Method and device for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs

Abstract

The present invention provides a method and device for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir. The prediction method comprises: obtaining a distance r from a critical boundary to the horizontal well; c , the critical boundary is the gas-water boundary corresponding to the moving speed of the water tongue point of the gas-water boundary is 0; obtain the distance a from the initial gas-water boundary to the horizontal well, and determine the distance a from the initial gas-water boundary to the horizontal well and r c The size relationship; if a>r c , then the time t1 of the gas-water boundary moving from the initial gas-water boundary to the critical boundary and the time t2 of the gas-water boundary water tongue point moving from the critical boundary to the horizontal well are obtained. bt =t1+t2 to determine the water breakthrough time t of the horizontal well bt ; If a<r c , then the time for the water tongue point of the gas-water boundary to move from the initial gas-water boundary to the horizontal well is obtained, that is, the water breakthrough time t of the horizontal well is obtained. bt The present invention can efficiently determine the water breakthrough time of a horizontal well.

Description

Technical Field

[0001] The invention relates to a method and a device for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir, belonging to the field of determining water breakthrough time of a gas well. Background Art

[0002] Water intrusion will harm the development of gas reservoirs. After water is seen in a gas well (horizontal well), if the gas flow rate is too low to carry the liquid out, the gas well will continue to accumulate liquid. At the same time, the gas-liquid mixture will increase the pressure loss in the wellbore, resulting in lower gas well production, forming a vicious cycle until the gas well is completely flooded, thereby reducing the recovery rate of the gas reservoir. Therefore, accurately predicting the time when water will appear in a gas well is important for the formulation of a gas reservoir development plan.

[0003] At present, there are usually three methods for predicting the water breakthrough time of water-driven gas reservoirs. The first is to use numerical simulation methods, which is not convenient for actual on-site operation, has many parameters and is complex to operate. The second is to use the volume balance principle, but the required water body parameters (such as shape, etc.) are difficult to obtain accurately in practice, so the error is large. The third is based on the porous media fluid particle seepage theory. However, the existing calculation methods of this type only study the tongue-entry process of water particles, which has a large error. Summary of the invention

[0004] The present invention provides a method and device for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir, which can effectively predict the water breakthrough time of the horizontal well and has the advantages of simple operation, etc., and can effectively overcome the defects of the prior art.

[0005] In one aspect of the present invention, a method for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir is provided, comprising: obtaining a distance r from a critical boundary to the horizontal well; c , the critical boundary is the gas-water boundary corresponding to the moving speed of the water tongue point of the gas-water boundary is 0; obtain the distance a from the initial gas-water boundary to the horizontal well, and determine the distance a from the initial gas-water boundary to the horizontal well and r c The size relationship; if a>r c , then the time t of the gas-water boundary moving from the initial gas-water boundary to the critical boundary is obtained 1 , the time t for the water tongue point at the gas-water boundary to move from the critical boundary to the horizontal well 2 , according to t bt =t 1 +t 2 Determine the water breakthrough time t of horizontal well bt ; If a<r c , then the time for the water tongue point of the gas-water boundary to move from the initial gas-water boundary to the horizontal well is obtained, that is, the water breakthrough time t of the horizontal well is obtained. bt .

[0006] According to one embodiment of the present invention, the distance r from the critical boundary to the horizontal well is obtained. c The process includes: obtaining v w The relationship between r and v w is the moving speed of the water tongue point at the gas-water boundary, r is the distance from the gas-water boundary to the horizontal well; according to v w The relationship between v and r is determined by w = 0, the corresponding r value, the v w = 0, the corresponding r value is r c .

[0007] According to one embodiment of the present invention, based on the seepage mechanics theory that the seepage model of a horizontal well is an ellipsoidal type, v is obtained. g The relationship between r and v g is the gas phase seepage velocity corresponding to the horizontal well; according to the gas-water motion equation based on the gas-water two-phase seepage law, gravity influence and gas non-Darcy effect, v is obtained w With v g According to the relationship between v w With v g The relationship between g The relationship between v and r is obtained w The relationship between r.

[0008] According to one embodiment of the present invention, the distance r from the critical boundary to the horizontal well is obtained. c The process includes:

[0009] Obtain characteristic parameters of the horizontal well, wherein the characteristic parameters include gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal section length L of horizontal well, reservoir thickness h;

[0010] according to Determine r c ;

[0011] in,

[0012]

[0013]

[0014]

[0015] g is the acceleration of gravity; β is the coefficient describing the turbulence effect of porous media.

[0016] According to one embodiment of the present invention, the process of determining the water breakthrough time of a horizontal well includes:

[0017] Obtain characteristic parameters of the horizontal well, wherein the characteristic parameters include gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , water phase viscosity μ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal well horizontal section length L, reservoir thickness h, porosity φ, irreducible water saturation S wi , residual gas saturation S gr , water intrusion speed v w ', gas phase relative permeability k under bound water rgwi , water phase relative permeability k under residual gas rwgr ;

[0018] If a>r c According to formula (22), the water breakthrough time t of the horizontal well is determined bt :

[0019]

[0020] If a<r c According to formula (25), the water breakthrough time t of the horizontal well is determined bt :

[0021]

[0022] in,

[0023]

[0024] D=M rgwi v w '+B;

[0025]

[0026]

[0027]

[0028] g is the acceleration of gravity; β is the coefficient describing the turbulence effect of porous media.

[0029] A method for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir provided in one embodiment of the present invention comprises:

[0030] Obtain characteristic parameters of the horizontal well, wherein the characteristic parameters include gas phase density ρg , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , water phase viscosity μ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal well horizontal section length L, reservoir thickness h, porosity φ, irreducible water saturation S wi , residual gas saturation S gr , water intrusion speed v w ', gas phase relative permeability k under bound water rgwi , water phase relative permeability k under residual gas rwgr ;

[0031] according to Determine r c ;

[0032] Determine a and r c The size relationship, and

[0033] If a>r c , according to formula (22) to determine the water breakthrough time t bt ;

[0034]

[0035] If a<r c , according to formula (25) to determine the water breakthrough time t bt :

[0036]

[0037] in,

[0038]

[0039] D=M rgwi v w '+B;

[0040]

[0041]

[0042]

[0043] g is the acceleration of gravity; β is the coefficient describing the turbulence effect of porous media.

[0044] Another aspect of the present invention provides a device for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir, comprising:

[0045] A characteristic parameter acquisition module is used to obtain the characteristic parameters of the horizontal well, and the characteristic parameters include: gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , water phase viscosity μ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal well horizontal section length L, reservoir thickness h, porosity φ, irreducible water saturation S wi , residual gas saturation S gr , water intrusion speed v w ', gas phase relative permeability k under bound water rgwi , water phase relative permeability k under residual gas rwgr , the distance a from the initial gas-water boundary to the horizontal well;

[0046] r c Determine the module for Determine r c ;

[0047] Water breakthrough time determination module, used to determine a and r c The size relationship, and

[0048] If a>r c , according to formula (22) to determine the water breakthrough time t bt ;

[0049]

[0050] If a<r c , according to formula (25) to determine the water breakthrough time t bt :

[0051]

[0052] in,

[0053]

[0054] D=M rgwi v w '+B;

[0055]

[0056]

[0057]

[0058] g is the acceleration of gravity; β is the coefficient describing the turbulence effect of porous media.

[0059] According to another aspect of the present invention, there is provided an electronic device, comprising: a processor, a memory and a computer program; wherein the computer program is stored in the memory and is configured to be executed by the processor to implement the above-mentioned method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs.

[0060] In another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored, and the computer program is executed by a processor to implement the above-mentioned method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs.

[0061] In another aspect of the present invention, a computer program product is provided, comprising a computer program, wherein the computer program is executed by a processor to implement the above-mentioned method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs.

[0062] The method for predicting the water breakthrough time of a horizontal well in an edge-water gas reservoir provided by the present invention realizes the prediction of the water breakthrough time of a horizontal well based on the movement state of water particles at the gas-water boundary at different stages. It can determine the water breakthrough time of a horizontal well more accurately and efficiently, and at the same time has the advantages of being simple and easy to operate, and is convenient for promotion and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a schematic diagram of a horizontal well in an edge water gas reservoir in one embodiment of the present invention;

[0064] Figure 2 It is a schematic diagram of an approximately elliptical equipotential surface of a horizontal well in one embodiment of the present invention. DETAILED DESCRIPTION

[0065] In order to enable those skilled in the art to better understand the scheme of the present invention, the present invention is further described in detail below. The specific implementation methods listed below are only for describing the principles and features of the present invention. The examples are only used to explain the present invention and are not intended to limit the scope of the present invention. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention.

[0066] At present, there are usually three methods for predicting the water breakthrough time of water-driven gas reservoirs. The first method is to use numerical simulation methods for research. This method is not convenient for actual field operation, has many parameters and is relatively complicated to operate. The second method is to use the volume balance principle, but the parameters of the required water body (such as shape, etc.) are difficult to obtain accurately in practice, so the error is large. The third method is based on the porous medium fluid particle seepage theory. However, the existing calculation methods of this type only study the tongue-intrusion process of water particles. However, when the reservoir inclination and the gas-water boundary are both large and the gas well production is small, according to the analysis of the gas-liquid motion equation, the driving force of the water particles at the gas-water boundary may be less than gravity. At this time, the tongue-intrusion speed of the water particles will not exist. Therefore, for the calculation of the water breakthrough time of the gas well, it is not enough to only consider the tongue-intrusion of the water particles. Based on this, the present invention proposes a method for predicting the water breakthrough time of horizontal wells in edge water gas reservoirs that comprehensively considers the influence of gas phase non-Darcy effect, reservoir inclination and water invasion speed. It can effectively determine the water breakthrough time of edge water gas reservoirs, and it is simple and easy to operate, which is convenient for promotion and application.

[0067] In addition, accurate prediction of water breakthrough time of horizontal wells in edge water gas reservoirs is of great theoretical and practical significance for the rational development of gas reservoirs. Research on water breakthrough time of horizontal wells in edge water gas reservoirs that comprehensively considers the influence of multiple factors has not been reported. The present invention analyzes the stress characteristics of water particles during water invasion and establishes a water breakthrough time prediction model for horizontal wells in edge water gas reservoirs that comprehensively considers the influence of gas phase non-Darcy effect, reservoir inclination and water invasion velocity. The model can effectively predict the water breakthrough time of horizontal wells with high credibility and is simple and easy to operate.

[0068] The method for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir provided by the present invention comprises: obtaining the distance r from the critical boundary to the horizontal well; c , the critical boundary is the gas-water boundary corresponding to the moving speed of the water tongue point of the gas-water boundary (i.e., the tongue advance speed) is 0; obtain the distance a from the initial gas-water boundary to the horizontal well, and judge the distance a from the initial gas-water boundary to the horizontal well and r c The size relationship; if a>r c , then the time t of the gas-water boundary moving from the initial gas-water boundary to the critical boundary is obtained 1 , the time t for the water tongue point at the gas-water boundary to move from the critical boundary to the horizontal well 2 , according to t bt =t 1 +t 2 Determine the water breakthrough time t of horizontal well bt ; If a<r c , then the time for the water tongue point of the gas-water boundary to move from the initial gas-water boundary to the horizontal well is obtained, that is, the water breakthrough time t of the horizontal well is obtained. bt .

[0069] According to the research of the present invention, considering the non-Darcy effect, reservoir inclination and water invasion velocity, there is a critical boundary in the process of water particles at the gas-water boundary migrating to the horizontal well. Specifically, when the driving force of the water particles at the water boundary is equal to the gravity, the water particles have no tongue-forward velocity (i.e., the tongue-forward velocity is 0), and the gas-water boundary at this time is the critical boundary. When a>r c (i.e., the distance from the initial gas-water boundary to the horizontal well is greater than the distance from the critical boundary to the horizontal well), the entire migration process of the water particle at the gas-water boundary is divided into two stages. The first stage is the stage of migration from the initial gas-water boundary to the critical boundary, and the second stage is the stage of migration from the critical boundary to the horizontal well. In the first stage, during the migration process to the horizontal well, the distance r from the gas-water boundary to the horizontal well is always greater than r c , the driving force on the water particle is smaller than the gravity component. At this time, there is only water invasion velocity but no tongue advance velocity. In the second stage, during the migration process to the horizontal well, the distance r from the gas-water boundary to the horizontal well is always less than r c , the driving force on the water particle is greater than the gravity component, at this time there is both water invasion velocity and tongue advance velocity; and when a<r c (i.e., the distance from the initial gas-water boundary to the horizontal well is less than the distance from the critical boundary to the horizontal well), during the migration process to the horizontal well, the distance r from the gas-water boundary to the horizontal well is always less than r c , the driving force on the water particle is greater than the gravity component, and at this time there is both water invasion velocity and tongue advance velocity. Therefore, the water breakthrough time of the horizontal well can be determined based on the migration state of the gas-water boundary at each stage.

[0070] In some embodiments, the distance r from the critical boundary to the horizontal well is obtained. c The process includes: obtaining v w The relationship between r and v w is the moving speed of the water tongue point at the gas-water boundary (i.e., tongue advance speed), r is the distance from the gas-water boundary to the horizontal well; according to v w The relationship between v and r is determined by w = 0 when the corresponding r value, v w = 0, the corresponding r value is r c .

[0071] In some preferred embodiments, based on the seepage mechanics theory that the seepage model of a horizontal well is an ellipsoidal type, v is obtained. g The relationship between r and v g is the gas phase seepage velocity corresponding to the horizontal well; according to the gas-water motion equation based on the gas-water two-phase seepage law, gravity influence and gas non-Darcy effect, v is obtained w With v g The relationship: According to v w With v g The relationship between gGet v by the relationship with r w The relationship between and r;

[0072] v g The relationship with r is:

[0073] v w With v g The relationship is:

[0074] Will Substitution And order Get v w The relationship with r is:

[0075]

[0076] according to Take v w = 0, calculate and determine the value of r, which is r c .

[0077] In specific implementation, characteristic parameters of the horizontal well can be obtained, including gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal section length L of horizontal well, reservoir thickness h; according to Determine r c .

[0078] In some embodiments, characteristic parameters of the horizontal well are obtained, and the characteristic parameters include gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , water phase viscosity μ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal well horizontal section length L, reservoir thickness h, porosity φ, irreducible water saturation S wi , residual gas saturation S gr , water intrusion speed v w ', gas phase relative permeability k under bound water rgwi , water phase relative permeability k under residual gas rwgr ;

[0079] If a>r cAccording to formula (22), the water breakthrough time t of the horizontal well is determined bt :

[0080]

[0081] If a<r c According to formula (25), the water breakthrough time t of the horizontal well is determined bt :

[0082]

[0083] A method for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir provided in one embodiment of the present invention comprises:

[0084] Obtain the characteristic parameters of the horizontal well, including gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , water phase viscosity μ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal well horizontal section length L, reservoir thickness h, porosity φ, irreducible water saturation S wi , residual gas saturation S gr , water intrusion speed v w ', gas phase relative permeability under bound water (gas phase relative permeability corresponding to bound water) k rgwi , relative permeability of water phase under residual gas (relative permeability of water phase corresponding to residual gas) k rwgr ;

[0085] according to Determine r c ;

[0086] Determine a and r c The size relationship, and

[0087] If a>r c , according to formula (22) to determine the water breakthrough time t bt ;

[0088]

[0089] If a<r c , according to formula (25) to determine the water breakthrough time t bt :

[0090]

[0091] The device for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir of the present invention is used to implement the above-mentioned method for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir, and comprises:

[0092] Characteristic parameter acquisition module, used to obtain the characteristic parameters of horizontal wells, including: gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , water phase viscosity μ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal well horizontal section length L, reservoir thickness h, porosity φ, irreducible water saturation S wi , residual gas saturation S gr , water intrusion speed v w ', gas phase relative permeability k under bound water rgwi , water phase relative permeability k under residual gas rwgr , the distance a from the initial gas-water boundary to the horizontal well;

[0093] r c Determine the module for Determine r c ;

[0094] Water breakthrough time determination module, used to determine a and r c The size relationship, and

[0095] If a>r c , according to formula (22) to determine the water breakthrough time t bt ;

[0096]

[0097] If a<r c , according to formula (25) to determine the water breakthrough time t bt :

[0098]

[0099] In addition, for a = r c In the case of a>r, we can c The water breakthrough time of the horizontal well can also be determined according to a<r c Determine the water breakthrough time of the horizontal well according to the situation of a = r c The corresponding t 1 =0, the water breakthrough time of the horizontal well can generally be determined directly according to formula (25).

[0100] In the present invention, the above-mentioned M rgwi, D, A, B, C are as follows:

[0101]

[0102] D=M rgwi v w '+B

[0103]

[0104]

[0105]

[0106] In the present invention, the above parameters can be measured by conventional technical means in the art, and no special restrictions are imposed on this. Unless otherwise specified, the units of the above parameters are shown in Table 1.

[0107] Table 1

[0108] parameter unit <![CDATA[Gas permeability of gas reservoir in original state, k g > mD Porosity, φ Dimensionless Reservoir thickness (effective reservoir thickness), h m <![CDATA[Gas density, ρ g > <![CDATA[kg / m 3 ]]> <![CDATA[Vapor viscosity (gas viscosity), μ g > mPa·s <![CDATA[Density of aqueous phase (formation water density), ρ w > <![CDATA[kg / m 3 ]]> <![CDATA[Viscosity of aqueous phase (formation water viscosity), μ w > mPa·s <![CDATA[Irreducible water saturation, S wi > Dimensionless <![CDATA[Residual gas saturation, S gr > Dimensionless <![CDATA[Restrained gas-phase relative permeability underwater, k rgwi > Dimensionless <![CDATA[Relative permeability of water phase under residual gas, k rwgr > Dimensionless <![CDATA[Gas volume factor, B g > <![CDATA[m 3 / sm 3 ]]> <![CDATA[Water invasion rate, v w ’]]> m / d Horizontal section length of horizontal well, L m Reservoir dip (formation dip), θ ° The distance from the initial gas-water boundary to the horizontal well, a m <![CDATA[Gas well production, q g > <![CDATA[m 3 / d]]> Gravitational acceleration, g <![CDATA[m / s 2 ]]> The coefficient describing the turbulence effect in porous media, β <![CDATA[m -1 ]]> <![CDATA[Distance from the critical boundary to the horizontal well, r c > m <![CDATA[Water breakthrough time of horizontal well, t bt > sky

[0109] The electronic device of the present invention comprises: a processor, a memory and a computer program; wherein the computer program is stored in the memory and is configured to be executed by the processor to implement the above-mentioned method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs.

[0110] The computer-readable storage medium provided by the present invention stores a computer program thereon, and the computer program is executed by a processor to implement the above-mentioned method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs. The computer-readable storage medium is, for example, a memory including instructions (computer program), and the instructions can be executed by the processor of the above-mentioned electronic device to complete the method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs. For example, the computer-readable storage medium is a non-temporary computer-readable storage medium, which can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, etc.

[0111] The computer program product provided by the present invention includes a computer program, which is executed by a processor to implement the above-mentioned method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs. According to an embodiment of the present application, at least one processor of the above-mentioned electronic device can read the computer program from a readable storage medium, and at least one processor executes the computer program so that the electronic device executes the above-mentioned method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs.

[0112] The present invention will be described more clearly in principle below with reference to the accompanying drawings. Figure 1 This is a schematic diagram of a horizontal well in an edge water gas reservoir. Figure 2 Figure 1 is a schematic diagram of the approximate elliptical equipotential surface of a horizontal well. To simplify the model derivation process, the following assumptions are made: (1) Figure 1As shown in Figure 1, there is a water-at-edge gas reservoir whose initial gas-water boundary is a straight line. There is a horizontal well at a distance a from the initial gas-water boundary. The length of the horizontal section of the horizontal well is L. The horizontal section of the horizontal well is perpendicular to the depth direction (or axial direction) of the horizontal well. The reservoir thickness is h, the reservoir dip is θ, and the other geometric parameters are shown in Figure 1. Figure 1 ( Figure 1 The gas in the equation represents the gas phase, and the water represents the water phase (i.e., formation water). The water phase and the gas phase infiltrate each other to form a transition phase); (2) During the gas-water seepage process, the influence of capillary force is ignored.

[0113] According to the seepage mechanics theory, the seepage model of a horizontal well is an ellipsoid. After the gas well starts production, the initial gas-water boundary moves toward the horizontal well and gradually advances toward the horizontal well in the form of a water tongue (generally toward the bottom of the horizontal well). Figure 1 and Figure 2 As shown in the figure, the equipotential surface of the horizontal well is approximately an elliptical torus. The front edge point M of the gas-water interface (gas-water boundary) (i.e., the front edge point of the water tongue) is on the surface. The line connecting the front edge point M of the gas-water boundary and the midpoint N of the horizontal well in the horizontal direction is approximately a straight line. The migration speed of the front edge point M of the water tongue (i.e., the tongue advance speed) is the largest. It first breaks through the midpoint N of the horizontal well, and the gas well begins to see water. The time from the initial gas-water boundary to the front edge point M of the water tongue breaking through the midpoint N of the horizontal well is the time when the horizontal well sees water. The gas permeability k of the original state of the gas reservoir is g It is the gas phase permeability of the gas reservoir before gas well production.

[0114] According to the law of gas-water two-phase seepage, the gas-water motion equation considering the influence of gravity and the non-Darcy effect (i.e. the gas-water motion equation based on the law of gas-water two-phase seepage, the influence of gravity and the non-Darcy effect of gas) is:

[0115]

[0116]

[0117] The units of the physical quantities (parameters) in equations (1) and (2) are Darcy units (also the International System of Units).

[0118] Ignoring the influence of capillary force, according to The units of each physical quantity (parameter) are converted into mine units (the subsequent process is calculated in mine units, and the mine units of each parameter are shown in Table 1 above), and the water phase seepage velocity (i.e. tongue advance velocity) v is obtained. w The calculation equation (also known as v w With v g )

[0119]

[0120] Among them, M rgw is the gas-water mobility ratio, dimensionless; β is the coefficient describing the turbulence effect of porous media, unit is m -1 , whose expression is:

[0121]

[0122]

[0123] To further simplify subsequent calculations, let:

[0124]

[0125]

[0126] Then formula (3) is transformed into:

[0127]

[0128] Therefore, we can use formula (8) as v w With v g The subsequent calculation process is carried out by using the relationship between g Less than ρ w , B is less than 0.

[0129] Based on the equipotential surface of the horizontal well, the elliptical torus is approximated (such as Figure 2 As shown in the figure, the leading edge point M of the gas-water interface (gas-water boundary) is on this surface, and the gas phase seepage velocity (or gas seepage velocity) v is obtained. g The calculation equation (also known as v g The relationship between (and r) is:

[0130]

[0131] Substituting equation (8) into equation (9), we can get v w The relationship with r is:

[0132]

[0133] To further simplify the subsequent calculations, let:

[0134]

[0135] Then formula (10) is transformed into:

[0136]

[0137] Therefore, we can use formula (12) as v w The relationship with r is used for subsequent calculations.

[0138] Considering the non-Darcy effect, reservoir inclination and water invasion velocity, there is a critical boundary in the process of water particles at the gas-water boundary migrating to the horizontal well, that is, when the driving force is equal to the gravity component, the water particles have no tongue velocity (i.e., v w =0), the corresponding gas-water boundary is called the critical boundary, and the distance from the critical boundary to the horizontal well is r c , v w =0 Substituting into formula (12), we get:

[0139]

[0140] In porous media, the true seepage velocity of a water particle is equal to its Darcy seepage velocity divided by φ, which satisfies:

[0141]

[0142] Where φ is the porosity; v is the Darcy seepage velocity, in m / d; the minus sign “-” in the formula indicates that the seepage velocity is opposite to the positive direction of the coordinate system.

[0143] Formula (14) can be transformed into:

[0144]

[0145] Considering the influence of residual gas and bound water, equation (15) is transformed as follows:

[0146]

[0147] Among them, S wi , S gr are irreducible water saturation and residual gas saturation, respectively.

[0148] Based on formula (16), the water breakthrough time of the horizontal well is determined according to the migration state of the gas-water boundary at each stage, as follows:

[0149] (a) a>r c

[0150] The entire migration process of water particles at the gas-water boundary is divided into two stages. The first stage is the stage of migration from the initial gas-water boundary to the critical boundary, and the second stage is the stage of migration from the critical boundary to the horizontal well. In the first stage, during the migration process to the horizontal well, the distance r from the gas-water boundary to the horizontal well is always greater than r c , the driving force on the water particle is smaller than the gravity component, and at this time only the water invasion velocity v w ', without tongue velocity v w In the second stage, during the migration to the horizontal well, the distance r from the gas-water boundary to the horizontal well is always less than r c , the driving force on the water particle is greater than the gravity component, at this time there is both water invasion velocity vw ', there is also a tongue velocity v w ;

[0151] Therefore, the water breakthrough time of the horizontal well is equal to the migration time of the first stage (i.e., the time for the gas-water boundary to move from the initial gas-water boundary to the critical boundary t 1 ) and the migration time of the second stage (i.e., the time it takes for the water tongue point at the gas-water boundary to move from the critical boundary to the horizontal well t 2 ), and the migration time is calculated based on formula (16):

[0152]

[0153] Substituting formula (12) into formula (17), we get:

[0154]

[0155] Rearranging formula (18) yields:

[0156]

[0157] To further facilitate calculation, let πr+L=x, r from 0 to r c Integral transformation from L to πr c +L integral, then equation (19) is transformed into:

[0158]

[0159] In general, k corresponding to the water tongue leading edge point M g k gwi , k w k wgr , k gwi is the relative permeability of the gas phase under bound water, k wgr is the relative permeability of water phase under residual gas, gas-water mobility ratio M rgw It can be expressed as:

[0160]

[0161] Among them, M rgwi It is the ratio of the gas phase mobility under bound water to the water phase mobility under residual gas; k rgwi k is the relative permeability of the gas phase under bound water, dimensionless; rwgr is the relative permeability of water phase under residual gas, dimensionless.

[0162] Substituting formula (21) into formula (20), we get:

[0163]

[0164] in,

[0165] D=M rgwi v w '+B (23)

[0166] (ii) a<r c

[0167] In this case, during the migration process to the horizontal well, the distance r from the gas-water boundary to the horizontal well is always less than r c , the driving force on the water particle is greater than the gravity component, at this time there is both water invasion velocity v w ', there is also a tongue velocity v w Based on formula (16), we can get:

[0168]

[0169] According to the integral of formula (24), we can get:

[0170]

[0171] The present invention can solve the above equations such as Formula (22) and Formula (25) by conventional methods in the art, for example, by solving them by Python numerical integration library Scipy.

[0172] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with specific embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0173] Example 1

[0174] 1. Obtain the characteristic parameters of horizontal well N1, see Table 2.

[0175] Table 2 Characteristic parameters of horizontal well N1

[0176] parameter Numeric unit <![CDATA[Gas-phase permeability of the gas reservoir in its original state, k g > 61.27 mD Porosity, φ 0.166 Dimensionless Effective thickness, h 17.3 m <![CDATA[Gas density, ρ g > 164 <![CDATA[kg / m 3 ]]> <![CDATA[Gas viscosity, μ g > 0.022 mPa·s <![CDATA[Density of formation water, ρ w > 1007 <![CDATA[kg / m 3 ]]> <![CDATA[Formation water viscosity, μ w > 0.287 mPa·s <![CDATA[Irreducible water saturation, S wi > 0.273 Dimensionless <![CDATA[Residual gas saturation, S gr > 0.074 Dimensionless <![CDATA[The gas-phase relative permeability corresponding to the bound water, k rgwi > 0.557 Dimensionless <![CDATA[Relative permeability of the aqueous phase corresponding to the residual gas, k rwgr > 0.671 Dimensionless <![CDATA[Gas volume factor, B g > 0.00479 <![CDATA[m 3 / sm 3 ]]> <![CDATA[Water invasion rate, v w ’]]> 0.0453 m / d Horizontal section length of horizontal well, L 266.6 m Formation dip, θ 2.4 ° The distance from the initial gas-water boundary to the horizontal well, a 585 m <![CDATA[Gas well production, q g > 381600 <![CDATA[m 3 / d]]>

[0177] 2. Determine the distance r from the critical boundary to the horizontal well c

[0178] According to the above formulas (5), (6), (7) and (11), we can calculate β = 1.59386 × 10 8 (m -1 ), A=0.00084(d / m), B=-0.08333(m / d), C=52.82844(m 2 / d).

[0179] Substituting the calculated values ​​of A, B, C and L into the above formula (13), we can calculate r c =116.95(m).

[0180] 3. Determine the water breakthrough time of horizontal wells (a>r c )

[0181] According to the above formula (21), M rgwi =10.82909, and then according to D = v w 'M rgwi + B is calculated to obtain D = 0.40723 (m / d); then according to formula (22), the Python numerical integration library Scipy is used to solve it and the water breakthrough time of the horizontal well is 1379 days (i.e., t bt =1379 days)

[0182] Example 2

[0183] 1. Obtain the characteristic parameters of horizontal well N2, see Table 3.

[0184] Table 3 Characteristic parameters of horizontal well N2

[0185] parameter Value unit <![CDATA[Gas permeability of gas reservoir in original state, k g > 66.375 mD Porosity, φ 0.201 Dimensionless Effective thickness, h 18.4 m <![CDATA[Gas density, ρ g > 157.576 <![CDATA[kg / m 3 ]]> <![CDATA[Gas viscosity, μ g > 0.022 mPa·s <![CDATA[Density of formation water, ρ w > 940.575 <![CDATA[kg / m 3 ]]> <![CDATA[Formation water viscosity, μ w > 0.205 mPa·s <![CDATA[Irreducible water saturation, S wi > 0.150 Dimensionless <![CDATA[Residual gas saturation, S gr > 0.09 Dimensionless <![CDATA[The gas-phase relative permeability corresponding to the bound water, k rgwi > 0.531 Dimensionless <![CDATA[Relative permeability of the aqueous phase corresponding to the residual gas, k rwgr > 0.701 Dimensionless <![CDATA[Volume coefficient, B g > 0.00529 <![CDATA[m 3 / sm 3 ]]> <![CDATA[Water invasion rate, v w ’]]> 0.0501 m / d Horizontal well length, L 100 m Formation dip, θ 1.8 ° The distance between the gas-water boundary and the horizontal well, a 150 m <![CDATA[Gas well production, q g > 301100 <![CDATA[m 3 / d]]>

[0186] According to the above formula (5), formula (6), formula (7), and formula (11), we can calculate β = 1.41356 × 10 9 (m -1 ), A=0.00078(d / m), B=-0.06289(m / d), C=43.28313(m 2 / d).

[0187] Substituting the calculated values ​​of A, B, C and L into the above formula (13), we can calculate r c =187.24(m).

[0188] 3. Determine the water breakthrough time of horizontal wells (a<r c )

[0189] According to the above formula (21), M rgwi =7.05842, and then according to D = v w 'M rgwi + B is calculated to obtain D = 0.29073 (m / d); then according to formula (25), the Python numerical integration library Scipy is used to solve it and the water breakthrough time of the horizontal well is 370 days (i.e., t bt =370 days).

[0190] The above describes the embodiments of the present invention. However, the present invention is not limited to the above embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir, characterized in that: include: Get the distance r from the critical boundary to the horizontal well c , the critical boundary is the gas-water boundary corresponding to the moving speed of the water tongue point of the gas-water boundary is 0; Obtain the distance a from the initial gas-water boundary to the horizontal well, and determine the distance a from the initial gas-water boundary to the horizontal well and r c The size relationship of If a>r c , then the time t1 of the gas-water boundary moving from the initial gas-water boundary to the critical boundary and the time t2 of the gas-water boundary water tongue point moving from the critical boundary to the horizontal well are obtained. bt =t1+t2 to determine the water breakthrough time t of the horizontal well bt ; If a<r c , then the time for the water tongue point of the gas-water boundary to move from the initial gas-water boundary to the horizontal well is obtained, that is, the water breakthrough time t of the horizontal well is obtained. bt .

2. The method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs according to claim 1, characterized in that: Get the distance r from the critical boundary to the horizontal well c The process includes: Get v w The relationship between r and v w is the moving speed of the water tongue point at the gas-water boundary, and r is the distance from the gas-water boundary to the horizontal well; According to v w The relationship between v and r is determined by w = 0, the corresponding r value, the v w = 0, the corresponding r value is r c .

3. The method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs according to claim 2, characterized in that: Based on the seepage mechanics theory that the seepage model of horizontal wells is an ellipsoid, v g The relationship between r and v g is the gas phase seepage velocity corresponding to the horizontal well; According to the gas-water motion equation based on the gas-water two-phase seepage law, gravity influence and gas non-Darcy effect, v is obtained. w With v g The relationship between According to v w With v g The relationship between g The relationship between v and r is obtained w The relationship between r.

4. The method for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir according to claim 1 or 2, characterized in that: Get the distance r from the critical boundary to the horizontal well c The process includes: obtaining characteristic parameters of the horizontal well, wherein the characteristic parameters include gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal section length L of horizontal well, reservoir thickness h; according to Determine r c ; in, g is the acceleration of gravity; β is the coefficient describing the turbulence effect of porous media.

5. The method for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs according to claim 1 or 2, characterized in that: Determine the water breakthrough time t of the horizontal well bt The process includes: Obtain characteristic parameters of the horizontal well, wherein the characteristic parameters include gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , water phase viscosity μ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal well horizontal section length L, reservoir thickness h, porosity φ, irreducible water saturation S wi , residual gas saturation S gr , water intrusion speed v w ', gas phase relative permeability k under bound water rgwi , water phase relative permeability k under residual gas rwgr ; If a>r c According to formula (22), the water breakthrough time t of the horizontal well is determined bt : If a<r c According to formula (25), the water breakthrough time t of the horizontal well is determined bt : in, D=M rgwi v w '+B; g is the acceleration of gravity; β is the coefficient describing the turbulence effect of porous media.

6. A method for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir, characterized in that: include: Obtain characteristic parameters of the horizontal well, wherein the characteristic parameters include gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , water phase viscosity μ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal well horizontal section length L, reservoir thickness h, porosity φ, irreducible water saturation S wi , residual gas saturation S gr , water intrusion speed v w ', gas phase relative permeability k under bound water rgwi , water phase relative permeability k under residual gas rwgr ; according to Determine r c ; Determine a and r c The size relationship, and If a>r c , according to formula (22) to determine the water breakthrough time t bt ; If a<r c , according to formula (25) to determine the water breakthrough time t bt : in, D=M rgwi v w '+B; g is the acceleration of gravity; β is the coefficient describing the turbulence effect of porous media.

7. A device for predicting water breakthrough time of horizontal wells in edge-water gas reservoirs, characterized in that: include: A characteristic parameter acquisition module is used to obtain the characteristic parameters of the horizontal well, and the characteristic parameters include: gas phase density ρ g , gas phase permeability k of the gas reservoir in its original state g , gas phase viscosity μ g , water phase density ρ w , water phase viscosity μ w , reservoir inclination θ, gas well production q g , Gas volume coefficient B g , horizontal well horizontal section length L, reservoir thickness h, porosity φ, irreducible water saturation S wi , residual gas saturation S gr , water intrusion speed v w ', gas phase relative permeability k under bound water rgwi , water phase relative permeability k under residual gas rwgr , the distance a from the initial gas-water boundary to the horizontal well; r c Determine the module for Determine r c ; Water breakthrough time determination module, used to determine a and r c The size relationship, and If a>r c , according to formula (22) to determine the water breakthrough time t bt ; If a<r c , according to formula (25) to determine the water breakthrough time t bt : in, D=M rgwi v w '+B; g is the acceleration of gravity; β is the coefficient describing the turbulence effect of porous media.

8. An electronic device, characterized in that: include: A processor, a memory and a computer program; wherein the computer program is stored in the memory and is configured to be executed by the processor to implement the method for predicting water breakthrough time of horizontal wells in edge water gas reservoirs as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and the computer program is executed by a processor to implement the method for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir as described in any one of claims 1-6.

10. A computer program product, characterized in that The method comprises a computer program which is executed by a processor to implement the method for predicting water breakthrough time of a horizontal well in an edge-water gas reservoir as described in any one of claims 1 to 6.

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