scholarly journals A dual-tube model for gas dynamics in fractured nanoporous shale formations

2014 ◽  
Vol 757 ◽  
pp. 943-971 ◽  
Author(s):  
I. Lunati ◽  
S. H. Lee
Keyword(s):  
Production Rate ◽  
Shale Gas ◽  
Structural Parameters ◽  
Knudsen Diffusion ◽  
Effective Diffusion ◽  
Reliable Estimate ◽  
Hydraulic Fractures ◽  
Late Time ◽  
Transport Mechanisms ◽  
Shale Formations

AbstractGas flow through fractured nanoporous shale formations is complicated by a hierarchy of structural features (ranging from nanopores to microseismic and hydraulic fractures) and by several transport mechanisms that differ from the standard viscous flow used in reservoir modelling. In small pores, self-diffusion becomes more important than advection; also, slippage effects and Knudsen diffusion might become relevant at low densities. We derive a nonlinear effective diffusion coefficient that describes the main transport mechanisms in shale-gas production. In dimensionless form, this coefficient depends only on a geometric factor (or dimensionless permeability) and on the kinetic model that describes the gas. To simplify the description of the complex structure of fractured shales, we observe that the production rate is controlled by the flow from the shale matrix (which has the smallest diffusivity) into the fracture network, which is assumed to produce instantaneously. Therefore, we propose to model the flow in the shale matrix and estimate the production rate with a simple bundle-of-dual-tubes model (BoDTM), in which each tube is characterized by two diameters (one for transport and the other for storage). The solution of a single tube is approximately self-similar at early time, but not at late time, when the gas flux decays exponentially owing to the finite length of the tube. To construct a BoDTM, a reliable estimate of the joint statistics of the matrix-porosity parameters is required. This can be either inferred from core measurements or postulated on the basis of somea prioriassumptions when information from laboratory and field measurements is scarce. By comparison with field production data from the Barnett shale-gas field, we demonstrate that BoDTM can be calibrated to estimate structural parameters of the shale formation and to predict the cumulative production of shale gas. Our framework has enough flexibility to construct models of increasing complexity that can be employed in the presence of a complex dataset or when more information is available.

scholarly journals A Review of Gas Flow and Its Mathematical Models in Shale Gas Reservoirs

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Bo-ning Zhang ◽  
Xiao-gang Li ◽  
Yu-long Zhao ◽  
Cheng Chang ◽  
Jian Zheng
Keyword(s):  
Mathematical Models ◽  
Shale Gas ◽  
Gas Flow ◽  
Knudsen Diffusion ◽  
Model Description ◽  
Transport Mechanisms ◽  
Gas Reservoirs ◽  
Flow Process ◽  
Type Curves ◽  
Shale Gas Reservoirs

The application of horizontal wells with multistage hydraulic fracturing technologies has made the development of shale gas reservoirs become a worldwide economical hotspot in recent years. The gas transport mechanisms in shale gas reservoirs are complicated, due to the multiple types of pores with complex pore structure and special process of gas accumulation and transport. Although there have been many attempts to come up with a suitable and practical mathematical model to characterize the shale gas flow process, no unified model has yet been accepted by academia. In this paper, a comprehensive literature review on the mathematical models developed in recent years for describing gas flow in shale gas reservoirs is summarized. Five models incorporating different transport mechanisms are reviewed, including gas viscous flow in natural fractures or macropores, gas ad-desorption on shale organic, gas slippage, diffusion (Knudsen diffusion, Fick diffusion, and surface diffusion), stress dependence, real gas effect, and adsorption layer effect in the nanoshale matrix system, which is quite different from conventional gas reservoir. This review is very helpful to understand the complex gas flow behaviors in shale gas reservoirs and guide the efficient development of shale gas. In addition to the model description, we depicted the type curves of fractured horizontal well with different seepage models. From the review, it can be found that there is some misunderstanding about the essence of Knudsen/Fick diffusion and slippage, which makes different scholars adopt different weighting methods to consider them. Besides, the contribution of each mechanism on the transport mechanisms is still controversial, which needs further in-depth study in the future.

scholarly journals Production Behavior of Fractured Horizontal Well in Closed Rectangular Shale Gas Reservoirs

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Qiguo Liu ◽  
Ke Li ◽  
Weihong Wang ◽  
Xiaohu Hu ◽  
Hua Liu
Keyword(s):  
Production Rate ◽  
Shale Gas ◽  
Superposition Principle ◽  
Stable State ◽  
Hydraulic Fractures ◽  
Gas Reservoirs ◽  
Desorption Process ◽  
Shale Gas Reservoirs ◽  
Wellbore Pressure ◽  
Production Behavior

This paper established a triple porosity physical model in rectangular closed reservoirs to understand the complex fluid flowing mechanism and production behavior of multifractured horizontal wells in shale gas reservoirs, which is more appropriate for practical situation compared with previous ones. According to the seepage theory considering adsorption and desorption process in stable state, the gas production rate of a well producing at constant wellbore pressure was obtained by utilizing the methods of Green’s and source function theory and superposition principle. Meanwhile, the volume of adsorbed gas (GL) and the number of hydraulic fractures (M) as well as permeabilities of matrix system (km) and microfractures (kf) were discussed in this paper as sensitive factors, which have significant influences on the production behavior of the wells. The bigger the value ofGLis, the larger the well production rate will be in the later flowing periods, and the differences of production rate with the increasing ofMare small, which manifest that there is an optimumMfor a given field. Therefore, the study in this paper is of significant importance to understand the dynamic production declining performance in shale gas reservoirs.

scholarly journals A Semianalytical Model for Analyzing the Infill Well-Caused Fracture Interference from Shale Gas Reservoirs

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Sidong Fang ◽  
Yonghui Wu ◽  
Cheng Dai ◽  
Liqiang Ma ◽  
Hua Liu
Keyword(s):  
Shale Gas ◽  
Control Volume ◽  
Material Balance ◽  
Production Performance ◽  
Production Data ◽  
Model Parameters ◽  
Hydraulic Fractures ◽  
Late Time ◽  
Fracture Characterization ◽  
Proposed Model

Drilling infill well has been widely used in many plays to enhance the recovery of shale gas, but the infill well-caused fracture interference is a very important issue that should be taken into consideration. The well interference makes it difficult for the conventional models to make production predictions, fracture characterization, and production data analysis. In this paper, a semianalytical model is proposed for this purpose by discretizing the whole control volume of the parent and infill wells into several linear flow zones. In this way, three important issues can be further handled very naturally, including fracture connection between the parent and infill wells, different SRV properties for zones with different distances to the wellbore, and different production times for adjacent wellbores. The approximate expressions for different flow regimes are used in making production predictions in the time domain, and a flowing material balance method and a simple iteration are used to update the model parameters step by step. The proposed model is shown to be reasonable and accurate for handling multiwell interference problems after comparing with the commercial numerical simulator tNavigator. The synthetical cases show that the fracture parameters, SRV properties, and well infill time have a significant influence on the production performance of both the parent and infill wells. The results show that the production of the parent well will be dramatically enhanced when it is connected with the infill well via high-conductive hydraulic fractures. Longer unconnected fractures and more fracturing stages/clusters for the infill well will result in higher production for the infill well, but a negative effect is observed for the parent well. The permeability of the distant well SRV has a similar influence on the parent and infill wells. The results also show that late time well interference will result in a more significant increase in production rate on the log-log plots for the severe depletion around the parent well. Finally, the proposed model is used to analyze the production data of a field case from Fuling shale in Southwestern China. After analyzing the production data, several parameters can be obtained for both parent and infill wells, including the fracture lengths and conductivities, numbers of connected fractures, and the near and distant well permeabilities of the SRV. This gives a basic and practical technique for production prediction, formation and fracture evaluation, and well connectivity analysis from shale gas wells with fracture connection.

A NEW FRACTAL TRANSPORT MODEL OF SHALE GAS RESERVOIRS CONSIDERING MULTIPLE GAS TRANSPORT MECHANISMS, MULTI-SCALE AND HETEROGENEITY

Fractals ◽  
2018 ◽  
Vol 26 (06) ◽  
pp. 1850096 ◽  
Author(s):  
WEIPENG FAN ◽  
HAI SUN ◽  
JUN YAO ◽  
DONGYAN FAN ◽  
KAI ZHANG
Keyword(s):  
Shale Gas ◽  
Gas Flow ◽  
Knudsen Diffusion ◽  
Gas Production ◽  
Transport Mechanisms ◽  
Apparent Permeability ◽  
Multi Scale ◽  
Inorganic Systems ◽  
Inorganic Matter ◽  
Fractal Characteristics

Duo to different transport mechanisms and gas storage in organic and inorganic systems, a new triple-continuum model coupling Discrete Fracture Model (DFM) was established to investigate gas flow in shale gas reservoir. Considering the multi-scale and heterogeneity of shale matrix, fractal theory was used to calculate the apparent permeability of organic and inorganic systems while multiple gas transport mechanisms such as viscous flow, Knudsen diffusion, surface diffusion, gas absorption/desorption effect and real gas effect were incorporated. This coupled mathematical model was solved by Finite Element Method (FEM) and the presented fractal apparent permeability model was validated with the experimental data. The results show that fractal characteristics of shale matrix have great impact on gas reservoir performance. The model without considering the influence of fractal characteristics could lead to underestimate gas production by approximately 17%. Viscous flow is the dominate transport mechanisms of shale gas and Knudsen diffusion has an impact on gas flow when the pressure declines. Surface diffusion should be only considered in organic systems and can be ignored. Then the results of sensitivity analysis show that the characteristic parameters of inorganic matter have a greater impact than those of organic matter and establishing a triple-continuum model with considering comprehensive effect of organic and inorganic matter is necessary. In addition, gas production would decrease as the pore fractal dimension and tortuosity fractal dimension increase, which results from the increasing number of small pores and more tortuous path for gas flow.

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.

Shale Gas Transport in Nanopores: Contribution of Different Transport Mechanisms and Influencing Factors

2021 ◽  
Vol 35 (3) ◽  
pp. 2033-2047
Author(s):  
Xiangyu Liu ◽  
Liehui Zhang ◽  
Yulong Zhao ◽  
Xiao He ◽  
Jianfa Wu ◽  
...  
Keyword(s):  
Influencing Factors ◽  
Shale Gas ◽  
Gas Transport ◽  
Transport Mechanisms ◽  
Shale Gas Transport

scholarly journals Candida albicans exhibits distinct cytoprotective responses to anti-fungal drugs that facilitate the evolution of drug resistance

2020 ◽  
Author(s):  
V Bettauer ◽  
S Massahi ◽  
S Khurdia ◽  
ACBP Costa ◽  
RP Omran ◽  
...  
Keyword(s):  
Drug Resistance ◽  
Candida Albicans ◽  
Drug Exposure ◽  
Fluorescent Imaging ◽  
Late Time ◽  
Transport Mechanisms ◽  
Short Term ◽  
Anti Fungal ◽  
Initial Drug

AbstractWe developed a modified protocol for nanolitre droplet-based single cell sequencing appropriate for fungal settings, and used it to transcriptionally profiled several thousands cells from a prototrophic Candida albicans population and several drug exposed colonies (incl. fluconazole, caspofungin and nystatin). Thousands of cells from each colony were profiled both at early and late time points post-treatment in order to infer survival trajectories from initial drug tolerance to drug resistance. We find that prototrophic C. albicans populations differentially and stochastically express cytoprotective epigenetic programs. For all drugs, there is evidence that tolerant individuals partition into distinct subpopulations, each with a unique survival strategy involving different regulatory programs. These responses are weakly related to changes in morphology (shift from white to opaque forms, or shift from yeast to filamentous forms). In turn, those subpopulations that successfully reach resistance each have a distinct multivariate epigenetic response that coordinates the expression of efflux pumps, chaperones, transport mechanisms, and cell wall maintenance. Live cell fluorescent imaging was used to validate predictions of which molecular responses most often led to survival after drug exposure. Together our findings provide evidence that C. albicans has a robust toolkit of short-term epigenetic cytoprotective responses designed to “buy time” and increase the chance of acquiring long-term resistance.

A Novel Design Method for Optimizing the Diverter Dosage in Hydraulic Fracturing Using Three-Dimensionally Printed Fractures

2021 ◽  
Author(s):  
Meng Wang ◽  
Mingguang Che ◽  
Bo Zeng ◽  
Yi Song ◽  
Yun Jiang ◽  
...  
Keyword(s):  
Shale Gas ◽  
Design Method ◽  
Pressure Rise ◽  
Horizontal Wells ◽  
Optimization Method ◽  
Darcy Law ◽  
Hydraulic Fractures ◽  
Fracture Conductivity ◽  
Fracture Simulation ◽  
3D Printed

Abstract Application of diversion agents in temporarily plugging fracturing of horizontal wells of shale has becoming more and more popular. Nevertheless, the studies on determining the diverter dosage are below adequacy. A novel approach based on laboratory experiments, logging data, rock mechanics tests and fracture simulation was proposed to optimizing the dosage of diversion agents. The optimization model is based on the classic Darcy Law. A pair of 3D-printed rock plates with rugged faces was combined to simulate the coarse hydraulic fractures with the width of 2.0 ~ 7.0 mm. The mixture of the diversion agents and slickwater was dynamically injected to simulate the fracture in Temco fracture conductivity system to mimic the practical treatment to temporarily plugging the fracture. The permeability of the temporary plugging zone in the 3D-printed fractures was measured in order to optimize the dosage of the selected diversion agents. The value of Pnet (also the value of ΔP in Darcy Formula) required for creation of new branched fractures was determined using the Warpinski-Teufel Failure Rules. The hydraulic fractures of target stages were simulated to obtain the widths and heights. The experimental results proved that the selected suite of the diversion agents can temporarily plug the 3D-printed fractures of 2.0 ~ 7.0 mm with blocking pressure up to 15 MPa. The measured permeability of the resulting plugging zones was 0.724 ~ 0.933 D (averaging 0.837 D). The value of Pnet required for creation of branched fractures in shale of WY area (main shale gas payzone of China) was determined as 0.4 ~ 15.6 MPa (averaging 7.9 MPa) which means the natural fractures and/or weak planes with approaching angle less than 70° could be opened to increase the SRV. The typical dosage of the diversion agents used for one stage of the horizontal wells (averaging TVD 3600 m) was calculated as 232 ~ 310 kg. The optimization method was applied to the design job of temporarily plugging fracturing of two shale gas wells. The observed surface pressure rise after injection of diversion agents was 0.6 ~ 11.7 MPa (averaging 4.7 MPa) and the monitored microseismic events of the test stages were 37% more than those of the offset stages.

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