D Wang on TCLB Solver

Optimal packing ratio of proppant monolayer for partially-propped horizontal bedding fractures of shale

Sat, 01 Mar 2025 00:00:00 +0000

Abstract

Hydraulic fracturing, which aims at creating highly-connected fracture networks and a successful delivery of proppant to these fractures, has emerged as one of the primary techniques to improve the production of shale oil and gas. Considering the unique layered structure and the strong heterogeneity of shale in the Qingshankou Formation, Songliao Basin, China, an effective propping of the horizontal bedding fractures could potentially boost the oil and gas production. In this study, the permeability of proppant packs within the horizontal bedding fractures is investigated both experimentally and numerically. Specifically, we focus on the propping effect of a partial monolayer, aiming for an optimal packing ratio (OPR) of proppant particles with which the resultant fracture permeability reaches the maximum. An experimental workflow is firstly established to evaluate the permeability of the partially-propped fractures using the selected shale. The non-linear variation between the permeability of natural bedding fractures and the proppant packing ratio is demonstrated experimentally for the first time, and the critical OPR falls within the range of 0.2 – 0.4. Numerical simulations using the lattice Boltzmann-modified partially saturated method (LB-MPSM) provide further investigations on fracture porosity and aperture under confining stress, which shed light on the permeability results. Numerical results indicate that the fracture porosity reaches the maximum when the proppant packing ratio ranges between 0.3 and 0.4 under confining stress, and the increase in fracture aperture retards above a proppant packing ratio of 0.4. The research outcome contributes towards an improved understanding of the permeability of propped shale fractures filled with a partial proppant monolayer, which facilitates a better hydraulic fracturing design as well as an improved well productivity.

An Analytical Relative Permeability Model Considering Flow Path Structural Characteristics for Gas-Liquid Two-Phase Flow in Shale Fracture

Mon, 01 Jul 2024 00:00:00 +0000

Abstract

Relative permeability models are essential in describing the multiphase fluid flow in reservoir rocks. Literature work has shown that the existing theoretical models of relative permeability cannot perfectly describe the two-phase flow experimental data in fractures because those models are mostly developed for porous media (such as sandstone) or proposed without fully taking the specific characteristics of two-phase flow into consideration. In this paper, we propose a theoretical two-phase flow relative permeability model based on the tortuous flow channels, considering the structural characteristics of two-phase flow in the fractures. This model considers that the gas and liquid flow through different channels of different shapes and sizes at the same time. The formula for two-phase relative permeability was derived from cubic law in fracture and Darcy’s law, with the influence of the slip effect of the gas phase also considered. The results from different models were compared using several series of experimental data. The model proposed in this paper has a better fit than the others for the raw experimental data. This study demonstrates that it is crucial to take the flow paths and distribution of the two phases into consideration to model the two-phase flow in fracture accurately. This work also found that the tortuosity of the gas channel at the irreducible liquid saturation has a negative effect on gas relative permeability but positive to liquid relative permeability. Moreover, the model demonstrates that the decrease in aperture leads to an increase in the gas relative permeability due to gas slippage, while the impact of gas slippage reduces under high pressure.

Evaluating the stability and volumetric flowback rate of proppant packs in hydraulic fractures using the lattice Boltzmann-discrete element coupling method

Sat, 01 Jun 2024 00:00:00 +0000

Abstract

The stability and mobility of proppant packs in hydraulic fractures during hydrocarbon production are numerically investigated by the lattice Boltzmann-discrete element coupling method (LB-DEM). This study starts with a preliminary proppant settling test, from which a solid volume fraction of 0.575 is calibrated for the proppant pack in the fracture. In the established workflow to investigate proppant flowback, a displacement is applied to the fracture surfaces to compact the generated proppant pack as well as further mimicking proppant embedment under closure stress. When a pressure gradient is applied to drive the fluid-particle flow, a critical aperture-to-diameter ratio of 4 is observed, above which the proppant pack would collapse. The results also show that the volumetric proppant flowback rate increases quadratically with the fracture aperture, while a linear variation between the particle flux and the pressure gradient is exhibited for a fixed fracture aperture. The research outcome contributes towards an improved understanding of proppant flowback in hydraulic fractures, which also supports an optimised proppant size selection for hydraulic fracturing operations.

An Experimental Method for Obtaining Optimal Proppant Packing Ratios for Micro-Sized Proppant Placement in Unconventional Reservoirs

Mon, 01 Jan 2024 00:00:00 +0000

Abstract

Coal bed methane and shale gas reservoirs are extensively developed in China, not only because of their large reserves, but also because they are clean energy resources and contribute to the net zero emissions. However, these reservoirs are usually typical unconventional reservoirs with tight matrix and natural fractures. Hydraulic fracturing with micro-sized proppants is used to develop them cost-effectively. However, a quantitative design for micro-sized proppant injection is not mature and is still raising attention in industry. Different from traditional proppants, micro-sized proppants (<100 mesh) are required to be placed in fractures in a partial-monolayer manner in order to obtain maximum conductivity. Many previous theoretical studies have shown that propped fracture conductivity changes parabolically with proppant concentration and there is an optimal proppant packing ratio. However, no one has observed this phenomenon in the laboratory. In this paper, we will introduce a laboratory method for obtaining an optimal packing ratio and the corresponding test results using 140/200 mesh and 200/300 mesh silica sands. The results are then compared with our numerical modeling results based on the LBM (lattice Boltzmann) algorithm. Micro-sized sands are selected and sorted from a silica sand mine in Chifeng, Inner Mongolia. The sorting coefficient of the sand particles is strictly controlled within 1.20. The proppant breakage rate under 4000 psi is controlled within 10%. Naturally cracked cores with natural rough surfaces, which are obtained from a shale formation in China, are used to make the test units. A GCTS Rock Triaxial System instead of a traditional fracture conductivity tester is used to test the conductivity of fractures propped by micro-sized proppants. A Transient Pulse Method is used to test the propped fracture permeability. The permeability and conductivity of 140/200 mesh and 200/300 mesh silica sands are measured at six different proppant packing ratios, 0, 0.25, 0.375, 0.50, 0.75 and 1.0, under two different closure pressures, 3000psi (21MPa) and 4000psi (28MPa). The regression analysis results show that the optimal packing ratios of 140/200 and 200/300 mesh silica sands are 40.30% and 52.09% respectively, regardless of the closure pressure. However, the conductivity curves of 200/300 mesh silica sands show that their optimal packing ratio under 4000psi is 78.14%, much higher than the result under 3000psi, which is 52.09%. This is the first time in industry to obtain the optimal proppant packing ratios for micro-sized proppant placement by direct conductivity tests on real shale cores. Our numerical modeling results based on the LBM algorithm under the same conditions show a lower optimal packing ratio (30%-40%) than the measured results. This makes our laboratory tests more beneficial in targeting the causes of the discrepancies and rectifying mathematical models.

Understanding and predicting proppant bedload transport in hydraulic fracture via numerical simulation

Wed, 01 Mar 2023 00:00:00 +0000

Abstract

The transport mechanism of densely-packed proppant bed is numerically investigated by the lattice Boltzmann-discrete element coupling method (LB-DEM). While many of the previous studies aimed at proppant-laden slurry flow, this study focuses on the bedload transport of the settled proppant in the primary fracture. By constructing an ideal horizontal fracture, a detailed study on proppant bed motion induced by shearing flow is performed. The results show that the particle flux increases quadratically with the fluid flux, from which a nonlinear relationship is concluded. Further investigations on sediment rheology indicate that the shear-thinning property of the proppant bed leads to such nonlinear variation. With the decrease of shear viscosity, an increasing portion of the proppant bed is driven by the fluid. The current research devotes to an optimised design for fracturing fluid injection scheme as well as a better proppant flowback control, which further contributes to an improved hydraulic fracturing operation.

Numerical investigation of proppant transport at hydraulic-natural fracture intersection

Sat, 01 Jan 2022 00:00:00 +0000

Abstract

The transport mechanism of particles at fracture intersection is numerically studied by the coupled lattice Boltzmann-discrete element methods. First, the numerical method is validated via a benchmark test of the relative suspension viscosity. Second, a comprehensive parametric study on proppant transport through a T-junction is performed. The impacts of various parameters, including particle concentration, particle size, the Reynolds number and the fracture intersection angle are investigated. The results show that the proppant leak-off ratio decreases with particle concentration due to retardation and the Reynolds number due to inertial migration, and increases with fracture aperture. Particularly, the results also reveal a critical intersection angle of 60° at which the particle leak-off ratio reaches a maximum. Finally, an empirical expression is proposed to evaluate the particle leak-off ratio. The outcomes provide new insights into proppant transport in fracture networks and assist in an improved fracturing fluid design for naturally fractured reservoirs.

Numerical investigation of the effects of proppant embedment on fracture permeability and well production in Queensland coal seam gas reservoirs

Tue, 01 Jun 2021 00:00:00 +0000

Abstract

This paper introduces the development of a new predictive model in support of proppant injection in naturally fractured coal seam gas (CSG) reservoirs. In the proposed model, the finite element method (FEM) is used for the prediction of proppant embedment and elastoplastic deformation of the coal. The lattice Boltzmann method (LBM) is applied to the modelling of fluid flow through propped fractures, in which the modified partially saturated method (MPSM) is implemented to characterise the fluid–solid interactions. Permeability diagrams of the fractures are then generated as functions of particle packing ratio and effective stress. Finally, these results are incorporated into a radial Darcy flow analytical solution to predict the productivity index of the CSG wells under various proppant injection pressures and cleat compressibilities. The developed model is applied to selected coal samples from the Bowen and Surat Basins in Queensland, Australia. Modelling results indicate that proppant injection leads to increased fracture permeabilities and enhanced well productivity indexes. The elastoplastic deformation results in smaller permeability increase and less production enhancement when compared to the traditional linear elastic models. Although focused on Australian coals, the developed workflow can be broadly applicable to the assessment of potential stimulation efficacy in other unconventional reservoirs. In addition, a better understanding and implementation of the proppant injection scheme can effectively improve the post-fracturing performance, particularly in low-permeability coal intervals, which benefits the CSG industry.

Development of predictive models in support of micro-particle injection in naturally fractured reservoirs

Tue, 01 Jan 2019 00:00:00 +0000

Abstract

New models for particle embedment during micro-particle injection into naturally fractured reservoirs are developed. The proposed models aim to predict production benefit from the application of micro-particle injection during coal seam gas (CSG) stimulation with broader applications to other naturally fractured reservoirs. The elastoplastic finite element modelling is applied to coal sample from Surat basin (Australia), to predict micro-particle embedment and fracture deformation under various packing densities and closure stresses. The coupled lattice Boltzmann-discrete element model (LBM-DEM) is then used for permeability prediction. These results are combined in a radial Darcy flow analytical solution to predict the productivity index of CSG wells. Modelling results indicate that considering elastoplastic fracture surface deformation leads to smaller permeability increase and less production enhancement, if compared with the linear elastic deformation of fracture implemented in traditional models. Although focused on Australian coals, the developed workflow is more broadly applicable in other unconventional resources. Modelling of particle transport and leak-off in coal fracture intersected with a cleat using LBM-DEM approach demonstrates the effects of particle and cleat sizes, particle concentration and sedimentation on the leak-off process. The leak-off is significantly affected if the particle-cleat size ratio is higher than 0.5. Particle sedimentation increases leak-off into vertical cleat substantially, but has no effect on horizontal cleat. Suspensions of higher concentration result in higher leak-off for cleats with different apertures.

Improved coupling of time integration and hydrodynamic interaction in particle suspensions using the lattice Boltzmann and discrete element methods

Sun, 01 Apr 2018 00:00:00 +0000

Abstract

This paper introduces improvements to the simulation of particle suspensions using the lattice Boltzmann method (LBM) and the discrete element method (DEM). First, the benefit of using a two-relaxation-time (TRT) collision operator, instead of the popular Bhatnagar–Gross–Krook (BGK) collision operator, is demonstrated. Second, a modified solid weighting function for the partially saturated method (PSM) for fluid–solid interaction is defined and tested. Results are presented for a range of flow configurations, including sphere packs, duct flows, and settling spheres, with good accuracy and convergence observed. Past research has shown that the drag, and consequently permeability, predictions of the LBM exhibit viscosity-dependence when used with certain boundary conditions such as bounce-back or interpolated bounce-back, and this is most pronounced when the BGK collision operator is employed. The improvements presented here result in a range of computational viscosities, and therefore relaxation parameters, within which drag and permeability predictions remain invariant. This allows for greater flexibility in using the relaxation parameter to adjust the LBM timestep, which can subsequently improve synchronisation with the time integration of the DEM. This has significant implications for the simulation of large-scale suspension phenomena, where the limits of computational hardware persistently constrain the resolution of the LBM lattice.

Characterising the behaviour of hydraulic fracturing fluids via direct numerical simulation

Fri, 01 Jan 2016 00:00:00 +0000

Abstract

Current design tools used for predicting the placement of proppant in fractures are based on the solution of a simplified conservation equation that is heavily dependent on empirical relationships for particle settling and suspension viscosity. In light of these shortcomings, this paper presents the development of a computational fluid dynamics (CFD) model capable of micromechanical simulation of hydraulic fracturing fluids. The model developed in this research employs the discrete element method (DEM) to represent the proppant for a range of sizes and densities. For the fluid phase, the lattice Boltzmann method (LBM) is utilised in a generalised-Newtonian form. Full hydrodynamic coupling of the LBM and DEM is achieved via an immersed moving boundary condition. The developed model has the ability to simulate Navier-Stokes hydrodynamics, a range of rheological models (e.g. Bingham, power law), thermal effects as well as electromagnetic and electrostatic forces between particles and walls. The model captures the detailed interactions of proppant particles as well as the non-Newtonian rheology of the fracturing fluid in both experimental and fracture geometries. Simulations of small-scale experiments are used to describe suspension rheology as a function of proppant concentration while small-scale fracture models explore the settling and injection of a number of candidate formulations. These results show that the direct numerical simulation (DNS) approach presented in this paper represents a potentially valuable complement to contemporary models which can provide insight on the rheology of new or novel fracturing fluid formulations as well as explore the influence of complex in-situ features on the efficacy of a hydraulic fracture. More detailed knowledge of how proppant is transported from the wellbore to the fracture tip will provide insights that could be used in the optimisation of the hydraulic fracturing process. This is particularly relevant in coal seam gas reservoirs which can include bi-directional fracture networks, non-planar fracture paths, interburden terminations and other leak-off points.