Numerical Simulation of the Propagation of Hydraulic and Natural Fracture Using Dijkstra’s Algorithm

Abstract

Utilization of hydraulic-fracturing technology is dramatically increasing in exploitation of natural gas extraction. However the prediction of the configuration of propagated hydraulic fracture is extremely challenging. This paper presents a numerical method of obtaining the configuration of the propagated hydraulic fracture into discrete natural fracture network system. The method is developed on the basis of weighted fracture which is derived in combination of Dijkstra's algorithm energy theory and vector method. Numerical results along with experimental data demonstrated that proposed method is capable of predicting the propagated hydraulic fracture configuration reasonably with high computation efficiency. Sensitivity analysis reveals a number of interesting observation results: the shortest path weight value decreases with increasing of fracture density and length, and increases with increasing of the angle between fractures to the maximum principal stress direction. Our method is helpful for evaluating the complexity of the discrete fracture network, to obtain the extension direction of the fracture.

Experimental and Simulation Studies of Energized Fracturing Fluid Efficiency in Tight Gas Formations

“…After opening the valve at the bottom of the chamber, the measurement was initiated by measuring the value of filtration after 1, 4, 9, 16, 25, 36, 49 min. Taking into account data on the amount of filtrate as a function of time, the relationship between the amount of filtrate (cm 3 ) and the root of time (min 1 2 ) was plotted and leakoff coefficients were calculated: C w and Spurt Loss ( Figure 1, Table 1).…”

“…Considering the continuing depletion of energy resources in the world [1,2], the extraction of natural gas has become a priority and it is believed to be a more ecological solution than the extraction of high-emission solid fossils. Hydraulic fracturing is the most efficient method for stimulating hydrocarbon deposits [3] and has been used for many years to produce gas from deep and poorly permeable geological formations. Multistage fracturing of horizontal wells significantly improves the production performance of low and ultralow permeability gas reservoirs.…”

Identification of Critical Transmission Lines in Complex Power Networks

“…Some new approaches, such as the compressive sensing-based approach [35] and graphical learning-based approach [36,37] were proposed in recent years. Based on Dijkstra's algorithm [38], CAA is proposed in this study. The sensitive regions can be obtained through the cyclic addition of different lines.…”

Dijkstra algorithm-based ray tracing for tunnel-like structures

“…This algorithm has often been used not only in graph theory but also in many other applications such as Operations Research (OR), management science, transportation, and Geographic Information System (GIS) (Zhan and Noon, 1998). On the other hand, since the movements of wavefront of any waves are governed by the Fermat's principle (Schuster, 1904), we can simulate propagation of various types of waves by use of DA-based computational methods; for examples, tsunami wave propagation in ocean by Uchida et al (2014), tracing of optical rays in free space with obstacles by Uchida (2015), and propagation of hydraulic and natural fractures by Wu and Li (2016) were reported.…”