<p>The size of fractures is a crucial parameter for accurately characterizing the development of near-borehole fractures. It not only provides essential data support for investigating the wellbore's surrounding structure but also serves as a prerequisite for examining the mechanical behavior of the wellbore wall and performing coupled analysis of fractures, stress, and seepage. In this study, the imaging data from electrical imaging logging is utilized to consider the position, direction, and density of fractures, treating parameters such as dip direction, dip angle, rotation angle, and size parameters as random variables. A formula for estimating the mean size of fractures around the wellbore is derived based on the stereological relationship between the wellbore and the fractures. The errors associated with various approximation methods are analyzed, and the three-dimensional models of fractures around the wellbore are reconstructed using the Monte Carlo method. The results can be applied for subsequent theoretical analysis and numerical simulations. Furthermore, the correlation between fracture size and angle is examined under a predefined fracture size distribution. The main conclusions are as follows: (1) Polynomial approximation yields results that are closer to the true value compared to linear approximation. However, linear approximation ensures that the function remains consistent at the boundary without altering the overall trend. (2) For errors arising from the distribution characteristics of Euler angles <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10706_2025_3300_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha$</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10706_2025_3300_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\beta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>, when <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10706_2025_3300_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$K > 4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>></mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>, the calculation results are relatively consistent. Notably, modifying the probability density function of the Fisher distribution not only improves the calculation accuracy but also provides clearer physical interpretation. (3) The effects of simplifications and approximations during the formula derivation process on the two assumed fracture size distributions (uniform and exponential) in the Monte Carlo simulations are discussed. However, further research is needed to explore other commonly used distribution types.</p>

Estimation of Fracture Size Near Boreholes Using Truncated Traces from Electrical Imaging Logging

期刊论文
发表日期：

2025年8月21日

查看全文

Chen Ye,
Liming Jiang,
Chunli Lu,
Xiao Zhou

摘要

The size of fractures is a crucial parameter for accurately characterizing the development of near-borehole fractures. It not only provides essential data support for investigating the wellbore's surrounding structure but also serves as a prerequisite for examining the mechanical behavior of the wellbore wall and performing coupled analysis of fractures, stress, and seepage. In this study, the imaging data from electrical imaging logging is utilized to consider the position, direction, and density of fractures, treating parameters such as dip direction, dip angle, rotation angle, and size parameters as random variables. A formula for estimating the mean size of fractures around the wellbore is derived based on the stereological relationship between the wellbore and the fractures. The errors associated with various approximation methods are analyzed, and the three-dimensional models of fractures around the wellbore are reconstructed using the Monte Carlo method. The results can be applied for subsequent theoretical analysis and numerical simulations. Furthermore, the correlation between fracture size and angle is examined under a predefined fracture size distribution. The main conclusions are as follows: (1) Polynomial approximation yields results that are closer to the true value compared to linear approximation. However, linear approximation ensures that the function remains consistent at the boundary without altering the overall trend. (2) For errors arising from the distribution characteristics of Euler angles $\alpha$ $α$ and $\beta$ $β$ , when $K > 4$ $K > 4$ , the calculation results are relatively consistent. Notably, modifying the probability density function of the Fisher distribution not only improves the calculation accuracy but also provides clearer physical interpretation. (3) The effects of simplifications and approximations during the formula derivation process on the two assumed fracture size distributions (uniform and exponential) in the Monte Carlo simulations are discussed. However, further research is needed to explore other commonly used distribution types.