Experimental test and theoretical calculation of the fracture height limit of gas pipe flow to Darcy flow

Low-speed flow experiments in which ultra-fine copper tubes are used to simulate micro-fractures in carbonate strata are conducted to analyze the variations of gas flow state in fractures of different fracture heights,determine flow state transition limit and transition interval,and establish the calculation method of flow state transition limit.The results show that the ideal Hagen-Poiseuille flow is the main form of gas flow in large fractures.Due to the decrease of fracture height,the gas flow in the fracture changes from Hagen-Poiseuille flow with ideal smooth seam surface to non-Hagen-Poiseuille flow,and the critical point of the transition is the boundary of flow state transition.After the fracture height continues to decrease to a certain extent below the boundary of the flow state transition fracture height,the form of gas flow gradually changes to the ideal Darcy flow,thus the transition interval of the gas flow state in the closing process of fracture can be determined.Based on the three-dimensional microconvex body scanning of the fracture surface,the material properties of fracture and properties of fluid in the fracture,a method for calculating the boundary of flow state transition is established.The experimental test and theoretical calculation show that the limit of the fracture height for the transition from pipe flow to Darcy flow is about twice the sum of the maximum height of the microconvex bodies on the upper and lower sides of the fracture.

A method for predicting the water-flowing fractured zone height based on an improved key stratum theory

In the process of using the original key stratum theory to predict the height of a water-flowing fractured zone(WFZ),the influence of rock strata outside the calculation range on the rock strata within the calculation range as well as the fact that the shape of the overburden deformation area will change with the excavation length are ignored.In this paper,an improved key stratum theory(IKS theory)was proposed by fixing these two shortcomings.Then,a WFZ height prediction method based on IKS theory was established and applied.First,the range of overburden involved in the analysis was determined according to the tensile stress distribution range above the goaf.Second,the key stratum in the overburden involved in the analysis was identified through IKS theory.Finally,the tendency of the WFZ to develop upward was determined by judging whether or not the identified key stratum will break.The proposed method was applied and verified in a mining case study,and the reasons for the differences in the development patterns between the WFZs in coalfields in Northwest and East China were also fully explained by this method.

Formation mechanism and height calculation of the caved zone and water-conducting fracture zone in solid backfill mining

To study the heights of the caved zone and water-conducting fracture zone in backfill mining,the failure mechanism of strata during backfill mining was analyzed,and a method for determining the heights of the two zones was proposed based on key strata theory.The movement and failure regularity of the strata above the backfilling panel were revealed through numerical simulation.Considering the geologic conditions of the CT101 backfilling panel,the height of the fracture zone was determined using the proposed method along with empirical calculation,numerical simulation,and borehole detection.The results of the new calculation method were similar to in situ measurements.The traditional empirical formula,which is based on the equivalent mining height model,resulted in large errors during calculation.The findings indicate the reliability of the new method and demonstrate its significance for creating reference data for related studies.

New P3D Hydraulic Fracturing Model Based on the Radial Flow

Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on the basis of the fundamental theory and the original 1D fluid flow is replaced with a more representatively radial flow. The distribution of the fluid in the modified fluid field is analyzed and a sound explanation to the problem is given. Due to the consideration of the fluid flow in the vertical direction, the modified model can predict the fracture height much better. To validate the rationality of the radial fluid flow assumption, the distribution of the fluid in the modified fluid field is simulated with the plane potential flow by using finite element method. And the results agree effectively with those from the assumption. Through comparing with the full 3D model, the results show that this new P3D model can be used to aid the fracturing design and predict the fracture height under poorly contained situation.

Analysis of a constant height hydraulic fracture driven by a power-law fluid

The focus of this study is to analyze a parametric space for the problem of a constant height hydraulic fracture driven by a power-law fluid.The interplay of physical mechanisms related to toughness,fluid resistance,and leakoff is considered,but the model is restricted to local elasticity for simplicity.The problem of a semi-infinite constant height fracture is first analyzed:limiting solutions are obtained analytically and their locations inside the dimensionless parametric space are obtained.Then,the problem of a finite constant height fracture is investigated.Similarly,limiting vertex solutions are first outlined and then their locations in the parametric space are quantified.Results demonstrate that the effect of the power-law factor is relatively mild,as it does not significantly distort the parametric spaces.At the same time,there are quantitative differences,which are also determined by the obtained results.Numerical examples highlighting the effect of fracture regime on morphology of multiple fractures are presented at the end.