Nonlinear Model for Gas Flow into a Horizontal Well from a Shale Reservoir with a Branched Fracture Network

2016 ◽  
Vol 52 (2) ◽  
pp. 224-236
Author(s):  
Cheng-yong Li ◽  
Jun Zhou ◽  
Yi Luo ◽  
Ran Zhang
Energies ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2348 ◽  
Author(s):  
Syed Haider ◽  
Wardana Saputra ◽  
Tadeusz Patzek

We assemble a multiscale physical model of gas production in a mudrock (shale). We then tested our model on 45 horizontal gas wells in the Barnett with 12–15 years on production. When properly used, our model may enable shale companies to gain operational insights into how to complete a particular well in a particular shale. Macrofractures, microfractures, and nanopores form a multiscale system that controls gas flow in mudrocks. Near a horizontal well, hydraulic fracturing creates fractures at many scales and increases permeability of the source rock. We model the physical properties of the fracture network embedded in the Stimulated Reservoir Volume (SRV) with a fractal of dimension D < 2 . This fracture network interacts with the poorly connected nanopores in the organic matrix that are the source of almost all produced gas. In the practically impermeable mudrock, the known volumes of fracturing water and proppant must create an equal volume of fractures at all scales. Therefore, the surface area and the number of macrofractures created after hydrofracturing are constrained by the volume of injected water and proppant. The coupling between the fracture network and the organic matrix controls gas production from a horizontal well. The fracture permeability, k f , and the microscale source term, s, affect this coupling, thus controlling the reservoir pressure decline and mass transfer from the nanopore network to the fractures. Particular values of k f and s are determined by numerically fitting well production data with an optimization algorithm. The relationship between k f and s is somewhat hyperbolic and defines the type of fracture system created after hydrofracturing. The extremes of this relationship create two end-members of the fracture systems. A small value of the ratio k f / s causes faster production decline because of the high microscale source term, s. The effective fracture permeability is lower, but gas flow through the matrix to fractures is efficient, thus nullifying the negative effect of the smaller k f . For the high values of k f / s , production decline is slower. In summary, the fracture network permeability at the macroscale and the microscale source term control production rate of shale wells. The best quality wells have good, but not too good, macroscale connectivity.


2021 ◽  
Vol 12 ◽  
pp. 19-23
Author(s):  
Mohamed B. El_Mashede ◽  
Magdy M. Zaky ◽  
A. A. Saleh ◽  
M. EL_Hanash

This paper introduces the Ozone generator parameters analysis and its engineering design aspects. Practically, Ozone is successfully used in water treatment applications; furthermore, it can be used to treat the secondary system cooling water in nuclear research reactors. The main element in this process is the Ozone generator; it has many parameters that need to be set at its design. These parameters can be divided into those related to the electrical equivalent circuit of corona dielectric barrier discharge (DBD), those associated with injected gas flow between the two electrodes, and those belonging to temperature of the electrodes. This paper is intended to those parameters that are related to the electrical equivalent circuit which has two standard models: linear and nonlinear. In this regard, the determination of the component values of nonlinear model can be achieved very hardly. To handle such determination, the nonlinear model can be approximately treated as a linear model in an approaching fashion. Based on this approximation, Lissajous plot and differential evolution (DE) methodologies are used for the computation of DBD ozone chamber parameters. Additionally, a new theoretical technique will be presented


Materials ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2387 ◽  
Author(s):  
Bo Zhang ◽  
Yong Li ◽  
Nicholas Fantuzzi ◽  
Yuan Zhao ◽  
Yan-Bao Liu ◽  
...  

Coal contains a large number of fractures, whose characteristics are difficult to describe in detail, while their spatial distribution patterns may follow some macroscopic statistical laws. In this paper, several fracture geometric parameters (FGPs) were used to describe a fracture, and the coal seam was represented by a two-dimensional stochastic fracture network (SFN) which was generated and processed through a series of methods in MATLAB. Then, the processed SFN image was able to be imported into COMSOL Multiphysics and converted to a computational domain through the image function. In this way, the influences of different FGPs and their distribution patterns on the permeability of the coal seam were studied, and a finite element model to investigate gas flow properties in the coal seam was carried out. The results show that the permeability of the coal seam increased with the rising of fracture density, length, aperture, and with the decrease of the angle between the fracture orientation and the gas pressure gradient. It has also been found that large-sized fractures have a more significant contribution to coal reservoir permeability. Additionally, a numerical simulation of CBM extraction was carried out to show the potential of the proposed approach in the application of tackling practical engineering problems. According to the results, not only the connectivity of fractures but also variations of gas pressure and velocity can be displayed explicitly, which is consistent well with the actual situation.


Author(s):  
Yingzhong Yuan ◽  
Wende Yan ◽  
Fengbo Chen ◽  
Jiqiang Li ◽  
Qianhua Xiao ◽  
...  

AbstractComplex fracture systems including natural fractures and hydraulic fractures exist in shale gas reservoir with fractured horizontal well development. The flow of shale gas is a multi-scale flow process from microscopic nanometer pores to macroscopic large fractures. Due to the complexity of seepage mechanism and fracture parameters, it is difficult to realize fine numerical simulation for fractured horizontal wells in shale gas reservoirs. Mechanisms of adsorption–desorption on the surface of shale pores, slippage and Knudsen diffusion in the nanometer pores, Darcy and non-Darcy seepage in the matrix block and fractures are considered comprehensively in this paper. Through fine description of the complex fracture systems after horizontal well fracturing in shale gas reservoir, the problems of conventional corner point grids which are inflexible, directional, difficult to geometrically discretize arbitrarily oriented fractures are overcome. Discrete fracture network model based on unstructured perpendicular bisection grids is built in the numerical simulation. The results indicate that the discrete fracture network model can accurately describe fracture parameters including length, azimuth and density, and that the influences of fracture parameters on development effect of fractured horizontal well can be finely simulated. Cumulative production rate of shale gas is positively related to fracture half-length, fracture segments and fracture conductivity. When total fracture length is constant, fracturing effect is better if single fracture half-length or penetration ratio is relatively large and fracturing segments are moderate. Research results provide theoretical support for optimal design of fractured horizontal well in shale gas reservoir.


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