CN111520132A - Method and system for determining distance of hole in stratum - Google Patents

Method and system for determining distance of hole in stratum Download PDF

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CN111520132A
CN111520132A CN201910101759.1A CN201910101759A CN111520132A CN 111520132 A CN111520132 A CN 111520132A CN 201910101759 A CN201910101759 A CN 201910101759A CN 111520132 A CN111520132 A CN 111520132A
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bottom hole
hole pressure
function
dimensionless
representing
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CN111520132B (en
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徐燕东
李冬梅
张宁
陶杉
邹宁
宋海
李丹丹
马国锐
王勤聪
谷海霞
李双贵
陈东波
黄传艳
张�杰
苏鹏
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China Petroleum and Chemical Corp
Sinopec Northwest Oil Field Co
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Sinopec Northwest Oil Field Co
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH DRILLING; MINING
    • E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A10/00—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE at coastal zones; at river basins
    • Y02A10/40—Controlling or monitoring, e.g. of flood or hurricane; Forecasting, e.g. risk assessment or mapping

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Abstract

A method and system for determining a hole distance in a formation, wherein the method comprises: establishing a fracture-cavity type oil reservoir well testing model, and taking a karst cave in a stratum as a point source; step two, obtaining a real space bottom hole pressure solution when a plurality of karst caves in the stratum exist simultaneously by adopting a superposition principle according to a fracture-cavity type oil reservoir well testing model; and step three, fitting the real space bottom hole pressure solution when a plurality of karsts exist at the same time with the actually measured bottom hole pressure data, and determining the distance from the karsts to the shaft according to the fitting result. The method provides a matched interpretation method for calculating the reservoir parameters and the reserves of the fracture-cavity oil reservoir, can directly interpret the number and the distance of the karst caves in the fracture-cavity oil reservoir, and provides technical support for formulating an oil field development scheme.

Description

Method and system for determining distance of hole in stratum
Technical Field
The invention relates to the technical field of oil and gas exploration and development, in particular to a method and a system for determining a hole distance in a stratum.
Background
The carbonate fracture-cavity type oil reservoir matrix is basically free of oil, the reservoir space mainly comprises cracks and karst caves, and pipe flow and seepage exist in the flowing of crude oil in the cracks and the karst caves. When crude oil flows in deep fracture cracks and karst caves, the vertical flow is obvious. At present, a well testing interpretation method for a fracture-cavity reservoir stratum has two theories of a triple medium and an equipotential body, and whether karst caves exist in the stratum or not can not be judged based on the two theories, and a cave distance is given.
The triple medium theory divides the oil storage space of the fracture-cavity reservoir into a cavity, a seam and a matrix. Wherein the substrate is a main oil storage space. The fracture is directly communicated with the shaft, the solution cavity supplies liquid to the fracture, and the matrix supplies liquid to the fracture and the solution cavity, and a set of complete well testing theoretical system is established based on the seepage theory.
The theory of equipotential bodies assumes: 1) the reservoir space of the fracture-cavity reservoir is only provided with a karst cave, but the flow of fluid in the karst cave is not considered, pressure waves are instantaneously propagated in the cave, 2) fractures are not oil storage spaces but are only seepage channels, and 3) matrix is not oil storage spaces nor seepage channels.
At present, the two theories are both based on a conventional well testing explanation theory, and the results given by the conventional well testing explanation are parameters such as permeability, storage volume ratio and channeling coefficient, the parameters are only average values in parameters of cracks, matrixes and karst caves in a stratum, the characteristics of the karst caves cannot be known by using the parameters, the volume parameters of the karst caves cannot be determined, the size, the number and the distance of the karst caves and other parameters directly serving the development of the karst caves type oil field cannot be determined (especially when a plurality of karst caves exist in the stratum, the distance from the caves to a shaft is an important parameter in the development of the oil field).
Disclosure of Invention
To solve the above problems, the present invention provides a method for determining a hole distance in an earth formation, the method comprising:
establishing a fracture-cavity type oil reservoir well testing model, and taking a karst cave in a stratum as a point source;
step two, obtaining a real space bottom hole pressure solution when a plurality of karst caves in the stratum exist simultaneously by adopting a superposition principle according to the fracture-cavity type oil reservoir well testing model;
and step three, fitting the real space bottom hole pressure solution when a plurality of karsts exist at the same time with the actually measured bottom hole pressure data, and determining the distance from the karsts to the shaft according to the fitting result.
According to an embodiment of the present invention, the second step includes:
step a, performing Laplace transformation on the fracture-cavity oil reservoir well testing model to obtain a first Laplace space bottom hole pressure solution function;
b, determining a dimensionless pressure function of a source and a sink at a shaft by adopting a superposition principle;
c, performing Laplace transformation according to the dimensionless pressure function of the source sink at the position of the shaft to obtain a second Laplace space bottom hole pressure solution function;
d, determining a bottom hole pressure solution function on the Laplace space after the point source function is considered according to the first Laplace space bottom hole pressure solution function and the second Laplace space bottom hole pressure solution function;
and e, obtaining a real space bottom hole pressure solution when a plurality of karst caves in the stratum exist at the same time according to the bottom hole pressure solution function inversion on the Laplace space after the point source function is considered.
According to an embodiment of the invention, in the step a, the first laplace space bottom hole pressure solution function is expressed as:
Figure BDA0001965815900000021
wherein the content of the first and second substances,
Figure BDA0001965815900000022
representing a first Laplace space bottom hole pressure solution function, u representing a Laplace variable, M1And B represent intermediate parameters, respectively.
According to one embodiment of the invention, the intermediate parameters are calculated according to the following expression:
Figure BDA0001965815900000023
Figure BDA0001965815900000024
Figure BDA0001965815900000025
Figure BDA0001965815900000026
Figure BDA0001965815900000027
Figure BDA0001965815900000028
wherein M is1、M2、M3、M4T represents an intermediate parameter, K0Representing a zero-order Bessel function of the second kind, swRepresenting the skin coefficient, s, of the wellborevDenotes the epidermal coefficient of the cavern, rvDDenotes dimensionless cavern radius, K1Representing a first order Bessel function of the second kind, CwDRepresenting a dimensionless wellbore reservoir coefficient, λ represents a dimensionless height, CvDRepresenting dimensionless cavern reservoir coefficients, α a correction coefficient, β a fluctuation coefficient, and γ a damping coefficient.
According to one embodiment of the invention, in step b, a dimensionless pressure function of the source at the wellbore is determined according to the following expression:
Figure BDA0001965815900000031
wherein, PDwfLRepresenting dimensionless pressure of the source at the wellbore, tDDenotes dimensionless time, EiRepresenting an exponential integral function, QjDRepresents the flow ratio, L, provided by the jth cavernjDDenotes the dimensionless distance of the jth cavern from the wellbore, J denotes the total number of caverns.
According to an embodiment of the invention, in step d, the bottom hole pressure solution function on the laplace space after considering the point source function is determined according to the following expression:
Figure BDA0001965815900000032
wherein the content of the first and second substances,
Figure BDA0001965815900000033
representing the bottom hole pressure solution function over laplace space after considering the point source function,
Figure BDA0001965815900000034
representing a first laplace space bottom hole pressure solution function,
Figure BDA0001965815900000035
a second laplace space bottom hole pressure solution function is represented.
According to an embodiment of the invention, in the step e, the true spatial bottom hole pressure solution when a plurality of karsts exist in the stratum at the same time is determined according to the following expression:
Figure BDA0001965815900000036
wherein p iswDRepresenting the true spatial bottom hole pressure solution, t, when multiple caverns exist simultaneously in the formationDRepresenting a dimensionless time, N represents a constant,
Figure BDA0001965815900000037
representing the bottom hole pressure solution function over laplace space after considering the point source function.
According to an embodiment of the invention, in said step three,
fitting the real space bottom hole pressure solution when a plurality of karsts exist at the same time with actually measured bottom hole pressure data to obtain the dimensionless distance from each karst cave to the shaft;
and determining the distance from each karst cave to the shaft according to the dimensionless distance and the shaft radius.
According to one embodiment of the invention, the distance of the cavern to the wellbore is determined according to the following expression:
L＝LD×rw
wherein L represents the distance from the karst cave to the shaft, and LDDenotes the dimensionless distance, r, of the cavern to the wellborewRepresenting the wellbore radius.
The invention also provides a system for determining the distance from a cavity in an earth formation, which is characterized in that the system determines the distance from a karst cave in the earth formation to a shaft by adopting the method as described in any one of the above.
The method and the system for determining the hole distance in the stratum provide a matched interpretation method for calculating the reservoir parameters and the reserves of the fracture-cavity oil reservoir, can directly interpret the number and the distance of the karst holes in the fracture-cavity oil reservoir, and provide technical support for the formulation of an oil field development scheme.
The fracture-cavity type oil reservoir well testing model used in the method is simple in model result and convenient to solve, an analytic solution can be given in the Laplace space, the analytic solution does not involve calculation of complex functions, and the calculation speed is high. Meanwhile, the method can conveniently give the number and the distance of the karst caves through the interpretation result of curve fitting.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required in the description of the embodiments or the prior art:
FIG. 1 is a schematic flow chart illustrating an implementation of a method for determining a hole distance in a formation according to one embodiment of the present invention;
FIG. 2 is a simplified schematic diagram of a fracture-cavity reservoir well testing model according to one embodiment of the present invention;
FIG. 3 is a schematic diagram of a fluid microcell in a wellbore, according to one embodiment of the present invention;
FIG. 4 is a schematic flow diagram illustrating an implementation of obtaining a true spatial bottom hole pressure solution when multiple vugs in a formation coexist using a superposition principle according to an embodiment of the present invention;
FIG. 5 is a bottom hole pressure and derivative log plot for different dimensionless distances of a formation having a cavern therein according to one embodiment of the invention;
FIG. 6 is a schematic illustration of an exemplary plot of a plurality of vugs in a formation in accordance with an embodiment of the present invention;
FIG. 7 is a log-log pressure and derivative fit plot for a well example in accordance with an embodiment of the present invention.
Detailed Description
The following detailed description of the embodiments of the present invention will be provided with reference to the drawings and examples, so that how to apply the technical means to solve the technical problems and achieve the technical effects can be fully understood and implemented. It should be noted that, as long as there is no conflict, the embodiments and the features of the embodiments of the present invention may be combined with each other, and the technical solutions formed are within the scope of the present invention.
Additionally, the steps illustrated in the flow charts of the figures may be performed in a computer system such as a set of computer-executable instructions and, although a logical order is illustrated in the flow charts, in some cases, the steps illustrated or described may be performed in an order different than here.
Aiming at the problems in the prior art, the invention provides a novel method for determining the distance of a hole in a stratum and a system for determining the distance of the hole in the stratum by using the method. The method and the system adopt a fracture-cavity reservoir well testing interpretation method based on the combination of the energy conservation law and karst cave fluctuation, and determine the number of the cavities in the stratum and the distance between the karst cave and a drilling well through pressure recovery well testing curve interpretation.
Fig. 1 shows a schematic flow chart of an implementation of the method for determining a hole distance in a formation according to the embodiment.
In this embodiment, as shown in fig. 1, the method preferably establishes a fracture-cavity reservoir well testing model in step S101, and dissolves the solution in the formationThe hole is considered a point source. Specifically, in this embodiment, the fracture-cavity reservoir well testing model is a model of a plurality of karsts existing in a formation, which can be simplified as shown in fig. 2 (taking 2 karsts existing in the formation as an example), where a distance L from a first karst cave 202 to a drilling well 201 is provided1The distance from the second karst cave 203 to the well 201 is L2. The method provided by the invention is to determine the number of the karst caves in the stratum and the distance L between each karst cave and the shaft by using a well testing analysis and oil reservoir engineering methodi。
In this embodiment, the fracture-cavity reservoir well testing model may preferably be represented by the following expression:
Figure BDA0001965815900000051
wherein r isDRepresenting a dimensionless radius, d is the derivative symbol,
Figure BDA0001965815900000061
representing a dimensionless pressure, p, of a first type of medium in Laplace space1DExpressed as a dimensionless pressure in the first type of medium; u represents the variable of the laplace (Laplace),
Figure BDA0001965815900000062
representing the dimensionless pressure, p, of the second medium type in Laplace space2DExpressed as dimensionless pressure in the second type of medium.
Figure BDA0001965815900000063
Denotes dimensionless bottom hole pressure in Laplace space, swRepresenting the skin coefficient, s, of the wellborevThe coefficient of the karst cave epidermis is shown,
Figure BDA0001965815900000064
denotes dimensionless cavern pressure in Laplace space, rvDDenotes dimensionless cavern radius, CwDRepresenting a dimensionless wellbore storage constant, λ representing a dimensionless height, α representing an equation correction coefficient, β representing a dimensionless fluctuation coefficient, γ representing a dimensionless fluctuation coefficientA damping coefficient.
Dimensionless pressure pjDIt can be calculated using the following expression:
Figure BDA0001965815900000065
wherein k represents the permeability of the external medium, h1Indicates the thickness of the formation to which the wellbore is connected, h2Denotes the thickness of the formation connected to the cavern, piRepresenting the original formation pressure, pvDenotes the pressure of the cavern, pfDenotes fracture pressure, Q denotes yield, B denotes volume factor, μ denotes fluid viscosity.
Dimensionless time tDIt can be calculated according to the following expression:
Figure BDA0001965815900000066
wherein φ represents the external medium porosity, CtRepresenting the compression factor of the external medium, t representing time, rwRepresenting the wellbore radius.
Dimensionless radius rDIt can be calculated according to the following expression:
Figure BDA0001965815900000067
where r denotes the detection radius.
Dimensionless wellbore reservoir coefficient CwDIt can be calculated according to the following expression:
Figure BDA0001965815900000068
wherein, CwRepresenting the wellbore reservoir coefficient, CtRepresenting the compression factor of the external medium, rvIndicating the cavern radius.
Dimensionless cavern storage coefficient CvDIt can be calculated according to the following expression:
Figure BDA0001965815900000069
wherein, CvIndicating the cavern reservoir coefficient.
The dimensionless height λ can be calculated according to the following expression:
Figure BDA0001965815900000071
the dimensionless fluctuation coefficient β can be calculated according to the following expression:
Figure BDA0001965815900000072
where ρ represents the fluid density, D represents the wellbore diameter, v0Indicating the initial velocity (which can be calculated by the flow meter).
The dimensionless damping coefficient γ can be calculated according to the following expression:
Figure BDA0001965815900000073
the mathematical function (x) can be expressed as:
Figure BDA0001965815900000074
in the above description, the subscript f represents a fracture, the subscript v represents a karst cave, and the subscript w represents an oil well.
In the fracture-cavity reservoir well testing model shown in expression (1), the last equation is a dimensionless equation established based on the law of conservation of energy.
The continuity equation, the momentum conservation equation and the energy conservation equation which are satisfied by the fluid flow in the process that the fluid flows into the well bore from the karst cave and then flows out of the ground surface from the well bore can be respectively expressed as follows:
Figure BDA0001965815900000075
Figure BDA0001965815900000076
Figure BDA0001965815900000077
where ρ represents fluid density, t represents time, v represents fluid flow velocity, x axis represents a one-dimensional coordinate axis established from the center of the wellbore downward, p represents pressure, f represents the coefficient of friction resistance experienced by the fluid, D represents wellbore diameter, p represents the velocity of the fluid flowing through the wellbore, andwfand pvIndicating pressure, v, in the wellbore and in the cavern, respectivelywfIndicating the velocity of the fluid at the junction of the wellbore and the cavern.
Taking a fluid infinitesimal in the wellbore as shown in fig. 3, the conservation of mass can be obtained:
Figure BDA0001965815900000078
wherein A represents the cross-sectional area of the infinitesimal.
Under high pressure, the fluid is compressible, the oil pipe is also an elastomer, the deformation of the oil pipe is determined by the diameter and the wall thickness of the oil pipe and the Young modulus of the material of the oil pipe, and the expansion expression (14) can be obtained:
Figure BDA0001965815900000081
according to the relation between the full derivative and the partial derivative in the fluid mechanics, the following can be obtained:
Figure BDA0001965815900000082
Figure BDA0001965815900000083
the above expression may be modified as:
Figure BDA0001965815900000084
considering the compressibility of the fluid, the density term in expression (18) can be expressed as a function of pressure, i.e. there is:
Figure BDA0001965815900000085
wherein G represents the volumetric flow rate of the fluid.
Assuming that the tubing is elastically deformed, for a thin-walled tubular, when the pressure increases dp, the relationship between the radial deformation dD and dp can be expressed as:
Figure BDA0001965815900000086
wherein D represents the diameter of the oil pipe, E represents the wall thickness of the oil pipe, and E represents the Young's modulus of the oil pipe.
The tubing area expression may be expressed as:
Figure BDA0001965815900000087
combining expression (19) and expression (20), expression (18) may become:
Figure BDA0001965815900000088
for the wave speed C in the pipe and fluid system, there are:
Figure BDA0001965815900000089
specifically, with the full derivative formula, expression (22) may become:
Figure BDA00019658159000000810
it can be seen that the propagation of the pressure in the x-axis direction is in the form of a wave with a wave velocity C.
If the cavern is also considered as a cylinder, the continuity equation is the same as expression (24), but the velocity of pressure propagation, C, can be expressed as:
Figure BDA0001965815900000091
combining the continuity equation with conservation of momentum can yield:
Figure BDA0001965815900000092
investigating the flow of fluid in the cavern, neglecting gravity and fluid friction force due to small velocity v, and considering the storage constant C of the cavernvSince the friction is a quadratic term of the velocity v, a second order small quantity can be omitted, then:
Figure BDA0001965815900000093
the solution of expression (27), i.e. the fluid flow rate in the cavern:
Figure BDA0001965815900000094
wherein v is0Representing the velocity at the initial moment, which can be determined by the ground production. Due to the radius r of the large karst cavevIs large, therefore
Figure BDA0001965815900000099
The term is also larger and is a constant, which can be added to the additional pressure drop. By modifying the equation, the second term on the right in expression (28) can be ignored, i.e. there is:
Figure BDA0001965815900000095
the yield Q provided by the caverns can thus be obtained, i.e. there are:
Figure BDA0001965815900000096
the velocity v of the fluid flowing into the wellborewfIt can also be calculated according to the following expression:
Figure BDA0001965815900000097
according to the energy conservation equation at the position of the shaft and the karst cave, the following are provided:
Figure BDA0001965815900000098
the expression (32) can be converted into the last equation in the fracture-cavity type oil reservoir well testing model according to dimensionless definition.
As shown in fig. 1, in this embodiment, in step S102, according to the created fracture-cavity reservoir well testing model, the method obtains a true spatial bottom-hole pressure solution when multiple karst caves in the formation exist simultaneously by using a superposition principle.
Fig. 4 shows a schematic implementation flow chart of obtaining a true spatial bottom hole pressure solution when multiple karst caves simultaneously exist in the formation by using the superposition principle in this embodiment.
As shown in fig. 4, in this embodiment, the method performs laplace transform on the fracture-cavity reservoir well testing model in step S401, so as to obtain a first laplace space bottom-hole pressure solution function. Specifically, in this embodiment, the first laplace space bottom hole pressure solution function obtained by the method may be preferably expressed as:
Figure BDA0001965815900000101
wherein the content of the first and second substances,
Figure BDA0001965815900000102
represents the first laplace space bottom hole pressure solution function and u represents the laplace variable.
Calculating the volume factor B according to the following expression:
Figure BDA0001965815900000103
Figure BDA0001965815900000104
Figure BDA0001965815900000105
Figure BDA0001965815900000106
Figure BDA0001965815900000107
Figure BDA0001965815900000108
wherein, M is1、M2、M3、M4T represents an intermediate parameter, and the specific meaning is shown above. K0Representing a zero-order Bessel function of the second kind, svDenotes the epidermal coefficient of the cavern, rvDDenotes dimensionless cavern radius, K1Representing a first order Bessel function of the second kind, CwDRepresenting a dimensionless wellbore reservoir coefficient, λ represents a dimensionless height, CvDRepresenting dimensionless cavern reservoir coefficients, α a correction coefficient, β a fluctuation coefficient, and γ a damping coefficient.
Of course, in other embodiments of the present invention, according to actual needs, the method may also perform laplace transform on the fracture-cavity reservoir well testing model by using other reasonable manners to obtain the first laplace space bottom hole pressure solution function.
In the present embodiment, as shown in fig. 4, the method employs the superposition principle in step S402 to determine the dimensionless pressure of the source and sink at the wellboreA force function. Specifically, referring to the simplified well testing model of fractured reservoir shown in FIG. 2, when multiple vugs (2 vugs for example) exist in the formation, the first vug 202 will provide the production Q for the wellbore 2011The second cavern 203 will provide production Q to the wellbore 2012。
During the provision of flow to the wellbore, the pressure of the first cavern 202 and the second cavern 203 may decrease. Thus, for the wellbore 201, the presence of the first cavern 202 and the second cavern 203 corresponds to 2 production zones in the formation, each having a Q1And Q2While the well is producing. The real space bottom hole pressure solution when the first cavern 202 and the second cavern 203 exist simultaneously can be obtained by utilizing the superposition principle.
If the first cavern 202 and the second cavern 203 are regarded as point sources, then according to the source-sink theory, the continuity equation for multiple sources in the formation is considered as follows:
Figure BDA0001965815900000111
wherein q isi(i ═ 1, 2. -) denotes the strength of the ith sink (i.e., the ith cavern), M1And M2Each represents a position of a first point source and a second point source in space, and M represents a position of an arbitrary point in space, and represents a centrally distributed physical quantity (for example, a mass point, a charge of a point, a heat of a point, a concentration force, and the like).
A function is a mathematical tool that describes a centrally distributed physical quantity. If a function is used to mathematically describe these centrally distributed physical quantities, it satisfies the following two requirements:
Figure BDA0001965815900000112
Figure BDA0001965815900000113
an important property of the function is: for any continuous function f (x, y, z), there is:
Figure BDA0001965815900000114
another important property of the function is symmetry, i.e. the presence:
(M-MO)＝(MO-M) (44)
using the slightly compressible assumption and substituting darcy's law into expression (40), one can obtain:
Figure BDA0001965815900000115
defining a dimensionless quantity and solving a dimensionless source-sink equation, the dimensionless pressure of the source-sink at the wellbore can be obtained, i.e. there is:
Figure BDA0001965815900000116
wherein, PDwfLRepresenting dimensionless pressure of the source at the wellbore, tDDenotes dimensionless time, EiRepresenting an exponential integral function, L1DDenotes the dimensionless distance, Q, of the 1 st cavern from the wellbore1DRepresents the flow ratio, L, provided by the 1 st cavern2DDenotes the dimensionless distance, Q, of the 2 nd cavern from the wellbore2DIndicating the flow ratio provided by the 2 nd cavern.
If a plurality of karsts exist in the fracture-cavity type oil reservoir well testing model, the expression (45) can be written as follows:
Figure BDA0001965815900000121
wherein Q isjDRepresents the flow ratio, L, provided by the jth cavernjDDenotes the dimensionless distance of the jth cavern from the wellbore, J denotes the total number of caverns.
Dimensionless pressure P at the source-sink wellboreDwfLCan be expressed as:
Figure BDA0001965815900000122
dimensionless time tDCan be expressed as:
Figure BDA0001965815900000123
dimensionless distance L of the 1 st karst cave from the shaft1DCan be expressed as:
Figure BDA0001965815900000124
dimensionless distance L of No. 2 karst cave from shaft2DCan be expressed as:
Figure BDA0001965815900000125
exponential integral function EiCan be expressed as:
Figure BDA0001965815900000126
the 1 st cave (i.e. the first cave) provides a flow ratio Q1DCan be expressed as:
Figure BDA0001965815900000127
the 2 nd cave (i.e. the second cave) provides a flow ratio Q2DCan be expressed as:
Figure BDA0001965815900000128
as shown in fig. 4, in this embodiment, after obtaining the dimensionless pressure function of the source at the wellbore, the method performs laplace transform on the dimensionless pressure function of the source at the wellbore in step S403, so as to obtain a second laplace space bottom hole pressure solution function
Figure BDA0001965815900000129
The method then proceeds to step S404 with a first Laplace space bottom hole pressure solution function determined in step S401
Figure BDA0001965815900000131
And the second Laplace space bottom hole pressure solution function determined in the step S403
Figure BDA0001965815900000132
To determine a bottom hole pressure solution function over laplace space after considering the point source function.
Specifically, in the present embodiment, the bottom hole pressure solution function in laplace space after considering the point source function can be expressed as:
Figure BDA0001965815900000133
wherein the content of the first and second substances,
Figure BDA0001965815900000134
representing the bottom hole pressure solution function over laplace space after considering the point source function.
Bottom hole pressure solution function on Laplace space after point source function is considered
Figure BDA0001965815900000135
The method may preferably solve the function in step S405 from the bottom hole pressure over laplace space after considering the point source function
Figure BDA0001965815900000136
And (4) carrying out inversion to obtain a true space bottom hole pressure solution when a plurality of karst caves in the stratum exist simultaneously.
Specifically, in this embodiment, the method preferably determines a true spatial bottom hole pressure solution when multiple karst caves exist simultaneously in the formation by using a Stehfest numerical inversion technique in step S405. For example, a true spatial bottom hole pressure solution when multiple vugs in the formation exist simultaneously may be determined according to the following expression:
Figure BDA0001965815900000137
wherein p iswDRepresenting the true spatial bottom hole pressure solution, t, when multiple caverns exist simultaneously in the formationDRepresenting a dimensionless time, N represents a constant,
Figure BDA0001965815900000138
representing the bottom hole pressure solution function over laplace space after considering the point source function.
In this embodiment, the constant N is preferably an even number between [8,16 ]. Of course, in other embodiments of the present invention, the constant N may also be configured to be other reasonable values according to actual needs, and the present invention does not limit the specific value of the constant N.
It should be noted that, in other embodiments of the present invention, according to practical needs, the method may also use other reasonable ways to obtain the true spatial bottom-hole pressure solution when multiple karst caves exist in the formation simultaneously by using the superposition principle, which is not limited to this.
As shown in fig. 1 again, in this embodiment, after obtaining the real space bottom hole pressure solution when multiple karsts exist at the same time, the method performs fitting by using the real space bottom hole pressure solution when multiple karsts exist at the same time obtained in step S102 and the measured bottom hole pressure data in step S103, and determines the distance from the karst cave to the wellbore according to the fitting result in step S104.
Specifically, in this embodiment, in step S104, the method preferably first obtains a typical curve plate by using a true space bottom hole pressure solution when multiple karsts exist simultaneously, and then obtains a dimensionless distance L from each karst cave to the wellbore according to the log-log pressure and derivative fitting of the actual pressure recovery curveD. The method will then be based on the resulting dimensionless distance LDAnd wellbore radius rwAnd determining the distance L from each karst cave to the shaft.
In this embodiment, the method preferably determines the distance of the cavern to the wellbore according to the following expression:
L＝LD×rw(57)
wherein L represents the distance of the cavern to the wellbore.
It should be noted that, in this embodiment, when curve fitting is performed, the number of the karst caves included in the formation may also be determined according to the upwarp segment number (for example, the segment number with the slope equal to 1 in the curve) of the curve corresponding to the real space bottom hole pressure solution obtained in step S102.
To more clearly illustrate the reliability and advantages of the method for determining the hole distance in the formation provided by the embodiment, taking a certain formation as an example, the bottom hole pressure and derivative log curves of different dimensionless distances when there is a karst hole in the formation can be obtained as shown in fig. 5. Wherein, the calculation parameters in fig. 5 are respectively: cDe2S100, dimensionless distance LDRespectively 200, 300 and 400.
The resulting typical curve may also change when multiple vugs are present in the formation, and fig. 6 shows a schematic diagram of a typical curve when multiple vugs are present in the formation. Wherein, the calculation parameters in FIG. 6 are C respectivelyDe2S100, dimensionless distance L1DIs 100, dimensionless distance L2DIs 600.
As can be seen from fig. 5 and 6, when there is a cavern in the formation, the pressure derivative curve will warp upward, the number of caverns can be determined from the number of warp of the derivative curve, and the dimensionless distance can be obtained by a curve fitting value.
By deriving the actual pressure recovery curve, a pressure derivative log-log curve can be drawn to fit the chart shown in fig. 5. Table 1 shows the basic parameters of the well case, and fig. 7 shows the log-log pressure and derivative fit plot of the well case. Wherein, the calculation parameter C of the chartDe2S＝3.28×1016，LD＝1290.6。
TABLE 1
Figure BDA0001965815900000141
Figure BDA0001965815900000151
According to the dimensionless distance L from the karst cave to the shaftDThe distance from the cavern to the wellbore can be obtained, i.e. the existence of:
L＝LD×rw＝1290.6×0.67＝86.47 (58)
meanwhile, only one karst cave is formed in the stratum as can be seen from the number of the upwarping sections of the measured curve.
The method and the system for determining the distance between the holes in the stratum provide a matched interpretation method for calculating the reservoir parameters and the reserves of the fracture-cavity oil reservoir, can directly interpret the number and the distance of the karst holes in the fracture-cavity oil reservoir, and provide technical support for the formulation of an oil field development scheme.
The fracture-cavity type oil reservoir well testing model used in the method is simple in model result and convenient to solve, an analytic solution can be given in the Laplace space, the analytic solution does not involve calculation of complex functions, and the calculation speed is high. Meanwhile, the method can conveniently give the number and the distance of the karst caves through the interpretation result of curve fitting.
It is to be understood that the disclosed embodiments of the invention are not limited to the particular structures or process steps disclosed herein, but extend to equivalents thereof as would be understood by those skilled in the relevant art. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting.
Reference in the specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Thus, the appearances of the phrase "one embodiment" or "an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment.
While the above examples are illustrative of the principles of the present invention in one or more applications, it will be apparent to those of ordinary skill in the art that various changes in form, usage and details of implementation can be made without departing from the principles and concepts of the invention. Accordingly, the invention is defined by the appended claims.

Claims (10)

1. A method of determining a hole distance in an earth formation, the method comprising:
establishing a fracture-cavity type oil reservoir well testing model, and taking a karst cave in a stratum as a point source;
step two, obtaining a real space bottom hole pressure solution when a plurality of karst caves in the stratum exist simultaneously by adopting a superposition principle according to the fracture-cavity type oil reservoir well testing model;
and step three, fitting the real space bottom hole pressure solution when a plurality of karsts exist at the same time with the actually measured bottom hole pressure data, and determining the distance from the karsts to the shaft according to the fitting result.
2. The method of claim 1, wherein step two comprises:
step a, performing Laplace transformation on the fracture-cavity oil reservoir well testing model to obtain a first Laplace space bottom hole pressure solution function;
b, determining a dimensionless pressure function of a source and a sink at a shaft by adopting a superposition principle;
c, performing Laplace transformation according to the dimensionless pressure function of the source sink at the position of the shaft to obtain a second Laplace space bottom hole pressure solution function;
d, determining a bottom hole pressure solution function on the Laplace space after the point source function is considered according to the first Laplace space bottom hole pressure solution function and the second Laplace space bottom hole pressure solution function;
and e, obtaining a real space bottom hole pressure solution when a plurality of karst caves in the stratum exist at the same time according to the bottom hole pressure solution function inversion on the Laplace space after the point source function is considered.
3. The method of claim 2, wherein in step a, the first laplace space bottom hole pressure solution function is represented as:
Figure FDA0001965815890000011
wherein the content of the first and second substances,
Figure FDA0001965815890000012
representing a first Laplace space bottom hole pressure solution function, u representing a Laplace variable, M1And B represent intermediate parameters, respectively.
4. A method according to claim 3, wherein the intermediate parameters are calculated according to the expression:
Figure FDA0001965815890000013
Figure FDA0001965815890000014
Figure FDA0001965815890000015
Figure FDA0001965815890000021
Figure FDA0001965815890000022
Figure FDA0001965815890000023
wherein M is1、M2、M3、M4T represents an intermediate parameter, K0Representing a zero-order Bessel function of the second kind, swRepresenting the skin coefficient, s, of the wellborevDenotes the epidermal coefficient of the cavern, rvDDenotes dimensionless cavern radius, K1Representing a first order Bessel function of the second kind, CwDRepresenting a dimensionless wellbore reservoir coefficient, λ represents a dimensionless height, CvDRepresenting dimensionless cavern reservoir coefficients, α a correction coefficient, β a fluctuation coefficient, and γ a damping coefficient.
5. The method of any one of claims 2 to 4, wherein in step b, the dimensionless pressure function of source convergence at the wellbore is determined according to the expression:
Figure FDA0001965815890000024
wherein, PDwfLRepresenting dimensionless pressure of the source at the wellbore, tDDenotes dimensionless time, EiRepresenting an exponential integral function, QjDRepresents the flow ratio, L, provided by the jth cavernjDDenotes the dimensionless distance of the jth cavern from the wellbore, J denotes the total number of caverns.
6. A method according to any one of claims 2 to 5, wherein in step d, the bottom hole pressure solution function over Laplace space after considering the point source function is determined according to the expression:
Figure FDA0001965815890000025
wherein the content of the first and second substances,
Figure FDA0001965815890000026
representing the bottom hole pressure solution function over laplace space after considering the point source function,
Figure FDA0001965815890000027
is shown asA laplace space bottom hole pressure solution function,
Figure FDA0001965815890000028
a second laplace space bottom hole pressure solution function is represented.
7. The method of any one of claims 2 to 6, wherein in step e, the true spatial bottom hole pressure solution is determined for the simultaneous presence of multiple vugs in the formation according to the following expression:
Figure FDA0001965815890000029
wherein p iswDRepresenting the true spatial bottom hole pressure solution, t, when multiple caverns exist simultaneously in the formationDRepresenting a dimensionless time, N represents a constant,
Figure FDA00019658158900000210
representing the bottom hole pressure solution function over laplace space after considering the point source function.
8. The method according to any one of claims 1 to 7, wherein, in step three,
fitting the real space bottom hole pressure solution when a plurality of karsts exist at the same time with actually measured bottom hole pressure data to obtain the dimensionless distance from each karst cave to the shaft;
and determining the distance from each karst cave to the shaft according to the dimensionless distance and the shaft radius.
9. The method of claim 8, wherein the distance of the cavern to the wellbore is determined according to the following expression:
L＝LD×rw
wherein L represents the distance from the karst cave to the shaft, and LDDenotes the dimensionless distance, r, of the cavern to the wellborewRepresenting the wellbore radius.
10. A system for determining the distance of a cavity in a formation, wherein the system determines the distance of a cavern in the formation to a wellbore using the method of any one of claims 1 to 9.
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