Sensitivity Analysis of Mechanical Parameters of Collapse Roof of Carbonate Rock Deep Buried Oilfield

Abstract

Carbonate rock oilfields account for two-thirds of proven marine carbonate oilfield reserves, which are the primary way to increase future oil and gas energy reserves. Cave collapses occur during the process of oil reservoir development, seriously affecting oil production. In order to reveal the collapse failure mechanism of carbonate karst caves and predict whether the fracture cave type oil reservoir will collapse before drilling, a binary depth reduction method for determining the critical collapse depth of karst caves is proposed based on the Tahe fracture cave type oil reservoir. The sensitivity of karst cave collapses to multiple factors is analyzed, and a prediction formula for the critical collapse depth of karst caves with changes in the deformation modulus, the internal friction angle, and the cohesion is established through multiple regression analysis. By calculating and analyzing the numerical values of a large number of operating conditions under different mechanical parameters, the failure process, failure mode, and the change law of collapse depth during the Tahe oilfield destruction process were obtained. We used the established formula for predicting the collapse depth of karst caves to predict and analyze the actual distribution of karst caves in the Tahe oilfield. The calculation and analysis results showed that in the karst cave failure mode characterized by vertical shear failure, the cohesive force is the most sensitive factor affecting cave collapse, followed by the internal friction angle. The deformation modulus is hardly sensitive to the influence of the karst collapse. Through the geomechanical model test, the result verified the accuracy and reliability of the calculation results. The research results will provide necessary theoretical support for the large-scale safe extraction of deep petroleum resources, increase oil production in China, and have important theoretical significance and engineering application value.

1. Introduction

As the main development field of oil reserves, the fractured-vuggy reservoir is the focus area of oil exploitation for the future [1]. It is an important type of carbonate reservoir and accounts for two-thirds of proven oil reserves [2,3]. The Ordovician oilfield in Tahe is a typical fracture-cavity carbonate oilfield. Its oilfield space mainly comprises two basic structures: caves and cracks. The cave is the main oilfield space, and the crack mainly communicates between the caves. As the formation pressure decreases during the oil recovery process, the collapse of the cavern or the closure of the large fracture outlet channel occurs, which seriously affects the production of the well and the recovery of the oilfield [4,5,6]. Therefore, it is of great theoretical significance and practical application value to carry out a prediction analysis of the collapse of the caverns in the Tahe oilfield.

At present, domestic and foreign scholars’ research on cave collapse and damage mainly relies on drilling cores and analyzing imaging logging data to determine the form of cave collapse and damage [7,8]. In addition, Tang et al. [9] systematically summarized the structural characteristics of ancient karst collapse, believing that modern karst collapse is mainly caused by the collapse of roofs and side walls triggered by cracks under gravity. Zhu et al. [10] proposed a new compaction failure model for carbonate rocks, which explains the mechanism of carbonate cave failure from a microscopic perspective. Although some achievements have been made in development techniques, the description of collapse phenomena, and leakage mechanisms for fractured and vuggy reservoirs, as well as the quantitative understanding of the collapse depth of fractured and vuggy reservoirs, is still relatively vague and cannot provide direct guidance for practical engineering implementation. Meanwhile, in terms of methods for quantitatively analyzing the impact of key factors, M. Geurey [11] proposed the PaD2 method for sensitivity analysis, and M. Beiki [12] used a neural network to analyze the sensitivity of factors affecting the stability of surrounding rock. Zhu Weishen [13] conducted a single-factor sensitivity analysis on the mechanical parameters affecting the stability of underground rock, whose results have a certain reference value for the stability analysis of the Yellow River Laxiwa groundwater power station project. Hou Zhesheng [14] used the nonlinear elastoplastic finite element method to analyze the influence of mechanical parameters of surrounding rock in a roadway of Jinshan No. 2 Mine on deformation and successfully applied it to the optimization analysis of engineering. Li Xiaojing [15] selected the sensitivity analysis of the mechanical parameters that have a great influence on the Langya Mountain underground powerhouse project. Xia Yuanyou [16] used neural networks to analyze the sensitivity of factors affecting slope stability. Nie Weiping [17] used the gray correlation analysis method to analyze the sensitivity of the parameters affecting the stability of underground caverns. Most of the existing analyses are for single indicators. However, in the mining process of the Tahe oilfield, the factors controlling the stability of surrounding rock are diverse, and a simple one-factor sensitivity analysis could not meet the requirements. At present, regarding the sensitivity of oilfield cave collapses, domestic and foreign research results are rare. Wang Chao [18] systematically analyzed the susceptibility of cave holes, roof thickness, and lateral pressure coefficient to the collapse depth of the cave, but did not study the sensitivity of the roof collapse of the oilfield to the surrounding rock mechanical parameters.

Based on previous research, this article establishes a binary depth reduction method for determining the collapse depth of karst caves in fractured and vuggy reservoirs through numerical analysis and rock fracture process analysis software (RFPA). The collapse failure morphology, collapse impact range, and collapse depth of different types of karst caves are obtained, and a prediction model for the critical collapse depth of karst caves under the influence of multiple factors is established through multiple regression analysis. Additionally, the accuracy of the prediction model was verified through physical and mechanical model experiments, providing a theoretical basis for oil extraction in the Tahe oilfield.

2. Brief Introduction of Sensitivity Analysis Method

Sensitivity analysis is a method of analyzing system stability in systems analysis. This is a system whose system characteristic $P=f\left({\alpha }_1,{\alpha }_2,{\cdots \alpha }_n\right)$ is mainly determined by factors $\alpha =\left({\alpha }_1,{\alpha }_2,{\cdots \alpha }_n\right).$ In a certain reference state ${\alpha }^{*}=\left({{\alpha }_1}^{*},{{\alpha }_2}^{*},{{\cdots \alpha }_n}^{*}\right)$, the system characteristic is $P^{*}$. The factors are changed within their respective possible ranges, and the trend and degree of deviation of the system characteristic P from the reference state $P^{*}$ due to the change in these factors are analyzed. This analysis method is called sensitivity analysis [19].

The above analysis could only understand the sensitivity of system characteristics to single factors. In an actual system, the factors that determine the characteristics of the system are often different physical quantities, and the units are different. With the above analysis, it is impossible to compare the sensitivity between various factors. Therefore, it is necessary to perform dimensionless processing. To this end, we define a dimensionless form of sensitivity and sensitivity factors. That is, the ratio of the relative error ${\delta }_P=\frac{\left|∆P\right|}{P}$ of the system characteristic P to the relative error ${\delta }_k=\frac{\left|∆{\alpha }_k\right|}{{\alpha }_k}$ of the parameter ${\alpha }_k$ is defined as the sensitivity function $S_k\left({\alpha }_k\right)$ of the parameter ${\alpha }_k$.

$$S_k\left({\alpha }_k\right)=\left(\frac{\left|∆P\right|}{P}\right)/\left(\frac{\left|∆{\alpha }_k\right|}{{\alpha }_k}\right)=\left|\frac{∆P}{∆{\alpha }_k}\right|\frac{{\alpha }_k}{P},K=1,2,\dots \dots ,n$$

(1)

In the case where $\frac{\left|∆{\alpha }_k\right|}{{\alpha }_k}$ is small, $S_k\left({\alpha }_k\right)$ could be approximated as

$$S_k\left({\alpha }_k\right)=\left|\frac{d{\psi }_k\left({\alpha }_k\right)}{d{\alpha }_k}\right|\frac{{\alpha }_k}{P},K=1,2,\dots \dots ,n$$

(2)

Take ${\alpha }_k={{\alpha }_k}^{*}$ to obtain the sensitivity factor ${S_k}^{*}$ of ${\alpha }_k$.

$${S_k}^{*}=S_k\left({\alpha }_k\right)=\left|{\frac{d{\psi }_k\left({\alpha }_k\right)}{d{\alpha }_k}}_{{\alpha }_k={{\alpha }_k}^{*}}\right|\frac{{{\alpha }_k}^{*}}{P^{*}},K=1,2,\dots \dots ,n$$

(3)

${S_k}^{*}$ (K = 1, 2, ……, n) is a set of dimensionless non-negative real numbers. The larger the ${S_k}^{*}$ value is, the more sensitive P is to ${\alpha }_k$ in the baseline state. By comparing ${S_k}^{*}$, it is possible to compare and evaluate the sensitivity of various factors affecting the collapse of the cave.

3. Sensitivity Analysis of Physical and Mechanical Parameters of the Karst Cave Collapse

3.1. Project Background

The exploration and development of carbonate rock oil and gas in China are gradually moving towards deep (burial depth > 4500 m) and ultra-deep (burial depth > 6000 m) fields, and significant breakthroughs have been made in ancient marine carbonate rock formations in basins such as Tarim, Sichuan, and Ordos, with karst fracture cave type reservoirs occupying an important position [20,21,22]. The Tahe oilfield is located in the Akekule Uplift on the Shaya Uplift of the Tarim Basin. The Ordovician reservoir is buried at a depth of 5300~6200 m. It is a typical deep carbonate rock fracture cave-type oil and gas reservoir formed through multi-stage reservoir formation and multi-stage reconstruction. The large-scale paleokarst karst cave system is the main type of reservoir space [23,24,25]. The filling phenomenon of paleokarst fractures and caves is common in the Tahe oilfield. More than 70% of the space in karst caves in some block reservoirs is filled with sedimentary sand, mud, and collapse breccias, of which collapse breccias account for about 30%. Through comprehensive interpretation of logging and seismic data from over 160 wells in Tahe, it is shown that collapse breccias are relatively developed near faults and water holes. When the original rock is thin limestone, collapse breccias are also easy to form. The presence of filling and collapse enhances the heterogeneity of karst fracture cave-type reservoirs. This will have a significant impact on oil and gas production capacity [26,27,28]. Production practice has shown that the collapse of karst caves can form a larger range of breccia and fracture distribution zones, thereby improving the reservoir’s storage and permeability performance, and becoming an important oil and gas storage space, enabling oil wells to achieve good production capacity. Therefore, research on the collapse mechanism, collapse mode, and influencing factors of karst caves, establishes seismic prediction methods for deep reservoir karst cave collapse bodies, reveals the distribution law of collapse filling, and guides the deployment of high-yield wells. It is of great significance for the efficient development of such reservoirs.

3.2. Numerical Analysis Model and Calculation Conditions

In the caves developed in the Ordovician, the thickness of the upper Ordovician carbonate roof varies from a few meters to several tens of meters; the rock around the cave is a very dense mudstone with very low matrix porosity and permeability [29]. The main factors affecting the collapse of the cave are cohesion c, internal friction angle ψ, and deformation modulus E. The karst caves in the fracture-cavity oilfield were generalized, and the karst morphology was simplified into a rectangular analysis. Because the force is constant along the axial direction of the hole, the plane strain model was used to numerically analyze the collapse of the cave.

Figure 1 shows the numerical analysis model and boundary conditions of deep-buried oilfield caves. The vertical stress on the top of the karst roof in Figure 1 was expressed by multiplying the average unit weight γ of the formation by the actual buried depth H of the karst. The horizontal stress was applied to the left and right boundaries of the model. According to the literature [30], the vertical stress gradient was Tv = 25 kPa/m, and the lateral pressure coefficient was K = 0.62. The grid was divided into 100 × 500. The numerical calculation of the cave size was consistent with the actual cave size. The bottom surface was a fixed boundary.

According to the literature [30], the physical and mechanical parameters of carbonate rock are shown in

Table 1. Physical mechanical parameters of carbonate rock.

Bulk Density (KN/m3)	Poisson’s Ratio	Elastic Modulus (GPa)	Compressive Strength (MPa)	Tensile Strength (MPa)	Internal Friction Angle (°)	Cohesion (MPa)
27	0.25	36.3	74.2	3.8	36	2

.

3.3. Criteria for Karst Cave Collapse

The RFPA-2D software based on the finite element could simulate the deformation process and the non-continuous behavior of material through the weakening of the unit [31,32]. It could be used to study the whole process of the rock mass material, from microscopic damage to macroscopic damage. It can be used to calculate and dynamically demonstrate the complete process of rock mass from loading to fracture. In this paper, the discontinuous and irreversible behavior of material failure was simulated by considering the parameter weakening of the element after material failure (including stiffness degradation). Figure 2 shows the collapse process of a rectangular cave.

It can be seen from Figure 2 that the RFPA calculation software could well simulate the whole process of the gradual destruction of the roof of the cave until it collapses. In the process of model loading, firstly, the stress of the local element exceeded its strength due to stress concentration, the strength attenuation of the rock mass was generated, and the redistribution of stress and unit information in the model were systematically completed. In this process, the number of failures of the unit was gradually increased, and the local cracks were gradually expanded, which eventually caused the shear stress at both ends of the top plate to exceed the shear strength and cause instability failure. The judgment of the collapse of the cave in this paper was the state of the roof of the cavern.

3.4. Determination Method of Critical Collapse Depth of Karst Cave

Based on the method of calculating the safety factor by using the strength reduction, the critical collapse depth reduction method for the deep cavern was proposed. That is, by continuously adjusting the buried depth of the cave until it reached a critical instability state, the corresponding depth was the critical collapse depth of the cavern, and the essence was to find the depth of the cave when the cave was in a critical state. For the critical collapse depth of the cavern, if the stepwise solution was used, the numerical analysis was multiple times [33]. Therefore, the dichotomy in the optimization theory was used for processing, and the specific solution flow is shown in Figure 3.

The above solution process was a depth of the binary subtraction method for determining the critical depth of the cave. This method could not only control the error but also obtain the critical collapse depth of the cave, and the simplified dichotomy could simplify the calculation and reduce the calculation workload.

3.5. Deformation and Failure Characteristics of Caves

It could be seen from Figure 2 that after loading the model, the roof rock mass in the upper part of the cavern had a tendency to form an independent beam from the surrounding rock main body. When the loading started, stress concentration was first formed around the cavity, and the shear stress was concentrated on both sides of the cavity and at the top corner end, as shown in Figure 2a,b.

As the shear stress in the roof area gradually increased and the strength of the rock mass in the stress concentration area decreased, when the shear stress exceeded the shear strength of the roof beam, the wall rock first produced micro-cracks at both ends of the top plate. The micro-cracks interacted with each other during the loading process, gradually penetrating, forming local damage, and the top plate produced a downward deflection, as shown in Figure 2c,d.

With the further decreases in the strength of the rock mass, the cracks at both ends of the surrounding rock around the karst cave gradually expanded from top to bottom, and the crack at the end gradually expanded and penetrated, eventually leading to the instability of the rock mass and the roof’s collapse, while the damage range extended along the top plate to both sides as shown in Figure 2e,h. The deformation and failure characteristics of the surrounding rock of the cavern were characterized by the direct collapse of the roof along the cave wall and was a kind of vertical shear failure.

3.6. Critical Collapse Depth of Karst Cave under the Influence of Single Factor

According to the calculation method for determining the critical collapse depth of the cave by the dichotomy method, the variation of the critical collapse depth of the cave under a different deformation modulus, different internal friction angles, and a different cohesive force could be obtained. The results are shown in Figure 4.

It can be seen from Figure 4 that the critical collapse depth of the cavern increased with the increase in the modulus of deformation, the angle of internal friction, and the cohesion. That is, the smaller the deformation modulus, the internal friction angle, and the cohesive force are, the smaller is the critical collapse depth of the cave, and the more likely it is that the cavern would collapse.

From the fitting results, the deformation modulus, internal friction angle, and cohesion force had a higher fitting degree to the critical collapse depth of the cavern, and the correlation coefficient R² was above 0.9. The deformation modulus was lower than that of the other two variables, and the correlation coefficient R² was small. From

Table 2. Fitting expression of critical collapse depth to factors.

The Expression of the Fitting Relationship between the Critical Collapse Depth of the Cavity and Various Factors
The expression of the fitting relationship between the critical collapse depth H of the cavity and the deformation modulus E	Fitting method	Fitting formula	Correlation coefficient R2
	Linear fitting	H = 15.239 E + 1275.4	0.95008
	Exponential fitting	H = 1343.8 e0.00842E	0.94443
	Logarithmic fitting	H = 540.23 ln(E) − 99.039	0.96762
	Second-order polynomial fitting	H = −0.33057 E2 + 39.238 E + 859.63	0.97073
The expression of the fitting relationship between the critical collapse depth H of the cavity and the internal friction angle ψ	Fitting method	Fitting formula	Correlation coefficient R2
	Linear fitting	H = 41.667 ψ+ 331.56	0.96335
	Exponential fitting	H = 760.65 e0.02392ψ	0.92764
	Logarithmic fitting	H = 1468.2 ln(ψ) − 3394.3	0.98668
	Second-order polynomial fitting	H = −1.0135 ψ2 + 114.64 ψ − 921.09	0.98968
The expression of the fitting relationship between the critical collapse depth H of the cavity and the cohesion C	Fitting method	Fitting formula	Correlation coefficient R2
	Linear fitting	H = 608.17 C + 610.56	0.9829
	Exponential fitting	H = 899.55 e0.34618C	0.95525
	Logarithmic fitting	H = 1166.5 ln(C) + 1059.8	0.99753
	Second-order polynomial fitting	H = −159.52 C2 + 1246.3 C + 15	0.99678

, we could obtain the following:

• Four different fitting methods were used, and all of the fitting results reached 0.9 or more. It showed that the critical collapse depth of the cavern had a good correlation with the surrounding rock mechanics parameters.
• When we used these four methods to fit, the correlation coefficient R² was higher in the critical collapse depth and cohesive force fitting results of the cavern; the largest was the logarithmic fitting where the correlation coefficient was 0.99753, and the smallest was the index fitting where the correlation coefficient was 0.95525.
• Overall, the linear fitting could be used to describe the influence of various factors on the critical collapse depth of the cavern.

It could be seen from the above that the linear function could well describe the relationship between the critical collapse depth of the cavern and the thickness of the roof or the cross-section or lateral pressure coefficient.

H = 15.239 E + 1275.4, R² = 0.95008;

H = 41.667 ψ + 331.56, R² = 0.96335

H = 608.17 C + 610.56, R² = 0.9829;

3.7. Multi-Factor Sensitivity of Cave Collapse

Sensitivity analysis can determine the main and secondary factors that affect cave collapse. Based on the relationship between the critical collapse depth of karst caves under the influence of single factors, the deformation modulus, the internal friction angle, and the cohesion obtained in this article, the sensitivity of karst cave collapse to single factors can be analyzed. However, in practical engineering, cave collapse is caused by multiple factors, and these parameters need to be treated in a dimensionless manner. As mentioned earlier, the sensitivity function of each factor can be deduced through Formulas (1)–(3)

$$S_E\left(E\right)=\left|\frac{15.239E}{15.239E+1275.4}\right|$$

(4)

$$S_{\Psi }\left(\Psi \right)=\left|\frac{41.667\Psi }{41.667\Psi +610.56}\right|$$

(5)

$$S_C\left(C\right)=\left|\frac{608.17C}{608.17C+331.56}\right|$$

(6)

The sensitivity curve of the collapse depth of the cavern as a function of various factors was plotted within the range of values of the three factors, as shown in Figure 4.

It could be seen from Figure 5 that with the increasing deformation modulus, internal friction angle, and cohesive force, the sensitivity factor affecting the collapse of the cave increased; the cohesion was the most sensitive factor affecting the collapse of the cave, followed by the internal friction angle; the deformation modulus was the least sensitive to the collapse of the cave.

3.8. Prediction Formula of Critical Collapse Depth of the Karst Cave

Because the cave is affected by many influencing factors, it is necessary to consider the effects of multiple factors, such as the modulus of deformation, the internal friction angle, and the cohesive force, on the collapse depth of the cave. There was a good linear function between the critical collapse depth and the single factor of deformation modulus, internal friction angle, and cohesion. Therefore, when establishing a critical collapse depth prediction model with multi-factor effects, it could be assumed that there was a linear relationship between the critical collapse depth and the deformation modulus, and between the internal friction angle and the cohesion, as shown below:

H = a₁E + a₂ψ + a₃C + a₄

(7)

In the formula, a₁, a₂, a₃, and a₄ were undetermined coefficients.

According to the numerical calculation results, the multivariate linear regression optimization method was used to obtain the prediction formula of the critical collapse depth of the rectangular cavity with the deformation modulus, the internal friction angle, and the cohesion:

H = 15.2 E + 41.7 ψ + 608.2 C − 1440.5

(8)

When the deformation modulus took a fixed value of 36.3 GPa, the relationship curve of the critical collapse depth of the cavity under the internal friction angle and the cohesion force could be plotted according to Formula (8). The results are shown in Figure 6 and Figure 7.

4. Engineering Calculation Case

4.1. Geomechanical Model Test

Because most of the fracture-cavity oilfields are at a relatively high burial depth, it is difficult to carry out engineering field testing. As a physical simulation method that could fully and accurately display the whole process of karst cave collapse under similar conditions, the geomechanical test uses a scaled geological model to study the engineering construction and deformation and damage based on the similarity principle, which is the reproduction of the real physical entity. On the premise of meeting the similarity principle, it could truly reflect the spatial relationship between the geological structure and the engineering structure and could effectively simulate the nonlinear deformation and failure law of deep caverns, which is an irreplaceably important role in verifying the above numerical simulation research results [34,35]. Therefore, this paper carried out a three-dimensional model test of collapse failure for the Tahe fractured-vuggy oilfield and further verified the accuracy of the above formula through the analysis of the test results.

4.2. Test Scheme Design

In this paper, the self-developed three-dimensional geomechanical model test system of high stress was used to load the initial stress in the tunnel area, as shown in Figure 8. The prototype simulation range was long × wide × height =35 m × 35 m × 35 m. The mmodel geometric similarity scale was C_L = 50. The model size was length × wide × height = 0.7 m × 0.7 m × 0.7 m. The prototype size of the karst cave was diameter = 5 m, the model karst cave diameter = 100 mm. The size of the high angle crack of the vertically arranged model was long × high × thickness = 100 mm × 60 mm × 10 mm, and the center distance of the model was 60 mm. The prototype tunnel area was located at 7500 m underground, and the in situ stress was vertical stress σ₁ × maximum horizontal principal stress σ₂ × minimum horizontal principal stress σ₃ = 205 MPa × 90 MPa × 54 MPa; the in situ stress in the model hole area was vertical stress σ₁ × maximum horizontal principal stress σ₂ × minimum horizontal principal stress σ₃ = 4.1 MPa × 1.8 MPa × 1.08 MPa. Figure 9 shows the loading diagram of the geological model. The physical and mechanical parameters of the prototype are shown in

Table 3. Physical and mechanical parameters of the original rock.

Material	Bulk Density (KN/m3)	Elastic Modulus (GPa)	Compressive Strength (MPa)	Tensile Strength (MPa)	Cohesion (MPa)	Internal Friction Angle (°)	Poisson’s Ratio
Carbonate	27	36	74	3.8	12	36	0.25

, and the physical and mechanical parameters of the model are shown in

Table 4. Theoretical calculations of physical and mechanical parameters of the model’s similar materials.

Similar Material	Bulk Density (KN/m3)	Elastic Modulus (GPa)	Compressive Strength (MPa)	Tensile Strength (MPa)	Cohesion (MPa)	Internal Friction Angle (°)	Poisson’s Ratio
Carbonate	26.8~27.1	710~820	1.38~1.61	0.71~0.82	0.23~0.26	35.4~36.5	0.23~0.26

.

4.3. Analysis of Test Results

During the model test, the rock displacement around the cave was monitored by embedded monitoring elements (Figure 10). The monitoring results of the upper part of the cave roof are shown in Figure 11. According to the analysis, under the action of tectonic stress and self-weight stress in the middle and late Caledonian period, when the loading stress reached 50% of the final load, the displacement at the top of the cave suddenly increased from 53 mm to 120 mm, with the increase of 126%, indicating that the roof of the cave had cracks; when the final stress was loaded, the displacement curve experienced a significant mutation, and the displacement of the top of the cave increased by 600%, indicating that the roof of the cave had fallen and the cave had finally collapsed.

In order to further verify the accuracy of the analysis results of the model test data, the model body after the cave loading test was opened for observation. The cavity damage results are shown in Figure 12. Through the comparison before and after the positioning, it was found that the karst cave roof experienced overall subsidence. The karst cave was relatively weak near the top of the crack, which was more prone to collapse damage, resulting in the collapse of the karst cave. The roof was M-shaped, the lower half of the karst cave was oblate, and there was a shear slip failure line around the cave. The two clusters of fracture zones intersected and cut each other around the bottom of the cave, and there was a cleavage failure zone around the cave wall. A large number of cracks and loose fracture zones appeared in the inner wall of the cleaned cavity.

The test showed that under the middle and late Caledonian stress loading, the karst cave collapsed, and the karst cave’s bearing capacity decreased due to prefabricated cracks. The actual critical collapse depth should be more than 7500 m. At the same time, the collapse depth of the karst cave under this condition could be calculated by using the collapse depth prediction formula above, which was 7878 m. By comparing the test results and the formula prediction results, we established that the error between the two was within the allowable range. It met a particular safety factor and verified the accuracy of the prediction formula for the critical collapse depth of karst caves.

In addition to the geomechanical model test, this paper used the examples in other documents for calculation and verification. In order to verify the reliability of the calculation method and the prediction formula of the collapse depth of the cave, this paper selected two calculation cases in the shale gas block excavation drilling in the literature [8] for verification. The specific calculation method was as follows: the deformation modulus of the Longmaxi Formation shale in Sichuan Province was 11.4 GPa, the internal friction angle was 250, and the cohesion was 5 MPa, according to the prediction Formula (8) H = 15.2 E + 41.7 ψ + 608.2 C − 1440.5. The predicted collapse depth of the excavation drilling was calculated to be 2816 m, and the actual buried depth was 2823 m, which had collapsed; the shale deformation modulus of the Qiongzhusi Formation was 52 GPa, the friction angle was 530, and the cohesion was 10 MPa, according to the prediction Formula (8). The predicted collapse depth of the excavation drilling was calculated to be 7642 m, and the actual buried depth was 3848 m, which indicated that it had not collapsed. Both predictions were consistent with the actual results. It could be seen that the formula for predicting the collapse depth was reasonable and reliable.

5. Discussion

Through the combination of true three-dimensional model test and numerical simulation, we discussed the cause of the collapse of fractured-vuggy reservoirs, and established a prediction model of the critical collapse depth of karst caves under the influence of multiple factors through numerical analysis. The fracture process and its failure modes of karst caves under different mechanical parameters were obtained. According to the critical collapse depth prediction model, the cohesive force in the Tahe fracture-cavity oilfield is the most sensitive factor affecting the collapse of the cave, followed by the internal friction angle, while the deformation modulus is the least sensitive to the collapse of the cave. In the process of oil drilling and development, we should pay more attention to the cohesion of rocks. Because the cave is too deep, the previous scholars could only analyze the drilling core by pure numerical simulation and imaging logging data, without being able to confirm the accuracy of the results [36,37]. We used a true three-dimensional geomechanical model. The combination of experiment and numerical simulation made up for the deficiencies of previous studies. However, there are still many important parameters worth studying. What is more, the physical and mechanical parameters included in our research are not comprehensive enough at present, and numerical calculations are still two-dimensional, which is our next direction.

6. Conclusions

Based on the RFPA software which was based on the finite element method, the model of carbonate caverns in fracture-cavity oilfields was established. The collapse criterion of caverns in fracture-cavity oilfields was proposed, and the critical collapse depth analysis method of caves was established. The surrounding rock failure of the cavern first occurred due to the stress concentration on both sides of the cavern and the top of the apex. As the local crack gradually expanded, the shear stress at the two ends of the roof exceeded the shear strength, and instability occurred, which is a shear failure of a rocking beam.

Through the numerical calculation and analysis of a large number of different working conditions, the critical collapse depth of the caverns in the Tahe oilfield under different deformation moduli, internal friction angles, and cohesion force was obtained. The effects of the deformation modulus, internal friction angle, and cohesive force on the critical collapse depth of the cave were defined. The law of the collapse of the caverns in the Tahe oilfield with the change in sensitivity of various influencing factors was revealed. The formula for predicting the critical collapse depth, deformation modulus, internal friction angle, and cohesion of the cave was established. It was verified by a geomechanical model test, and the test results proved the accuracy of the calculation model.

According to the critical collapse prediction model, for the caverns of surrounding rock with different mechanical parameters, drilling should be carried out in the process of oil drilling development in the stratum with a large deformation modulus, large internal friction angle, and high cohesion. It has essential reference value and theoretical significance for the development of an oilfield. Next, we will establish a collapse prediction formula containing more physical and mechanical parameters to meet the actual project. At the same time, we will extend the working conditions of numerical simulation from 2D to 3D. Further research will make the application of our research results more extensive and accurate.