Method and device for determining formation pressure and dynamic reserve of water invasion gas reservoir

Abstract

The embodiment of the invention provides a formation pressure and dynamic reserve determination method and device of a water invasion gas reservoir, and belongs to the technical field of gas reservoir development. The determination method comprises the following steps: determining a first productivity function in any horizontal plane and a second productivity function in any vertical plane in a horizontal characteristic well; determining a first viscosity function between the viscosity of the natural gas and the formation pressure, a first volume function between the volume coefficient of the natural gas and the formation pressure, and a first permeability function between the relative permeability of the natural gas and the formation pressure; and according to the gas-water two-phase quasi-pressure function, the first productivity function, the second productivity function, the first viscosity function, the first volume function and the first permeability function, the formation pressure is determined. Under the condition that a gas well lacks formation pressure data, the method for calculating the average formation pressure of the water-invaded gas reservoir suitable for the horizontal well is established, and the problem that an existing method for calculating the dynamic reserves of the water-invaded gas reservoir lacks static pressure test data is solved.

Description

Technical Field

[0001] The invention relates to the technical field of gas reservoir development, and in particular to a method and device for determining the formation pressure and dynamic reserves of a water-invaded gas reservoir. Background Art

[0002] In the field of gas reservoir engineering, the early classic water invasion gas reservoir water invasion volume and dynamic reserve calculation method is mainly realized by assuming water invasion model. However, the water body parameters required for calculating the water invasion model, such as water invasion angle, inner and outer boundary radius of the water body, etc., are often difficult to determine accurately, which is not conducive to practical application.

[0003] In addition, based on the material balance principle, existing studies have proposed some methods for calculating the dynamic reserves of water-invaded gas reservoirs that are simple to calculate and easy to apply on site. However, these methods also rely on static pressure test data and have large visual errors.

[0004] At the same time, in practical applications, many gas wells on site lack pressure measurement data, making it difficult to calculate the dynamic reserves of water-invaded gas reservoirs. Therefore, a calculation method with small visual error and capable of solving formation pressure is urgently needed to calculate the dynamic reserves of water-invaded gas reservoirs. Summary of the invention

[0005] The purpose of the embodiment of the present invention is to provide a method and device for determining the formation pressure and dynamic reserves of a water-invaded gas reservoir. In the absence of on-site pressure measurement data, the determination method can use production data, fluid high-pressure physical properties and rock relative permeability data to quickly determine the formation pressure and dynamic reserves of a water-invaded gas reservoir.

[0006] In order to achieve the above-mentioned purpose, an embodiment of the present invention provides a method for determining the formation pressure of a water-invaded gas reservoir, the determination method comprising: determining a first productivity function between the pressure at the outer boundary of the gas reservoir in any horizontal plane in the horizontal feature well and the pressure at the junction of the internal and external seepage fields according to the daily gas production of the natural gas in the horizontal feature well under standard conditions, the length of the horizontal feature well, and the length of the major axis of the oil displacement ellipse; determining a second productivity function between the pressure at the junction of the internal and external seepage fields in any vertical plane of the horizontal feature well and the pressure at the bottom of the well according to the daily gas production, relative permeability and viscosity of the natural gas under standard conditions, the length of the horizontal feature well, and the wellbore radius; determining a first viscosity function between the viscosity of the natural gas and the formation pressure, a first volume function between the volume coefficient of the natural gas and the formation pressure, and a first permeability function between the relative permeability of the natural gas and the formation pressure; and determining the formation pressure according to the gas-water two-phase pseudo-pressure function, the first productivity function, the second productivity function, the first viscosity function, the first volume function, and the first permeability function.

[0007] Optionally, determining the first productivity function includes: determining the first productivity function according to the length L of the horizontal characteristic well and the length 2a of the major axis of the oil discharge ellipse, the daily gas production q of the natural gas under standard conditions gsc , the pressure at the outer boundary of the gas reservoir in any horizontal plane in the horizontal characteristic well is determined by the following formula: Pressure at the interface between internal and external seepage fields The first capacity function between: Wherein, h is the thickness of the water-invaded gas reservoir, K is the air permeability of the water-invaded gas reservoir, R wg is the water-gas mass ratio of the water-invaded gas reservoir, ρ gsc is the density of the natural gas under standard conditions; and / or determining the second productivity function includes: according to the length L of the horizontal characteristic well and the wellbore radius r w The daily gas production of natural gas under standard conditions is q gsc , relative permeability K rg and viscosity μ g The pressure at the junction of the internal and external seepage fields of the horizontal characteristic well in any vertical plane is determined by the following formula: The pressure at the bottom of the well The second capacity function between: Wherein, h is the thickness of the water-invaded gas reservoir, K is the air permeability of the water-invaded gas reservoir, R wg is the water-gas mass ratio of the water-invaded gas reservoir, ρ gsc is the density of the natural gas under standard conditions.

[0008] Optionally, determining the first viscosity function and the first volume function includes: fitting a first viscosity function between the viscosity of natural gas and formation pressure and a first volume function between the volume coefficient of the natural gas and formation pressure based on historical high-pressure physical property test data of horizontal wells in the water-invaded gas reservoir.

[0009] Optionally, determining the first permeability function includes: determining a second viscosity function between the viscosity of the formation water and the formation pressure and a second volume function between the volume coefficient of the formation water and the formation pressure according to the formation temperature and salinity of the formation water in the horizontal characteristic well; determining a first relative permeability function between the gas-water relative permeability ratio and the formation pressure according to the first viscosity function, the first volume function, the second viscosity function, the second volume function and the water-gas ratio between the formation water and the natural gas, wherein the gas-water relative permeability ratio is the ratio between the relative permeability of the natural gas and the relative permeability of the formation water; fitting a second permeability function between the relative permeability of the natural gas and water saturation and a second relative permeability function between the gas-water relative permeability ratio and the water saturation according to the core relative permeability experimental data of the historical horizontal well; and determining the first permeability function between the relative permeability of the natural gas and the formation pressure according to the second permeability function, the first relative permeability function and the second relative permeability function.

[0010] Optionally, determining the second viscosity function comprises: determining the second viscosity function according to the formation temperature T of the formation water F and salinity w s , the viscosity of the formation water is determined by the following formula μ w The second viscosity function with the formation pressure p: in, and / or determining the second volume function comprises: determining the second volume function according to the formation temperature T of the formation water F The viscosity of the formation water B is determined by the following formula: w The second viscosity function between the formation pressure p: B w =(1-a)*(1-b), where a=10 -7 *(3.58922+0.0195301*T F )*p+10 -10 *(2.25341+0.00172834*T F )*p, b=0.010001-(0.000133391+0.000000550654*T F )*T F .

[0011] Optionally, determining the first relative permeability function comprises: according to the first viscosity function μ g (p), the first volume function B p (p), the second viscosity function μ w(p), the second volume function B w (p) and the water-gas ratio WGR, the gas-water relative permeability ratio is determined by the following formula The first relative permeability function with the formation pressure:

[0012] Optionally, determining the formation pressure includes: determining a third production capacity function of the horizontal characteristic well of the water-invaded gas reservoir with respect to the formation pressure based on the gas-water two-phase pseudo-pressure function, the first production capacity function and the second production capacity function; and determining the formation pressure through the first viscosity function, the first volume function, the first permeability function and the third production capacity function.

[0013] On the other hand, the present invention also provides a method for determining the dynamic reserves of a water-invaded gas reservoir, the determination method comprising: determining the formation pressure of the water-invaded gas reservoir according to the method for determining the formation pressure of the water-invaded gas reservoir described above; determining the water saturation of the water-invaded gas reservoir according to the formation pressure of the water-invaded gas reservoir and a saturation function between the water saturation of the water-invaded gas reservoir and the formation pressure; and determining the dynamic reserves of the water-invaded gas reservoir according to the material balance equation of the water-invaded gas reservoir and the water saturation of the water-invaded gas reservoir.

[0014] Optionally, determining the saturation function includes: fitting a first viscosity function between the viscosity of the natural gas and the formation pressure and a first volume function between the volume coefficient of the natural gas and the formation pressure according to the high-pressure physical property test data of the historical horizontal wells of the water-invaded gas reservoir; determining a second viscosity function between the viscosity of the formation water and the formation pressure and a second volume function between the volume coefficient of the formation water and the formation pressure according to the formation temperature and salinity of the formation water in the horizontal characteristic well; and calculating the saturation function according to the first viscosity function, the first volume function, the second viscosity function, the second volume function, and the second volume function. and the water-gas ratio between the formation water and the natural gas, determining a first relative permeability function between the gas-water relative permeability ratio and the formation pressure, wherein the gas-water relative permeability ratio is the ratio between the relative permeability of the natural gas and the relative permeability of the formation water; fitting a second relative permeability function between the gas-water relative permeability ratio and the water saturation according to the core relative permeability experimental data of the historical horizontal wells; and determining a saturation function between the water saturation of the water-invaded gas reservoir and the formation pressure according to the first relative permeability function and the second relative permeability function.

[0015] Optionally, determining the dynamic reserves of the water-invaded gas reservoir includes: according to the cumulative production G of the natural gas in the water-invaded gas reservoir P , Volume coefficient B gand the volume coefficient B at the original formation pressure gi , the cumulative production of formation water in the water-invaded gas reservoir is W p , Volume coefficient B w and isothermal compressibility C w , the pressure drop Δp and isothermal compressibility coefficient C of the water-invaded gas reservoir p , water saturation S w and initial water saturation S wi , the dynamic reserve G of the water-invaded gas reservoir is determined by the following formula: Among them, W e is the water invasion amount of the water-invaded gas reservoir.

[0016] On the other hand, the present invention also provides a device for determining the formation pressure of a water-invaded gas reservoir, the determination device comprising: a first productivity function determination module, for determining a first productivity function between the pressure at the outer boundary of the gas reservoir and the pressure at the junction of the internal and external seepage fields in any horizontal plane in the horizontal characteristic well according to the daily gas production of the natural gas in the horizontal characteristic well in the water-invaded gas reservoir under standard conditions, the length of the horizontal characteristic well, and the length of the major axis of the oil discharge ellipse; a second productivity function determination module, for determining the first productivity function between the pressure at the outer boundary of the gas reservoir and the pressure at the junction of the internal and external seepage fields in any horizontal plane in the horizontal characteristic well according to the daily gas production, relative permeability and viscosity of the natural gas under standard conditions, the length of the horizontal characteristic well, and the length of the wellbore radius of the horizontal characteristic well. a second productivity function between the pressure at the junction of the internal and external seepage fields of the well in any vertical plane and the pressure at the bottom of the well; a natural gas physical property parameter determination module, used to determine the first viscosity function between the viscosity of the natural gas and the formation pressure, the first volume function between the volume coefficient of the natural gas and the formation pressure, and the first permeability function between the relative permeability of the natural gas and the formation pressure; and a formation pressure determination module, used to determine the formation pressure according to the gas-water two-phase pseudo-pressure function, the first productivity function, the second productivity function, the first viscosity function, the first volume function and the first permeability function.

[0017] On the other hand, the present invention also provides a device for determining the dynamic reserves of a water-invaded gas reservoir, the determination device comprising: a device for determining the formation pressure of the water-invaded gas reservoir as described above, used to determine the formation pressure of the water-invaded gas reservoir; a water saturation determination module, used to determine the water saturation of the water-invaded gas reservoir according to the formation pressure of the water-invaded gas reservoir and a saturation function between the water saturation of the water-invaded gas reservoir and the formation pressure; and a dynamic reserves determination module, used to determine the dynamic reserves of the water-invaded gas reservoir based on the material balance equation of the water-invaded gas reservoir and the water saturation of the water-invaded gas reservoir.

[0018] Through the above technical scheme, the beneficial effect of the present invention is that: in the case of a lack of formation pressure data in gas wells, a calculation method for the average formation pressure of water-invaded gas reservoirs suitable for horizontal wells is established, which solves the problem of lack of static pressure test data in the existing calculation method of dynamic reserves of water-invaded gas reservoirs.

[0019] Other features and advantages of the embodiments of the present invention will be described in detail in the subsequent detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The accompanying drawings are used to provide a further understanding of the embodiments of the present invention and constitute a part of the specification. Together with the following specific implementations, they are used to explain the embodiments of the present invention, but do not constitute a limitation on the embodiments of the present invention. In the accompanying drawings:

[0021] Figure 1 It is a flow chart of a method for determining the formation pressure of a water-invaded gas reservoir provided according to an embodiment of the present invention;

[0022] Figure 2 A schematic diagram showing the relationship between the viscosity and volume coefficient of natural gas and the formation pressure according to an embodiment of the present invention;

[0023] Figure 3 A schematic diagram showing the relationship between the viscosity and volume coefficient of formation water and the formation pressure according to an embodiment of the present invention;

[0024] Figure 4 A schematic diagram of the gas-water relative permeability relationship of a core provided according to an embodiment of the present invention;

[0025] Figure 5 A schematic diagram of the relationship between the average water saturation of a gas reservoir and the formation pressure under a certain water-gas ratio condition according to an embodiment of the present invention;

[0026] Figure 6 A schematic diagram of the relationship between gas phase relative permeability and formation pressure under a certain water-gas ratio condition provided according to an embodiment of the present invention;

[0027] Figure 7 This is a schematic diagram of the overall process of a method for determining the dynamic reserves of a water-invaded gas reservoir provided in accordance with an embodiment of the present invention;

[0028] Figure 8 It is a flowchart of specific steps of a method for calculating dynamic reserves of a water-invaded gas reservoir provided in accordance with an embodiment of the present invention;

[0029] Fig. 9 is a schematic diagram of a device for determining formation pressure of a water-invaded gas reservoir provided according to an embodiment of the present invention;

[0030] Fig.10It is a schematic diagram of a device for determining the dynamic reserve of a water-invaded gas reservoir provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0031] The specific implementation of the embodiment of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the embodiment of the present invention, and is not used to limit the embodiment of the present invention.

[0032] The present invention first provides a method for determining the formation pressure of a water-invaded gas reservoir, such as Figure 1 As shown, the determination method may include steps S110 - S140 .

[0033] Step S110, determining a first productivity function between the pressure at the outer boundary of the gas reservoir in any horizontal plane in the horizontal characteristic well and the pressure at the junction of the internal and external seepage fields according to the daily gas production of the natural gas in the horizontal characteristic well in the water-invaded gas reservoir under standard conditions, the length of the horizontal characteristic well, and the length of the major axis of the oil drainage ellipse.

[0034] Wherein, determining the first capacity function may include:

[0035] According to the length L (in m) of the horizontal characteristic well and the length 2a (in m) of the major axis of the oil discharge ellipse, the daily gas production q of natural gas under the standard conditions of set temperature and pressure (for example, the standard conditions of temperature 20°C and pressure 0.1 MPa) gsc (Unit: m 3 / d), the pressure at the outer boundary of the gas reservoir in any horizontal plane in the horizontal characteristic well is determined by the following formula (Unit: MPa) Pressure at the interface between the internal and external seepage fields The first capacity function between (in MPa):

[0036]

[0037] Where h is the thickness of the water-invaded gas reservoir (m), K is the air permeability of the water-invaded gas reservoir (mD), R wg is the water-gas mass ratio of water-invaded gas reservoir (g / g), ρ gsc is the density of natural gas under standard conditions (g / cm 3 ).

[0038] Step S120, determining a second production capacity function between the pressure at the junction of the internal and external seepage fields of the horizontal characteristic well in any vertical plane and the pressure at the bottom of the well according to the daily gas production, relative permeability and viscosity of natural gas under standard conditions and the length and wellbore radius of the horizontal characteristic well.

[0039] Wherein, determining the second capacity function may include:

[0040] According to the horizontal characteristic well length L and wellbore radius r w (unit: m), the daily gas production of natural gas at the standard conditions of set temperature and pressure (for example, at a temperature of 20°C and a pressure of 0.1 MPa) gsc , relative permeability K rg and viscosity μ g (unit: cp), the pressure at the junction of the internal and external seepage fields of the horizontal characteristic well in any vertical plane is determined by the following formula The pressure at the bottom of the well The second capacity function between:

[0041]

[0042] Where h is the thickness of the water-invaded gas reservoir, K is the air permeability of the water-invaded gas reservoir, and R wg is the water-gas mass ratio of water-invaded gas reservoir, ρ gsc is the density of natural gas under standard conditions.

[0043] Step S130, determining a first viscosity function between the viscosity of the natural gas and the formation pressure, a first volume function between the volume coefficient of the natural gas and the formation pressure, and a first permeability function between the relative permeability of the natural gas and the formation pressure.

[0044] Wherein, step S130 may include determining a first viscosity function and a first volume function, and may specifically include step S131.

[0045] Step S131, fitting a first viscosity function between the viscosity of natural gas and the formation pressure and a first volume function between the volume coefficient of natural gas and the formation pressure based on the historical high-pressure physical property test data of horizontal wells in water-invaded gas reservoirs.

[0046] In one embodiment, the viscosity μ of natural gas can be fitted based on the high-pressure physical property test data of historical horizontal wells on site, or based on the experimental data provided by the laboratory. g And the volume factor B g The relationship between the change of the target parameters (such as the viscosity and volume coefficient of natural gas) and the formation pressure p respectively. Among them, the historical horizontal wells are the horizontal wells with relatively complete data in the water-invaded gas reservoir, while the horizontal characteristic wells are the horizontal wells with relatively insufficient data in the water-invaded gas reservoir. Therefore, some historical data of the historical horizontal wells can be used to fit the relationship between the change of the target parameters (such as the viscosity and volume coefficient of natural gas) and the formation pressure, and then infer the formation pressure of the horizontal characteristic wells.

[0047] The fitting diagram can be referred to Figure 2 As shown, the specific formula is as follows:

[0048] μ g=0.0134*e 0.0135*p ,

[0049] B g =0.1376*p -0.0975 ,

[0050] Where: the unit of formation pressure p is MPa; the viscosity of natural gas is μ g The unit is cp.

[0051] Wherein, step S130 may include determining a first permeability function, and specifically may include steps S132 - S135 .

[0052] Step S132, determining a second viscosity function between the viscosity of the formation water and the formation pressure and a second volume function between the volume coefficient of the formation water and the formation pressure according to the formation temperature and salinity of the formation water in the horizontal characteristic well.

[0053] Wherein, determining the second viscosity function may include:

[0054] According to the formation water temperature T F (in °F) and salinity w s (Unit: %), and the viscosity of formation water is determined by the following formula: w The second viscosity function between the formation pressure p:

[0055]

[0056] in,

[0057] Wherein, determining the second volume function may include:

[0058] According to the formation water temperature T F , the viscosity of formation water B is determined by the following formula w The second viscosity function between the formation pressure p:

[0059] B w =(1-a)*(1-b),

[0060] Where a = 10 -7 *(3.58922+0.0195301*T F )*p+10 -10 *(2.25341+0.00172834*T F )*p, b=0.010001-(0.000133391+0.000000550654*T F )*T F .

[0061] in, Figure 3 The curves showing the changes of volume coefficient and viscosity of formation water with formation pressure are shown.

[0062] Step S133, determining the first relative permeability function between the gas-water relative permeability ratio and the formation pressure based on the first viscosity function, the first volume function, the second viscosity function, the second volume function and the water-gas ratio between formation water and natural gas, wherein the gas-water relative permeability ratio is the ratio between the relative permeability of natural gas and the relative permeability of formation water.

[0063] Among them, determine The first relative permeability function may include:

[0064] According to the first viscosity function μ g (p), the first volume function B g (p), the second viscosity function μ w (p), the second volume function B w (p) and water vapor ratio WGR (in m 3 / m 3 ), the gas-water relative permeability ratio is determined by the following formula The first relative permeability function k between the formation pressure p rg / k rw :

[0065]

[0066] In one embodiment, the gas-water relative permeability ratio can be obtained according to the definition of the produced water-gas ratio when the water-gas ratio WGR is 0.00025 cubic meters / cubic meters. The relationship between it and the formation pressure p is:

[0067]

[0068] Step S134, fitting a second permeability function between the relative permeability of natural gas and water saturation and a second relative permeability function between the gas-water relative permeability ratio and water saturation based on the core relative permeability experimental data of the historical horizontal wells.

[0069] In one embodiment, if Figure 4 As shown in the figure, based on the core relative permeability experiment, according to the initial water saturation S of the gas reservoir w , corrected to obtain the actual gas-water two-phase permeability curve, that is, to obtain the second permeability function k rg and the third permeability function k between the relative permeability of formation water and water saturation rw :

[0070]

[0071]

[0072] Then, combined with the gas-water two-phase permeability curve, the gas-water relative permeability ratio is obtained. and water saturation S w The relationship between the second relative permeability function is:

[0073]

[0074] in, With S w There are two ways to obtain the mathematical relationship curve:

[0075] 1. Through phase permeability experiments, a series of S w K rg With k rw , and then fit k according to these scattered points rg , k rw as well as With S w 3 relationship curves.

[0076] 2. Through phase permeability experiments, a series of S w K rg With k rw , and then according to these scattered points, first fit k rg , k rw With S w The two relationship curves are then calculated by fitting formula With S w The relationship curve of , that is, the third relationship curve is obtained.

[0077] There will be some error between these two treatment methods, but the impact is not significant.

[0078] Step S135: according to the second permeability function k rg , The first relative permeability function and the second relative permeability function are used to determine the relative permeability of natural gas. The first permeability function between and the formation pressure p.

[0079] In the above embodiment where the water-gas ratio is 0.00025 cubic meters, the water saturation S w The saturation function of the formation pressure p is as follows: Figure 5 shown.

[0080] S w =0.6324*p 0.0287 .

[0081] Combined with the second permeability function k of natural gas mentioned above rg and water saturation S w The relationship between the second permeability function k rg The relationship with the formation pressure p is as follows: Figure 6 shown.

[0082] k rg =0.5252*p -0.43 .

[0083] Step S140, determining the formation pressure according to the gas-water two-phase pseudo-pressure function, the first productivity function, the second productivity function, the first viscosity function, the first volume function and the first permeability function.

[0084] Among them, step S140 may include steps S141-S142.

[0085] Step S141, determining a third productivity function of a horizontal characteristic well in a water-invaded gas reservoir with respect to formation pressure according to the gas-water two-phase pseudo-pressure function, the first productivity function and the second productivity function.

[0086] Among them, the gas-water two-phase pseudo-pressure function is defined as:

[0087]

[0088] Where: is the pseudo pressure; ρ g is the density of natural gas under formation conditions (in g / cm 3 );ρ w is the density of formation water under formation conditions (in g / cm 3 ).

[0089] Then, by adding the first productivity function in the horizontal direction and the second productivity function in the vertical direction, the third productivity function of the horizontal characteristic well of the water-invaded gas reservoir with respect to the formation pressure can be obtained:

[0090]

[0091] Step S142, determining the formation pressure through the first viscosity function, the first volume function, the first permeability function and the third productivity function.

[0092] According to the first viscosity function μ g (p r ), the first volume function B g (p r ) and the first permeability function K rg (p r ), in the third productivity function, the formation pressure p rTaking the derivative, we obtain the following ordinary differential equation for formation pressure:

[0093]

[0094] Among them, ρ g (p r )=ρ gsc B g (p r ).

[0095] In one embodiment, the Newton iteration method or the bisection method may be used to solve the ordinary differential equation.

[0096] For example, in one embodiment, a computer program software may be used to solve the ordinary differential equation using the bisection method, and the main program Visual Basic code is:

[0097]

[0098] In the absence of formation pressure data in gas wells, the present invention establishes a method for calculating the average formation pressure of water-invaded gas reservoirs suitable for horizontal wells, solving the problem of lack of static pressure test data in existing methods for calculating dynamic reserves of water-invaded gas reservoirs.

[0099] On the other hand, the present invention also provides a method for determining the dynamic reserves of a water-invaded gas reservoir, the overall flow chart of which can be shown as follows: Figure 7 shown.

[0100] 1) Prepare a set of high-pressure physical property calculation equations for natural gas and formation water based on historical high-pressure physical property experimental data;

[0101] 2) Based on the core relative permeability experiment, according to the initial water saturation S of the gas reservoir wi , corrected to obtain the actual gas-water relative permeability relationship (k rg ~S w With k rw ~S w );

[0102] 3) Obtain the isothermal compressibility coefficient of the fluid through the overburden porosity test, where the isothermal compressibility coefficient refers to the rate of change of fluid volume under unit pressure difference. The overburden porosity test of gas is to obtain the isothermal compressibility coefficient C of the gas. g The purpose of the water overburden permeability test is to obtain the isothermal compressibility coefficient C of water. w ;

[0103] 4) Based on the expression of the gas-water ratio in the production data (wherein the production data specifically includes daily gas production, daily water production, cumulative gas production, cumulative water production, etc.) and the gas-water two-phase permeability curve, the relationship between the average water saturation and the gas phase relative permeability and the formation pressure (S w=f(p) and k rg =f(p));

[0104] 5) Based on the seepage theory and the gas-water two-phase production capacity equation, a differential equation for solving the average formation pressure of water-invaded gas reservoirs applicable to horizontal characteristic wells is derived;

[0105] 6) Use Newton iteration method or bisection method to solve the differential equation and obtain the average formation pressure p of the water-driven gas reservoir at a certain time;

[0106] 7) Based on the relationship between water saturation and formation pressure, first calculate the average water saturation S w Then, the dynamic reserve G and water invasion W are solved by using the material balance equation of water drive gas reservoir. e .

[0107] Specifically, Figure 8 As shown, the method for determining the dynamic reserves of a water-invaded gas reservoir of the present invention may include steps S210-S230.

[0108] Step S210: determining the formation pressure of the water-invaded gas reservoir according to the method for determining the formation pressure of the water-invaded gas reservoir described above.

[0109] In one embodiment, the formation pressure is obtained to be 30.4 MPa.

[0110] Step S220, determining the water saturation of the water-invaded gas reservoir according to the formation pressure of the water-invaded gas reservoir and the saturation function between the water saturation of the water-invaded gas reservoir and the formation pressure.

[0111] Among them, step S220 may include steps S221-S226.

[0112] Step S221, fitting a first viscosity function between the viscosity of natural gas and the formation pressure and a first volume function between the volume coefficient of natural gas and the formation pressure based on the historical high-pressure physical property test data of horizontal wells in water-invaded gas reservoirs.

[0113] In one embodiment, the viscosity μ of the natural gas in the horizontal characteristic well can be fitted based on the high-pressure physical property test data of the historical horizontal well on site, or based on the experimental data provided by the laboratory. g And the volume factor B g The relationship between them and the formation pressure p is as follows: Figure 2 shown.

[0114] μ g =0.0134*e 0.0135*p ,

[0115] B g =0.1376*p -0.0975 ,

[0116] Where: the unit of formation pressure p is MPa; the viscosity of natural gas is μ g The unit is cp.

[0117] Step S222, determining a second viscosity function between the viscosity of the formation water and the formation pressure and a second volume function between the volume coefficient of the formation water and the formation pressure according to the formation temperature and salinity of the formation water in the horizontal characteristic well.

[0118] Wherein, determining the second viscosity function may include:

[0119] According to the formation water temperature T F (in °F) and salinity w s (Unit: %), and the viscosity of formation water is determined by the following formula: w The second viscosity function between the formation pressure p:

[0120]

[0121] in,

[0122] Wherein, determining the second volume function may include:

[0123] According to the formation water temperature T F , the viscosity of formation water B is determined by the following formula w The second viscosity function between the formation pressure p:

[0124] B w =(1-a)*(1-b),

[0125] Where a = 10 -7 *(3.58922+0.0195301*T F )*p+10 -10 *(2.25341+0.00172834*T F )*p, b=0.010001-(0.000133391+0.000000550654*T F )*T F .

[0126] in, Figure 3 The curves showing the changes of volume coefficient and viscosity of formation water with formation pressure are shown.

[0127] Step S223, determining a first relative permeability function between the gas-water relative permeability ratio and the formation pressure based on the first viscosity function, the first volume function, the second viscosity function, the second volume function, and the water-gas ratio between formation water and natural gas, wherein the gas-water relative permeability ratio is the ratio between the relative permeability of natural gas and the relative permeability of formation water.

[0128] Among them, determine The first relative permeability function may include:

[0129] According to the first viscosity function μ g (p), the first volume function B g (p), the second viscosity function μ w (p), the second volume function B w (p) and water vapor ratio WGR (in m 3 / m 3 ), the gas-water relative permeability ratio is determined by the following formula The first relative permeability function between and the formation pressure p:

[0130]

[0131] In one embodiment, the gas-water relative permeability ratio can be obtained according to the definition of the produced water-gas ratio when the water-gas ratio WGR is 0.00025 cubic meters / cubic meters. The relationship between it and the formation pressure p is:

[0132]

[0133] Step S224, fitting a second relative permeability function between the gas-water relative permeability ratio and the water saturation based on the core relative permeability experimental data of the historical horizontal wells.

[0134] In one embodiment, if Figure 4 As shown in Figure 2, the gas-water relative permeability ratio can be obtained based on the core relative permeability experiment. and water saturation S w The relationship between the second relative permeability function is:

[0135]

[0136] Step S225, according to The first relative permeability function and the second relative permeability function are used to determine the water saturation and S of the water-invaded gas reservoir. w Saturation function between formation pressure p.

[0137] In the above embodiment where the water-gas ratio is 0.00025 cubic meters, the water saturation S wThe saturation function of the formation pressure p is as follows: Figure 5 shown.

[0138] S w =0.6324*p 0.0287 .

[0139] Step S226, determining the water saturation of the water-invaded gas reservoir according to the formation pressure and saturation function of the water-invaded gas reservoir.

[0140] In the above embodiment, according to the obtained formation pressure of 30.4 MPa, the average water saturation of the gas reservoir is obtained as 0.7 using the obtained saturation function.

[0141] Step S230, determining the dynamic reserves of the water-invaded gas reservoir according to the material balance equation of the water-invaded gas reservoir and the water saturation of the water-invaded gas reservoir.

[0142] Among them, determining the dynamic reserves of water-invaded gas reservoirs may include:

[0143] According to the cumulative production of natural gas in water-invaded gas reservoirs G p , Volume coefficient B g and the volume coefficient B at the original formation pressure gi , the cumulative production of formation water in water-invaded gas reservoirs W p , Volume coefficient B w and isothermal compressibility C w (Unit: MPa -1 ), pressure drop Δp of water-invaded gas reservoir, isothermal compressibility coefficient C p (Unit: MPa -1 ), water saturation S w and initial water saturation S wi The water invasion amount W of the water-invaded gas reservoir is determined by the following formula: e (Unit is 10 4 m 3 ) and dynamic reserve G (unit: 10 4 m 3 ):

[0144]

[0145] W e =W p B w +GB gi (S w -S wi ).

[0146] In one embodiment, based on the material balance equation of the water-invaded gas reservoir, according to the average water saturation of the gas reservoir being 0.7, the water invasion volume of the water-invaded gas reservoir is calculated to be 297,000 cubic meters, and the dynamic reserves of the water-invaded gas reservoir are approximately 310 million cubic meters.

[0147] Through the above scheme, the present invention solves the problem of large errors in the commonly used dynamic reserve calculation methods on site (such as the water invasion replacement coefficient plate method and the apparent geological reserve method). At the same time, when the formation pressure is known, the average water saturation can be directly calculated based on the relationship between the average water saturation and the formation pressure at a certain moment, and then the dynamic reserve can be obtained based on the material balance equation of the water-invaded gas reservoir. The problem of difficult parameter acquisition and large visual error in the existing dynamic reserve calculation method of the water-invaded gas reservoir is solved.

[0148] On the other hand, the present invention also provides a device 300 for determining the formation pressure of a water-invaded gas reservoir, such as Figure 8 As shown, the determining device 300 may include:

[0149] The first productivity function determination module 310 is used to determine the first productivity function between the pressure at the outer boundary of the gas reservoir and the pressure at the junction of the inner and outer seepage fields in any horizontal plane in the horizontal characteristic well according to the daily gas production of the natural gas in the horizontal characteristic well in the water-invaded gas reservoir under standard conditions, the length of the horizontal characteristic well, and the length of the major axis of the oil drainage ellipse;

[0150] The second productivity function determination module 320 is used to determine the second productivity function between the pressure at the junction of the inner and outer seepage fields of the horizontal characteristic well in any vertical plane and the pressure at the bottom of the well according to the daily gas production, relative permeability and viscosity of the natural gas under standard conditions and the length and wellbore radius of the horizontal characteristic well;

[0151] The natural gas physical property parameter determination module 330 is used to determine a first viscosity function between the viscosity of the natural gas and the formation pressure, a first volume function between the volume coefficient of the natural gas and the formation pressure, and a first permeability function between the relative permeability of the natural gas and the formation pressure; and

[0152] The formation pressure determination module 340 is used to determine the formation pressure according to the gas-water two-phase pseudo-pressure function, the first productivity function, the second productivity function, the first viscosity function, the first volume function and the first permeability function.

[0153] On the other hand, the present invention also provides a device 400 for determining the dynamic reserve of a water-invaded gas reservoir, such as Fig. 9 As shown, the determining device 400 may include:

[0154] The device 300 for determining the formation pressure of a water-invaded gas reservoir described above is used to determine the formation pressure of a water-invaded gas reservoir;

[0155] A water saturation determination module 410, for determining the water saturation of the water-invaded gas reservoir according to the formation pressure of the water-invaded gas reservoir and a saturation function between the water saturation of the water-invaded gas reservoir and the formation pressure; and

[0156] The dynamic reserve determination module 420 is used to determine the dynamic reserve of the water-invaded gas reservoir based on the material balance equation of the water-invaded gas reservoir and the water saturation of the water-invaded gas reservoir.

[0157] The beneficial effects of the device for determining the formation pressure and dynamic reserves of a water-invaded gas reservoir provided by the present invention can be referred to the above description of the method for determining the formation pressure and dynamic reserves of a water-invaded gas reservoir, which will not be repeated here.

[0158] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0159] The above are only embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included within the scope of the claims of the present application.

Claims

1. A method for determining the formation pressure of a water-invaded gas reservoir, characterized in that: The determination method comprises: Determine a first productivity function between the pressure at the outer boundary of the gas reservoir and the pressure at the junction of the inner and outer seepage fields in any horizontal plane in the horizontal characteristic well according to the daily gas production of the natural gas in the horizontal characteristic well in the water-invaded gas reservoir under standard conditions, the length of the horizontal characteristic well, and the length of the major axis of the oil drainage ellipse; Determine a second productivity function between the pressure at the junction of the inner and outer seepage fields of the horizontal feature well in any vertical plane and the pressure at the bottom of the well according to the daily gas production, relative permeability and viscosity of the natural gas under standard conditions and the length and wellbore radius of the horizontal feature well; determining a first viscosity function between the viscosity of the natural gas and the formation pressure, a first volume function between the volume coefficient of the natural gas and the formation pressure, and a first permeability function between the relative permeability of the natural gas and the formation pressure; and The formation pressure is determined according to the gas-water two-phase pseudo-pressure function, the first productivity function, the second productivity function, the first viscosity function, the first volume function and the first permeability function.

2. The determination method according to claim 1, characterized in that: Determining the first capacity function includes: According to the length L of the horizontal characteristic well and the length 2a of the major axis of the oil discharge ellipse, the daily gas production q gsc , the pressure at the outer boundary of the gas reservoir in any horizontal plane in the horizontal characteristic well is determined by the following formula: Pressure at the interface between internal and external seepage fields The first capacity function between: Wherein, h is the thickness of the water-invaded gas reservoir, K is the air permeability of the water-invaded gas reservoir, R wg is the water-gas mass ratio of the water-invaded gas reservoir, ρ gsc is the density of the natural gas at standard conditions; and / or Determining the second capacity function includes: According to the length L of the horizontal characteristic well and the wellbore radius r w The daily gas production of natural gas under standard conditions is q gsc , relative permeability K rg and viscosity μ g The pressure at the junction of the internal and external seepage fields of the horizontal characteristic well in any vertical plane is determined by the following formula: The pressure at the bottom of the well The second capacity function between: Wherein, h is the thickness of the water-invaded gas reservoir, K is the air permeability of the water-invaded gas reservoir, R wg is the water-gas mass ratio of the water-invaded gas reservoir, ρ gsc is the density of the natural gas under standard conditions.

3. The determination method according to claim 1, characterized in that: Determining the first viscosity function and the first volume function includes: According to the high-pressure physical property test data of the historical horizontal wells in the water-invaded gas reservoir, a first viscosity function between the viscosity of the natural gas and the formation pressure and a first volume function between the volume coefficient of the natural gas and the formation pressure are fitted.

4. The determination method according to claim 3, characterized in that: Determining the first permeability function includes: Determining a second viscosity function between the viscosity of the formation water and the formation pressure and a second volume function between the volume coefficient of the formation water and the formation pressure according to the formation temperature and salinity of the formation water in the horizontal characteristic well; Determine a first relative permeability function between a gas-water relative permeability ratio and the formation pressure according to the first viscosity function, the first volume function, the second viscosity function, the second volume function, and a water-gas ratio between the formation water and the natural gas, wherein the gas-water relative permeability ratio is a ratio between the relative permeability of the natural gas and the relative permeability of the formation water; Fitting a second permeability function between the relative permeability of the natural gas and water saturation and a second relative permeability function between the gas-water relative permeability ratio and the water saturation according to the core relative permeability experimental data of the historical horizontal well; and A first permeability function between the relative permeability of the natural gas and the formation pressure is determined according to the second permeability function, the first relative permeability function, and the second relative permeability function.

5. The determination method according to claim 4, characterized in that: Determining the second viscosity function includes: determining the second viscosity function according to the formation temperature T of the formation water F and salinity w s , the viscosity of the formation water is determined by the following formula μ w The second viscosity function with the formation pressure p: in, and / or Determining the second volume function includes: According to the formation temperature T of the formation water F The viscosity of the formation water is determined by the following formula: w The second viscosity function with the formation pressure p: B w =(1-a)*(1-b), where a = 10 -7 *(3.58922 + 0.0195301*T F )*p + 10 -10 *(2.25341 + 0.00172834*T F )*p, b = 0.010001 - (0.000133391 + 0.000000550654*T F )*T F .

6. The determination method according to claim 4, characterized in that: Determining the first relative permeability function includes: According to the first viscosity function μ g (p), the first volume function B g (p), the second viscosity function μ w (p), the second volume function B w (p) and the water-gas ratio WGR, the gas-water relative permeability ratio is determined by the following formula The first relative permeability function with the formation pressure:

7. The determination method according to claim 1, characterized in that: Determining the formation pressure includes: Determining a third productivity function of the horizontal characteristic well of the water-invaded gas reservoir with respect to the formation pressure according to the gas-water two-phase pseudo-pressure function, the first productivity function, and the second productivity function; and The formation pressure is determined by the first viscosity function, the first volume function, the first permeability function, and the third productivity function.

8. A method for determining the dynamic reserves of a water-invaded gas reservoir, characterized in that: The determination method comprises: Determine the formation pressure of the water-invaded gas reservoir according to the method for determining the formation pressure of the water-invaded gas reservoir according to any one of claims 1 to 7; determining the water saturation of the water-invaded gas reservoir according to the formation pressure of the water-invaded gas reservoir and a saturation function between the water saturation of the water-invaded gas reservoir and the formation pressure; and The dynamic reserves of the water-invaded gas reservoir are determined according to the material balance equation of the water-invaded gas reservoir and the water saturation of the water-invaded gas reservoir.

9. The determination method according to claim 8, characterized in that: Determining the saturation function includes: According to the high-pressure physical property test data of the historical horizontal wells in the water-invaded gas reservoir, a first viscosity function between the viscosity of the natural gas and the formation pressure and a first volume function between the volume coefficient of the natural gas and the formation pressure are fitted; Determining a second viscosity function between the viscosity of the formation water and the formation pressure and a second volume function between the volume coefficient of the formation water and the formation pressure according to the formation temperature and salinity of the formation water in the horizontal characteristic well; Determine a first relative permeability function between a gas-water relative permeability ratio and the formation pressure according to the first viscosity function, the first volume function, the second viscosity function, the second volume function, and a water-gas ratio between the formation water and the natural gas, wherein the gas-water relative permeability ratio is a ratio between the relative permeability of the natural gas and the relative permeability of the formation water; Fitting a second relative permeability function between the gas-water relative permeability ratio and the water saturation according to the core relative permeability experimental data of the historical horizontal well; and A saturation function between the water saturation of the water-invaded gas reservoir and the formation pressure is determined according to the first relative permeability function and the second relative permeability function.

10. The determination method according to claim 8, characterized in that: Determining the dynamic reserves of the water-invaded gas reservoir includes: according to the cumulative production G of the natural gas in the water-invaded gas reservoir p , Volume coefficient B g and the volume coefficient B at the original formation pressure gi , the cumulative production of formation water in the water-invaded gas reservoir is W p , Volume coefficient B w and isothermal compressibility C w , the pressure drop Δp and isothermal compressibility coefficient C of the water-invaded gas reservoir p , water saturation S w and initial water saturation S wi , the dynamic reserve G of the water-invaded gas reservoir is determined by the following formula: IN e =In p B w +GB gi (S w -S wi ), Among them, W e is the water invasion amount of the water-invaded gas reservoir.

11. A device for determining the formation pressure of a water-invaded gas reservoir, characterized in that: The determining device comprises: A first productivity function determination module is used to determine a first productivity function between the pressure at the outer boundary of the gas reservoir and the pressure at the junction of the inner and outer seepage fields in any horizontal plane in the horizontal feature well according to the daily gas production of the natural gas in the horizontal feature well in the water-invaded gas reservoir under standard conditions, the length of the horizontal feature well, and the length of the major axis of the oil drainage ellipse; A second productivity function determination module is used to determine a second productivity function between the pressure at the junction of the inner and outer seepage fields of the horizontal feature well in any vertical plane and the pressure at the bottom of the well according to the daily gas production, relative permeability and viscosity of the natural gas under standard conditions and the length and wellbore radius of the horizontal feature well; a natural gas physical property parameter determination module, used to determine a first viscosity function between the viscosity of the natural gas and the formation pressure, a first volume function between the volume coefficient of the natural gas and the formation pressure, and a first permeability function between the relative permeability of the natural gas and the formation pressure; and The formation pressure determination module is used to determine the formation pressure according to the gas-water two-phase pseudo-pressure function, the first productivity function, the second productivity function, the first viscosity function, the first volume function and the first permeability function.

12. A device for determining the dynamic reserve of a water-invaded gas reservoir, characterized in that: The determining device comprises: The device for determining the formation pressure of a water-invaded gas reservoir according to claim 11, used to determine the formation pressure of the water-invaded gas reservoir; a water saturation determination module, configured to determine the water saturation of the water-invaded gas reservoir according to the formation pressure of the water-invaded gas reservoir and a saturation function between the water saturation of the water-invaded gas reservoir and the formation pressure; and The dynamic reserve determination module is used to determine the dynamic reserve of the water-invaded gas reservoir based on the material balance equation of the water-invaded gas reservoir and the water saturation of the water-invaded gas reservoir.

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