RU2540716C1 - Leak-tightness determination method for underground gas storage facilities with water drive operation mode - Google Patents

Abstract

FIELD: oil and gas industry.

SUBSTANCE: stratum is impact cyclically, at that each cycle of impact includes gas injection to the stratum with further gas extraction. The stratum is impacted during 10 cycles at least. In each cycle current formation pressure as well as gas extraction (or injection) volume is measured simultaneously in gas- $$\left(P_t^{\text{'}\text{'}ф\text{'}\text{'}}\right)$$

and water-bearing $$\left(P_t^{\text{'}\text{'}фв\text{'}\text{'}}\right)$$

zone of the storage facility, then considering the measured parameters the design pressure in the underground storage facility $$\left(P_t^{\text{'}\text{'}P\text{'}\text{'}}\right)$$

is defined for the facility operation mode without gas losses and operation mode with gas losses. Then function (F) is defined as arithmetic mean value of deviations $$\left(P_t^{\text{'}\text{'}P\text{'}\text{'}}\right)$$

from $$\left(P_t^{\text{'}\text{'}ф\text{'}\text{'}}\right)$$

, which are received for each i^th measurement for the facility operation mode without gas losses and the function (Fy) for the facility operation mode with gas losses and when inequality Fy<F is satisfied the summary is made about available gas leaks in the storage facility.

EFFECT: simplifying control of gas leak-tightness, improving reliability and safety of the underground storage facilities made in the water-bearing strata.

1 tbl

Description

The invention relates to the gas industry and can be used to control the safety of underground gas storages (UGS) with a water-pressure mode of operation.

A well-known hydrogeochemical method for determining inter-layer gas flows in gas fields (Agishev A.P. Inter-layer gas flows in the development of gas fields. M: Nedra, 1966, p. 79-88), in which the constant hydrogeochemical background is determined throughout the vertical cutaway. Then, the accumulated data on the hydrogeochemical situation of the studied intervals of the section are compared with the natural background of the field and determine the trends of emerging changes in a particular area. The disadvantage of this method is the difficulty of its implementation, due to the need to study the initial hydrogeochemical background before gas injection into the storage. In addition, the application of this method for underground gas storage is associated with significant costs for drilling control wells, because hydrogeochemical studies must be carried out in specially drilled control wells located in the gas reservoir circuit, and water samples must be taken in well-isolated wells, while maintaining reservoir conditions (temperature and pressure), which leads to errors in determining the tightness of underground gas storage facilities.

Closest to the proposed method (prototype) is a method for studying the dynamic processes of the UGS gas environment (RF patent No. 2167288, E21B 47/00, publ. 05/20/2001), which includes introducing indicators into the reservoir through various injection wells of a gas carrier, sampling gas from producing wells and determining the concentration of indicators over time in the production of producing wells. During the period of maximum gas pressure, central injection wells located in one or several production horizons are selected based on the area of the production wells by their location, in this case indicators of several colors are used, and an indicator of the same color is pumped in the form of gas-filled microgranules with a degree of dispersion of 0.5- 0.6 μm, consisting of a mixture of a polycondensation resin and an organic luminescent substance in an estimated amount. In the period of pressure reduction to a minimum area-weighted average, gas samples are simultaneously taken from production wells located in one or more production horizons, and the concentration changes of the indicators of each color and the gas volume velocity of all production wells are determined over time, the total number of indicator of each color is found, received in each production well, according to a given formula. Maps are built and, by the magnitude of the shares of the migrating gas, the directions of in-situ and inter-layer flows are identified and the gas-dynamic zones are outlined. The disadvantage of this method is the need for identification of indicators by five parameters, which complicates the implementation of the method and reduces the reliability of the study of dynamic processes of the gas environment.

The problem to which the invention is directed, is to develop a method for determining the tightness of underground gas storage facilities created in an aquifer with a water-pressure mode of operation, which allows timely detection of gas leaks from underground gas storage facilities throughout the entire period of operation.

The technical result, the achievement of which the present invention is directed, is to simplify the tightness control, which leads to an increase in the reliability and safety of operation of underground gas storage facilities created in aquifers.

и водоносной $$\left(P_t^{фв}\right)$$

зоне хранилища, а также объем отбора (или закачки) газа (q_t). Затем с учетом измеренных параметров определяют расчетное давление в подземном хранилище газа $$\left(P_t^P\right)$$

для режима эксплуатации хранилища без утечек газа из соотношенияThe specified technical result is achieved due to the fact that in the proposed method for determining the tightness of underground gas storage facilities, a cyclic impact on the formation is carried out, in which each cycle includes the injection of gas through production wells into the formation until the formation pressure reaches a maximum permissible design value, followed by gas extraction until the value of reservoir pressure is not lower than the minimum permissible design value. The impact on the reservoir is carried out for at least 10 cycles, while in each cycle the current reservoir pressure in the gas is periodically simultaneously measured $$\left(P_t^f\right)$$

and aquifer $$\left(P_t^{f\mathrm{at}}\right)$$

storage area, as well as the volume of gas extraction (or injection) (q _t ). Then, taking into account the measured parameters, the calculated pressure in the underground gas storage is determined $$\left(P_t^P\right)$$

for the operation mode of the storage without gas leaks from the ratio

$$\left({\Omega }_o-q_{\mathrm{at}}\right)P_t^p/Z_t-{\Omega }_o{P}_o/Z_o={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt},\left(\mathrm{one}\right)$$

where Ω _o - gas-saturated pore volume of underground gas storage facilities,

P _o - initial reservoir pressure,

- расчетное пластовое давление на момент времени t, $$P_t^P$$

- the estimated reservoir pressure at time t,

Z _o - the initial coefficient of supercompressibility of the gas,

Z _t is the coefficient of supercompressibility of the gas at time t,

q _t is the volume of gas injection (or withdrawal) at time t;

q _in - the volume of displaced (or invading) formation water into the gas zone of the storage at time t, while

$$q_{\mathrm{at}}=C_{\mathrm{at}}\left(P_t^P-P_t^{f\mathrm{at}}\right),\left(2\right)$$

where C _in is the proportionality coefficient of the displaced (or embedded) formation water into the gas zone of the storage facility;

and for the operating mode of the store with gas leaks from the ratio

$$\left({\Omega }_o-q_{\mathrm{at}}\right)P_t^p/Z_t-{\Omega }_o{P}_o/Z_o={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt-C_y{\displaystyle \underset{0}{\overset{t}{\int }}\frac{P_t^p}{Z_t}dt}},\left(3\right)$$

where C _y is the coefficient of proportionality of the gas leak.

от $$\left(P_t^{ф}\right)$$

, полученных при каждом i-м измерении, для режима эксплуатации хранилища без утечек газаThen determine the function (F) as the arithmetic mean of the deviations $$\left(P_t^P\right)$$

from $$\left(P_t^f\right)$$

obtained at each i-th measurement for the operation mode of the storage without gas leaks

$$F=\frac{\mathrm{one}}{n}{\displaystyle \sum _{i=\mathrm{one}}^n\left|\left(P_{ti}^P-P_{ti}^f\right)\right|},\left(\mathrm{four}\right)$$

where n is the number of measurements of reservoir pressure,

i - serial number of the measurement of reservoir pressure;

and function (F _y ) for operating mode of a gas leak storage facility

$$Fy=\frac{\mathrm{one}}{n}{\displaystyle \sum _{i=\mathrm{one}}^n\left|\left(P_{ti}^P-P_{ti}^f\right)\right|},\left(5\right)$$

and when the inequality Fy <F is satisfied, they conclude that there are gas leaks in the storage.

During the operation of the UGSF, gas leaks are mainly recorded at a late stage of their development, that is, with the manifestation of gas on the surface and gas contamination of the control horizons, which complicates further searches for a specific cause of gas leakage and can lead to serious complications in the operation of UGS facilities.

For UGS, the change in gas volume in the formation over time is determined from the equation:

$$d{V}_t/dt=q_t,\left(6\right)$$

where V _t is the volume of gas in the reservoir at time t;

t is the time;

q _t is the volume of gas extraction (or injection) per unit time t.

Passing to the integral form, we obtain:

$${\displaystyle \underset{0}{\overset{t}{\int }}d{V}_t={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt\left(7\right)}}$$

$$V_t-V_o={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt,\left(8\right)}$$

where V _o is the volume of gas at the initial time;

From the equation of material balance (Zakirov SN "Design and development of gas fields." M: Nedra, 1974, p. 28-35) it is known

$$V_t={\Omega }_t{P}_t/Z_t,\left(9\right)$$

where Ω _t is the gas-saturated pore volume of the formation at time t;

P _t is the reservoir gas pressure at time t;

Z _t is the coefficient of supercompressibility of the gas at time t.

Equation (9) for underground gas storage in an aquifer with a water-pressure mode of operation will take the form

$$\left({\Omega }_o-q_{\mathrm{at}}\right)P_t^p/Z_t-{\Omega }_o{P}_o/Z_o={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt},\left(10\right)$$

The coefficient of supercompressibility (Z) depends on the composition of the gas, temperature, pressure and is a reference indicator (Trebin F. A. "Natural gas production." M: Nedra, 1976, p. 78-85). The values of Z can be approximated with high accuracy by a polynomial of the form

$$Z_t=a{P}_t^2-b{P}_t+c,\left(\mathrm{eleven}\right)$$

where a , b, c are the coefficients of the polynomial.

Thus, the operating mode of underground storage facilities with a water-pressure mode is described through the measured parameters of gas extraction (injection) and reservoir pressure in the gas and aquifer zones of the formation using the following system of equations

$$\{\begin{array}{l}\left({\Omega }_o-q_{\mathrm{at}}\right)\frac{P_t^p}{Z_t}-{\Omega }_o\frac{P_o}{Z_o}={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt}\\ Z_t=a{P}_t^2-b{P}_t+c\left(12\right)\\ Z_0=a{P}_0^2-b{P}_0+c\\ q_{\mathrm{at}}={\mathrm{from}}_{\mathrm{at}}\left(P_t^p-P^{f\mathrm{at}}\right)\end{array}$$

In case of leakage (presence of gas overflow), i.e. for the operating mode of underground gas storage with gas leaks, equation (6) takes the form

$$d{V}_t/dt=q_t-q_t^y,\left(13\right)$$

- дебит утечки газа из ПХГ в единицу времени t.Where $$q_t^y$$

- the rate of gas leakage from the underground gas storage facility per unit time t.

The rate of gas leakage from underground gas storages can be described by an equation of the form (SN Zakirov, “Design and development of gas fields.” M: Nedra, 1974, p. 220-226)

$$Q_y=C_y{\displaystyle \underset{0}{\overset{t}{\int }}\frac{P_t}{Z_t}dt,\left(\mathrm{fourteen}\right)}$$

where C _y is the gas leakage coefficient.

Then, for the operation of the UGS facility under water pressure conditions with gas leaks, equation (14) takes the form

$$\left({\Omega }_o-q_{\mathrm{at}}\right)P_t/Z_t-{\Omega }_o{P}_o/Z_o={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt-C_y{\displaystyle \underset{0}{\overset{t}{\int }}\frac{P_t}{Z_t}dt}}\left(\mathrm{fifteen}\right)$$

эксплуатацию ПХГ с водонапорным режимом можно описать системой уравнений:To calculate reservoir pressure $$\left(P_t^P\right)$$

UGS operation with a water-pressure mode can be described by a system of equations:

- without gas leaks

$$\{\begin{array}{l}\left({\Omega }_o-q_{\mathrm{at}}\right)\frac{P_t^p}{Z_t}-{\Omega }_o\frac{P_o}{Z_o}={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt}\\ Z_t=a{P}_t^2-b{P}_t+c\left(16\right)\\ Z_0=a{P}_0^2-b{P}_0+c\\ q_{\mathrm{at}}={\mathrm{from}}_{\mathrm{at}}\left(P_t^p-P^{f\mathrm{at}}\right)\end{array}$$

- with gas leaks

$$\{\begin{array}{l}\left({\Omega }_o-q_{\mathrm{at}}\right)\frac{P_t^p}{Z_t}-{\Omega }_o\frac{P_o}{Z_o}={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt-C_y{\displaystyle \underset{0}{\overset{t}{\int }}\frac{P_t^p}{Z_t}dt}}\\ Z_t=a{P}_t^2-b{P}_t+c\left(17\right)\\ Z_0=a{P}_0^2-b{P}_0+c\\ q_{\mathrm{at}}={\mathrm{from}}_{\mathrm{at}}\left(P_t^p-P^{f\mathrm{at}}\right)\end{array}$$

от фактического $$\left(P_t^{ф}\right)$$

используют функцию (F), характеризующую технологическую модель эксплуатации ПХГ, полученную в результате решения систем уравнений (16) и (17), относительно пластового давления $$\left(P_t^P\right)$$

To estimate the deviation of the estimated reservoir pressure $$\left(P_t^P\right)$$

from the actual $$\left(P_t^f\right)$$

use the function (F), which characterizes the technological model of the operation of underground gas storage, obtained by solving systems of equations (16) and (17), relative to reservoir pressure $$\left(P_t^P\right)$$

$$F=\frac{\mathrm{one}}{n}{\displaystyle \sum _{i=\mathrm{one}}^n\left|\left(P_{ti}^P-P_{ti}^f\right)\right|}\left(\mathrm{eighteen}\right)$$

The method is as follows.

для режима эксплуатации хранилища без утечек газа и для режима эксплуатации хранилища с утечками газа по формулам (16) и (17). После чего вычисляют функцию (F), характеризующую режим эксплуатации ПХГ без утечек газа и с утечками газа (F_y) по формуле (18). Выполняют сравнение значений (F) и (F_y). Если F_y<F, делают вывод о наличии утечек газа в ПХГ, т.е. о нарушении герметичности хранилища.During operation, underground storage facilities with a water-pressure regime carry out a cyclical effect on the reservoir. In each cycle, gas is pumped through production wells into the reservoir with subsequent gas extraction. Gas injection is carried out until the reservoir pressure in the UGS facility is reached, not exceeding the maximum permissible design value. Gas sampling is carried out until the reservoir pressure is not lower than the minimum permissible design value. The cyclic impact on the reservoir is carried out for at least 10 cycles. During each cycle, once a day, the current reservoir pressure in the gas and aquifer zones of the storage facility is measured, as well as the volume of gas injection (selection). Then calculate the pressure in the underground gas storage facility $$\left(P_t^P\right)$$

for the operating mode of the storage without gas leaks and for the operating mode of the storage with gas leaks according to formulas (16) and (17). Then calculate the function (F) characterizing the operating mode of the UGSF without gas leaks and gas leaks (F _y ) according to the formula (18). A comparison of the values of (F) and (F _y ) is performed. If F _y <F, conclude that there are gas leaks in the underground gas storage facility, i.e. about violation of the tightness of the storage.

The proposed method was investigated Osipovichi UGS. Obtained during the study, the measured values of reservoir pressure in the gas and aquifer zones of the reservoir, the volume of injection (selection) of gas, as well as the calculated values of reservoir pressures are shown in the table.

By comparing the measured and calculated parameters, it was concluded that there are gas leaks in the indicated underground gas storage facility (F _y = 2.3, F = 4.4), i.e. F _y <F).

Thus, the proposed method improves the reliability and safety of operation of underground storage facilities created in aquifers by simplifying the tightness control, as well as by increasing the reliability of determining tightness.

Table Measured parameters (actual data) Design parameters (water pressure mode) Design parameters (water pressure mode with gas leak) No. per measure Injection / Selection (-), mln.m ³

, ПаPressure measured in the gas zone $$\left(P_t^F\right)$$

, Pa Pressure measured in an aquifer $$\left(P_t^{F\mathrm{at}}\right)$$

, Pa Pressure $$\left(P_t^P\right)$$

, Pa $$P_t^P-P_t^F$$

, Pa Pressure $$\left(P_t^P\right)$$

, Pa $$P_t^P-P_t^F$$

, Pa one 2 3 four 5 6 7 8 one -5.96 21.6 47.0 21.6 0 21.6 0 2 56.46 40.5 47.0 38,0 2,5 37.8 2.7 3 75 53.1 47.0 55,2 -2.1 54.7 -1.6 four 77.61 61.1 47.0 65,4 -4.3 64.8 -3.7 5 77.23 67.9 47.1 70.3 -2.4 69.6 -1.7 6 44.21 67.7 47.1 68.5 -0.8 67.7 0 7 -2.65 63.8 47.2 62,2 1,6 61.3 2,5 8 -35.54 54,4 47.3 54.5 -0.1 53,4 one

Table continuation one 2 3 four 5 6 7 8 9 -79.54 43.8 47.3 43.7 0.1 42,4 1.4 10 -82.54 32 47.2 34.0 -2 32,3 -0.3 eleven -60.44 23.7 47.1 27.6 -3.9 25,4 -1.7 12 -45 17.3 47.0 23.1 -5.8 20.5 -3.2 13 -6.42 19.8 47.0 25,4 -5.6 22.8 -3 fourteen 39.17 39.1 47.0 37.6 1,5 36.6 2,5 fifteen 85.09 55,4 47.0 56.5 -1.1 57.7 -2.3 16 77.98 61.8 47.0 66.0 -4.2 67.1 -5.3 17 80.57 68,4 47.0 70.9 -2.5 71,4 -3 eighteen 52.65 69,4 47.1 70.0 -0.6 69.8 -0.4 19 -11.79 61 47.2 62.3 -1.3 61.3 -0.3 twenty -54.71 51 47.2 52.6 -1.6 51.0 0 21 -82.39 41 47.2 42.1 -1.1 39.7 1.3 22 -77.41 thirty 47.1 33.3 -3.3 30.1 -0.1 23 -55.24 19,4 47.1 27.7 -8.3 23.7 -4.3 24 -29.76 14.9 47.0 25.8 -10.9 21,2 -6.3 25 0 20.9 47.0 29.2 -8.3 25.3 -4.4

Table continuation one 2 3 four 5 6 7 8 26 42.49 43.7 46.9 40.7 3 40.6 3,1 27 81.92 57.8 46.9 56.8 one 60,4 -2.6 28 81.26 64.5 47.0 66.1 -1.6 69.1 -4.6 29th 73.76 69.7 47.0 69.8 -0.1 71.5 -1.8 thirty 54.42 69.9 47.1 69.5 0.4 70.0 -0.1 31 7.25 69.6 47.2 64,4 5.2 63.8 5.8 32 -78.3 50.3 47.2 52,2 -1.9 50,0 0.3 33 -81.13 40.5 47.2 42,4 -1.9 39.0 1,5 34 -76.41 30.8 47.1 34.2 -3.4 29.6 1,2 35 -54.45 19.9 47.1 29.0 -9.1 23.3 -3.4 36 -21.84 15.9 47.0 28,4 -12.5 22.5 -6.6 37 17.04 32,5 47.0 34.0 -1.5 30.3 2.2 38 46,42 48.7 47.0 44.0 4.7 44.7 four 39 53.54 56.9 47.0 52.9 four 56.1 0.8 40 77.16 64.9 47.0 62.1 2,8 66.0 -1.1 41 75.17 70 47.0 67.2 2,8 70.1 -0.1 42 55.47 70.7 47.1 68.0 2.7 69,4 1.3

Table continuation one 2 3 four 5 6 7 8 43 36.38 70.5 47.2 66.6 3.9 66.8 3,7 44 -70.89 53.7 47.3 55.3 -1.6 53.3 0.4 45 -88.39 43 47.3 45.0 -2 41.2 1.8 46 -80.8 32.6 47.2 36.7 -4.1 31,4 1,2 47 -60.47 21.9 47.1 31,2 -9.3 24.5 -2.6 48 -28.5 17 47.0 29.7 -12.7 22.5 -5.5 49 33.03 38.5 47.0 36.7 1.8 32.9 5,6 fifty 50.09 50,5 47.0 45.4 5.1 46.0 4,5 51 66.48 58.8 47.0 54,4 4.4 58.0 0.8 52 87.64 66,2 47.0 63.1 3,1 67.7 -1.5 53 71.36 70.9 47.1 66.9 four 70.1 0.8 54 46.66 70.7 47.2 66.9 3.8 68.5 2.2 55 25.92 68 47.3 65.1 2.9 65.3 2.7 56 -61.01 56.1 47.4 56.2 -0.1 54,2 1.9 57 -77.09 46.1 47.4 47.9 -1.8 44.1 2 58 -96.13 34 47.3 38.8 -4.8 33.0 one 59 -67.62 24.1 47.2 33,2 -9.1 25.8 -1.7

Table continuation one 2 3 four 5 6 7 8 60 -49 17,2 47.1 29.5 -12.3 20.8 -3.6 61 54.56 37.6 47.0 38,2 -0.6 33.7 3.9 61 57.33 47.1 47.0 46.3 0.8 46.2 0.9 63 37.77 53.6 47.0 50.8 2,8 52,2 1.4 64 93.85 63,2 47.1 60.1 3,1 64.3 -1.1 65 78.73 68.3 47.1 65,2 3,1 68.9 -0.6 66 56.35 69.3 47.2 66.6 2.7 68.9 0.4 67 13.64 57.6 47.4 64.1 -6.5 64,4 -6.8 68 -63.09 55.3 47.6 56.0 -0.7 53.8 1,5 69 -110.04 42,2 47.6 45.5 -3.3 40.6 1,6 70 -108.05 28.3 47.4 36,2 -7.9 28.6 -0.3 71 -65.29 19.7 47.2 31,2 -11.5 21.9 -2.2 72 -34.78 fifteen 47.1 29.4 -14.4 19.0 -four 73 29.35 31.6 47.0 34.9 -3.3 27.9 3,7 74 94.7 fifty 47.0 47.4 2.6 49.0 one 75 35.98 47.4 47.0 51.3 -3.9 54.1 -6.7 76 100.3 65.3 47.0 60.9 4.4 66.7 -1.4

Table continuation one 2 3 four 5 6 7 8 77 72.57 67.4 47.1 65.0 2,4 69.6 -2.2 78 52.72 68.6 47.2 66,2 2,4 68.9 -0.3 79 24.28 67.4 47.4 64.7 2.7 65.5 1.9 80 -65.01 54.3 47.6 56.7 -2.4 54,4 -0.1 81 -94 44,2 47.6 47.8 -3.6 42.8 1.4 82 -98.84 33.8 47.4 39.6 -5.8 31.9 1.9 83 -78.03 22.7 47.2 33.5 -10.8 23.6 -0.9 84 -43.77 14.7 47.1 30.9 -16.2 19,4 -4.7 85 13.52 25,2 47.0 34.3 -9.1 25.1 0.1 86 59.43 42 47.0 42.5 -0.5 40,0 2 87 84.19 55.8 47.0 52.1 3,7 56.3 -0.5 88 90,99 63.6 47.0 60,2 3.4 66.8 -3.2 89 80.62 68 47.1 65.1 2.9 70.7 -2.7 90 66.43 69.5 47.2 67.4 2.1 71.1 -1.6 91 21.73 67.8 47.4 65.6 2.2 66.7 1,1 92 -65.09 57.3 47.6 57.7 -0.4 55,4 1.9 93 -86.34 47 47.6 49.8 -2.8 44.6 2,4

Table continuation one 2 3 four 5 6 7 8 94 -103.02 32.1 47.5 41.5 -9.4 33.3 -1.2 95 -79.73 22.4 47.3 35.5 -13.1 25.0 -2.6 96 -50.02 15,5 47.1 32,4 -16.9 20,0 -4.5 97 10.22 14,4 47.1 35,2 -20.8 24.9 -10.5 Function F = 4.4 F _y = 2,3

Claims (1)

A method for determining the tightness of underground gas storages with a water-pressure mode of operation, characterized by a cyclic impact on the formation, in which each cycle includes pumping gas through production wells into the formation until a formation pressure value does not exceed the maximum permissible design value, followed by gas extraction until the formation value is reached pressure not lower than the minimum permissible design value, and the impact on the formation is carried out for at least 10 cycles in, while at the same time in each cycle are periodically measured current pressure in the gas reservoir $$\left(P_t^f\right)$$

and aquifer $$\left(P_t^{f\mathrm{at}}\right)$$

storage area, as well as the volume of gas extraction (or injection) (q _t ), then, taking into account the measured parameters, the design pressure in the underground gas storage is determined $$\left(P_t^P\right)$$

for the operation mode of the storage without gas leaks from the ratio
$$\left({\Omega }_o-q_{\mathrm{at}}\right)P_t^p/Z_t-{\Omega }_o{P}_o/Z_o={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt}$$

,
where Ω _o - gas-saturated pore volume of underground gas storage facilities,
P _o - initial reservoir pressure,
$$P_t^P$$

- the estimated reservoir pressure at time t,
Z _o - the initial coefficient of supercompressibility of the gas,
Z _t is the coefficient of supercompressibility of the gas at time t,
q _t is the volume of gas injection (or withdrawal) at time t;
q _in - the volume of displaced (or invading) formation water into the gas zone of the storage at time t, while
$$q_{\mathrm{at}}=C_{\mathrm{at}}\left(P_t^P-P_t^{f\mathrm{at}}\right)$$

,
where C _in is the proportionality coefficient of the displaced (or embedded) formation water into the gas zone of the storage facility;
and for the operating mode of the store with gas leaks from the ratio
$$\left({\Omega }_o-q_{\mathrm{at}}\right)P_t^p/Z_t-{\Omega }_o{P}_o/Z_o={\displaystyle \underset{0}{\overset{t}{\int }}{q}_{t}dt-C_y{\displaystyle \underset{0}{\overset{t}{\int }}\frac{P_t^p}{Z_t}dt}}$$

,
where C _y is the coefficient of proportionality of the gas leak,
then determine the function (F) as the arithmetic mean of the deviations $$\left(P_t^P\right)$$

from $$\left(P_t^f\right)$$

obtained at each i-th measurement for the operation mode of the storage without gas leaks
$$F=\frac{\mathrm{one}}{n}{\displaystyle \sum _{i=\mathrm{one}}^n\left|\left(P_{ti}^P-P_{ti}^f\right)\right|}$$

,
where n is the number of measurements of reservoir pressure,
i - serial number of the measurement of reservoir pressure;
and function (F _y ) for operating mode of a gas leak storage facility
$$Fy=\frac{\mathrm{one}}{n}{\displaystyle \sum _{i=\mathrm{one}}^n\left|\left(P_{ti}^P-P_{ti}^f\right)\right|}$$

,
and when the inequality Fy <F is satisfied, they conclude that there are gas leaks in the storage.