A Semi-Analytical Fractal-Fractional Mathematical Model for Multi-Fractured Horizontal Wells in Coalbed Methane Reservoirs

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Ruizhong Jiang ◽  
Xiuwei Liu ◽  
Xing Wang ◽  
Qiong Wang ◽  
Yongzheng Cui ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Coalbed Methane ◽  
Fractal Theory ◽  
Superposition Principle ◽  
Horizontal Wells ◽  
Clean Energy ◽  
Stress Sensitivity ◽  
Element Discretization ◽  
Proposed Model ◽  
Fractured Horizontal Wells

Abstract Coalbed methane (CBM) which is clean energy has received great emphasis recently, and the multi-fracturing technology is widely applied in the exploitation of CBM. Due to the complexity, the randomness, and the anisotropism of the porous medium and the anomalous diffusion process, the fractal theory and fractional calculus are utilized to establish a semi-analytical fractal-fractional mathematical model considering the stress sensitivity of the cleat system for multi-fractured horizontal wells in CBM reservoirs. Through line-sink theory, Pedrosa transformation, perturbation theory, Laplace transformation, element discretization, superposition principle, and Stehfest numerical inversion, the pressure-transient analysis curves are plotted in the double logarithmic coordinates. By comparing with the existing model, the validation of the proposed model is illustrated. Also, nine flowing stages are identified according to different characteristics. Then, sensitivity analysis is conducted and influence laws are summarized. At last, a field application is introduced to furtherly verify the reliability of the proposed model. The relevant results analysis can provide some new significant guidance for interpreting the field data more precisely.

Production Performance Analysis for Multi-Branched Horizontal Wells in Composite Coal Bed Methane Reservoir Considering Stress Sensitivity

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Ruizhong Jiang ◽  
Xiuwei Liu ◽  
Yongzheng Cui ◽  
Xing Wang ◽  
Yue Gao ◽  
...  
Keyword(s):  
Superposition Principle ◽  
Horizontal Wells ◽  
Stress Sensitivity ◽  
Field Application ◽  
Model Verification ◽  
Production Performance ◽  
Coal Bed ◽  
Coal Bed Methane ◽  
Element Discretization ◽  
Type Curves

Abstract Coal bed methane (CBM) significantly contributes to unconventional energy resources. With the development of the drilling technology, multi-branched horizontal wells (MBHWs) have been put into the exploitation of CBM. In this paper, a semi-analytical mathematical model is introduced to study the production characteristics of MBHWs in the composite CBM reservoir. Stress sensitivity, composite reservoir, and complex seepage mechanisms (desorption, diffusion, and Darcy flow) are taken into consideration. Through Pedrosa transformation, Perturbation transformation, Laplace transformation, Finite cosine transformation, element discretization, superposition principle, and Stehfest numerical inversion, pseudo-pressure dynamic curves and production decline curves are plotted and 13 flow regimes are divided. Then, the sensitivity analysis of related parameters is conducted to study the influences of these parameters based on these two type curves. Model verification and field application are introduced which shows that the model is reliable. The model proposed in this paper and relevant results analysis can provide some significant guidance for a better understanding of the production behavior of MBHWs in the composite CBM reservoir.

Mathematical Model for Rate Transient Analysis with Additional Interface Skin for Fractured Horizontal Well With Weak Fluid Supply

2021 ◽  
Author(s):  
Jiali Zhang ◽  
Xinwei Liao ◽  
Nai Cao
Keyword(s):  
Mathematical Model ◽  
Transient Analysis ◽  
Horizontal Wells ◽  
Tight Gas ◽  
Fracture Conductivity ◽  
Multi Stage ◽  
Rate Transient Analysis ◽  
Proposed Model ◽  
Fluid Supply ◽  
Fractured Horizontal Wells

Abstract This paper develops a mathematical model for rate transient analysis in multi-stage fractured horizontal wells with considering weak fluid supply. A new concept of additional skin factor is introduced in the proposed model to characterize the fluid supply. Then, the mathematical model are solved by using the perturbation transformation, point source integration method, Laplace transform, and numerical inversion, while the fracture flow equations are solved by fracture discretization and superposition principle. First, the flow regimes of multi-stage fractured horizontal wells with considering weak fluid supply are identified based on the rate transient behaviors, including wellbore storage and skin effect, bilinear flow, linear flow, pseudo-radial flow in the fractured zone, interface skin effect, pseudo-radial flow in the original zone, and boundary-dominated flow. The effect of additional interface skin makes the double logarithmic curve of production rate appear an abrupt "overlap". The results of the sensitivity study show that the abrupt "overlap" becomes more obvious with the increase of the fracture conductivity, fracture number, the stress sensitivity coefficient, especially the interface skin. Finally, the proposed mathematical model is used to perform a case study on the production data of actual tight-gas wells from the Ordos Basin. The interface skin factor, fracture half-length, fracture conductivity, and boundary radius are evaluated. Through the proposed model, the characteristics of weak fluid supply in tight gas reservoirs are fully understood.

A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

2018 ◽  
Vol 29 (02) ◽  
pp. 1850019 ◽  
Author(s):  
X.-H. Tan ◽  
C.-Y. Liu ◽  
X.-P. Li ◽  
H.-Q. Wang ◽  
H. Deng
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Stress Sensitivity ◽  
Maximum Diameter ◽  
Proposed Model ◽  
Fractal Parameters ◽  
Stress Changes ◽  
Capillary Bundle ◽  
Definition Of

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster [Formula: see text] become bigger with an increase of stress. However, the pore fractal dimension of solid cluster [Formula: see text] and capillary bundle [Formula: see text] remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

scholarly journals GPU-Based Computation of Formation Pressure for Multistage Hydraulically Fractured Horizontal Wells in Tight Oil and Gas Reservoirs

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Rongwang Yin ◽  
Qingyu Li ◽  
Peichao Li ◽  
Yang Guo ◽  
Yurong An ◽  
...  
Keyword(s):  
Oil And Gas ◽  
Superposition Principle ◽  
Horizontal Wells ◽  
Tight Oil ◽  
Formation Pressure ◽  
Gas Reservoirs ◽  
Integral Forms ◽  
Oil And Gas Reservoirs ◽  
Fractured Horizontal Wells ◽  
Tight Oil And Gas

A mathematical model for multistage hydraulically fractured horizontal wells (MFHWs) in tight oil and gas reservoirs was derived by considering the variations in the permeability and porosity of tight oil and gas reservoirs that depend on formation pressure and mixed fluid properties and introducing the pseudo-pressure; analytical solutions were presented using the Newman superposition principle. The CPU-GPU asynchronous computing model was designed based on the CUDA platform, and the analytic solution was decomposed into infinite summation and integral forms for parallel computation. Implementation of this algorithm on an Intel i5 4590 CPU and NVIDIA GT 730 GPU demonstrates that computation speed increased by almost 80 times, which meets the requirement for real-time calculation of the formation pressure of MFHWs.

ANALYSIS OF THE COMPLEX FRACTURE FLOW IN MULTIPLE FRACTURED HORIZONTAL WELLS WITH THE FRACTAL TREE-LIKE NETWORK MODELS

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550014 ◽  
Author(s):  
WENDONG WANG ◽  
YULIANG SU ◽  
XIAO ZHANG ◽  
GUANGLONG SHENG ◽  
LONG REN
Keyword(s):  
Superposition Principle ◽  
Network Models ◽  
Horizontal Wells ◽  
Seepage Flow ◽  
Fracture Network ◽  
Fractal Model ◽  
Complex Fracture ◽  
Flow Mechanisms ◽  
Fractured Horizontal Wells ◽  
Shale Oil Reservoirs

This paper formulates a fractal-tree network model to address the challenging problem of characterizing the hydraulic fracture network in unconventional reservoirs. It has been proved that the seepage flow in tight/shale oil reservoirs is much more complicated to the conventional formation. To further understand the flow mechanisms in such a complex system, a semi-analytical model considering "branch network fractures" was established stage by stage using point source method and superposition principle. Fractal method was employed to generate and represent induced fracture network around bi-wing fractures. In addition, based on the new established model and solution, deterministic fractal-tree-like fracture network patterns and heterogeneity were carefully investigated and compared with the simulation model. Results show that the fractal dimension for the fracture network has significant effect on the connectivity of the stimulated reservoir. The proposed fractal model may capture the characteristics of the heterogeneous complex fracture network and help in understanding the flow and transport mechanisms of multiple fractured horizontal wells.

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