Fractal Scaling of Storage Capacity Fluctuations in Well Logs from Southeastern Mexican Reservoirs

Abstract

This study focuses on a hydrocarbon reservoir located in southeastern Mexico. The analysis uses well log data derived from petrophysical evaluations of storage capacity. The structural complexity of the reservoir and observed heterogeneity in Cretaceous units motivate a fractal-based characterization of spatial fluctuations. The objective is to assess the fractal scaling of storage capacity fluctuations using the dynamic Family–Vicsek framework. Critical exponents $\alpha$ (roughness), $\beta$ (growth), and z (dynamic) are obtained through structure function metrics. Data collapse techniques and local Hurst exponent distributions are used to explore long-range memory and spatial heterogeneity across wells. This study aims to classify storage capacity fluctuation records based on Euclidean or fractal geometries. This analysis allows a novel characterization of storage trends in the reservoir. The analysis reveals persistent scaling behavior, indicating long-range correlations in the storage capacity fluctuations. Multiscale patterns and variations in local Hurst exponents highlight the presence of multifractality and regional heterogeneity. Specifically, the spatial distribution of local Hurst exponents obtained in this study enables the inference of statistical properties in synthetic wells, providing key input for the structural and functional characterization of the reservoir’s geological model. This approach aims to identify preferential subsurface flow pathways for hydrocarbons and gas.

1. Introduction

The heterogeneity of petroleum reservoirs poses a significant challenge for their accurate characterization. This characterization is based on two complementary approaches: static and dynamic evaluations. The static approach includes various types of assessments such as petrography (porosity, permeability, fluid saturation, storage and flow capacity), geology (structure, stratigraphy, lithology, faults, etc.), and geophysics (seismic data and well logs). The dynamic approach involves reservoir behavior under flow conditions (reservoir pressure, production rate) as well as fluid properties (e.g., viscosities, compressibilities). Both evaluations are necessary and complementary for a comprehensive understanding of reservoir behavior [1,2,3,4,5,6,7,8].

Within the static evaluation framework, several authors have pointed out that variations in the petrophysical properties of reservoir rocks affect both storage capacity and fluid flow behavior, directly influencing hydrocarbon production performance within the reservoir [9,10,11,12]. In this context, the storage capacity in porous media associated with rock formations (oil or gas reservoirs) constitutes a key parameter to be determined. In the petroleum industry, the estimation and characterization of storage capacity, represented as $\varphi h$, is fundamental for the development of reservoir characterization models, with the aim of optimizing and maximizing hydrocarbon production [13,14,15].

The characterization of heterogeneities through petrophysical properties such as porosity $\varphi$ or storage capacity $\varphi h$ (where h denotes the thickness of the porous medium) has been widely investigated. These studies have been developed within both the Euclidean and fractal geometry frameworks in response to the complex topology of porous networks.

Classical Euclidean models assume that the geometric forms of the porous medium are smooth, continuous, and differentiable functions. Examples of such approaches, which consider various pore configurations, can be found in [16,17,18,19,20]. In contrast, fractal models address this complexity by considering non-smooth curves—often continuous but non-differentiable in the Euclidean sense. This perspective has led to various research paths, among which the use of fractional calculus tools—such as fractional integro-differential equations—and fractal statistical analysis stands out, especially for identifying power-law behaviors with fractional exponents [21,22,23,24,25,26,27].

Within Euclidean-based characterization approaches, several relevant investigations have been conducted, such as the analysis of transient pressure tests. For example, in the model proposed by Flamenco et al. [28], storage ratios at different scales (0.0001, 0.01, 0.1, and 0.5) are used to generate pressure curves. These curves reflect transient pressure and production responses, which are influenced by the flow dynamics of the fluid within media of either Euclidean or fractal topology, as discussed in [26,29,30,31], when considering various pore structures and distributions.

In the laboratory-based experimental study conducted by Balankin et al. [31], two reservoirs were compared: one with a Euclidean porous structure and the other with fractal characteristics. The results indicate a greater loss of mechanical energy in the fluid flowing through the Euclidean reservoir compared to the fractal one, suggesting greater flow efficiency in fractal porous media.

In the context of real reservoir systems, local petrophysical measurements and interpretations from core and well data are commonly used to infer the predominant type of medium in the formation. By applying either Euclidean or fractal theoretical models, the goal is to describe the general properties of the formation [32,33,34,35]. Several studies based on scalar well logs have demonstrated that some formations exhibit fractal structures at multiple levels, such as core textures, pore distributions, fractures, stratigraphy, seismic faults, and flow capacities. These behaviors follow scaling laws and are governed by fractal dimensions [36,37,38,39,40].

The present study investigates whether scalar records obtained from the petrophysical interpretation and measurement of storage capacity—acquired from wells located in southeastern Mexico—exhibit fractal characteristics. These wells were selected because they belong to a producing reservoir region. Petrophysical analysis of these logs is a standard practice that, together with other static and dynamic evaluations, contributes to understanding reservoir behavior and efficiency. For instance, such characterization would allow the identification of zones with higher flow capacity based on the fractal properties of the logs, in line with previous studies [31,40]. Furthermore, this study investigates whether a complete $\varphi h$ information sequence can be characterized by a family of Hurst exponents associated with different sampling intervals, thereby revealing heterogeneity in terms of short- and long-range correlations.

Commercial petrophysical characterization software—although widely used in industry—is often expensive and usually based on Euclidean-type descriptions. In this work, no commercial software was employed. Instead, we introduce a fractal statistical analysis of storage capacity records that provides a Euclidean and fractal classification suitable for integration into static evaluation. For this purpose, this study applies the theoretical framework of the dynamic Family–Vicsek scaling approach. This framework involves the calculation of the Hurst exponent to quantify power-law behavior of the associated fluctuations. Several estimation methods for the Hurst exponent have been established in the literature, including fluctuation analysis (FA), detrendend fluctuation analysis (DFA), and multifractal detrendend fluctuation analysis (MF-DFA). These methods are theoretically equivalent and differ primarily in the way they handle trend elimination and noise filtering in non-stationary series [41,42,43]. In contrast to MF-DFA and spectral analysis methods, which are typically applied to time series, the dynamic Family–Vicsek scaling framework is specifically suited for analyzing spatially extended data in multiple directions (e.g., depth and lateral axes). One key methodological advantage of the Family–Vicsek approach is its ability to capture anisotropic scaling behavior through the joint analysis of roughness, growth, and dynamic exponents ($\alpha$, $\beta$, and z), which provides insight into the directional correlation structure of the data. Additionally, MF-DFA yields a spectrum of scaling exponents $h\left(q\right)$, from which the particular case of $q=2$ corresponds to the generalized Hurst exponent, equivalent to the DFA-based Hurst exponent. This equivalence allows for comparative validation of results. In our study, Hurst exponents obtained from well log data are compared with results from other domains using different estimation techniques, thereby supporting the robustness and consistency of the observed correlations. Overall, the Family–Vicsek framework complements conventional multifractal methods by emphasizing spatial correlation and dynamic scaling properties, making it a suitable tool for reservoir-scale heterogeneity characterization. The Hurst values derived from the well logs are compared with results from other fields using different estimation techniques in order to validate the robustness of the correlation. For instance, from the multifractal spectrum obtained via MF-DFA, the value at statistical moment $q=2$ coincides with the Hurst exponent obtained via DFA as a particular case [42,44,45,46,47].

The structure of this paper is as follows: Section 2.1 outlines the study area, specifically the location of the wells from which the storage capacity logs $\varphi h$ were obtained. Section 2.2 presents the method based on the dynamic Family–Vicsek scaling theory, applying its mathematical formulation to the scalar $\varphi h$ records in order to analyze their fluctuations. Section 3 discusses and interprets the obtained results. Section 4 presents limitations and scope. Finally, Section 5 presents the main conclusions of this study.

2. Materials and Methods

2.1. Study Area

A hydrocarbon reservoir located in southeastern Mexico served as the primary source of data used in this study for analyzing storage capacity records. This information, previously interpreted, calibrated, and evaluated, was employed to determine local storage capacities associated with several wells. That is, these records were derived from porosity logs, which were obtained using different measurement techniques such as sonic porosity (SP), gamma ray (GR), neutron porosity (NPHI), and other estimation techniques for cores and plugs using the reservoir quality index (RQI).

Specifically, five data series relating a petrophysical property to depth were analyzed. The storage capacity logs correspond to five wells located in the northern portion of southeastern Mexico. For confidentiality reasons, the following notation is used to refer to each well: scW1, scW2, scW3, scW4, and scW5. The logs correspond to the following depths: scW1 4936 m, scW2 3302 m, scW3 3297 m, scW4 3596 m, scW5 3293 m.

The heterogeneity of the study area is illustrated through the description and observation of general features from both the region and core samples. The analysis focuses on four Cretaceous units: Breccia, Upper, Middle, and Lower Cretaceous.

Regarding the Breccia unit, data from core samples reveal marked heterogeneity associated with sedimentary variations, which suggests possible diagenetic changes both vertically and laterally. The observed facies correspond to dolomitized floatstone and rudstone, with varying degrees of fracturing and dissolution, resulting in porosity of variable size.

The degree of fracturing in the Breccia unit ranges from scarce to abundant and is commonly associated with good residual porosity and hydrocarbon saturation. Some core samples display significant vertical variability, with column sections where flow capacity is not uniformly distributed, i.e., interbedded intervals with lower porosity and permeability are identified. Matrix porosity associated with the generation of secondary intercrystalline porosity due to dolomitization is limited, implying a minor contribution to the effective flow of the rock. The porous medium presents dissolution cavities and moldic porosity connected through multidirectional fractures, which also exhibit good residual porosity and hydrocarbon impregnation.

In the KS and KM units, cryptocrystalline to mesocrystalline dolomite is observed, often clay-rich and/or enriched in organic matter, with the presence of stylolites. These units exhibit poor intercrystalline porosity and little evidence of significant dissolution; however, in some fractured zones, appreciable residual porosity is preserved. Additionally, abundant dissolution is reported, generating vugs between 1 and 2 cm in diameter, some of which are impregnated with hydrocarbons (see Figure 1a).

Other cores display microcrystalline dolomite with a dark gray base, attributable to clay and/or organic matter content, becoming cleaner toward the top. This dolomite exhibits low intercrystalline porosity, although centimeter-scale vugs (Figure 1a–c) are distributed throughout the core and are typically saturated with residual oil. At the top, a dolomitized breccia is present with small clasts, dissolution cavities, and partially open fractures impregnated with hydrocarbons.

In the Lower Cretaceous unit (KI), micro- to mesocrystalline dolomite is identified, ranging in color from dark gray to black and possibly rich in organic matter. In some cases, this unit includes interbedded intraformational dolomitized conglomerates with light-colored clasts embedded in a dark matrix. Intercrystalline porosity is generally poor, although some sections exhibit abundant fracturing—partially cemented—along (see Figure 1c) with residual porosity and oil saturation (see Figure 1a).

2.2. Methodology

The Family–Vicsek methodology is used to model phenomena associated with interface growth and has been widely applied to the analysis of time series in economic, biological, physical, and geological systems, among others [48,49,50,51]. The main goal of this methodology is to identify power-law dependencies in the temporal and spatial fluctuations observed in time series. See the flow diagram in Figure 2 for a clearer understanding of the methodology.

The metric used to capture this dependency is known as the q-th-order structure function, $G_q(L,t)$. This function enables the analysis of the scaling behavior of the q-th statistical moment (particularly roughness or standard deviation for $q=2$) as a function of the interface height relative to the system size L.

For spatial records of storage capacity, two scaling exponents are estimated to describe the self-similar properties in vertical and horizontal directions. These exponents correspond to the parameters $\alpha$ and $\beta$ in Family–Vicsek theory, known, respectively, as the roughness exponent (or Hurst exponent) and the growth exponent. A third exponent, the dynamic exponent $z=\alpha /\beta$, is also defined to quantify the correlation between directions.

Applying the structure function to records of storage capacity fluctuations reveals a generic scaling behavior that is invariant with respect to spatial variables—provided a correlation exists. In such cases, the behavior is expected to follow Equation (1) [52,53,54]:

$$G_q=\left\{\begin{array}{cc}{L}^{\alpha }\hfill & \mathrm{if}{t}^{\ast }\ll t\hfill \\ t^{\beta }\hfill & \mathrm{if}t\ll t^{\ast }\hfill \end{array}\right.$$

(1)

The function $G_q$ is referred to as the generalized q-th-order moment function and is more specifically defined by Equation (2):

$$G_q={\left({\displaystyle \frac{1}{N-{\delta }_n}}\sum _{n=1}^{N-{\delta }_n}{\left|M_{n+{\delta }_n}-M_n\right|}^q\right)}^{1/q}$$

(2)

Here, N is the total length of the series, and ${\delta }_n$ represents the observation window width—that is, the distance between the paired values $M_{n+{\delta }_n}$ and $M_n$ (${\delta }_n$ ranging from 1 to $n\le N$) within the fluctuation function used for this analysis (see Figure 3).

Furthermore, when the interface width $G_2(L,t)$ reaches saturation, the dynamic exponent z is used to determine the characteristic time $t^{\ast }$ as a function of system size L, following the relation $t^{\ast }\sim L^z$.

This study analyzes scalar records of storage capacity expressed as ${\varphi }_n\Delta h$, where $\Delta h$ is defined as $h_{i+1}-h_i$, with $i=1:L-1$, in order to evaluate the scaling behavior of the fluctuation function. This function is referred to hereafter as the relative storage capacity (RSC). The RSC (see Figure 3) is constructed by accumulating the storage capacities along the depth record, i.e.,

$$F\left({\varphi }_n\Delta h\right)=\sum _{i=1}^{n}M\left({\varphi }_i\Delta h\right)$$

This cumulative function is then fitted using a first-degree polynomial $\xi {\varphi }_n\Delta h$, and the RSC is defined as the difference between the two terms, expressed mathematically by Equation (3):

$$RSC\left({\varphi }_n\Delta h\right)=F\left({\varphi }_n\Delta h\right)-\xi {\varphi }_n\Delta h$$

(3)

where $\xi$ is the slope (see Figure 3a).

3. Empirical Results and Discussion

3.1. Results for Well scW1

The application of the structure function (note: All variables used in the structure and fluctuation functions are dimensionless, as the analysis focuses on relative variations across scales) (Equation (2)) to the fluctuation function RSC (see Figure 3b) for well scW1 exhibits scaling behavior in the vertical direction along the y-axis, where $G_q\propto {\left({\delta }_n\right)}^H$ for $q = 1, 2, 3, 4, 5$. This indicates that $G_q\left({\delta }_n\right)$ follows a power-law behavior across three orders of magnitude, revealing autocorrelation in the RSC with respect to depth (y) in the sampled records. Furthermore, this correlation is of long-range type, as $H_q=H=\alpha =0.93$ for all values of q analyzed. Therefore, the RSC fluctuations are classified as self-affine [37].

The exponents obtained, as well as those listed in

Table 1. Scaling exponents and data collapse results for each analyzed well.

Well	$\mathit{\alpha }$	$\mathit{\beta }$	z	Collapse
scW1	0.90	1.03	0.92	Yes
scW2	0.83	0.76	1.11	Yes
scW3	0.86	0.40	2.23	No
scW4	0.99	0.81	1.38	Yes
scW5	0.97	0.71	2.70	No

, are of the same order as those reported by Yu et al. [25] for groundwater level fluctuations. On the other hand, Dashian et al. [27] report scaling or Hurst exponents ranging from $H=0.72$ to $H=0.99$ for well log data in large-scale porous media. The latter employed techniques such as spectral density $S\left(w\right)$, multifractal random walk (MFRW), and multifractal detrended fluctuation analysis (MF-DFA), considering records from various oil and gas fields.

Likewise, Hernández-Martinez et al. [35] demonstrated that porosity logs can be modeled through self-affine distributions characterized by two scaling exponents associated with the behavior of the fluctuation function applied to complete well log sequences. Additionally, they present a spatial distribution of scaling exponents with respect to a reference facies pattern; however, such depth-dependent facies information is not always available. In contrast Ferreira et al. [55] reported cases characterized by short-range memory processes with Hurst exponents ranging from $H=0.35$ to $H=0.40$, further emphasizing the complexity and heterogeneity of petroleum reservoirs in terms of pore distribution topology. The main difference between persistent and antipersistent Hurst exponents lies in their ability to characterize fluctuations with homogeneous and heterogeneous interface widths, respectively. That is, when $H>0.5$, the fluctuation interface tends to be smoother, whereas when $H<0.5$, the interface becomes rougher [56].

Horizontal scaling (along the x-axis, parallel to the y-axis) is analyzed by constructing standard deviation series $A_n$ (see Figure 3d) using the following expression:

$$h(n,\Delta )=\sqrt{{\displaystyle \frac{1}{\Delta }}\sum _{k=n-\Delta +1}^n{\left(A_k-\langle A_k\rangle \right)}^2}$$

(4)

Here, $\Delta$ represents the sampling window width, analogous to a temporal variable, and $h(n,\Delta )$ describes the fluctuations in a moving interface in the x–y plane. This treatment accounts for spatial correlations along the x-direction, following the approach proposed by Balankin et al. [48]. By applying the structure function (Equation (2)) to these newly constructed profiles, the growth exponent $\beta =1.03$ is obtained.

It is worth noting that the profiles used in this analysis differ from those suggested by Hewet [57], who proposed the use of fractional Gaussian noise (FGN) to model porosity logs perpendicular to stratification. However, the current results do not contradict those observations, as the differences arise from the construction of the profiles via Equation (4).

Finally, the dynamic exponent z is determined by plotting $log{\delta }_c$ versus $log\Delta$, where ${\delta }_c\propto {\Delta }^{1/z}$ (see Figure 4c). For well scW1, the result is $z=0.97$. The x–y correlation between the $\alpha$ and $\beta$ exponents is established through a data collapse analysis (Figure 4d) using the coordinates $f=G_2/{\Delta }_n^{\beta }$ and window ${\delta }_c/{\Delta }_n^{1/z}$.

Unlike studies such as that of Dashian et al. [58], which explicitly conduct cross-correlation analysis between porosity log series using techniques like MF-DXA and logs such as DT, RHOB, NPHI, and GR, the present analysis does not apply such techniques, although multifractal patterns are identified that support their inclusion in future work.

3.2. Results for Well scW2

Similar to well scW1, well scW2 exhibits a fractal correlation with an exponent $\alpha = 0.83 \pm 0.02$ for $q = 1, 2, 3, 4, 5$ (see Figure 5a), indicating self-affinity of the RSC with respect to depth y. Regarding scaling parallel to the y-axis, i.e., along the x-direction, a value of $\beta =0.76$ is obtained (Figure 5b), suggesting long-range memory in both directions.

$\alpha -\beta$ correlation is reflected in the dynamic exponent (Figure 5c), and the data collapse shown in Figure 5d suggests a difference $\alpha -\beta$ correlation than that observed for well scW1.

3.3. Results for Well scW3

Well scW3 is characterized by the exponents $\alpha = 0.86 \pm 0.02$, $\beta =0.40$, and $z=2.72$ (see Figure 6). However, as seen in Figure 6a, no fractal scaling behavior is observed for the RSC in the vertical (y) direction or in the horizontal parallel (x) direction, as indicated by Figure 6b. Similarly, the estimation of the z exponent is inconclusive, as evidenced by the absence of data collapse in Figure 6d.

Therefore, although fractal parameters can be typically estimated, they do not adequately describe the behavior of the well log data and may be more appropriately interpreted from a Euclidean perspective, given the topological complexity of the porous structure.

3.4. Summary of Exponents and Data Collapse

The estimated exponents $\alpha$, $\beta$, and z for each analyzed well, along with the presence or absence of data collapse, are summarized in Table 1.

3.5. Classification of Observed Cases

Based on the application of the fractal analysis methodology to the storage capacity log series from wells scW1 to scW5, three types of behavior were identified:

• Case 1: Autocorrelation is present in both directions (y and x), with strong $\alpha$–$\beta$ correlation and a well-defined data collapse (e.g., well scW1).
• Case 2: Fractal behavior is observed in both directions but with $\alpha$–$\beta$ correlation and less-defined data collapse (e.g., well scW2). Better connectivity is suggested in the vertical direction compared to the horizontal direction.
• Case 3: No fractal correlation is present in either direction, and no data collapse is observed (e.g., wells scW3 and scW5). Such behavior would be due to the scarce or null connectivity between well logs, which could suggest records with minimal porosity, that is, a solid non-porous matrix. In such cases, a Euclidean analysis may be more suitable than a fractal approach.

In at least three of the presented cases, the wells exhibit characteristics that can be modeled using the self-affine fractal approach. However, it is worth noting that the literature also reports the presence of multifractality in various studies on porosity logs using different sampling and analysis techniques [27,59,60].

The results obtained in this study do not contradict such findings. As shown in Figure 7, the existence of a family of local Hurst exponents provides a better characterization of the log series depending on the analysis size L. This figure highlights the heterogeneous behavior of the series, showing how Hurst exponents vary across different intervals. Additionally, short-range memory processes are identified (see Figure 7), as described by Ferreira et al. [55].

These short-term memory processes may not be noticed if only a single global Hurst exponent is estimated, which would lead to a limited representation of the spatial heterogeneity in the porosity or storage capacity matrix. Thus, it is concluded that the system’s heterogeneity should be incorporated into the characterization of the rock formation, regardless of the metric used for estimation. That is, a single exponent is not sufficient to describe the heterogeneity of porosity logs or, by analogy, storage capacity logs. A multiscale approach or an alternative description, such as that proposed through the calculation of Hurst exponents from a physical and monofractal perspective, is required (see Figure 7).

4. Limitations and Scope

• The correlation between the scaling exponents $\alpha$ and $\beta$ is not presented quantitatively through explicit power-law relationships, as has been developed in previous studies [58].
• The correlation between the scaling results of storage capacity fluctuations and Cretaceous stratigraphic units is not included due to confidentiality constraints in data management. Similarly, the relationship between storage capacity and well stratigraphy is not addressed. Furthermore, the anisotropy induced by stress or thermal/mechanical compaction dependent on depth is not addressed. However, such correlation could be readily established by a specialist with access to both variables and data from a different geological formation.
• The petrophysical heterogeneity of the reservoir, as observed through petrographic analysis, could be associated with the spatial heterogeneity observed in the distribution of Hurst exponents.
• The local heterogeneity illustrated in Figure 7 from individual well records could be integrated into the modeling of a global storage capacity and/or porosity matrix for a petroleum reservoir using an appropriate interpolation method; that is, a connection between the static and dynamic reservoir models could be evaluated.

5. Conclusions

The Family–Vicsek methodology was applied to scalar log profiles of storage capacity $\varphi h$ from five wells located in an oil field in southeastern Mexico. Correlations were established in the perpendicular direction corresponding to depth y, and in the horizontal direction along the x-axis. $\alpha$–$\beta$ correlation was identified through information collapse analysis. The Euclidean and fractal classification is evidenced by the three distinct patterns identified in the well log records of storage capacity $\varphi h$.

An auto-affine behavior was observed in the RSC of wells scW1, scW2, scW4, and scW5, characterized by long-range memory, that is, statistical persistence in the fluctuations associated with the scalar records. The field’s heterogeneity was evidenced by a spectrum of scaling exponents ranging from antipersistent to random and persistent behaviors, suggesting multifractal features in the series of records analyzed at different scales.

Two types of statistical correlation were identified using Hurst exponents derived from the power-law relationship between the structure function and the observation window widths $\delta$, considering $q=2$: statistical persistence ($H>0.5$) and antipersistence ($H<0.5$). Wells characterized by $H>0.5$ indicate statistically persistent behavior, implying smoother growth fronts, i.e., lower variation in the magnitude of records. Conversely, wells with Hurst exponents $H<0.5$ indicate antipersistent behavior, associated with more heterogeneous growth fronts and greater variation in the recorded values.

The heterogeneity described through the different scaling exponents across the case studies suggests that such information should be taken into account in the construction of the storage capacity matrix, which serves as a key input for assessing the storage potential of the reservoir.

In addition to confirming the relevance of fractal and auto-affine models in the interpretation of geophysical records, the results underscore the importance of multiscale approaches in capturing the complex heterogeneity inherent in reservoir systems. The observed multifractal traits and cross-scale correlations support the hypothesis that the spatial variability in storage capacity cannot be accurately characterized by a single global exponent. Instead, a local or segmented treatment using Hurst exponent distributions provides a richer and more precise understanding of the spatial structure.

Furthermore, the methodology presented offers a physically grounded alternative for integrating petrophysical heterogeneity into reservoir modeling workflows. This is particularly useful in the absence of complete stratigraphic or lithological data, allowing the identification of internal organizational patterns solely from the statistical properties of the available records. As such, the proposed approach complements traditional deterministic techniques and opens new possibilities for the integration of fractal geometry and stochastic modeling in reservoir characterization and simulation.

While this study identified qualitative evidence of fractal characteristics in some of the analyzed wells—helping to establish more consistent indicators of flow capacity—this represents an initial approximation. A subsequent stage should include a more rigorous quantitative validation using formal statistical tools such as spectral analysis, goodness-of-fit tests, or long-range correlation functions. These tools would serve to reinforce the fractal hypothesis and facilitate its application within predictive flow models for porous media.