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Numerical calculation and multi-factor analysis of slurry diffusion in an inclined geological fracture

Calcul numérique et analyse multifactorielle de diffusion de boue dans Une fracture géologique inclinée

Cálculo numérico y análisis multifactorial de la difusión de lodos en una fractura geológica inclinada

倾斜地质裂缝中浆体扩散的数值计算及多因素分析

Calculo numérica e analise multifatorial da difusão de calda de cimento em uma fratura geológica inclinada

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Abstract

Slurry grouting plays an important role in water plugging for hydrogeological engineering and there are multiple factors that restrict the slurry flow. This study investigates the restriction mechanisms, based on a single inclined rough fracture, employing a space stepwise method (SSM) using multi-direction sectors (MDS) for calculating the diffusion of variable-viscosity slurry under constant flow. The specifically developed numerical algorithm is validated by experimental results. The spatio-temporal effects of major factors on the flow, and the rock hydraulic properties, were analyzed for cement-based slurry. The results show that the slurry flow calculated by MDS-SSM exhibits strong fitting with experimental results. The diffusion pattern no longer exhibits a circular plane, but rather a double semi-elliptical distribution. The fracture direction angle, especially for the upward vertical flow, must be considered in the case of a larger dip angle. The main controlling factor of the pressure field is the higher slurry viscosity in regions far from the injection hole, and the influence of dip angle is significantly greater closer to the hole. Roughness has an influence on the fracture hydraulic properties, and the required grouting pressure increases with an increase in roughness. The fracture aperture, viscosity coefficient, and diffusion radius are three key factors with strong sensitivity affecting the forecasting accuracy of grouting parameters. The role of the fracture dip angle can be neglected only in narrow fractures and long-distance diffusion with higher-viscosity slurry or larger pressure. The key threshold value can be obtained with a fitting formula under given conditions.

Résumé

La cimentation à base de boue joue un rôle important pour le bouchage de voie d’eau en ingénierie hydrogéologique et plusieurs facteurs restreignent les flux de boue. Cette étude investigue les mécanismes de restriction, sur la base d’une fracture unique inclinée et rugueuse, en employant une méthode par étape spatiale (MES) qui utilise des secteurs multidirectionnels (SMD) pour le calcul de la diffusion de boue à viscosité variable à débit constant. L’algorithme numérique développé spécifiquement est validé par des résultats expérimentaux. Les effets spatio-temporels des facteurs majeurs sur l’écoulement, et les propriétés hydrauliques de la roche, ont été analysés pour une boue à base de ciment. Les résultats montrent que le débit de boue calculé par SMD-MES montre un ajustement robuste avec les résultats expérimentaux. Les motifs de diffusion ne montrent plus un plan circulaire, mais plutôt une double distribution semi-elliptique. L’angle de direction de la fracture, en particulier pour les écoulements ascendants verticaux, devront être considérés pour le cas d’un angle de pendage élevé. Le principal facteur de contrôle du champ de pression est la plus grande viscosité de boue dans les régions éloignées du trou d’injection, et l’influence de l’angle de pendage est significativement plus élevée prêt du trou. La rugosité a une influence sur les propriétés hydrauliques de la fracture, et les pressions requises pour le scellement augmentent avec l’augmentation de rugosité. L’ouverture de la fracture, le coefficient de viscosité, et le rayon de diffusion sont trois facteurs clés avec une forte sensibilité qui affectent la précision les prédictions des paramètres de scellements. Le rôle de l’angle de pendage de la fracture peut être négligé seulement pour les fractures étroites et la diffusion à longue distance avec des boues à haute viscosité ou pour des pressions plus élevées. La valeur de seuil clé peut être obtenue à partir d’une formule empirique sous certaines conditions.

Resumen

El revestimiento por lodos juega un papel importante en el taponamiento de agua para la ingeniería hidrogeológica y existen múltiples factores que restringen el flujo de los lodos. Este estudio investiga los mecanismos de restricción, basados en una sola fractura inclinada en bruto, empleando un método espacial escalonado (SSM) que utiliza sectores multidireccionales (MDS) para calcular la difusión de lodos de viscosidad variable bajo flujo constante. El algoritmo numérico desarrollado específicamente es validado por resultados experimentales. Los efectos espacio-temporales de los principales factores en el flujo, y las propiedades hidráulicas de las rocas, fueron analizados para determinar la presencia de lodos a base de cemento. Los resultados muestran que el flujo de lodos calculado por el MDS-SSM muestra un ajuste fuerte con resultados experimentales. El patrón de difusión ya no presenta un plano circular, sino una doble distribución semielíptica. El ángulo de dirección de la fractura, especialmente para el flujo vertical ascendente, debe considerarse en el caso de un ángulo de inclinación mayor. El principal factor de control del campo de presión es la mayor viscosidad del lodo en regiones alejadas del pozo de inyección, y la influencia del ángulo de inclinación es significativamente mayor cerca del pozo. La rugosidad influye en las propiedades hidráulicas de la fractura, y la presión de inyección requerida aumenta con el aumento de la rugosidad. La apertura de la fractura, el coeficiente de viscosidad y el radio de difusión son tres factores clave con una gran sensibilidad que afectan a la precisión de las previsiones de los parámetros de inyección. El papel del ángulo de inclinación de la fractura sólo se puede descuidar en fracturas estrechas y en la difusión a larga distancia con lodos de mayor viscosidad o mayor presión. El valor umbral clave se puede obtener con una fórmula de ajuste bajo determinadas condiciones.

摘要

本研究以单斜粗糙裂缝为研究对象, 采用基于多方向扇形(MDS)的空间分步方法(SSM)计算变粘度浆体在恒定流量下的扩散作用, 调研了堵水的机理。 利用实验结果验证了开发的数值算法的有效性。本研究分析了影响水泥浆流动的主要因素的时空效应, 以及水泥浆的岩石水力特性。结果表明, 用MDS-SSM方法计算的泥浆流量与实验结果吻合较好。扩散模式不再是一个环形平面, 而是一个双半椭圆分布。在倾角较大的情况下, 必须考虑裂缝方位角, 特别是向上垂直流动的方位角。压力场的主要控制因素是远离注水井区域的泥浆粘度较高, 而靠近注水井区域倾角的影响明显较大。粗糙度对裂缝水力特性有影响, 随着粗糙度的增加, 所需灌浆压力也增大。裂缝宽度、粘滞系数和扩散半径是影响注浆参数预测精度的高敏感性三个关键因素。只有在狭窄的裂缝中和高粘度泥浆或较大压力的长距离扩散条件下, 裂缝倾角的影响才可以忽略。在给定的条件下, 通过拟合公式可以得到关键阈值。

Resumo

Cimentação usando calda de cimento tem um importante papel no tamponamento de água na engenharia hidrogeológica e existem múltiplos fatores que restringem o fluxo de injeção da calda. Este estudo investiga os mecanismos de restrição baseados e uma única fratura áspera, empregando o método space stepwise (MSS) usando setores multi-direcionais (SMD) para calcular a difusão da calda de cimento com viscosidade variável sob fluxo constante. O modelo numérico especificamente desenvolvido é validado por resultados experimentais. Os efeitos espaço-temporais dos principais fatores no fluxo, e a propriedades hidráulicas da rocha foram analisadas para calda de cimento. Os resultados mostram que o fluxo da calda calculado por SMD-SSM mostram boa correlação com os resultados experimentais. O padrão de difusão não mostra mais um plano circular, porém uma distribuição dupla semielíptica. O anglo e direção da fratura, especialmente pata o fluxo vertical ascendente, precisa ser considerado nos casos de alto angulo e mergulho. O principal fator de controle do campo de pressão é a alta viscosidade da calda em regiões distantes do furo de injeção, e a influência do ângulo de mergulho é significativamente próximo ao do poço. A rugosidade influencia as propriedades hidráulicas das fraturas, e requer aumento da pressão de injeção da calda de cimento com o aumento da rugosidade. A abertura da fratura, coeficiente de viscosidade e raio de difusão são três fatores com forte sensibilidade que afetam a precisão da estimativa dos parâmetros de cimentação. O papel do ângulo de mergulho da fratura pode ser negligenciado apenas em fraturas estreitas e difusão de longa distância com alta viscosidade ou alta pressão. O valor limite pode ser obtido com uma formula própria sob as condições dadas.

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Acknowledgements

The authors express their sincere thanks to the reviewers for their helpful comments and suggestions for improving this paper.

Funding information

This work is supported by the National Key R&D Program of China (Grant No. 2017YFC1503101), National Natural Science Foundation of China (Grant No. 51879041, U1710253), the Fundamental Research Funds for the Central Universities (grant No. N180105029) and Anhui Province Science and Technology Project of China (Grant No. 17030901023).

Author information

Correspondence to Lianchong Li.

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Mu, W., Li, L., Yang, T. et al. Numerical calculation and multi-factor analysis of slurry diffusion in an inclined geological fracture. Hydrogeol J (2020). https://doi.org/10.1007/s10040-019-02103-y

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Keywords

  • Fractured rocks
  • Diffusion
  • Hydraulic properties
  • Variable viscosity slurry