A Caprock Evaluation Methodology for Underground Gas Storage in a Deep Depleted Gas Reservoir: A Case Study for the X9 Lithologic Trap of Langgu Sag, Bohai Bay Basin, China

Abstract

The evaluation of caprocks’ sealing capacity is exceedingly important for depleted gas reservoirs to be reconstructed into gas storage. In this paper, based on the physical sealing mechanism of caprock, four aspects of ten indexes of caprock quality evaluation were firstly selected, and the related classification standards were established. Secondly, based on the rock mechanical sealing mechanism, elastic and plastic indexes were selected to characterize the mechanical brittleness of caprock, and a brittleness evaluation method of caprock based on complete stress-strain curves was established. Then, a systematic comprehensive evaluation model (including 5 aspects and 12 evaluation indexes) for the sealing capacity of gas storage caprock was proposed, and the analytic hierarchy process (AHP) was used to determine the weight of the 12 indexes in the evaluation model, and the formula for calculating the suitability of the caprock sealing capacity was established. Finally, the geological data, laboratory, and field test data, including X-ray diffraction, poro-permeability test, displacement pressure, and tri-axial compression test, were used for the caprock sealing capacity evaluation of the X9 depleted gas reservoir, and the result from this model showed that the caprock quality is suitable for underground gas storage.

1. Introduction

Underground gas storage is the main facility for natural gas safe supply, and an important part of national energy security. Accelerating the construction of domestic gas storage is a major strategic measure to ensure natural gas safe supply [1,2]. At present, there are more than 700 gas storage facilities in the world, of which more than 70% are depleted gas storage [1]. Among various types of underground gas storage, the performance of depleted gas reservoir underground gas storage is the best, because of its geology conditions, structural trap, gas storage volume have been basically clear, and it has a complete set of natural gas surface system engineering facilities available for selection [3]. Huabei oilfield is located in the Beijing-Tianjin-Hebei area. With the increasing demand for natural gas in the two cities and the surrounding cities, it is necessary to establish a certain scale of underground gas storage(s) to meet the gas supply needs of the cities. Therefore, it is very important to use depleted oil and gas reservoirs to rebuild underground gas storage.

The sealing condition is the first of the four bottlenecks in the construction of gas storage, and the sealing capacity of the caprock is an important part of it [4]. The sealing capacity of caprock refers to the ability to prevent natural gas from moving in the caprock after it is injected into the gas storage, which controls the vertical distribution, gas abundance, and working pressure of the gas storage. At present, the caprock evaluation of gas storage is mainly divided into two aspects: the macro- and the micro-effectiveness evaluation of caprock [5]. From the macro perspective, lithology, thickness, continuity, and brittle-ductile characteristic have a significant influence on the sealing capacity of caprock [6,7,8,9,10]. The physical sealing mechanism of the caprock means that the caprock realizes the function of gas sealing through its physical properties. The clay content and sedimentary characteristics are considered to be the key parameters affecting the sealing capacity of the caprock. Generally speaking, the higher the clay content, the better the sealing capacity, and the mudstone caprock formed by the semi-deep and deep lake facies has the best sealing capacity [10,11,12]. The caprock thickness refers to the effective thickness after subtracting the area with no sealing capacity, and statistics show that there is a thickness lower limit for the sealing capacity, beyond which, the thicker the caprock is, the higher the cap continuity is, the stronger the sealing capacity is, and the larger the gas field area formed [9,13,14,15]. The rock mechanics sealing mechanism means that in the process of injection and production, the stress state of the caprock will change, leading to the generation of cracks, which further makes the seal invalid. The construction practice of underground gas storage also shows that the key factor affecting the failure of the gas reservoir is the development of caprock fracture (mechanical failure). Although some caprocks have good physical property conditions, they still cannot play a sealing role. The generation of cracks is related to the caprock’s brittleness that is characterized by its mechanical properties. Many scholars have noticed the change of brittleness and ductility of mudstone for a long time, and carried out many experiments on mudstone rock mechanics, and defined the evaluation criteria of mudstone brittleness by using different parameters, but there are few studies specifically on mudstone caprock of gas storage [4,16,17]. From the microscopic perspective, porosity, permeability, pore size distribution, specific surface area, and displacement pressure are the main parameters to reflect the microscopic sealing capacity of caprock, among which displacement pressure is widely regarded as the most fundamental parameter that reflects the sealing capacity of caprock [8,13,14,18]. The sealing mechanism of hydrocarbon caprock can be divided into a capillary seal, hydraulic seal, overpressure seal, and hydrocarbon concentration seal, among which capillary seal is the most important sealing mechanism of depleted gas storage caprock. The requirement for gas seepage in caprock is that the difference between gas pressure and hydrostatic pressure exceeds capillary pressure at the gas-water interface in caprock, and this difference in pressure in the critical state is called displacement pressure, which is numerically equal to capillary pressure. The laboratory test of displacement pressure can be divided into the direct method (step-by-step method, continuous method, displacement method, and pulse method) and indirect method (mercury intrusion method), where the step-by-step method is based on the definition of breakthrough pressure and has a high accuracy [11,19,20,21]. The breakthrough pressure can also be obtained by fitting field data, such as the time difference of acoustic velocity [14,22,23].

You et al. systematically analyzed the geological factors influencing the caprock sealing performance, established the relationship between porosity, median radius, and burial depth, and breakthrough pressure, and proposed a quantitative evaluation method combining macro and microscopic [24]. Fu et al. classified the microscopic sealing characteristics of the caprock and the evaluation parameters of the macroscopic sealing characteristics, and discussed the comprehensive evaluation method of the sealing capacity of the caprock [25]. By analyzing the relationship between both the specific surface area and the breakthrough pressure with caprock sealing performance, Fan et al. proposed an evaluation template of mudstone caprock by combining specific surface area and breakthrough pressure [26]. In addition, some scholars [27,28] conducted statistical studies on more than 40 discovered gas reservoirs in China, and obtained the factors affecting the sealing capacity of caprocks, such as lithology, thickness, displacement pressure, damage degree of caprocks caused by faults, gas reservoir pressure, and natural gas viscosity, and established the corresponding evaluation standards. In spite of these, the current gas sealing capacity evaluation of caprock has the following shortcomings: (a) the evaluation indexes, which are the parameters that can reflect or affect the sealing capacity of the caprock when one carries out the sealing evaluation of the caprock, are quite a few, usually one or several, which cannot fully reflect the sealing capacity of caprock. For example, the influence of brittleness of caprock on sealing capacity is usually ignored [18]; (b) for the same evaluation index, the evaluation criteria are inconsistent. Generally, efficient sealing means that when the value of a parameter that can reflect the sealing capacity of the caprock is less or greater than a certain value, the caprock has the best gas sealing capacity. Taking permeability as an example, Bai et al. [14] considered the caprock with a permeability less than 0.1 mD as a highly efficient sealing caprock, while Zhou et al. [7] considered it as 0.00001 mD; (c) the evaluation work is not systematic, and the degree of influence of different evaluation indexes on the sealing performance of the caprock cannot be considered quantitatively.

Based on the analysis above, a caprock sealing capacity evaluation system based on the analytic hierarchy process (AHP) is proposed, which includes multiple key parameters related to caprock, such as the physical property parameters and the brittleness characterized by the mechanical properties. Then, the caprock sealing capacity of X9 gas storage is evaluated using this method.

2. Evaluation Indexes of Sealing Capacity of Caprock

This paper analyzes the sealing characteristics of caprock from five aspects: lithology, thickness, porosity-permeability characteristics, displacement pressure, and the brittleness of caprock of the depleted gas reservoir.

2.1. Lithologic Characteristics

Argillaceous shale, mudstone, gypsum, and salt rock are common lithology of caprock. According to the lithology classification, the caprock can be divided into three types: evaporite caprock, argillaceous caprock, and carbonate caprock. Grunau [10] conducted a statistical study of 334 oil and gas fields all over the world, and the results showed that argillaceous caprocks accounted for 65%, evaporite caprocks accounted for 33%, and other caprocks accounted for only 2%. The sealing performance of gypsum salt rock is the best of all, followed by aluminum mudstone. The formation of caprock is related to the sedimentary environment, and only a lake basin environment with wide distribution and deep sedimentary water can form the most effective regional caprock [10].

Referring to the previous research results [24,25,27,28], the sealing capacity of caprock can be classified from the perspective of lithologic characteristics (

Table 1. Lithology classification of gas storage caprock of depleted gas reservoir.

Classification	Sedimentary Environment	Lithology	Argillaceous Content/%
I	Semi deep-deep lake facies Basin facies Wide sea continental basin facies	Salt gypsum rock Gypsum mudstone	>75
II	Platform facies shore-shallow lake facies Delta front facies	Calcareous mudstone Mudstone	50~75
III	Platform margin Shoreline facies Delta diversion plain facies	Sandy mudstone Argillaceous siltstone	25~50
IV	River facies Alluvial fan facies	Argillaceous sandstone Dense limestone	<25

).

2.2. Caprock Thickness

The thickness is one of the important parameters affecting the caprock sealing capacity. It not only affects the spatial distribution of caprock, but also to some extent affects the sealing quality of the caprock. At present, there is no uniform evaluation standard for the thickness of the caprock [29].

Generally, the caprock is supposed to be the tight lithologic strata with a certain thickness and spatial distribution range, so as to have the basic capping conditions. Theoretically, a caprock of a few meters is sufficient to seal hydrocarbons at a large column height, but the probability that an area of a few meters thick stays intact over a significant hydrocarbon accumulation and maintains stable lithology is low [30]. For the same kind of caprock, the greater the thickness of the caprock and the larger the area of the spatial distribution, the more conducive to the preservation of natural gas; on the contrary, it is difficult to keep the thin caprock in a large area without breaking. The lateral distribution continuity of the caprock is closely related to the thickness of the caprock. The greater the thickness of the caprock is, the better the continuity of the transverse distribution is, and the easier it is to form regional caprock.

The continuity of the caprock is the key factor for the risk assessment of the gas storage. For the strata with large changes in the thickness of the caprock, the places where the caprock is relatively thinner are more likely to leak. Therefore, the thickness evaluation should be based on the smallest thickness of the caprock. The available data indicate that a thin layer with a thickness of fewer than 30 m can also serve as the oil and gas reservoir caprock [19], but caprock thicker than 30 m is more preferred [10]. The caprock thickness of China’s 30 large and medium-sized gas fields ranges from tens to hundreds of meters, of which 16.7% are those below 30 m, 6.6% are those between 30 m and 50 m, 16.7% are those between 50 m and 100 m, and 60% are those above 100 m [19]. To form medium efficiency natural gas reservoir, the thickness of the caprock must be greater than 40 m, and to form a high-efficiency natural gas reservoir, a direct caprock with a thickness of more than 100 m is required [27]. The quality of caprock according to thickness can be divided into four levels, as shown in

Table 2. Thickness classification of gas storage caprock of depleted oil and gas reservoir.

Classification	Continuity	Thickness/m
I	Continuous, stable	>100
II	Generally continuous, generally stable	50~100
III	Have a certain continuity, generally stable	30~50
IV	Poor continuity, instability	<30

.

2.3. Porosity and Permeability Characteristics of Caprock

Porosity is an indispensable parameter reflecting the degree of pore development and permeability of caprock. Permeability is a measure of the ability of gas to leak through caprock, which depends on the influence of rock pore structure, mineral filling mode, particle distribution, and particle size. The smaller the porosity, the higher the degree of rock diagenesis, the smaller the pore throat radius, the lower the permeability, and the tighter the rock. Porosity and permeability of caprock are the parameters related to the displacement pressure of rock, the porosity and permeability can be used to quantitatively evaluate the sealing capacity of caprock, the smaller the pore size that controls the flow path, the lower the permeability, the greater the capillary pressure of caprock and the better the sealing performance of the caprock [21]. According to relevant materials research [3], the quality of the caprock can be classified into four grades according to the hole-seepage characteristics, as shown in

Table 3. Porosity and permeability characteristics classification of gas storage caprock of depleted oil and gas reservoir.

Classification	Crack Development	Porosity/%	Permeability/(10−3 mD)
I	Crack not developed	<2.5	<1
II	Small amount of crack developed	2.5~5	1~10
III	Certain degree of developed crack, and no thorough crack is formed	5~8	10~100
IV	Crack developed with penetrating cracks	>8	>100

.

2.4. Displacement Pressure

2.4.1. Direct Displacement Method

Displacement pressure is the most intuitive parameter to determine the sealing capacity of the caprock. It refers to the minimum pressure at which the wetting phase in the caprock is displaced by the non-wetting phase, and essentially refers to the capillary pressure of the largest communicating channel of the rock. Previously, adsorption and mercury intrusion methods are usually adopted in the laboratory to indirectly measure the displacement pressure of the rock (Figure 1). At present, the direct method is mainly adopted to test the displacement pressure of caprock. Experimental procedure is as follows: (a) Saturate the caprock with formation water or insensitive fluid, (b) calibrate the circumferential pressure according to the depth of the well, (c) displace the wetting phase with non-wetting, and regularly pressurize until the non-wetting breakthrough (Figure 2), and the pressure increments and time settings follow standard SY/T 5748-1995. Pc means the capillary pressure, the Pc-entry is the pressure that the non-wetting phase enters the pores of the rock, Pc-threshold is the minimum differential pressure between the nonwetting phase and the wetting phase at which the gas starts to move continuously through the rock, and Pc-breakthrough is the “second threshold pressure” at which non-wetting phase flow at the downstream side increases sharply [20]. The breakthrough pressure measured by the direct displacement method is slightly higher than the actual displacement pressure, but when the long-term experiment is carried out, the breakthrough pressure of the rock is basically close to the displacement pressure [19].

The displacement pressure of caprock in more than 40 medium- and high-efficiency gas reservoirs in China is found statistically that all the displacement pressure values of caprock of high-efficiency gas reservoirs exceed 20 MPa, and that of medium-efficiency gas reservoirs all exceeded 15 MPa [27]. Therefore, the caprock sealing capacity according to the displacement pressure can be classified into four grades, as shown in

Table 4. Displacement pressure classification of gas storage caprock of depleted oil and gas reservoir.

Classification	Displacement Pressure/MPa
I	>20
II	5~20
III	1~5
IV	<1

.

2.4.2. Acoustic Time Method

The acoustic logging data is also used to study the capillary sealing capacity of mudstone caprock. Acoustic time difference is affected by many geological factors, such as lithology, rock structure, buried depth, and geological time. For mudstone caprock, density is an important factor in controlling the acoustic time difference, and mudstone density is closely related to rock porosity. Therefore, the acoustic time difference can effectively reflect the porosity of mudstone caprock.

A large number of statistics show that there is the following relationship between mudstone porosity and acoustic time difference [29]:

$$\Delta t=A\varphi +B$$

(1)

where, Δt is the mudstone acoustic time difference; ϕ is the mudstone porosity; A, B are empirical parameters.

The measured mudstone displacement pressure has a significant inverse relationship with the porosity. The smaller the porosity is, the higher the compaction degree of mudstone is, the denser the mudstone is, the better the capillary sealing ability is, and the higher the displacement pressure is. It is assumed that the mudstone displacement pressure and porosity satisfy the following relationship,

$$P_{\mathrm{dw}}=a\exp (-b\varphi )$$

(2)

where, P_dw is displacement pressure; a, b are empirical parameters.

According to Equations (1) and (2), the relationship between the mudstone displacement pressure and the acoustic time difference is obtained:

$$P_{\mathrm{dw}}=c\exp (d\Delta t)$$

(3)

where, c, d are empirical parameters.

2.5. Caprock Brittleness Based on Triaxial Compression Tests

For the underground gas storage caprock, the sealing performance depends more on the mechanical properties of the caprock. Different from conventional gas reservoir development, gas storage of depleted oil and gas reservoir requires strong injection and production, and the pressure on the caprock changes frequently. The instability and rupture of the caprock are the root causes of the failure of the gas storage caprock.

The brittleness of the caprock directly determines the quality of the caprock. Brittleness is the property of the rock when it is damaged under specific conditions (certain confining pressure and temperature). The stronger the brittleness of the caprock, the more prone the caprock is to crack, and the sealing capacity will be greatly reduced.

The brittleness of the caprock can be described by the method of full stress-strain characteristics [31]. The brittleness of the mudstone is related to the pre-peak elastic modulus, Poisson’s ratio, the slope of the post-peak curve, and the residual strength. Considering the mechanical characteristics of rock pre-peak and post-peak, elastic index and plastic index are defined to evaluate rock brittleness.

The elastic index B_e is used to describe the pre-peak curve shape [32],

$$B_e=(B_{EM}+B_{PR})/2$$

(4)

where, $B_{EM}=(E-E_{\min })/(E_{\max }-E_{\min })$, $B_{PR}=(\mu -{\mu }_{\max })/({\mu }_{\min }-{\mu }_{\max })$. E_max, E_min, ${\mu }_{\max },{\mu }_{\min }$ are the maximum and minimum values of the elastic modulus and the maximum and minimum values of the Poisson’s ratio, respectively.

The plasticity index B_p is used to describe the post-peak curve shape [33]. The solution steps of B_p are as follows:

(1)

Define the relative magnitude of post-peak stress drop:

$$B_1^{’}=({\tau }_p-{\tau }_r)/{\tau }_p$$

(5)

where, $B_1^{’}$ is the relative magnitude of stress drop, the value range is 0~1; τ_p and τ_r are the peak strength and residual strength respectively.

(2)

Define the absolute rate of post-peak stress drop:

$$B_2^{’}=\alpha \lg \left|k_{ac(AC)}\right|$$

(6)

where, $B_2^{’}$ is the absolute rate of stress drop; $\alpha$ is the adjustment factor, and the value is 0.6; the geometric meaning of $k_{ac(AC)}$ is the slope of the line connecting the starting point of the yield stage to the starting point of the residual stage. Since the slope is negative, an absolute value is added. Taking the common logarithm and multiplying α is to convert the absolute rate of stress drop between 0 and 1, and take $B_2^{’}=1$ when the post-peak stress falls vertically to zero. Combining Figure 3 and the magnitude of the relative stress drop and the absolute rate of the stress drop, it can be found that the values of $B_1^{’}$, $B_2^{’}$ calculated from curve OACE section are equal to that calculated from the OABCE section. However, due to the existence of the yield stage in the OABCE section, the rock brittleness corresponding to the two curves is different in fact. To this end, the yield influence coefficient $B_3^{’}$ is introduced.

(3)

Define the yield influence coefficient:

$$B_3^{’}=1-({\epsilon }_{q2}-{\epsilon }_{q1})/{\epsilon }_r$$

(7)

where: $B_3^{’}$ is the yield influence coefficient, the value range is 0~1; ${\epsilon }_{q1}$, ${\epsilon }_{q2}$, ${\epsilon }_r$ are the starting point strain of the yield stage, the endpoint strain of the yield stage, and the residual strain; when the stress and strain curve given by the test has no softening stage and residual stage, that is, the yielding stage is infinitely long, at this time $({\epsilon }_{q2}-{\epsilon }_{q1})>>{\epsilon }_{q1}$, take $B_3^{’}=0.01$.

(4)

Finally, define the plasticity index B_p:

$$B_p=B_1^{’}{B}_2^{’}{B}_3^{’}=\frac{{\tau }_p-{\tau }_r}{{\tau }_p}\alpha \lg \left|k_{ac(AC)}\right|(1-\frac{{\epsilon }_{q2}-{\epsilon }_{q1}}{{\epsilon }_r})$$

(8)

Based on the above analysis, the quality of the caprock can be classified into four grades from the perspective of rock brittleness, as shown in

Table 5. Rock mechanics Classification of gas storage caprock of depleted gas reservoir.

Classification	Elasticity Index/%	Plasticity Index/%
I	<30	>60
II	30~50	50~60
III	50~60	30~50
IV	>60	<30

.

3. Materials and Methods for Study Area

3.1. Study Area of X9 Lithologic Trap

Daxing conglomerate body is located in Langfang City, Hebei Province, China, and located in the downthrown side of the Daxing fault in the Gu’an-Jiuzhou fault structural zone of Langgu sag. It is close to Daxing uplift with the Daxing fault as the boundary to the northwest, and adjacent to the deep zone of Langgu sag to the southeast. Several conglomerates are distributed from north to south, and the X9 conglomerate is located in the middle of the downthrown side of the Daxing fault (Figure 4).

The lithology of the upper member of Es3 is consisting of gray mudstone, silty mudstone, and gray, gray-white argillaceous silty conglomerate, silty conglomerate, and fine conglomerate. The thickness is generally more than 300 m, and the maximum thickness is about 700 m. The upper member of Es3 is in conformable contact with the underlying middle member of Es3.

The lithology of the upper part of the middle member of Es3 is brown-gray mudstone mixed with gray and gray-white argillaceous silty conglomerate, silty conglomerate, and fine conglomerate, the thickness of which is generally more than 300 m. As well, the lithology of the lower part of the middle member of Es3 is interbedded with brownish-gray mudstone, dark mudstone, gray argillaceous silty conglomerate, silty conglomerate, fine conglomerate, conglomeratic conglomerate, and fine conglomerate. The thickness of the lower part of the middle member of Es3 is generally more than 400 m, and it is conformable contact with the underlying lower member of Es3.

The lower member of Es3 is a large set of brownish-gray and dark mudstone interbedded with fine conglomerate. The thickness is generally more than 400 m, and the thickest part is more than 1000 m. The composition of the gravel is mainly limestone and dolomite, and it is in unconformable contact with the underlying strata. The X9 conglomerate body is located in the lower member of Es3 (Figure 5).

According to the sedimentary characteristics of the conglomerate, it can be subdivided into two sets of producing layers, the I and II set of conglomerates. There are stable mudstone interlayers between the two sets of producing layers, making the two sets of producing layers closed and non-connected. As the main production layer, at present, a total of 15 wells have been drilled into the I conglomerate body, and the lateral development is stable.

The structure of the top surface of the I set of X9 conglomerate body is the strata dipping northward, and a lithologic trap is formed by the control of the pinch-out line of the conglomerate body in the east and south directions. The high point, with a buried depth of 3720 m, is located at X9-1 well. The trap amplitude is 400 m, and the trap area is 4.36 km². The structure of the bottom surface is the strata dipping northward, and a lithologic trap is formed by the control of the pinch-out line of the conglomerate body in the east and south directions. The high point, with a buried depth of 3840 m, is located at Well X9-1. The trap amplitude is 280 m, and the trap area is 1.71 km².

Up to 30 September 2013, 12 gas wells have been put into operation in this area, with cumulative gas production of 10.61 × 10⁸ m³ and cumulative oil production of 36.24 × 10⁴ t. Among them, cumulative gas production of the I conglomerate body is 10.41 × 10⁸ m³ and cumulative oil production of 35.72 × 10⁴ t. According to the reconstructed structure, the I set of gas geological reserves of conglomerate is calculated by volume method. The gas geological reserves of the conglomerate body are 18.03 × 10⁸ m³ and condensate oil reserves are 85.89 × 10⁴ t.

3.2. Evaluation Model Based on AHP Method

3.2.1. Target Hierarchy of Comprehensive Evaluation

Analytic Hierarchy Process (AHP) is a decision analysis method combining qualitative and quantitative methods, and is an effective method to determine weights [34]. The basic principle of the analytic hierarchy process (AHP) is to decompose a complex problem into several influencing factors (or evaluation indicators). These factors are organized into a hierarchical structure according to dominant relationships. Through pairwise comparison, the relative importance of each factor in the hierarchy is determined. It determines the order of importance of factors by clarifying vague concepts.

According to the sealing requirements of gas storage caprock in depleted gas reservoirs, the quality of gas storage caprock is taken as the target layer, and the lithology, thickness, porosity and permeability characteristics, displacement pressure, and rock mechanical properties of the caprock are taken as the criterion layer. Then, the 12 basic indicators were refined into evaluation layers, and a target hierarchy model based on AHP was established (Figure 6).

3.2.2. Weight Coefficient

After the objective hierarchy is established, it is necessary to carry out a quantitative analysis of each influencing factor. In order to facilitate the conversion from qualitative to quantitative values and determine the comparative weight vector, the “1–9” scale method proposed by T. Saaty [35], p_ij take the value 1, 2, …, 9 and its reciprocal 1, 1/2, …, 1/9. Where, p_ij represents the importance of i-th factor relative to j-th factor; 1/9 represents the lowest degree of importance; 1 represents the same degree of importance; 9 represents the highest degree of importance; the comparison rules are shown in

Table 6. Classification of the relative importance of indexes.

Value	Relative Importance
1	Equally important
3	Slightly important
5	Important
7	More important
9	Extremely important

.

According to Table 6, a number of influencing factors at a certain level were pairwise compared and the judgment matrix is obtained as follows:

$$P={(p_{ij})}_{n\times n}=\left[\begin{array}{cccc}{p}_{11}& p_{12}& \dots & p_{1n}\\ p_{21}& p_{22}& \dots & p_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ p_{n1}& p_{n2}& \dots & p_{nn}\end{array}\right]$$

(9)

For each judgment matrix $P$, the maximum eigenvalue and its corresponding feature vector are first obtained, and the feature vector is the weight of each evaluation factor. The method for calculating the factor weight vector $\omega$, the maximum eigenvalue ${\lambda }_{\max }$, and the random consistency ratio $CR$ is as follows:

$${\overline{\omega }}_i={\left({\displaystyle \prod _{j=1}^n{p}_{ij}}\right)}^{1/n}(j=1,2,\cdots ,n)$$

(10)

$${\omega }_i={\omega }_i/\left({\displaystyle \sum _{j=1}^n{\overline{\omega }}_j}\right)(i=1,2,\cdots ,n)$$

(11)

$$\mathsf{\omega }={\left({\omega }_1,{\omega }_2,\cdots ,{\omega }_n\right)}^T$$

(12)

$${\lambda }_{\max }=\frac{1}{n}{\displaystyle \sum _{i=1}^n[{(P\mathsf{\omega })}_i/{\omega }_i]}$$

(13)

$$CR=[({\lambda }_{\max }-n)/(n-1)]/RI$$

(14)

where, RI is a random consistency indicator. When n = 3~9, RI takes the value 0.58, 0.94, 1.12, 1.24, 1.32, 1.41 and 1.45, respectively.

When CR < 0.1, it can be considered that the judgment matrix P has satisfactory consistency, indicating that the weight distribution is reasonable; otherwise, the matrix needs to be re-evaluated until satisfactory random consistency is obtained. Based on the “1~9” scaling method, a questionnaire survey was conducted for underground gas storage experts to obtain the relative importance ratio between the influencing factors at the same level. The judgment matrix of each level is constructed, and then the specific weight values of each evaluation index can be calculated according to the Equations (10)–(14). The results are shown in

Table 7. Summary table of weight values.

Criteria Layer	Criteria Layer Weight Value Assignment ωiB	Indicator Layer	Indicator Layer Weight Value Assignment ωiC	Weight Value Relative to the Target Layer ωi
B1	0.044	C1	0.110	0.005
		C2	0.309	0.014
		C3	0.581	0.025
B2	0.096	C4	0.333	0.032
		C5	0.667	0.064
B3	0.196	C6	0.412	0.081
		C7	0.260	0.051
		C8	0.328	0.064
B4	0.560	C9	0.500	0.280
		C10	0.500	0.280
B5	0.104	C11	0.333	0.035
		C12	0.667	0.069

.

3.2.3. Comprehensive Evaluation Model

In order to facilitate the quantitative analysis of the specific indicators for the evaluation of caprock, according to the classification of caprock grades in Table 1, Table 2, Table 3, Table 4 and Table 5 above, “I”, “II”, “III” and “IV” caprock are quantified as 10, 8, 6 and 4 points respectively. Combined with the analytic hierarchy process (AHP), the weight of all indexes in the caprock quality evaluation system can be obtained, and the comprehensive suitability value M of caprock quality can be obtained,

$$M={\displaystyle \sum _{i=1}^{12}{\omega }_i{m}_i}$$

(15)

where: m_i is the quantified value of each evaluation index; ω_i is the weight value of each evaluation index; i = 1, 2, …, 12.

By substituting the comprehensive suitability value M of caprock calculated according to Equation (15) into

Table 8. Evaluation table of comprehensive suitability grade of gas storage caprock of depleted oil and gas reservoir.

Caprock Quality Suitability	Comprehensive Indicator Value
Optimal	9 < M ≤ 10
Suitable	7 < M ≤ 9
Basically suitable	6 < M ≤ 7
Not suitable	M ≤ 6

for comparison, the suitability degree of caprock can be obtained, and the feasibility of the gas storage construction project can be considered according to the corresponding countermeasures. The trap with “Optimal” caprock has a good sealing ability and high safety, and is very suitable for building the gas storage. The trap with “Suitable” caprock is the second choice to build gas storage, but it is necessary to strengthen the sealed investment and monitoring of gas storage during the operation period. The trap with “Basically suitable” caprock basically meets the requirement to build gas storage, but special funds shall be reserved during the construction period to evaluate the sealing of the gas storage. The trap with “Not suitable” caprock cannot be considered for building gas storage.

4. Results and Discussions

4.1. Results of Experiments and Comprehensive Evaluation

The X9 conglomerate body gas reservoir is surrounded by a large set of dark mudstone of the lower member of Es3. Mudstone is not only the oil and gas source rock, but also the caprock of conglomerate reservoir. The lower member of Es3 is characterized by the deep lake to semi-deep lake sedimentary system, with the lithology of brown gray, dark grey mudstone with thin layer of fine sandstone or silty stripe. The mineral composition of the caprock is mainly clay minerals and a small amount of sand-grade mineral debris. According to X-ray diffraction analysis (

Table 9. Rock composition comparison of Es2 & Es3 mudstone.

Well Number	Member	Lithology	Mineral Content/%
			Kaolinite	Chlorite	Illite	Illite-Montmorillonite Mixed Layer	Interlayer Ratio
RS 2X	Es2 + 3	Gray mudstone	6.9	6.7	33.3	53.1	45.8
XG 1	Es3	Gray mudstone	6.7	5.1	20.6	67.6	37.1

), clay minerals are mainly composed of illite, illite-montmorillonite mixed layer, kaolinite, and chlorite, in which illite-montmorillonite mixed layer accounts for more than 53% of the clay minerals, accounting for the largest proportion, followed by illite, and the proportion of kaolinite and chlorite are relatively small.

The X9 conglomerate body is located in the lower member of the Es3, and the caprock is a large set of brownish-gray and dark red mudstone with good continuity, and the thickness is generally more than 400 m. For the X9 lithologic trap gas reservoir, the mudstone caprock can not only perform vertical sealing but also play the role of lateral sealing (Figure 7).

Due to the lack of samples of the mudstone caprock in the X9 area, the caprock samples of the same layer in the adjacent area were selected for testing, and the results of the porosity and permeability test according to SY/T 5336-2019 are shown in

Table 10. Laboratory results of porosity and permeability characteristics of caprock samples of the adjacent well.

Number	Well Number	Porosity/%	Permeability/(10−3 mD)	Density/(g·cm−3)
1	G15	2.16	1.16	2.61
2		2.91	42.80	2.66
3		3.19	8.40	2.63
4		3.22	4.06	2.65
5		8.92	55.10	2.61
6	X8	6.66	0.79	2.53
7		4.98	0.63	2.54
8		5.86	821.00	2.45
9		4.84	15.10	2.51
10	T29	3.53	0.14	2.58
11		8.27	246.0	2.57
12		3.89	1.10	2.57

.

The porosity range of the caprock of the lower member of Es3 in the G15 well is 2.16~8.92%, with an average value of 4.08%. The permeability range of the caprock is 1.16 × 10⁻³~55.1 × 10⁻³ mD, with an average value of 22.3 × 10⁻³ mD. The porosity range of the caprock of the lower member of Es3 of the X8 well is 4.84%~6.66%, with an average value of 5.59%. The permeability of sample 8 is quite large with the value of 821 × 10⁻³ mD, and the main reason is that the stress release causes the micro-cracks of mudstone to open and the permeability of the caprock becomes larger. The permeability range of rest samples in X8 well is 0.63 × 10⁻³~15.10 × 10⁻³ mD, with the average value of 5.5 × 10⁻³ mD. The porosity range of the caprock of the lower member of Es3 of the T29 well is 3.53%~8.27%, and the lowest permeability of the caprock is 0.14 × 10⁻³ mD. The permeability of sample No.11 is 246 × 10⁻³ mD, which is also caused by crack opening due to stress release. Nevertheless, the porosity and permeability of these 12 samples still show a certain positive correlation, that is, the greater the porosity, the greater the permeability (Figure 8).

The breakthrough pressure laboratory test of mudstone caprock was carried out (Figure 9 and Figure 10) and the results are shown in

Table 11. Breakthrough pressure of caprock sample of adjacent well in X9 area (confining pressure 60 MPa, temperature 70 °C).

Number	Well Number	Sampling Depth/m	Permeability/(10−3 mD)	Breakthrough Pressure/MPa
1	G15	3904.54	0.39	31.35
2		3900.81	0.10	27.28
3		3901.21	1.09	26.66
4		3904.34	0.36	29.28
5	X8	2870.80	97.10	23.98
6	T29	2834.00	0.84	30.66
7		2836.00	0.51	31.14
8		2835.70	0.38	32.11

. The breakthrough pressure values measured are all greater than 20 MPa, the maximum value was about 32.11 MPa, and the permeability measured was basically within 0.10 × 10⁻³~1.1 × 10⁻³ mD. The permeability value of rock sample 5 is relatively large due to the existence of micro-cracks, and the corresponding breakthrough pressure value is the smallest, about 24 MPa. It is not difficult to see that there is an obvious negative relationship between permeability and breakthrough pressure, that is, the greater the permeability is, the smaller the breakthrough pressure is (Figure 11).

The breakthrough pressure test was also carried out in the same layer of mudstone in the No.102 well in the adjacent area. Under the conditions of temperature 26 °C and pressure 30 MPa, the breakthrough pressure reached 40 MPa, which also proved that the mudstone of this layer has good sealing capacity.

According to Equation (3), and the average acoustic time difference values of mudstone on the top of the conglomerate body in X9, the displacement pressure of mudstone caprock in X9 were calculated, in which the empirical parameters c, d are 3673.61 and −0.02764. The displacement pressure values are all greater than 6 MPa (

Table 12. Calculated results of displacement pressure of in each well of X9 area.

Well No.	Δt μs/m	Displacement Pressure/MPa	Well No.	Δt μs/m	Displacement Pressure/MPa
X9	226	7.11	X9-4	216	9.38
X9-1	232	6.03	X9-6	228	6.73
X9-2	229	6.55	X9-7	221	8.17
X9-3	221	8.17	X9-9	230	6.37

), indicating that the mudstone caprock in the area has good sealing performance.

Under simulated formation temperature and pressure, triaxial tests were carried out on four samples from Well G15 and three samples from Well T29. The triaxial rock mechanics test system RTR-1000 was used for the test (Figure 12). The test procedure is as follows: (1) Load the prepared sample into the triaxial chamber, and add axial pressure of 0.5 MPa to the sample; (2) Close the pressure chamber and inject hydraulic oil; (3) Heating to formation temperature; (4) Add confining pressure to formation pressure; (5) Compressing the sample with a strain rate of 0.002 mm/s until the sample is failed; (6) Save the experimental data.

Rock mechanics test results of mudstone caprock of two wells in the adjacent area are shown in Figure 13. Due to the existence of microcracks inside sample G3, it suddenly breaks when the stress value is at its peak strength, and the post-peak stage is very short. All other six samples all show obvious strain-softening characteristics, which indicate that the caprock in this area has certain plastic deformation ability under simulated formation conditions.

Table 13. Rock mechanics test results of caprock samples under formation conditions.

No.	Well No.	Elastic Modulus/MPa	Poisson’s Ratio	Peak Strain/%	Peak Strength/MPa	Residual Strain/%	Residual Strength/MPa	Elasticity Index/%	Plasticity Index/%
G1	G15	24,661.2	0.155	0.392	87.0	0.651	10.80	64.68	1.57
G2		18,369.1	0.140	1.756	185.80	2.490	159.90	58.19	19.98
G3		15,398.3	0.163	1.364	161.28	1.482	157.85	41.45	–
G4		9443.5	0.104	1.517	132.91	2.323	90.67	55.68	67.32
T1	T29	13,383.9	0.149	2.310	222.70	3.085	177.55	43.56	27.12
T2		9738.5	0.111	1.894	165.24	2.471	120.95	53.12	55.62
T3		7281.1	0.143	2.084	97.67	3.173	53.75	33.38	67.98

shows the laboratory test results of caprock. Under normal temperature and low confining pressure, the hard rock generally fails in brittle mode. When the stress reaches its peak value, the magnitude of the strain is generally 10⁻³. In this test, except for G1 (strain magnitude of 10⁻³, elasticity index of 64.68%, plasticity index of 1.57%), all failure modes of the other rocks were a ductile failure. Under the simulated formation conditions, the strain magnitude is 10⁻², in which the axial compression strain is 1.36–3.2%, the elastic index is 33.38–58.19%, and the average value is 47.56%. The plasticity index ranges from 19.98 to 67.98%, with an average value of 47.60%. Therefore, caprock is believed to have a certain plastic deformation capacity.

According to the above analysis, the scores of the 12 basic indicators of the X9 depleted gas reservoir caprock are: 10, 8, 8, 10, 10, 8, 8, 8, 10, 8, 8, 8. The scores of the respective indexes and the corresponding weight values corresponding to Table 7 are substituted into Equation (15) to obtain the comprehensive suitability value of the depleted gas reservoir caprock. According to the classification evaluation of Table 8, it can be seen that the caprock of the gas storage is of good quality, close to the requirements of optimal caprock, but the sealing performance monitoring of the gas storage should be strengthened during the operation phase of the gas storage. The evaluation results are consistent with the expert argumentation results [36].

4.2. Discussion

It is not difficult to see that the breakthrough pressure measured in the laboratory is significantly greater than the breakthrough pressure measured by the acoustic time difference. It is analyzed that: When drilling to plane A, the vertical stress overlying the core is reduced firstly. During the process of stress unloading in the vertical direction, the inhomogeneity in the rock mass leads to the incongruity of deformation, which produces a local stress field in the vertical direction and horizontal tensile cracks in the core. Then, when the core enters the drilling pipe, the horizontal stress gradually decreases, the wellbore tends to collapse, and the core expands laterally, resulting in vertical fractures (Figure 14). Once horizontal or vertical fractures occur in the core, the acoustic time difference increases, and the breakthrough pressure value decreases significantly. For laboratory tests, it is the samples with higher integrity that are selected, and correspondingly, the breakthrough pressure values are relatively higher.

According to the above analysis, the displacement pressure of the mudstone caprock calculated according to the acoustic time difference and the breakthrough pressure measured by laboratory experiments (Table 11 and Table 12) all indicate that the mudstone caprock of the X9 gas reservoir is of good sealing performance.

The existence of micro-cracks not only affects the breakthrough pressure, but also the permeability. The permeability measured by laboratory test is the permeable performance exhibited of the caprock after stress release, and the stress release of some samples causes the micro-cracks of the mudstone to change from the state of non-open to open, thus the permeability becomes larger. There is no significant difference in the appearance, density, and porosity of caprock samples from the same stratum, but the difference in permeability is relatively obvious, which indicates that there is a small amount of microfractures in the caprock. Therefore, it is necessary to adopt more specific methods to characterize the degree of micro-cracks development in the future when evaluating the sealing capacity of the caprock.

Hildenbrand et al. [20] carried out some breakthrough pressure tests and made statistics on some previous work. These results and the results of this paper show that the higher the permeability is, the lower the displacement pressure is. The correlation coefficient between permeability and breakthrough pressure of hundreds of samples counted in ref. [20] is 0.26–0.99, and that of the test carried out in ref. [20] is 0.71. The correlation coefficient between permeability and breakthrough pressure in this study is 0.74, indicating that the correlation is effective to some extent. Since the data amount is not abundant, this relationship may not be accurate enough to predict the breakthrough pressure through permeability. In further research, more laboratory tests can be carried out to enrich the database, so as to obtain a fitting relationship with less error.

On the other hand, it can be seen that the permeability measured in this paper is greater than the permeability in [20], but the breakthrough pressure is also greater than the breakthrough pressure in [20]. In addition to the difference in the core itself, the analysis believes that the difference in the testing process is the main reason. For example, the stepwise gas pressure increasing scheme (0.5 MPa per 120 h) is mentioned in ref [20], while the loading scheme in this paper follows the Chinese standard SY/T 5748-1995, in which the holding constant time of each stage pressure is relatively short (0.5–2 h), and the loading pressure increment is 15% of the previous stage. The pressure of externally applied gas has a good correlation with the time of gas breakthrough, which is the higher the pressure of externally applied gas, the shorter the breakthrough time, and vice versa [19]. In addition, the confining pressure is also one of the reasons for the difference. In this study, the confining pressure is set at 60 MPa, which is relatively high and also means that the same lithologic caprock with deeper depth may have better sealing ability since the confining pressure is usually positively correlated with depth.

Faults are one of the important factors controlling traps [37]. The research object of this paper, X9 gas storage, is reconstructed from the lithologic gas reservoir, as shown in the yellow part of Figure 8, which means there is no fault in the reservoir or caprock. Daxing fault is hundreds or thousands of meters away from X9 gas storage. Unlike fault-controlled gas reservoir that is laterally sealed by faults, it is the caprock that plays the role of the lateral and vertical seal of X9 gas storage. Naturally, the focus of trap sealing evaluation has become the evaluation of caprock sealing capacity as presented in this study.

Building a geological model and (then) performing both analytical or numerical geomechanical multiscale assessment using data from a mechanical earth model [38,39] is considered to be the “gold standard” for sealing and stability evaluation of caprock and even the whole trap. However, for many gas reservoirs, the pressure and production information of the reservoir were mainly concerned with the early development of the gas reservoir. Therefore, the geological model established by PETREL and other software usually contains only a reservoir model but no caprock, and due to the lack of some data, it is difficult to establish the entire trap geological model including reservoir, caprock, and fault, which will be the focus of the future work. By then, many factors can be more carefully reflected, such as rock heterogeneity based on well log analysis, mercury porosimetry derived pore size distribution for different rock types, assessment of fracture gradient across the reservoir and caprock lithologies, the correlation between the geomechanical state (stress field) and transport properties (permeabilities) of the caprock, the fault characterization, even the effects of cyclic loading and creep, and in the end, comparison can be made between a gold standard and the method proposed in this paper.

5. Conclusions

This paper was devoted to putting forward a new qualitative and quantitative systematic evaluation method, which can comprehensively evaluate the caprock quality of underground gas storage. By the means of geological data research, field and laboratory tests, and theoretical analysis, the following conclusions were obtained:

(1)

In this paper, the factors influencing the caprock quality are analyzed in detail from five aspects: caprock lithology, thickness, porosity and permeability characteristics, displacement pressure, and mechanical properties of caprock, and 12 basic evaluation indexes are selected. Based on the relevant research results, the classification criteria for each basic indicator are initially proposed, and the comprehensive evaluation model based on the Analytic Hierarchy Process method is established.

(2)

Based on the failure mechanism of mudstone caprock, an analytical method for evaluating the sealing capacity of mudstone caprock using the brittleness index is proposed. The method considers the full stress-strain curve characteristics of mudstone, based on the mechanical analysis of the whole process of rock failure, and comprehensively utilizes the peak strain and the post-peak curve shape to form an evaluation index.

(3)

Taking the X9 depleted gas reservoir as an example, the quality of the target caprock is evaluated by the above method. The caprock suitability value was M = 8.77, the caprock quality was suitable for underground gas storage, and the conditions for rebuilding into gas storage were available. The evaluation results are consistent with the expert demonstration results, which verified the effectiveness of the method.

(4)

Due to the difficulty of core drilling and preservation of mudstone caprock, the mechanics and deformation characteristics of the mudstone caprock are less understood at present, and the mechanical response which plays a key role in the sealing capacity of gas storage caprock still needs further study.