A method for formation pressure monitoring while drilling based on data physical double drive

Abstract

The present application relates to the technical field of oil drilling, and proposes a formation pressure while drilling monitoring method based on data-physical double driving, comprising: selecting comprehensive logging data and logging data of drilled adjacent wells in a target block; establishing an acoustic travel time logging curve inversion model based on the comprehensive logging data and logging data to obtain inverted acoustic travel time; calculating formation pressure according to the obtained inverted acoustic travel time; dynamically calculating a formation pressure profile while drilling; the present application is combined with Eaton formula and used for formation pressure monitoring of land conventional drilling. The method establishes a connection between comprehensive logging data and acoustic travel time logging curve, realizes intelligent, high-accuracy and reliable formation pressure calculation. It is suitable for field deployment, has a theoretical basis, can accurately calculate formation pressure while drilling in real time, and improves accuracy and reliability compared with the prior art.

Description

Technical Field

[0001] This invention relates to the field of oil drilling technology and proposes a method for monitoring formation pressure while drilling based on a data-physical dual-drive approach. Background Technology

[0002] In the process of oil and gas exploration and development, formation pressure, as a geological attribute, plays a crucial role in identifying favorable blocks, ensuring safe and efficient drilling, and achieving sustained and stable production in the later stages of development.

[0003] In drilling engineering, accurate pre-drilling prediction and monitoring of formation pressure are of great significance for avoiding downhole risks, optimizing drilling design, protecting oil and gas reservoirs, and achieving cost reduction and efficiency improvement.

[0004] Currently, formation pressure prediction in drilling design mainly relies on seismic layer velocity or adjacent well logging data. However, due to the lag in basic data, the low resolution of seismic layer velocity, and the lateral heterogeneity of the formation, the accuracy of formation pressure prediction is low, posing potential risks during drilling operations. Therefore, it is necessary to monitor formation pressure in real time based on comprehensive logging parameters acquired from the surface during drilling and downhole information obtained while drilling. This allows for dynamic adjustment of drilling parameters to avoid problems caused by abnormal formation pressure, such as blowouts, lost circulation, formation fracturing, ground subsidence, equipment damage, decreased production efficiency, and potential environmental impacts. These situations not only threaten the safety of operators but may also lead to huge economic losses and production interruptions.

[0005] Commonly used methods for monitoring formation pressure while drilling include the standard rotation speed method, shale density method, rock strength method, and DC index method. The standard rotational speed method assesses formation drillability by measuring the rotational speed during drilling. Its principle is based on variations in drill bit rotational speed in different formations, thereby inferring formation hardness and drilling efficiency. Its drawbacks include sensitivity to changes in drilling parameters and the inability to directly reflect the physical properties of the formation.

[0006] The shale density method assesses formation pore pressure and fracture pressure by measuring changes in drilling fluid density. Its principle is based on the change in drilling fluid density caused by the exchange of pore fluids within shale formations. However, it has drawbacks, requiring high-quality drilling fluid and a clean wellbore, and may be inaccurate in complex formations.

[0007] The rock strength method assesses formation hardness by measuring the compressive strength of rocks. Its principle is based on laboratory tests of rock samples, combined with field drilling parameters. Its drawbacks include the need for core sampling, the time-consuming laboratory testing, and the inability to reflect formation conditions in real time.

[0008] The DC index method calculates the drilling index by measuring the drilling pressure and rotational speed during drilling, thereby assessing the drillability of a formation. Its principle is based on the changes in drilling parameters generated when the drill bit interacts with the formation. Its drawbacks include the need for precise recording of drilling parameters and the potential for interference from various factors during drilling, such as changes in the performance of the drilling equipment. It is evident that the aforementioned traditional methods involve numerous parameters, are overly complex in their calculations, and rely on many assumptions, leading to difficulties in field application and significant errors in calculation and monitoring.

[0009] Chinese patent document with publication number CN115059448A discloses a formation pressure monitoring method based on a deep learning algorithm. The method uses well logging information of adjacent target blocks and assigns priority to the well location for model training based on the richness of geological logging information of the well location. The method uses a GA-BP neural network to monitor formation pore pressure and its changing trend.

[0010] Chinese patent document CN112966217A discloses a formation pressure monitoring method based on drilling machinery energy efficiency. It monitors formation pressure in real time by comprehensively utilizing mechanical specific energy and drilling efficiency data during the drilling process, and adjusts and optimizes drilling parameters such as drilling fluid density and displacement based on the real-time monitoring.

[0011] Chinese patent document CN115795840A discloses a formation pressure monitoring method based on the effective stress method. The method collects various drilling engineering parameters and formation pressure data from adjacent wells, calculates the corrected drilling pressure index and the vertical effective stress at the effective pressure measurement point of the adjacent well, substitutes the corrected drilling pressure index and the vertical effective stress into the effective stress model to obtain the correction formula, and obtains the formation pressure of the well being drilled according to the correction formula.

[0012] Chinese patent document CN114922614A discloses a method for monitoring formation pressure under controlled pressure drilling conditions. Under controlled pressure drilling conditions, the method directly measures the suction pressure and bottom hole pressure through PWD. Based on this, an RNN neural network model based on bee colony optimization algorithm is established. The pressure difference inside the wellbore is obtained through the trained neural network, and the formation pressure is obtained according to the pressure difference formula.

[0013] The methods described in the above patents all have limitations to varying degrees, facing challenges such as numerous formulas, lack of interpretability of the process, and the rarity of PWD applications in conventional onshore drilling.

[0014] In recent years, with the increasingly sophisticated application of artificial intelligence technology in the field of oil exploration and development, data-driven analysis methods can classify, regress, and predict engineering parameters by mining the correlations between data, bringing new research ideas to technicians in drilling design, rock mechanics, and other fields. For example, the gated recurrent unit (GRU) is a type of recurrent neural network widely used in deep learning. By introducing a gating mechanism, it can not only mine the spatial correlations between different time series data, but also take into account the temporal variation characteristics of the sequence data. It has been successfully applied in fields such as well logging curve reconstruction. However, artificial intelligence algorithms represented by GRU neural networks are black-box models, which lack interpretability and are difficult to meet the high reliability requirements of drilling engineering.

[0015] Therefore, it is necessary to establish a formation pressure monitoring method based on a combination of data-driven and physical models, combining GRU neural networks and Eaton formulas, for the purpose of monitoring formation pressure while drilling in the field of drilling technology. Summary of the Invention

[0016] The purpose of this invention is to address the shortcomings of existing technologies by proposing a data-physical dual-drive method for monitoring formation pressure while drilling, thus solving the following technical problems: 1. Traditional monitoring while drilling methods involve many parameters, the calculation process is too complicated, and there are many assumptions, which makes them difficult to use in the field and results in large calculation and monitoring errors. 2. The application of artificial intelligence algorithms in the field of drilling engineering is immature and has great limitations. It is a black box model with numerous formulas, lack of interpretability, and a lack of relevant equipment for onshore drilling. To achieve the above objectives, the present invention adopts the following technical solution: A data-physical dual-drive method for monitoring formation pressure while drilling includes: Select comprehensive logging and well logging data from adjacent wells that have been drilled in the target block; Based on the integrated logging data and well logging data, an inversion model for acoustic transit time logging curves is established to obtain the inverted acoustic transit time. The formation pressure is calculated based on the obtained inverted acoustic transit time. Dynamically calculate the formation pressure profile while drilling.

[0017] Furthermore, the sonic transit time logging curve inversion model is established using a GRU neural network, and the comprehensive logging parameters include engineering logging parameters and drilling fluid logging parameters. The steps for establishing the sonic transit time logging curve inversion model include: The collected integrated logging parameters and sonic transit logging parameters were interpolated for depth alignment, and correlation analysis was performed between the parameters. Logging parameters with high correlation to sonic transit and low correlation between parameters were extracted as input parameters for the inversion model. The dataset is divided into training, testing, and validation sets according to a certain ratio, and the dataset is standardized. Determine the topology and hyperparameters of the GRU neural network; The GRU neural network is trained by backpropagation of errors, and the weights and thresholds at each node of the network are updated until the training cycle ends. The output of the network is then denormalized to obtain the inverted acoustic time difference.

[0018] Furthermore, the calculation of the formation pressure includes: Based on the sonic transit time logging curves obtained from the inversion, the equation for the normal compaction trend line is fitted and constructed as follows: lgDT N =C1H+lgDT0——(1) In the formula, H is the well depth, in meters; DT N DT0 and DT0 represent the acoustic transit time of normally compacted mudstone and the surface acoustic transit time when H=0, respectively, in µs / ft. Substituting the inverted acoustic transit time and the fitted normal compaction trend line equation into the Eaton formula yields: In the formula, PP is the formation pressure, in g / cm³. 3 OBG represents the pressure of the overlying strata, in g / cm³. 3 ;PP N The hydrostatic pressure is expressed in g / cm³. 3 DT represents the actual inverted sonic transit time of mudstone, in µs / ft; n represents the Eaton exponent.

[0019] Furthermore, it also includes data preprocessing, which includes outlier removal from the curve data. The outlier removal uses the unknown rational number method to remove curve outliers, and the formula for the unknown rational number method is: In the formula, n i X represents i Within the neighborhood | X i -X j |≤λ;(i-δ<j<i+δ) contains X j The number of is determined by the expected value of the unknown rational number A. To replace A, we can remove outliers.

[0020] Furthermore, the data preprocessing also includes curve smoothing preprocessing, which uses a five-point bell function smoothing method. The five-point bell function is: P i =0.11(P) i-2 +Pi+2 )+0.24(P i-1 +P i+1 +0.3P i ——(4). Furthermore, the interpolation algorithm for curve depth alignment employs trispline interpolation. Furthermore, the correlation analysis employs the MIC (Maximum Information Coefficient) method, and the calculation formula for the MIC is as follows: In the formula, MIC[x,y] is the correlation coefficient between variables x and y; X and Y are the discrete vectors of variables x and y, respectively; and B is the threshold for dividing the two-dimensional spatial discrete grid.

[0021] Furthermore, the dataset is divided in a ratio of training set: validation set: test set = 7:2:1. Furthermore, the dataset is standardized using the z-score standardization method, which is as follows: In the formula, x * The data has been standardized. σ represents the mean and standard deviation of the original data, respectively.

[0022] Furthermore, the pressure of the overlying strata is calculated using the Gardner formula and by quadrature. The Gardner formula and integral formula are obtained through calculation: ρ b =a(304.8 / DT) b ——(8) In the formula: ρ b ρ is the density of the rock mass, g / cm3; a and b are model parameters, preferably a = 0.23 and b = 0.25; ΔH is the depth interval, m.

[0023] The beneficial effects of this invention are as follows: For formation pressure monitoring using integrated logging data in conventional onshore drilling, this invention establishes a link between sonic transit time logging curves and logging parameters, constructs a GRU-based sonic transit time inversion model, and calculates formation pressure using the Eaton formula. This method is highly intelligent, widely applicable, and theoretically supported, enabling accurate calculation of formation pressure during drilling. Compared to existing technologies, this invention offers higher accuracy and reliability, is easier to deploy in the field, and combines timeliness and realism. Attached Figure Description

[0024] Figure 1 This is a flowchart of the technical solution of the present invention. Figure 2 This is a correlation matrix diagram showing the relationships between the parameters. Figure 3 The optimal GRU neural network topology is set for this invention. Figure 4 This is an inversion diagram of the sonic transit time logging curve. Figure 5 This is a profile of formation pressure monitoring during drilling. Detailed Implementation

[0025] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Example 1: like Figure 1 As shown, a method for monitoring formation pressure while drilling based on a data-physical dual-drive approach includes the following steps: Step 1: Select comprehensive logging data (including but not limited to engineering logging parameters and drilling fluid logging parameters), well logging data, and formation pressure test data of the adjacent wells that have been drilled in the target block, and perform outlier removal and curve smoothing preprocessing on the curve data.

[0026] Step Two: Since logging parameters are engineering representations of the downhole geological environment under specific construction conditions, while well logging parameters are physical representations of the downhole geological environment, there is a certain correlation between the two types of data. Well logging acoustic data, with its elastic propagation characteristics in the medium, can quantitatively characterize abnormal formation overpressure. Therefore, the formation acoustic transit time can be dynamically inverted using logging parameters, and a GRU neural network can be used to establish an acoustic transit time logging curve inversion model.

[0027] The method for establishing the GRU sonic time-of-flight logging curve inversion model is as follows: Step 2-1: The collected integrated logging parameters and sonic transit logging parameters are interpolated for depth alignment, and correlation analysis is performed between the parameters. Logging parameters with high correlation to sonic transit and low correlation between parameters are extracted as input parameters for the inversion model.

[0028] Step 2-2: Divide the dataset into training set, test set and validation set according to the proportion, and standardize the dataset.

[0029] Steps 2-3: Determine the topology and hyperparameters of the GRU neural network. Hyperparameters include, but are not limited to: number of layers, initial learning rate, decay coefficient, decay period, batch size, dropout probability, sliding window size, training period, optimizer, and loss function.

[0030] Steps 2-4: Train the GRU neural network through error backpropagation, updating the weights and thresholds at each node until the training cycle ends. Inverse normalize the network output to obtain the retrieved acoustic time difference.

[0031] Step 3: For abnormally overpressured formations of conventional sandstone and mudstone, the Eaton method can be used for drilling pressure monitoring. The Eaton method is one of the most widely used quantitative methods for calculating formation pressure. This method is based on the relationship between formation pore pressure and logging parameters established by Eaton based on experience and theoretical analysis in regions such as the Gulf of Mexico.

[0032] The method for calculating formation pressure using Eaton's formula is as follows: Step 3-1: Based on the sonic transit time logging curve obtained from the inversion, the equation for the normal compaction trend line is fitted and constructed as follows: lgDT N =C1H+lgDT0——(1) In the formula, H is the well depth, in meters; DT N DT0 and DT0 represent the acoustic transit time of normally compacted mudstone and the surface acoustic transit time when H=0, respectively, in µs / ft. Step 3-2: Substitute the inverted acoustic transit time and the fitted normal compaction trend line equation into the Eaton formula: In the formula, PP is the formation pressure, in g / cm³. 3 OBG represents the pressure of the overlying strata, in g / cm³. 3 ;PP N The hydrostatic pressure is expressed in g / cm³. 3 DT represents the actual inverted sonic transit time of mudstone, in µs / ft; n represents the Eaton exponent.

[0033] Step 3-3: Dynamically calculate the formation pressure profile while drilling. Preferably, in step one, the unknown rational number method is used to remove outliers from the curve. The formula for the unknown rational number method is: In the formula, n i X represents i Within the neighborhood | X i -X j |≤λ;(i-δ<j<i+δ) contains X j The number of is determined by the expected value of the unknown rational number A. To replace A, we can remove outliers.

[0034] Preferably, in step one, the five-point bell-shaped function smoothing method is used for curve smoothing, wherein the five-point bell-shaped function is: Pi =0.11(P) i-2 +P i+2 )+0.24(P i-1 +P i+1 +0.3P i ——(4) Preferably, in step 2-1, the interpolation algorithm for curve depth alignment uses trispline interpolation.

[0035] Preferably, in step 2-1, the MIC (Maximum Information Coefficient) method is used to analyze the correlation between parameters. This method is suitable for measuring the degree of linear or nonlinear association between two variables. The calculation formula for the MIC method is as follows: In the formula, MIC[x,y] is the correlation coefficient between variables x and y; X and Y are the discrete vectors of variables x and y, respectively; B is the threshold for dividing the two-dimensional spatial discrete grid, which is generally set to about 0.6 times the amount of sample data.

[0036] Preferably, in step 2-2, the dataset is divided into the following ratios: (training set: validation set: test set) = (7:2:1).

[0037] Preferably, in step 2-2, the dataset is standardized using z-score standardization. The processed data has a mean of 0 and a standard deviation of 1. The z-score standardization method is as follows: In the formula, x * The data has been standardized. σ represents the mean and standard deviation of the original data, respectively.

[0038] Preferably, in step 3-2, the pressure of the overlying strata is obtained using the Gardner formula and integral calculation. The Gardner formula and integral formula are as follows: ρ b =a(304.8 / DT) b ——(8) In the formula: ρ b Density of the rock mass, g / cm³ 3 a and b are model parameters, preferably a = 0.23 and b = 0.25; ΔH is the depth interval, in meters.

[0039] Preferably, in step 3-2, the Eaton index is set to 1.6, which is determined by regression analysis of regional patterns and formation pressure test data. Example 2: like Figure 1As shown, a method for monitoring formation pressure while drilling based on a data-physical dual-drive approach includes the following steps: (1) Ten completed wells in a certain block were selected as the dataset. The collected logging parameters included: hook load, rotational speed, torque, standpipe pressure, inlet flow rate, outlet flow rate, inlet density, outlet density, mechanical drilling rate, inlet temperature, outlet temperature, total gas measurement value, as well as the sonic transit time logging curve and formation pressure test data for each well. The unknown rational number and five-point bell function smoothing method were used to preprocess the curves of each parameter. Among them, the unknown rational number sliding window length N = 80.

[0040] (2) The collected integrated logging parameters and sonic transit logging parameters were depth-aligned using trispline interpolation, and the correlation between each parameter was calculated using the MIC maximum information coefficient analysis method. Logging parameters with high correlation to sonic transit and low correlation among parameters were extracted. The correlation analysis results between each parameter are as follows: Figure 2 As shown, the following eight parameters were ultimately selected as network input parameters: hook load, rotational speed, torque, riser pressure, mechanical drilling speed, outlet flow rate, outlet density, and total gas measurement value.

[0041] (3) Divide the dataset into training set, test set and validation set according to the proportion, and standardize the dataset using z-score standardization.

[0042] Preferably, the dataset is divided into (training set: validation set: test set) = (7:2:1). For ease of comparison and analysis, 7 wells are used as the training set, 2 wells as the validation set, and 1 well as the test set.

[0043] (4) Substitute the dataset from step (3) into the GRU neural network for training to achieve dynamic inversion of the acoustic time difference curve.

[0044] The method for training the GRU sonic transit time logging curve inversion model is as follows: The curves in each dataset are sampled using a sliding window method, with the window size set to 300, or 30m. This sample length means that in this GRU model, the data within 30m in front of each sampling point has an impact on the inversion value of that sampling point.

[0045] Through multiple experiments, the topology of the GRU neural network was determined as follows: Figure 3As shown, it consists of 2 GRU layers (80 neurons each) + 1 fully connected layer (1 neuron). The loss function is the MSE function. The initial learning rate is set to 0.005, the decay coefficient Decay is 0.2, the decay period is 10 rounds, the batch size is 128, the dropout probability is 50%, the training period is 10 rounds, and the Adam optimizer is selected.

[0046] The MSE function is as follows: The GRU neural network is trained using backpropagation to update the weights and thresholds at each node until the training cycle ends. The network output is then denormalized to obtain the retrieved acoustic time difference, as shown below. Figure 4 As shown.

[0047] (5) Based on the acoustic time difference curve obtained by inversion in step (4), judge the curve change trend according to regional experience, extract the curve data of normal compaction trend segment, and fit the equation of normal compaction trend line.

[0048] By comparison and judgment, the acoustic time difference curve above 1300m was selected for fitting the normal compaction trend line equation, and the fitted equation is as follows: lgDT N =0.00016H+5.08——(11) (6) Calculate the formation pressure profile while drilling, including: Specifically, the acoustic transit time curve obtained from step (4) is substituted into the Gardner formula and integrated to obtain the pressure of the overlying strata. The Gardner formula is as follows: ρ b =0.23×(304.8 / DT) 0.25 ——(12) Based on the normal compaction trend line equation obtained by fitting in step (5), calculate the normal compaction sonic transit time corresponding to the well depth for each sampling point of the target well, and then substitute it into the Eaton formula to calculate the formation pressure at each point. The Eaton formula is: Finally, the formation pressure profile obtained from the drilling monitoring of the target well (i.e., the well location to which the test set belongs) is obtained, such as... Figure 5 As shown.

[0049] By comparing the measured formation pore pressure points, it can be seen that the formation pore pressure profile calculated using this invention has a good fit with the measured points, which improves the accuracy and reliability of formation pressure monitoring while drilling compared with traditional formation pressure monitoring methods.

[0050] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for monitoring formation pressure while drilling based on a data-physical dual-drive approach, comprising selecting comprehensive logging data and well logging data from adjacent wells already drilled in the target block, characterized in that: Based on the integrated logging data and well logging data, an inversion model for acoustic transit time logging curves is established to obtain the inverted acoustic transit time. The formation pressure is calculated based on the obtained inverted acoustic transit time. Dynamically calculate the formation pressure profile while drilling.

2. The method for monitoring formation pressure while drilling based on data and physical dual-drive as described in claim 1, characterized in that, The sonic transit time logging curve inversion model is established using a GRU neural network. The comprehensive logging parameters include engineering logging parameters and drilling fluid logging parameters. The steps for establishing the sonic transit time logging curve inversion model include: The collected integrated logging parameters and sonic transit logging parameters were interpolated for depth alignment, and correlation analysis was performed between the parameters. Logging parameters with high correlation to sonic transit and low correlation between parameters were extracted as input parameters for the inversion model. The dataset is divided into training, testing, and validation sets according to a certain ratio, and the dataset is standardized. Determine the topology and hyperparameters of the GRU neural network; The GRU neural network is trained by backpropagation of errors, and the weights and thresholds at each node of the network are updated until the training cycle ends. The output of the network is then denormalized to obtain the inverted acoustic time difference.

3. The method for monitoring formation pressure while drilling based on data and physical dual-drive as described in claim 2, characterized in that, The calculation of the formation pressure includes: Based on the sonic transit time logging curves obtained from the inversion, the equation for the normal compaction trend line is fitted and constructed as follows: lgDT N =C1H+lgDT0——(1) In the formula, H is the well depth, in meters; DT N DT0 and DT0 represent the acoustic transit time of normally compacted mudstone and the surface acoustic transit time when H=0, respectively, in µs / ft. Substituting the inverted acoustic transit time and the fitted normal compaction trend line equation into the Eaton formula yields: In the formula, PP is the formation pressure, in g / cm³. 3 OBG represents the pressure of the overlying strata, in g / cm³. 3 ;PP N The hydrostatic pressure is expressed in g / cm³. 3 DT represents the actual inverted sonic transit time of mudstone, in µs / ft; n represents the Eaton exponent.

4. The method for monitoring formation pressure while drilling based on data and physical dual-drive as described in claim 3, characterized in that, It also includes data preprocessing, which includes outlier removal from the curve data. The outlier removal uses the unknown rational number method to remove outliers from the curve. The formula for the unknown rational number method is: In the formula, n i X represents i Within the neighborhood | X i -X j |≤λ;(i-δ<j<i+δ) contains X j The number of is determined by the expected value of the unknown rational number A. To replace A, we can remove outliers.

5. The method for monitoring formation pressure while drilling based on data and physical dual-drive as described in claim 4, characterized in that, The data preprocessing also includes curve smoothing preprocessing, which uses a five-point bell function smoothing method. The five-point bell function is as follows: P i =0.11(P i-2 +P i+2 )+0.24(P i-1 +P i+1 )+0.3P i ——(4)。 6. The method for monitoring formation pressure while drilling based on data and physical dual-drive as described in claim 5, characterized in that, The interpolation algorithm for curve depth alignment uses trispline interpolation.

7. The method for monitoring formation pressure while drilling based on data and physical dual-drive as described in claim 6, characterized in that, The correlation analysis employs the MIC (Maximum Information Coefficient) method, and the calculation formula for the MIC method is as follows: In the formula, MIC[x,y] is the correlation coefficient between variables x and y; X and Y are the discrete vectors of variables x and y, respectively; and B is the threshold for dividing the two-dimensional spatial discrete grid.

8. The method for monitoring formation pressure while drilling based on data and physical dual-drive as described in claim 7, characterized in that, The dataset is divided in a ratio of training set: validation set: test set = 7:2:

1.

9. The method for monitoring formation pressure while drilling based on data and physical dual-drive as described in claim 8, characterized in that, The dataset was standardized using z-score standardization, which is as follows: In the formula, x * The data has been standardized. σ represents the mean and standard deviation of the original data, respectively.

10. The method for monitoring formation pressure while drilling based on data and physical dual-drive as described in claim 9, characterized in that, The pressure of the overlying strata is obtained using the Gardner formula and integral calculation. The Gardner formula and integral formula are as follows: r b =a(304.8DT) b ——(8) In the formula: ρ b ρ is the density of the rock mass, g / cm3; a and b are model parameters, preferably a = 0.23 and b = 0.25; ΔH is the depth interval, m.

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