is an island-free network model for estimating the permeability of shale gas
https://www.nature.com/articles/s41598-021-86829-4
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7p Authors: Di Zhang, Xinghao Zhang, Haohao Guo, Dantong Lin, Jay N. Meegoda & Liming HuResearch highlights:
In this study, the permeability of shale is the use of pore networks Model to predict. The characteristics of pore structure can be described by specific parameters, including pores, pore body and pore throat size and distribution and coordination numbers. The isotope was incorporated into the model using coordinated number ratios and an algorithm developed for pore connections in shale formation. The proposed three-dimensional pore network model was verified by predicting the hydraulic connection and comparing it with several high-pressure permeability tests.
Introduction to the results
Compared with the prediction based on the ectopic pore network model, the prediction from the non-tropical pore network model is closer to the test results. The predicted permeability values of the four shales in the Chinese Al-Qaeda Basin using the same-directional pore network model for numerical simulation are very similar to the values measured in laboratory tests. This study confirms that the smokeless three-dimensional pore network model developed can reasonably represent the natural gas flow in actual shale formation.Thus as a forecasting tool.
Key 1: The parameters of the proposed pore network
Using mathematical methods combined with the actual pore structure data, an equivalent pore network model with a variable coordination number was developed, which can accommodate different pore sizes , Pores, pore connections and pores have variable coordination numbers.
network model The conventional three-dimensional lattice of the pores connected by the throat represents the void space of the rock. Each pore throat hole or pore body is assumed to be cylindrical or spherical in a regularly spaced grid 16 , 24 . This assumption is the development of the prediction model to describe the main part of the actual formate porous network Foundation 25 . This model simplifies the geometric materials of complex leakage channels (holes, throats) into conventional geometric shapes, such as spheres, cylinders, etc., and arranges them in a grid on a regular basis. To construct the above-mentioned equivalent pore network, the following six key model parameters are needed:
- pore radius (R) p) and its distribution: the pore radius represents the large cavity in the entire geological medium Pore size.
- pore throat radius ( R th) and its distribution: The pore throat radius indicates the size of the leakage channel between the pore bodies. Since any liquid migration between the pore bodies must flow through the pore throat,Therefore, the size of the throat of the pore directly affects the leakage characteristics of the entire geological medium.
- coordination number (ζ) and its distribution: The pore coordination number indicates the connection between the pore bodies. For geological media with high permeability (such as sand), one pore may be connected to multiple surrounding pores, so the coordination number is very high (> 6). For geological media with low water permeability (such as shale), the pore coordination number is relatively small (<4).>
- porosity (n): porosity represents the proportion of voids in the geological medium. Here, the void includes all pore bodies and pore throats, including dead pore bodies and corresponding pore throats.
- feature length (L ): L is a concept that introduces the distance between adjacent pores of an equivalent mesh. L cannot be less than the average pore size of the two connecting pores.
- Isotope parameters: Due to the different deposition factors of geographic materials, their hydraulic properties are different in different directions, resulting in isotope permeability. Anaerobic parameters try to capture this hydraulic ectopic position.
Point 2: Building a non-ridged pore network
When the average coordination number in the equivalent pore network model is low,There may be some pores whose coordination number is less than 2, which becomes a dead end pore (ζ = 1) or isolated pore (ζ = 0). There may also be dead-end pore groups and isolated pore groups (multiple pores have less than two connections to the main permeation channel). These pores are in the actual pore structure, but they do not contribute to the flow, so in the equivalent pore network model, they can be eliminated, thereby reducing the calculation time. In order to eliminate unconnected pores in the model, it is necessary to first define isolated pores and dead ends as follows:
1. Starting from any upstream pore, the channel is connected to any downstream pores through non-repetitive pores called leakage channels.
2. If the pore is contained in any leakage channel, it is called a leaky pore: otherwise, it is called a non-leaky pore.
3. For interrelated non-permeable groups, if there are holes that can be connected to any leaky channel, this hole group is defined as a dead-end hole group. Otherwise, it becomes an isolated pore group.
According to the above definition, it can be seen that in the equivalent pore network shown in Figure 3 , pore A is isolated, pore B is dead pore, pore C belongs to the isolated pore group, and pore D belongs Dead hole group. The dark area in Figure 3
shows the leaky pores and pore throats after the pore structure pretreatment.
Point 3: Probability-based generation of ectopic and coordinated numbers
Due to deposition and bedding,Shale is extremely incompetent, so the vertical permeability is usually lower compared to the horizontal or the bedding plane. 26. The published permeability values vary by order of magnitude and are different from the applied effective stress (between limiting pressure and pore pressure). The difference) is directly related to the direction of the bedding relative to the direction of flow (parallel or normal to the bedding). The test results of the Mississippi Barnett Shale 27, 28, 29 show that the permeability ranges from 10+17 to 10+21m2. For Scandinavian alumni and Tal'an Shale, Ganizard, etc. people. 26 reported permeability between 10+17 and 10+22m2. In the Woodford Shale in Western Canada, Patty 4 reported three to four orders of magnitude difference in subtropical permeability. Tenny et al.30 discovered up to 100 times more heterotopes for the German and Aldovich shale samples. Figure 5 shows the changes in permeability in different directions. This undirected behavior is incorporated into the pore network described in this study.
Summary
This paper describes the use of a new algorithm to improve the development of the pore network model, which uses unparalleled coordination numbers and isolated pore elimination methods. The model was verified by comparing the permeability of the simulated shale with the measured data of four shale rocks in the Longmaxi formation. The construction of an equivalent isotope pore network model is described in detail for the first time, especially the proposed method of generating coordination numbers and the assignment of coordination numbers based on the connection probability of adjacent pores. Exploiting the probability of connection, it is found that the connection between two pores is not only related to the coordination number of the two pores, but also related to the average coordination number of the entire network. A ratio of nothingness and symbiosis (ax:ay:az) was then introduced to explain the formation of no gaps in gas shale. In order to accurately represent the permeability behavior of different isotope formations (such as soil, sandstone or shale), the isotope ratios in the three directions are defined as the pore connection ratio in each direction. For different formations, different isotropic ratios are used to simulate different gas flow behaviors. The four shale samples collected from the Longmaxi formation in eastern Sichuan are in good agreement in predicting and measuring permeability, indicating that the isotope model is more representative than the traditional isotope pore network model.Can represent pore connections in shale formations.
References:
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