Dynamic hydraulic fracture propagation micro-seismic data estimation methods

Abstract

A method of estimating a micro-seismic cloud related to a hydraulic fracturing operation. The method includes receiving a treating pressure signal generated during hydraulic fracture propagation, calculating a complex wavelet transform coefficient on the received treating pressure signal, calculating energy of the received treating pressure signal at multiple scales to create a signal-energy scalogram, normalizing the signal-energy scalogram to create a normalized signal-energy scalogram, and establishing a correlation between signatures of dynamic fracture propagation modes identified in the normalized signal-energy scalogram and corresponding fracture propagation mode influence on temporal development of a micro-seismic events cloud.

Description

DYNAMIC HYDRAULIC FRACTURE PROPAGATION MICRO-SEISMIC DATA ESTIMATION METHODSTECHNICAL FIELD

[0001] The present disclosure relates generally to micro-seismic data in hydraulic fracturing operations and more particularly, but not by way of limitation, to use of Continuous Wavelet Transforms in same.BACKGROUND

[0002] This section provides background information to facilitate a better understanding of the various aspects of the disclosure. It should be understood that the statements in this section of this document are to be read in this light and not as admissions of prior art.

[0003] Detection of fracture events is important for optimizing hydraulic fracture treatments. Failure to achieve optimal design during initial treatment can in many cases not be rectified. Therefore, taking the right action during fracture treatment is paramount to the success of the hydraulic fracture and achieving optimal post-fracture production. An understanding of fracture propagation events during the execution of the treatment would permit appropriate pumping rate, fluid viscosity, and timing of an early flush to be achieved.SUMMARY

[0004] This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not necessarily intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of claimed subject matter.

[0005] A method of estimating a micro-seismic cloud related to a hydraulic fracturing operation. The method includes receiving a treating pressure signal generated during hydraulic fracture propagation, calculating a complex wavelet transform coefficient on the received treating pressure signal, calculating energy of the received treating pressure signal at multiple scales to create a signal -energy scalogram, normalizing the signal-energy scalogram to create a normalized signal-energy scalogram, and establishing a correlation between signatures of dynamic fracture propagation modes identified in the normalized signal-energy scalogram and corresponding fracture propagation mode influence on temporal development of a micro-seismic events cloud.

[0006] The method may include that the complex wavelet transform coefficient is a function of the signal convolution with a short wavy signal, the preferred complex wavelet transform coefficient equation beinga is a scale parameter, b is a translation parameter that represents time-scale movement, * is a Complex Morlet mother wavelet function, and t is time.

[0007] The method may include that the complex Morlet mother wavelet function is the function of its bandwidth and central frequency and the preferred complex Morlet mother wavelet function iswhere B is the bandwidth and C is the center frequency.

[0008] The method may include that the energy of the received treating pressure signal is represented bywhereT(a,b) = l[Re(T(a, i>))]z+ [lm(r(a,W)]zV

[0009] The method may include integrating the establishing correlation into an artificialintelligence system to generate a synthetic micro-seismic cloud. The integrating may utilizes machine-learning techniques. The integrating may utilize deep-learning techniques. The method may include using the generated micro-seismic cloud to process treating pressure to simulate an outcome of a second hydraulic fracturing operation.

[0010] A method of estimating a micro- seismic cloud related to a hydraulic fracturing operation. The method includes calculating a complex wavelet transform coefficient on a treating pressure signal of the hydraulic fracturing operation, calculating energy of the treating pressure signal at multiple scales to create a signal-energy scalogram, establishing a correlation between signatures of dynamic fracture propagation modes identified in the signal-energy scalogram and corresponding fracture propagation mode influence on temporal development of a micro-seismic events cloud, integrating the establishing correlation into an artificial-intelligence system to generate a synthetic micro-seismic cloud, and using the generated micro-seismic cloud to process treating pressure to simulate an outcome of a second hydraulic fracturing operation.

[0011] The method may include that the complex wavelet transform coefficient equation isa is a scale parameter, b is a translation parameter that represents time-scale movement, * is a Complex Morlet mother wavelet function, and t is time; and the Complex mother Morlet wavelet function iswhere B is the bandwidth and C is the center frequency.

[0012] The method may include that the energy of the treating pressure signal is represented byThe integrating may utilize machine-learning techniques. The integrating may utilize deeplearning techniques.

[0013] A method of estimating a micro-seismic cloud related to a hydraulic fracturing operation includes establishing a correlation between signatures of dynamic fracture propagation modes identified in a normalized signal-energy scalogram from a calculated complex continuous wavelet transform coefficient on a treating pressure signal and corresponding fracture propagation mode influence on temporal development of a micro-seismic events cloud, integrating the establishing correlation into an artificial-intelligence system to generate a synthetic micro-seismic cloud, and using the generated micro-seismic cloud to process treating pressure to simulate an outcome of a second hydraulic fracturing operation. The integrating may utilize at least one of machine-learning techniques and deep-learning techniques.BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The disclosure is best understood from the following detailed description when read with the accompanying Figures. It is emphasized that, in accordance with standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of various features may be arbitrarily increased or reduced for clarity of discussion.

[0015] FIGURE 1 is a flow diagram that illustrates a workflow for validation and results of a method to generate a synthetic micro-seismic cloud;

[0016] FIGURE 2A is a schematic diagram of an enhanced geothermal system;

[0017] FIGURE 2B illustrates a recording of micro-seismic events in the enhanced geothermal system of FIGURE 2A;

[0018] FIGURE 3 illustrates examples of commonly used complex and real wavelet transform families;

[0019] FIGURE 4 illustrates wavelet transform mechanism and plotting of a signal energy scalogram;

[0020] FIGURE 5 illustrates an example of a hydraulic fracturing job pumping chart;

[0021] FIGURE 6 illustrates a continuous wavelet transform scalogram for the hydraulic fracturing job of FIGURE 5;

[0022] FIGURE 7 illustrates a normalized continuous wavelet transform scalogram for the hydraulic fracturing job of FIGURE 5;

[0023] FIGURE 8 illustrates a deep learning or machine learning framework that may be used to predict a micro- seismic events cloud; and

[0024] FIGURE 9 illustrates training Loss versus learning rate of the deep learning or machine learning model of FIGURE 8.DETAILED DESCRIPTION

[0025] Various embodiments will now be described more fully with reference to the accompanying drawings. The disclosure may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein.

[0026] A typical methodology disclosed herein includes two primary steps. First, a normalized continuous wavelet transform (“CWT”) scalogram is applied to treating pressure data from a hydraulic fracturing operation. Second, a deep-learning model is trained to estimate coordinates of the micro-seismic events (X, Y, and Z) using normalized CWT scalogram coefficients. These two steps are discussed in more detail below.

[0027] A typical CWT closure detection technique workflow includes the following: 1 ) obtain a treating pressure signal during hydraulic fracturing propagation; 2) calculate a wavelet transformcoefficient where a is scale parameter (from 0.1 to 256), b is a translation parameter that represents movement on the time scale, * is a mother wavelet function (e.g., a Complex Morlet wavelet), and t is time. A Complex Morlet wavelet, which is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window(envelope), is as follows: where is B = bandwidth (B= 1.5) C = center frequency (C = 1) ; 3) calculate log2 signal energy at multiple scales to create an energy scalogram from the magnitude of complex coefficientto create a normalized CWT scalogram; 5) establisha correlation between unique signatures of each dynamic fracture propagation mode, as identified in the normalized CWT scalogram, and the corresponding fracture propagation mode's influence on the temporal development of a micro-seismic events cloud; and 6) integrate the correlation into an artificial-intelligence (“Al”) system, utilizing machine-learning or deep-learning techniques, to generate a synthetic micro- seismic cloud that can be used for processing treating pressure in other wells to simulate the outcomes of hydraulic fracturing jobs. It will be appreciated that Al simulates human intelligence to perform tasks and make decisions. Machine learning is a subset of Al that uses algorithms to learn patterns from data, while deep learning is a subset of machine learning that employs artificial neural networks for complex tasks.

[0028] FIGURE 1 is a flow diagram that illustrates a workflow 100. The workflow 100 begins at step 102, at which step a mathematical technique is used to analyze treating pressure to understand fracture propagation behavior in dynamic fracture events. From step 102, execution proceeds to step 104, at which step the dynamic fracture events arc correlated with a signature. From step 104, execution proceeds to step 104. At step 104, the correlation of step 104 is validated using one or more of fracture simulation models, previously validated real field data using different dynamic-event analysis techniques, and physical measurements for the dynamic fracture events.

[0029] Following validation at step 106, at step 108 the validated correlation of step 106 is integrated into an artificial intelligence (“Al”) system that utilizes, for example, machine-learning or deep-learning techniques, to generate a synthetic micro-seismic cloud. From step 108, execution proceeds to step 1110, at which step the Al system is employed to process treating pressure in other wells to simulate outcomes of hydraulic fracturing jobs.

[0030] Various methodologies disclosed herein can be used to estimate the volume of a micro- seismic events cloud related to a hydraulic fracturing job. The resulting estimation can be achieved by establishing a correlation between unique signatures of each dynamic fracture propagation mode, as identified in the normalized CWT scalogram, and the corresponding fracture propagation mode's influence on the temporal development of the micro-seismic events cloud, and then integrating this correlation into an Al system, utilizing machine-learning or deep-learningtechniques, to generate a synthetic micro-seismic cloud. The methodologies can be used for processing treating pressure in other wells to simulate the outcomes of hydraulic fracturing jobs.

[0031] FIGURE 2A is a schematic diagram of an enhanced geothermal system. The enhanced geothermal system is used for electricity generation. FIGURE 2B illustrates a recording of micro- seismic events in the enhanced geothermal system of FIGURE 2A. Estimation of a micro-seismic events cloud related with hydraulic fracturing jobs can be used to estimate the volume of enhanced geothermal systems and can be used, for example, to optimize a distance between a production well and an injection well.

[0032] In addition, calibration of the detection of dynamic fracture events using CWT with a fiber optics signature for each dynamic fracture event can be used to understand fracture propagation. As such, various methodologies disclosed herein can be used to replace fiber optics technologies in an observation well by creating the correlation in, for example, a plurality of wells and populating the correlation using an Al system to other wells in the same basin in order to save the cost of deploying fiber optics in the other wells. Machine-learning modelling for hydraulic fracturing jobs as disclosed herein can be used to save considerable expense in comparison to prior methods.

[0033] Various normalized CWT scalogram techniques consider hydraulic fracturing propagation as a system with inputs and outputs. Pumping rate and proppant concentration are examples of inputs while treating pressure is an example of an output. Analysis of the output signal is used to reveal properties of the system. A primary concept behind various methodologies disclosed herein for fracture event detection is to magnify minute changes in the treating pressure versus time signal during hydraulic fracturing treatment to determine a mode of fracture propagation using wavelet transform techniques.

[0034] A wavelet transform is a mathematical technique that employs small wavelike functions called wavelets to extract additional information from signals that are not readily available in their raw format. Many signals encountered in practice are time-domain signals that are plotted as a time-amplitude representation. However, the time- amplitude representation may not be optimal for some signal-processing applications since valuable information about the signal's frequency content is often hidden. Fourier transforms are widely used for frequencyanalysis, but they do not provide information about the time at which frequency components occur. Fourier transforms are most useful for stationary signals that have properties that do not change over time. To analyze non-stationary signals, the short-time Fourier transform (“STFT”), which divides the signal into small stationary segments using window functions, is often used.

[0035] The wavelet transform is often a useful alternative to the STFT. The wavelet transform is suitable for analyzing signals that are periodic, noisy, intermittent, or transient. The wavelet transform can, in contrast to the STFT, be employed to examine signals in both time and frequency simultaneously. These benefits have led to popularity and applicability of the wavelet transform in various signal-processing applications, ranging from heart-condition monitoring to climate analysis.

[0036] FIGURE 3 illustrates examples of commonly used complex and real wavelet transform families. Wavelet transform analysis uses small wavelike functions known as wavelets, which can be real, such as Coeflets, Debauchies, and Haar, or complex, such as Complex Gaussian and Complex Morlet. Wavelets can be defined mathematically as the convolution of a signal function. The CWT serves as a form of mathematical microscope for diverse signals and has been adopted by numerous engineering and medical applications.

[0037] In the realm of wavelet analysis, two primary strategies are often employed: 1) shifting the wavelet along the signal's length; and 2) altering the wavelet’s size through one or both of compression and expansion. The wavelet transform is fundamentally a process in which a small specific wavelet function is combined with a signal in a focused manner. A typical process is dependent on two parameters: 1) the scale, which dictates how much the wavelet is compressed or expanded; and 2) the location, indicating the specific point of this interaction within the signal.

[0038] FIGURE 4 illustrates a wavelet transform mechanism and plotting of a signal energy scalogram. The scale parameter is a measure of the change in size of the wavelet, while the location parameter pinpoints the exact position in the signal where the analysis is conducted. The outcome of this transform is a measure of how closely the wavelet corresponds with the signal at various scales and positions. A smaller scale factor results in a more compressed wavelet. Equation 1 is as follows:where (b) is the location of the wavelet transform, (a) is the scale, x(t) is the signal, and w(a) is a weighting function, ip is the mother wavelet. In a typical embodiment, (a) is set as - = for energy conservation. The complex wavelet (^) becomes (p *) which indicates using the complex conjugate of the wavelet function. In a typical embodiment, the complex Morlet wavelet is used, where the mother wavelet function ( I / J *) can be obtained from equation 2where B is the bandwidth and C is the center frequency. In fracture-propagation event detection, a fixed bandwidth (B = 1.5) and center frequency (C = 1) have been empirically determined for optimal performance, although is some applications other fixed bandwidth and center frequency may be preferred. In some embodiments, a configuration of fixed bandwidth B of 1 .5 and a center frequency of C=1 has been found to balance sensitivity and specificity, such that accurate detection of relevant frequency components tends to be ensured while false positives are minimized. Such standardized values often serve to streamline analyses, providing consistency and repeatability for enhanced fracture characterization and monitoring.

[0039] Wavelet transforms can be undertaken at discrete points, thereby resulting in a discrete wavelet transform (“DWT”) or a smoothly resulting CWT filling the wavelet transform space. One feature of the signals that can observed and analyzed to identify the system properties is the signal energy. For any signal, the total energy contained in a signal x(t) is defined as its integrated squared magnitude as in equation 3 with the condition that the signal must contain finite energy.E = (0l2dt (3)The relative contribution of the signal energy contained at a specific (a) scale and (b) location is given by the two-dimensional wavelet energy density function of Equation 4.E(a, b) is depicted graphically over time by employing varying location parameters (b) and scale values (a) in a graphical representation known as a scalogram. In some embodiments, the scalogram utilizes a scale parameter (a) that spans from 0 to 256. The upper limit of 256 has been determined through multiple experiments as sufficient for identifying fracture propagation events in various applications.

[0040] The location parameter (b) begins at zero, aligning with the onset of the treating pressure signal (i.e., the start of hydraulic fracturing pumping) and continues until the termination of the signal (i.e., the end of hydraulic fracturing pumping), thereby mirroring the dynamic evolution of fracture propagation. This methodology conforms to the common sampling rate used in hydraulic fracturing procedures of 1 / 60 minutes. Through the scalogram, the location and scale of predominant energetic characteristics within the signal can be pinpointed. Moreover, the scalogram enables acquisition of the scale-dependent wavelet energy spectrum of the signal E(a) at a particular scale. At smaller scales (i.e., a compressed wavelet), it is possible to detect rapidly changing details (i.e., fine features) that induce high frequency in the signal. Conversely, at larger scales (i.e., a stretched wavelet), the scalogram identifies slowly evolving details (i.e., coarse features) that are associated with low frequency in the signal.

[0041] To extract both coarse and fine features within a signal using wavelet transform, a specific procedure as illustrated in FIGURE 4 may be utilized. First, a selected wavelet, such as the Complex Morlet Wavelet, is compared to a segment of the original signal at the beginning of the signal. A correlation coefficient, known as the wavelet transform value, is calculated. This process is repeated for the entire signal by incrementally shifting the wavelet along the signal. Second, the selected wavelet is stretched. The first and second steps are repeated for all desired scales. This process effectively fills the wavelet transform space with coefficients at different scales and locations, thereby providing a comprehensive representation of the signal's frequency content across various scales. Third, the coefficients at the same scales and locations are squared. The resulting values are then plotted with the logarithm of base 2 as the scale axis. This visual representation, known as the signal energy scalogram, helps identify dominant frequencies and scales within the analyzed signal.

[0042] FIGURE 5 illustrates an example of a hydraulic fracturing job pumping chart. Calculated bottom-hole pressure (“BHP”), slurry rate, and proppant concentration are illustrated versus time. Treating pressure versus time serves as a valuable output signal for monitoring hydraulic fracturing behavior. To gain insights into dominant frequencies and scales within this signal and potentially identify different fracture propagation events, the signal undergoes CWT processing.

[0043] FIGURE 6 illustrates a continuous wavelet transform scalogram for the hydraulic fracturing job of FIGURE 5 using the process illustrated in FIGURE 4. The process generates a CWT signal energy scalogram, which provides a visual representation of the signal's frequency content across various scales and time intervals.

[0044] For improved analysis and identification of distinct signatures associated with each fracture propagation mode, the CWT signal energy scalogram can be further processed through normalization. This normalization ensures the normalized signal energy falls within a range of 0 to 1 across any hydraulic fracturing job, enabling comparisons and interpretations across diverse datasets. The signal energy scalogram may undergo a minimum-maximum scaling process for normalization, which procedure involves assigning a value of 1 to the maximum base-2 logarithm of the squared CWT coefficient and a value of 0 to the minimum base-2 logarithm for each hydraulic fracturing pumping period. Subsequently, the base-2 logarithm of squared CWT coefficients within this normalized range may be further normalized using Equation 5.

[0045] FIGURE 7 illustrates a normalized continuous wavelet transform scalogram shown in FIGURE 6 for the hydraulic fracturing job of FIGURE 5. The normalization step serves to enhance the classification of fracture propagation events, facilitating clearer interpretation and comparison between different datasets. The resulting normalized CWT scalogram is generated using the same methodology as the signal energy scalogram shown in FIGURE 6.

[0046] The normalized CWT scalogram technique involves computing CWT of the treating pressure data to generate a time-scale energy scalogram showing energetic features. Normalizing the scalogram magnifies differences between energy values, helping to classify propagation events for interpretation. The technique detects coarse low-frequency features representing gradual change and fine high-frequency details from rapid changes. Using this technique can identify fracture propagation events like fracture height growth and fracture length propagation from the treating pressure.

[0047] The normalized scalogram of the CWT provides a visual interpretation of the events of hydraulic fracturing propagation over time as shown in FIGURE 7. Different shaded regions,which in some embodiments may be represented as different colored regions, on the CWT coefficient heat map indicate distinct fracture behaviors during different time intervals. In a typical embodiment, normalized CWT values from 0.4 to 0.6 primarily signify fracture length growth, while values between 0.8 and 0.95 suggest interactions with high leak-off zones or increases in fracture height, and values from 0.0 to 0.25 imply limited fracture width propagation. Thus, the CWT scalogram facilitates interpreting intricate 3D fracture geometry evolution using only recorded treating pressure data as inputs.

[0048] To evaluate the methodologies disclosed herein, the normalized CWT scalogram may be compared to existing methods such as, for example, the MRP and Nolte-Smith techniques. This comparison involves assessing fracture simulation, real field cases, and micro-seismic event locations (in x, y, and z dimensions) over time to gauge the present methodologies’ accuracy. Treating pressure undergoes analysis and is transformed into a normalized CWT scalogram map. This map then may be correlated with the relative location of micro- seismic events concerning the perforation midpoint for each fracture stage (dx, dy, dz). One benefit of incorporating treating pressure analysis via CWT is its ability to generalize distinctive signatures of fracture propagation events, overcoming valuations in factors such as friction, minimum horizontal stress, toughness, and fracture complexity.

[0049] Normalized CWT techniques as disclosed herein may be validated through simulations and real field applications and corroborated by a planar 3D model. Leveraging the extensive Marcellus Shale Energy and Environment Laboratory (“MSEEL”) public dataset, this study significantly contributes to calibrating the technique using micro-seismic events recorded during fracture propagation. Upon confirming the effectiveness of the normalized CWT in detecting dynamic fracture events, in various embodiments, a deep-learning model may be trained using data from hydraulic fracturing jobs. The model subsequently may be used to generate an estimated micro-seismic event cloud for various fracture stages within the formation in question. This integrated approach underscores the applicability and robustness of the methodologies for real- world fracture monitoring and analysis.

[0050] The application of a normalized CWT scalogram in hydraulic fracturing presents a novel approach to deep learning or machine learning. This technique transforms treating pressuredata into a normalized CWT scalogram, generating unique signatures associated with distinct hydraulic fracturing propagation events. These 256 features, constituting the normalized CWT scalogram, serve as input for training a machine-learning or deep-learning model. The trained model accurately predicts the three-dimensional locations (x, y, and z) of micro-seismic events, providing valuable insights into the geometry of hydraulic fracturings. The technique excels in accurately modeling hydraulic fracturings, regardless of induced complexity or fraction losses, thereby enhancing the understanding and optimization of hydraulic fracturing processes in various formations, and serves to translate fracture propagation events into the evolution of micro-seismic events' locations.

[0051] A compact neural network specifically tailored for regression tasks involving tabular data may be employed in accordance with principles disclosed herein. The neural network incorporates several crucial components to enhance its training and predictive capabilities. First, the network leverages Batch Normalization, which can serve to stabilize and accelerate a training process by normalizing the input for each mini-batch of data during training. This normalization helps to combat issues related to vanishing and exploding gradients, making the training process smoother and more efficient. The parameters associated with Batch Normalization include the number of features (e.g., 256) which are the output of each stage after applying the CWT transformation, a small constant for numerical stability (cps- lc-05). a momentum term (momentum=0.1) for maintaining running statistics being used.

[0052] In the presented model, the foundational architecture is encapsulated within a sequential container, delineating a structured series of computational layers. This architecture adheres to a predefined schema: initially, a Linear Layer (configured as Linear (input features=256, output features=200)) executes a linear' transformation of the input dataset, effectuating a mapping from 256 input features to 200 output features. Subsequently, this transformation is complemented by the integration of a Rectified Linear Unit (“ReLU”) activation function. This function imparts non-linearity into the computational process while its “inplace=True” parameter serves to enhance memory efficiency. This Linear- ReLU configuration is replicated in the ensuing stages of the model, with the second instantiation of the Linear Layer diminishing the feature count from 200 to 100. The architectural sequence culminates with an additional Linear Layer, which furtherrefines the output from 100 features to a trio, corresponding to the normalized dx, dy, and dz relative to the midpoint of the perforation of each fracture stage.

[0053] In the development of the deep-learning or machine-learning model, a comprehensive data set encompassing approximately 256,555 data points may be employed. These data points represent a series of 48 hydraulic fracturing stages, collated to ensure a representative sample of the operational scope. The model adheres to a rigorous training regimen, with the data set partitioned into two distinct subsets: 70% is allocated for training purposes, enabling the model to learn and adapt to the intricacies of the data, while the remaining 30% is reserved for testing, ensuring a robust evaluation of the model’s performance. Furthermore, to enhance the validity of the model's predictive capabilities, certain stages are deliberately excluded from the primary training and testing phases. These stages may be retained for a final comprehensive testing phase, providing an additional layer of assessment to gauge the model’s efficacy in real-world scenarios. This strategic division of data not only bolsters the model's accuracy but also increases the likelihood of more generalized and reliable performance across various future data scenarios.

[0054] In order to evaluate the model's performance, Stratified K-Fold cross-validation may be employed. Stratified K-Fold cross-validation is a robust technique that is particularly effective in dealing with class imbalance in tabular data. It improves upon standard K-Fold cross-validation by ensuring each fold contains approximately the same proportion of high values of micro-seismic events in dx, dy, and dz directions as the entire dataset, providing a more accurate estimate of the model's generalization performance. As an example, 10 folds may be used to stratify the data categorized in high, mid, and low dx, dy, dz, dividing it into 10 equally sized folds, each with a representative distribution of micro-seismic events.

[0055] In a typical embodiment, the training and evaluation process is repeated 15 times, involving training the model on K-l folds and evaluating the model on the remaining fold, recording metrics such as, for example, accuracy, precision, and recall. An average of these metrics across all folds provides a comprehensive performance estimate. Benefits of this approach include reduced bias, as the approach ensures training and testing on data with similar micro- seismic distribution, improved generalization by evaluating the model on various data subsets, and more reliable performance estimates through averaging metrics across multiple folds.

[0056] FIGURE 8 illustrates a deep-learning or machine-learning framework that may be used to predict a micro-seismic events cloud. The choice of a batch size of 64 in this model is critical for several reasons. It aligns with available hardware memory, balancing computational efficiency and memory usage. This size influences the model's generalization ability and training convergence, offering a middle ground between stable training and good generalization. Empirical studies suggest that batch sizes in a range of 32 to 128 are generally effective, making a batch size of 64 a well-founded choice based on practical experience.

[0057] FIGURE 9 illustrates training loss versus learning rate of the model of FIGURE 8. It shows that the selected learning rate achieves a minimum training loss.

[0058] Validation of the methodologies is achieved through three distinct cases, each serving a specific goal. Each case serves as a useful step, contributing uniquely to the comprehensive validation process, ensuring the technique's reliability and effectiveness across various scenarios. In the first case, the technique is carefully tested in a simulated fracture scenario, making sure the basic fracture mechanics and fluid flow principles are followed. This step aims to confirm that the technique works well under controlled settings. The second case is a real-world field scenario. This field case is intricately calibrated using a planar 3D fracture simulation that delves into the integration of comprehensive geomechanical and reservoir properties. The primary objective is to validate the methodologies’ applicability and accuracy in a practical and field-oriented context. In the third case, the focus sharpens on validation using recorded micro-seismic events during fracture propagation. This phase involves a detailed comparison of the detected fracture propagation events utilizing the new technique against the temporal evolution of micro-seismic events throughout the fracture propagation process. Case 3 specifically leverages hydraulic fracturing job data from stage 28 in MIP-3H, coupled with associated micro-seismic events from the MSEEL public dataset. The overarching goal in this case is to validate the methodologies’ performance under real- world conditions and its ability to accurately capture micro-seismic events during hydraulic fracturing propagation.

[0059] Confirmation of the normalized CWT scalogram efficacy in identifying dynamic fracture events is followed by a deep learning model trained using data derived from 48 hydraulic fracturing jobs conducted in wells MIP-3H and MIP-5H. The trained model then produces acomprehensive estimation of micro- seismic event cloud locations for different fracture stages within the Marcellus formation. This integrated approach highlights the versatility and reliability of the proposed methodologies, emphasizing practicality for real-world fracture monitoring and in-depth analysis.

[0060] Three distinct cases are examined below to evaluate the effectiveness of the normalized CWT scalogram for detecting dynamic fracture events. The first case involves a simulated scenario in which treating pressure is applied in a realistic mechanical earth model. This simulated environment, referred to as case 1, allows for controlled observation and analysis of how the CWT scalogram responds to theoretical inputs, setting a baseline for understanding its performance. The second case, known as case 2, shifts focus to actual treating pressure data. This real-world data provides a more complex and uncontrolled set of variables, offering insights into how the CWT scalogram operates under typical field conditions. The third and final case, case 3, presents a comprehensive real-field scenario. Here, the validation of the CWT scalogram’ s efficacy in detecting dynamic fracture events is undertaken by comparing interpreted dynamic fracture events with actual fracture events. These actual events are measured and tracked through the development of micro-seismic activities over time. This case is crucial as it tests the CWT scalogram in a fully realistic setting, confirming its practical utility and accuracy in interpreting dynamic fracture.

[0061] Using the normalized CWT scalograms provides a tool for visual representation and comprehension of the fracture propagation events. Each mode exhibits a distinct and discernible pattern within the normalized CWT scalogram. The normalized CWT technique offers distinct advantages over existing methodologies such as the Nolte-Smith and MRP techniques and expedites the analytical process without necessitating the closure pressure data or going through a complex workflow. The efficacy of the normalized CWT scalogram is proven with comparative analysis performed against fracture simulation data, real field cases calibrated with MRP technique, and finally using publicly available micro-seismic events data obtained from the MSEEL. The calibration of detecting dynamic fracture propagation events using the normalized CWT scalogram with micro-seismic events evolution with time enables the training of a deep learning model to create synthetic micro-seismic events from the observed treating pressure. The deep learning model allows estimation of micro-seismic events cloud and fracture geometrydirection solely from the treating pressure data. Testing using MSEEL data has demonstrated that the methodologies exhibit commendable accuracy in predicting micro-seismic cloud formations.

[0062] The term "substantially" is defined as largely but not necessarily wholly what is specified (and includes what is specified; e.g., substantially 90 degrees includes 90 degrees and substantially parallel includes parallel), as understood by a person of ordinary skill in the art. In any disclosed embodiment, the terms “substantially,” “approximately,” “generally,” and “about” may be substituted with “within 10% of’ what is specified.

[0063] Depending on the embodiment, certain acts, events, or functions of any of the algorithms described herein can be performed in a different sequence, can be added, merged, or left out altogether (e.g., not all described acts or events are necessary for the practice of the algorithms). Moreover, in certain embodiments, acts or events can be performed concurrently, e.g., through multi-threaded processing, interrupt processing, or multiple processors or processor cores or on other parallel architectures, rather than sequentially. Although certain computer- implemented tasks are described as being performed by a particular entity, other embodiments are possible in which these tasks are performed by a different entity.

[0064] Conditional language used herein, such as, among others, "can," "might," "may," “e.g.,” and the like, unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain embodiments include, while other embodiments do not include, certain features, elements and / or states. Thus, such conditional language is not generally intended to imply that features, elements and / or states are in any way required for one or more embodiments or that one or more embodiments necessarily include logic for deciding, with or without author input or prompting, whether these features, elements and / or states are included or are to be performed in any particular embodiment.

[0065] While the above detailed description has shown, described, and pointed out novel features as applied to various embodiments, it will be understood that various omissions, substitutions, and changes in the form and details of the devices or algorithms illustrated can be made without departing from the spirit of the disclosure. As will be recognized, the processes described herein can be embodied within a form that does not provide all of the features and benefits set forth herein, as some features can be used or practiced separately from others. Thescope of protection is defined by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.

Claims

What is claimed is:

1. A method of estimating a micro- seismic cloud related to a hydraulic fracturing operation, the method comprising: receiving a treating pressure signal generated during hydraulic fracture propagation; calculating a complex wavelet transform coefficient on the received treating pressure signal; calculating energy of the received treating pressure signal at multiple scales to create a signal-energy scalogram; normalizing the signal-energy scalogram to create a normalized signal-energy scalogram; and establishing a correlation between signatures of dynamic fracture propagation modes identified in the normalized signal-energy scalogram and corresponding fracture propagation mode influence on temporal development of a micro-seismic events cloud.

2. The method of claim 1, wherein: the complex Morlet mother wavelet function is the function of its bandwidth and central frequency and the preferred complex Morlet mother wavelet function iswhere B is the bandwidth and C is the center frequency.

3. The method of claim 1 , comprising integrating the establishing correlation into an artificialintelligence system to generate a synthetic micro-seismic cloud.

4. The method of claim 3, comprising using the generated micro-seismic cloud to process treating pressure to simulate an outcome of a second hydraulic fracturing operation.

5. The method of claim 1, comprising: integrating the establishing correlation into an artificial-intelligence system to generate a synthetic micro-seismic cloud; andusing the generated micro-seismic cloud to process treating pressure to simulate an outcome of a second hydraulic fracturing operation.

6. The method of claim 1 or 5, wherein: the complex wavelet transform coefficient equation isa is a scale parameter, b is a translation parameter that represents time-scale movement, T* is a Complex Morlet mother wavelet function, and t is time; and the Complex mother Morlet wavelet function iswhere B is the bandwidth and C is the center frequency.

7. The method of claim 2 or 10, wherein the energy of the treating pressure signal is represented by8. The method of claim 5, wherein the integrating utilizes machine-learning techniques.

9. The method of claim 5, wherein the integrating utilizes deep-learning techniques.

10. The method of claim 5 or 14, wherein the integrating utilizes at least one of machinelearning techniques and deep-learning techniques.

11. A computer-program product comprising a non-transitory computer-usable medium having computer-readable program code embodied therein, the computer-readable program code adapted to be executed to implement the method of claim 1.

12. The computer-program product of claim 11, the computer-readable program code adapted to be executed to implement the method of claim 2.

13. The computer-program product of claim 11, the computer-readable program code adapted to be executed to implement the method of claim 3.

14. The computer-program product of claim 11, the computer-readable program code adapted to be executed to implement the method of claim 4.

15. The computer-program product of claim 11, the computer-readable program code adapted to be executed to implement the method of claim 5.

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