scholarly journals Physical and mathematical modeling of gas production in shale matrix

2018 ◽  
Vol 73 ◽  
pp. 12 ◽  
Author(s):  
Wei Guo ◽  
Rongze Yu ◽  
Xiaowei Zhang ◽  
Zhiming Hu
Keyword(s):  
Mathematical Model ◽  
Shale Gas ◽  
Gas Production ◽  
Experimental Results ◽  
Factors Affecting ◽  
Adsorbed Gas ◽  
Decline Curve ◽  
Longmaxi Shale ◽  
The Mathematical Model ◽  
Pressure Propagation

Shale gas mainly stores in shale matrix, and gas production in shale matrix is very important during exploration. In order to clarify gas production and transport mechanism in shale matrix, an experimental modeling of gas production in shale matrix was designed and conducted with Longmaxi shale samples collected from South of Sichuan. The experimental results show that gas production decline curve displays a “L” pattern which indicates initial production is high and declines rapidly, while late production is low and declines moderately; meanwhile, pressure propagation in shale matrix is quite slow due to ultralow permeability. Based on the results, a mathematical model was derived to describe gas production in shale matrix. The comparison between numerical solution of mathematical model and experimental results shows that the mathematical model can well describe gas transport in shale matrix. In addition, factors affecting gas production were investigated on the basis of the mathematical model. Adsorbed gas can replenish gas pressure in pores by desorption and delay pressure propagation, and gas production decreases very quickly when there is no adsorbed gas. Other parameters (diffusion coefficient, permeability and porosity) also need to be considered in shale gas development.

scholarly journals Review of Formation and Gas Characteristics in Shale Gas Reservoirs

Energies ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 5427
Author(s):  
Boning Zhang ◽  
Baochao Shan ◽  
Yulong Zhao ◽  
Liehui Zhang
Keyword(s):  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Shale Gas ◽  
Physical Parameters ◽  
Gas Reservoirs ◽  
Shale Formations ◽  
Adsorbed Gas ◽  
Shale Gas Reservoirs ◽  
Longmaxi Shale

An accurate understanding of formation and gas properties is crucial to the efficient development of shale gas resources. As one kind of unconventional energy, shale gas shows significant differences from conventional energy ones in terms of gas accumulation processes, pore structure characteristics, gas storage forms, physical parameters, and reservoir production modes. Traditional experimental techniques could not satisfy the need to capture the microscopic characteristics of pores and throats in shale plays. In this review, the uniqueness of shale gas reservoirs is elaborated from the perspective of: (1) geological and pore structural characteristics, (2) adsorption/desorption laws, and (3) differences in properties between the adsorbed gas and free gas. As to the first aspect, the mineral composition and organic geochemical characteristics of shale samples from the Longmaxi Formation, Sichuan Basin, China were measured and analyzed based on the experimental results. Principles of different methods to test pore size distribution in shale formations are introduced, after which the results of pore size distribution of samples from the Longmaxi shale are given. Based on the geological understanding of shale formations, three different types of shale gas and respective modeling methods are reviewed. Afterwards, the conventional adsorption models, Gibbs excess adsorption behaviors, and supercritical adsorption characteristics, as well as their applicability to engineering problems, are introduced. Finally, six methods of calculating virtual saturated vapor pressure, seven methods of giving adsorbed gas density, and 12 methods of calculating gas viscosity in different pressure and temperature conditions are collected and compared, with the recommended methods given after a comparison.

Lithology and sedimentary heterogeneity of the Longmaxi Shale in the southern Sichuan Basin, China

2021 ◽  
pp. 1-49
Author(s):  
Boling Pu ◽  
Dazhong Dong ◽  
Ning Xin-jun ◽  
Shufang Wang ◽  
Yuman Wang ◽  
...  
Keyword(s):  
Continental Shelf ◽  
Deep Water ◽  
Shale Gas ◽  
Sichuan Basin ◽  
Sedimentary Environment ◽  
Gas Production ◽  
Carbonaceous Shale ◽  
Gas Wells ◽  
Longmaxi Shale ◽  
Siliceous Shale

Producers have always been eager to know the reasons for the difference in the production of different shale gas wells. The Southern Sichuan Basin in China is one of the main production zones of Longmaxi shale gas, while the shale gas production is quite different in different shale gas wells. The Longmaxi formation was deposited in a deep water shelf that had poor circulation with the open ocean, and is composed of a variety of facies that are dominated by fine-grained (clay- to silt-size) particles with a varied organic matter distribution, causing heterogeneity of the shale gas concentration. According to the different mother debris and sedimentary environment, we recognized three general sedimentary subfacies and seven lithofacies on the basis of mineralogy, sedimentary texture and structures, biota and the logging response: (1) there are graptolite-rich shale facies, siliceous shale facies, calcareous shale facies, and a small amount of argillaceous limestone facies in the deep - water shelf in the Weiyuan area and graptolite-rich shale facies and carbonaceous shale facies in the Changning area; (2) there are argillaceous shale facies and argillaceous limestone facies in the semi - deep - water continental shelf of the Weiyuan area and silty shale facies in the Changning area; (3) argillaceous shale facies are mainly developed in the shallow muddy continental shelf in the Weiyuan area, while silty shale facies mainly developed in the shallow shelf in the Changning area. Judging from the biostratigraphy of graptolite, the sedimentary environment was different in different stages.

Simulation of oscillatory processes in the MVSTUDIUM package

2022 ◽  
Vol 14 (4) ◽  
pp. 139-148
Author(s):  
Aleksandr Poluektov ◽  
Konstantin Zolnikov ◽  
V. Antsiferova
Keyword(s):  
Mathematical Model ◽  
Friction Force ◽  
Computer Models ◽  
3D Models ◽  
Oscillatory Process ◽  
Suspension Point ◽  
Factors Affecting ◽  
2D And 3D ◽  
The Mathematical Model ◽  
Oscillatory Processes

The mathematical model and algorithms of oscillatory movements are considered. Various factors affecting the oscillatory process are considered. Oscillatory movements are constructed in the MVSTUDIUM modeling environment. The schemes of three computer models demonstrating oscillatory processes are determined: a model of a pendulum with a non-movable suspension point, a model of a pushing pendulum with friction force and a model of a breaking pendulum. Classes are being built to execute models with embedded properties, as well as with the ability to export the created classes to other models, and embed classes created by the program developer into the model. Creation of 2D and 3D models of oscillatory processes, an experiment behavior map and a virtual stand.

scholarly journals Analysis on Present Mathematical Model for Predicting the Crop Production

2020 ◽  
Vol 9 (12) ◽  
pp. 168-170
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Real World ◽  
Crop Production ◽  
Ghg Emissions ◽  
Data Set ◽  
Factors Affecting ◽  
The Government ◽  
The Mathematical Model ◽  
Government Website

India is a worldwide agriculture business powerhouse. Future of agriculture-based products depends on the crop production. A mathematical model might be characterized as a lot of equations that speak to the conduct of a framework. By using mathematical model in agriculture field, we can predict the production of crop in particular area. There are various factors affecting crops such as Rainfall, GHG Emissions, Temperature, Urbanization, climate, humidity etc. A mathematical model is a simplified representation of a real-world system. It forms the system using mathematical principles in the form of a condition or a set of conditions. Suppose we need to increase the crop production, at that time the mathematical model plays a major role and our work can be easier, more significant by using the mathematical model. Through the mathematical model we predict the crop production in upcoming years. .AI, ML, IOT play a major role to predict the future of agriculture, but without mathematical models it is not possible to predict crop production accurately. To solve the real-world agriculture problem, mathematical models play a major role for accurate results. Correlation Analysis, Multiple Regression analysis and fuzzy logic simulation standards have been utilized for building a grain production benefit depending model from crop production. Prediction of crop is beneficiary to the farmer to analyze the crop management. By using the present agriculture data set which is available on the government website, we can build a mathematical model.

Mathematical Modeling of Electrochemical Deburring

2010 ◽  
Vol 126-128 ◽  
pp. 545-550 ◽  
Author(s):  
Wen Ji Xu ◽  
W. Wang ◽  
Xu Yue Wang ◽  
Gui Bing Pang
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Influencing Factors ◽  
Applied Voltage ◽  
Experimental Results ◽  
Electrode Gap ◽  
Workpiece Material ◽  
Burr Height ◽  
Object A ◽  
The Mathematical Model

The drilling burr is taken as the research object. A mathematical model of electrochemical deburring (ECD) is established and the effects of main influencing factors, such as inter-electrode gap, applied voltage and deburring time, on burr height have been analyzed. The results show that the deburring time increases with the increase of initial burr height, inter-electrode gap, with the decrease of volume of electrochemical equivalent of the workpiece material, conductivity of electrolyte and applied voltage. The deburring time for various burr heights can be predicted by the mathematical model. The calculated results obtained from the mathematical model are approximately consistent with the experimental results. The results show that initial burr height h0=0.722mm is removed, and the fillet radius R=0.211mm is obtained.

scholarly journals The Evaluation and Sensitivity of Decline Curve Modelling

Energies ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2765
Author(s):  
Prinisha Manda ◽  
Diakanua Nkazi
Keyword(s):  
Shale Gas ◽  
Goodness Of Fit ◽  
Accuracy Assessment ◽  
Gas Production ◽  
Production Performance ◽  
Logistic Growth ◽  
Gas Reservoirs ◽  
Shale Gas Reservoirs ◽  
Decline Curve ◽  
Exponential Decline

The development of prediction tools for production performance and the lifespan of shale gas reservoirs has been a focus for petroleum engineers. Several decline curve models have been developed and compared with data from shale gas production. To accurately forecast the estimated ultimate recovery for shale gas reservoirs, consistent and accurate decline curve modelling is required. In this paper, the current decline curve models are evaluated using the goodness of fit as a measure of accuracy with field data. The evaluation found that there are advantages in using the current DCA models; however, they also have limitations associated with them that have to be addressed. Based on the accuracy assessment conducted on the different models, it appears that the Stretched Exponential Decline Model (SEDM) and Logistic Growth Model (LGM), followed by the Extended Exponential Decline Model (EEDM), the Power Law Exponential Model (PLE), the Doung’s Model, and lastly, the Arps Hyperbolic Decline Model, provide the best fit with production data.

The Gas Content Characteristics of Nanopores Developed in a Normal Pressure Shale Gas Reservoir in Southeast Chongqing, Sichuan Basin, China

2021 ◽  
Vol 21 (1) ◽  
pp. 698-706
Author(s):  
Fangwen Chen ◽  
Qiang Zheng ◽  
Hongqin Zhao ◽  
Xue Ding ◽  
Yiwen Ju ◽  
...  
Keyword(s):  
Organic Carbon ◽  
Shale Gas ◽  
Normal Pressure ◽  
Gas Content ◽  
Organic Carbon Content ◽  
Gas Reservoir ◽  
Free Gas ◽  
Shale Gas Reservoir ◽  
Adsorbed Gas ◽  
Longmaxi Shale

To evaluate the gas content characteristics of nanopores developed in a normal pressure shale gas reservoir, the Py1 well in southeast Chongqing was selected as a case study. A series of experiments was performed to analyze the total organic carbon content, porosity and gas content using core material samples of the Longmaxi Shale from the Py1 well. The results show that the adsorbed gas and free gas content in the nanopores developed in the Py1 well in the normal pressure shale gas reservoir range from 0.46–2.24 m3/t and 0.27–0.83 m3/t, with average values of 1.38 m3/t and 0.50 m3/t, respectively. The adsorbed gas is dominant in the shale gas reservoir, accounting for 53.05–88.23% of the total gas with an average value of 71.43%. The Gas Research Institute (GRI) porosity and adsorbed gas content increase with increasing total organic carbon content. The adsorbed gas and free gas contents both increase with increasing porosity value, and the rate of increase in the adsorbed gas content with porosity is larger than that of free gas. Compared with the other five shale reservoirs in America, the Lower Silurian Longmaxi Shale in the Py1 well developed nanopores but without overpressure, which is not favorable for shale gas enrichment.

scholarly journals What Factors Control Shale-Gas Production and Production-Decline Trend in Fractured Systems: A Comprehensive Analysis and Investigation

SPE Journal ◽  
2016 ◽  
Vol 22 (02) ◽  
pp. 562-581 ◽  
Author(s):  
HanYi Wang
Keyword(s):  
Shale Gas ◽  
Gas Production ◽  
Reservoir Model ◽  
Reservoir Properties ◽  
Gas Reservoir ◽  
Gas Well ◽  
Field Development ◽  
Shale Gas Reservoir ◽  
Decline Curve ◽  
Realistic Prediction

Summary One of the most-significant practical problems with the optimization of shale-gas-stimulation design is estimating post-fracture production rate, production decline, and ultimate recovery. Without a realistic prediction of the production-decline trend resulting from a given completion and given reservoir properties, it is impossible to evaluate the economic viability of producing natural gas from shale plays. Traditionally, decline-curve analysis (DCA) is commonly used to predict gas production and its decline trend to determine the estimated ultimate recovery (EUR), but its analysis cannot be used to analyze which factors influence the production-decline trend because of a lack of the underlying support of physics, which makes it difficult to guide completion designs or optimize field development. This study presents a unified shale-gas-reservoir model, which incorporates real-gas transport, nanoflow mechanisms, and geomechanics into a fractured-shale system. This model is used to predict shale-gas production under different reservoir scenarios and investigate which factors control its decline trend. The results and analysis presented in the article provide us with a better understanding of gas production and decline mechanisms in a shale-gas well with certain conditions of the reservoir characteristics. More-in-depth knowledge regarding the effects of factors controlling the behavior of the gas production can help us develop more-reliable models to forecast shale-gas-decline trend and ultimate recovery. This article also reveals that some commonly held beliefs may sound reasonable to infer the production-decline trend, but may not be true in a coupled reservoir system in reality.

Shaping Law and Motion Design in NC-ECM under Effect of Twiste Angle

2011 ◽  
Vol 128-129 ◽  
pp. 1010-1014
Author(s):  
Rui Wu ◽  
Dan Wen Zhang ◽  
Juan Sun
Keyword(s):  
Mathematical Model ◽  
Electrochemical Machining ◽  
Experimental Results ◽  
Working Face ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Motion Design

The twiste angle has a great effect on shaping law and stability of Numerical Controlled Electrochemical Machining (NC-ECM) process. In order to avoid the disadvantages caused by twiste angle, a methode of study shaping law by dispersing cathode working face in NC-ECM was proposed, and a mathematical model of the shaping law with the effects of twiste angle has been established in this paper. The mathematical model disclosed the relationship of twiste angle β, feeding velocity vf and thickness of removal material h in NC-ECM. Theoretical and experimental results show the the mathematical model of shaping law described in this paper can be considered as a useful reference and is helpful for the analysis of the NC-ECM and general ECM process.

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