can be well depicted by the Herschel-Bulkley (H-B) model. Based on the rheological parameters obtained from curve fitting, the empirical correlations for the flow behavior index and the consistency coefficient were proposed. The consistency coefficient increases with the increase of cuttings amounts and the reduction of cuttings size. While the flow behavior index decreases with the increase of cuttings amounts and the reduction of the cuttings size. The proposed rheology determination approach in this study could give an orientative performance for cuttings-laden drilling fluids. Highlights • A new approach was developed to investigate the rheological behaviors of cuttings-laden drilling fluids. • An algorithm based on Tikhonov regularization was proposed. • The empirical correlations of rheological parameters for Herschel-Bulkley model were obtained. • Cuttings amounts and cuttings size have a combined effect on the rheological properties of drilling fluids. [ABSTRACT FROM AUTHOR]

Granular lost circulation materials (LCMs) are used to control fluid loss in naturally fractured thief zones. Rapid and automated identification of their optimal particle size distribution (PSD) is highly desirable. This paper proposes a PSD selection method for LCMs based on a PSD representation algorithm and the Monte Carlo method. The PSD representation algorithm describes the cumulative and compositional PSD curves of LCMs according to a piecewise cubic Hermite interpolation algorithm. Comparison with measured PSD data shows that the representation algorithm is more accurate than other commonly used PSD models in describing both homogeneous and mixed LCMs, and the relative errors are all within 10%. The Monte Carlo method is adopted to simulate LCMs with various compositions and select ones with PSDs that meet a proposed selection criterion. Experiments show that the PSD curves of the LCMs were all within the upper and lower bounds specified by the selection criterion. Plugging experiments show that LCMs with the recommended compositions can effectively enter fractures, and the fluid loss is less than 200 mL for half an hour under the pressure difference of 7 MPa. The proposed selection method can be used for the rapid and automatic design of granular LCMs used in fractured thief zones. • Common particle size distribution models are not suitable for complex systems. • Hermite interpolation is effective in describing the particle size distribution. • New selection method for particle size distribution are proposed and validated. • The selected lost circulation materials effectively reduce the fluid loss. [ABSTRACT FROM AUTHOR]