CN111520132B - Method and system for determining hole distance in stratum - Google Patents
Method and system for determining hole distance in stratum Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 56
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- 230000005465 channeling Effects 0.000 description 1
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- 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
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Abstract
A method and system for determining hole distance in a formation, wherein the method comprises: step one, establishing a fracture-cavity type oil reservoir well test model, and taking a karst cavity in a stratum as a point source; step two, according to a fracture-cavity type oil reservoir well test model, obtaining a true space bottom hole pressure solution when a plurality of karst cavities exist in a stratum at the same time by adopting a superposition principle; fitting the real space bottom hole pressure solution and the actually measured bottom hole pressure data when a plurality of karst cave exist simultaneously, and determining the distance from the karst cave to the shaft according to the fitting result. The method provides a matched interpretation method for fracture-cavity type oil reservoir parameter calculation and reserve calculation, can directly interpret the number and the distance of karst cavities in the fracture-cavity type oil reservoir, and provides technical support for the establishment of an oil field development scheme.
Description
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 is mainly a fracture and a karst cavity, and the flow of crude oil in the fracture and the karst cavity is provided with pipe flow and seepage. When crude oil flows in deep fracture cracks and karst cave, the vertical flow is obvious. The existing well testing interpretation method for the fracture-cavity type reservoir has two theories of triple medium and equipotential body, and whether karst cavities exist in the stratum or not cannot be judged based on the two theories, and the hole distance is given.
Triple medium theory divides the fracture-cavity reservoir oil storage space into a hole, a seam and a matrix. Wherein the matrix is the primary oil reservoir. The fracture is directly communicated with the shaft, the karst cave supplies liquid to the fracture, the matrix supplies liquid to the fracture and the karst cave, and a set of complete well testing theoretical system is established based on seepage theory.
Equipotential body theory assumes: 1) the fracture-cave reservoir has only karst cave space, but does not consider the flow of fluid in karst cave, pressure wave propagates instantaneously in karst cave, 2) the fracture is not oil storage space but seepage flow channel, 3) the matrix is neither oil storage space nor seepage flow channel.
At present, both theories are based on conventional well testing interpretation theory, and the results based on conventional well testing interpretation are parameters such as permeability, storage ratio, channeling coefficient and the like, wherein the parameters are just average values of fracture, matrix and karst cave parameters in a stratum, fracture and cave characteristics cannot be recognized by using the parameters, fracture and cave volume parameters cannot be determined, parameters of directly serving fracture and cave type oilfield development such as size, number and distance of fracture and cave cannot be determined (particularly when a plurality of karst cave exist in the stratum, the distance from a cave to a shaft is an important parameter in oilfield development).
Disclosure of Invention
To solve the above problems, the present invention provides a method of determining a hole distance in a formation, the method comprising:
step one, establishing a fracture-cavity type oil reservoir well test model, and taking a karst cavity in a stratum as a point source;
step two, according to the fracture-cavity type oil reservoir well test model, obtaining a true space bottom hole pressure solution when a plurality of karst cavities exist in a stratum at the same time by adopting a superposition principle;
fitting the real space bottom hole pressure solution and the actually measured bottom hole pressure data when a plurality of karst cave exist simultaneously, and determining the distance from the karst cave to the shaft according to the fitting result.
According to one embodiment of the present invention, the second step includes:
step a, carrying out Laplace transformation on the fracture-cavity oil reservoir well test model to obtain a first Laplace space bottom hole pressure solution function;
step b, determining a dimensionless pressure function of the source sink at the well bore by adopting a superposition principle;
step c, carrying out Laplace transformation according to the dimensionless pressure function of the source sink at the shaft to obtain a second Laplace space bottom hole pressure solution function;
step d, determining a bottom hole pressure solution function on the Laplace space after considering a point source function according to the first and second Laplace space bottom hole pressure solution functions;
and e, inverting according to a bottom hole pressure solution function on the Laplace space after the point source function is considered to obtain a real space bottom hole pressure solution when a plurality of karst caves in the stratum exist at the same time.
According to one embodiment of the present invention, in the step a, the first laplace space bottom hole pressure solution function is expressed as:
wherein,represents a first Laplace space bottom hole pressure solution function, u represents a Laplace variable, M 1 And B represent intermediate parameters, respectively.
According to one embodiment of the invention, the intermediate parameters are calculated according to the following expression:
wherein M is 1 、M 2 、M 3 、M 4 T represents an intermediate parameter, K 0 Representing zero-order Bessel functions of the second class, s w Represents the skin coefficient of the wellbore, s v Represents the skin coefficient of karst cave, r vD Represents the radius of the dimensionless karst cave, K 1 Representing a first order Bessel function of a second class, C wD Represents the dimensionless wellbore reservoir coefficient, lambda represents the dimensionless height, C vD The method is characterized in that the method is used for representing a dimensionless karst cave storage coefficient, alpha represents a correction coefficient, beta represents a fluctuation coefficient, and gamma represents a damping coefficient.
According to one embodiment of the invention, in said step b, a dimensionless pressure function of the source sink at the wellbore is determined according to the following expression:
wherein P is DwfL Representing dimensionless pressure of a source sink at a wellbore, t D Represent dimensionless time, E i Represents an exponential integral function, Q jD Represents the flow ratio provided by the jth karst cave, L jD The dimensionless distance of the jth karst cave from the wellbore is represented, and J represents the total number of karst cave.
According to one embodiment of the present invention, in the step d, a solution function of the bottom hole pressure in the laplace space taking the point source function into consideration is determined according to the following expression:
wherein,representing the solution function of the bottom hole pressure in Laplace space after considering the point source function, +.>Representing a first Laplace space downholePressure solution function->Representing a second laplace space bottom hole pressure solution function.
According to one embodiment of the present invention, in the step e, a true space bottom hole pressure solution when a plurality of karst holes exist in the formation at the same time is determined according to the following expression:
wherein p is wD Representing the real space bottom hole pressure solution when a plurality of karst cave exist in stratum at the same time, t D Represents the dimensionless time, N represents a constant,representing the solution function of the bottom hole pressure in the laplace space after considering the point source function.
According to one embodiment of the invention, in said step three,
fitting by utilizing real space bottom hole pressure solutions when a plurality of karst caves exist simultaneously and actually measured bottom hole pressure data to obtain dimensionless distances from each karst cave to a 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 karst cave to wellbore distance is determined according to the following expression:
L＝L D ×r w
wherein L represents the distance from the karst cave to the shaft, L D Representing the dimensionless distance from the karst cave to the shaft, r w Representing the wellbore radius.
The invention also provides a system for determining the hole distance in a stratum, which is characterized in that the system adopts the method for determining the hole-to-wellbore distance in the stratum.
The method and the system for determining the hole distance in the stratum provide a matched interpretation method for calculation of fracture-cavity type oil reservoir parameters and calculation of reserves, can directly interpret the number and the distance of the karst cavity in the fracture-cavity type oil reservoir, and provide technical support for formulation of an oil field development scheme.
The fracture-cavity oil reservoir well test model used by the method has the advantages of simple model result, convenient solution, capability of giving an analytical solution in the Laplace space, no relation to the calculation of complex functions, and high calculation speed. Meanwhile, the method can conveniently give the number and the distance of karst cave according to 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 description will briefly explain the drawings required in the embodiments or the description of the prior art:
FIG. 1 is a schematic flow diagram of an implementation of a method of determining hole distance in a formation according to one embodiment of the invention;
FIG. 2 is a simplified schematic diagram of a fracture-cave reservoir well test model in accordance with one embodiment of the present invention;
FIG. 3 is a schematic illustration of a fluid cell in a wellbore according to one embodiment of the invention;
FIG. 4 is a schematic diagram of an implementation flow of obtaining a true space bottom hole pressure solution for the simultaneous presence of multiple karst cave in a formation using superposition principles according to one embodiment of the invention;
FIG. 5 is a log plot of bottom hole pressure and derivative for different dimensionless distances with a karst cave in a formation according to one embodiment of the invention;
FIG. 6 is a schematic representation of an exemplary plot of the presence of multiple karst holes in a formation according to one embodiment of the invention;
FIG. 7 is a graph of a log-log pressure and derivative fit of a well case according to one embodiment of the invention.
Detailed Description
The following will describe embodiments of the present invention in detail with reference to the drawings and examples, thereby solving the technical problems by applying technical means to the present invention, and realizing the technical effects can be fully understood and implemented accordingly. It should be noted that, as long as no conflict is formed, each embodiment of the present invention and each feature of each embodiment may be combined with each other, and the formed technical solutions are all within the protection scope of the present invention.
Additionally, the steps illustrated in the flowcharts 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 flowcharts, in some cases the steps illustrated or described may be performed in an order other than that herein.
The invention provides a novel method for determining the hole distance in a stratum and a system for determining the hole distance in the stratum by using the method. The method and the system adopt a fracture-cavity type reservoir well test interpretation method based on the combination of energy conservation law and karst cavity fluctuation, and determine the number of holes in the stratum and the distance between the karst cavity and the well drilling through interpretation of a pressure recovery well test curve.
Fig. 1 is a schematic flow chart of an implementation of a method for determining a hole distance in a stratum according to the embodiment.
In this embodiment, as shown in fig. 1, the method preferably establishes a fracture-cavity reservoir test model in step S101, and regards the karst cavity in the formation as a point source. Specifically, in this embodiment, a model in which multiple karst cave exist in a stratum adopted by the fracture-cave type oil reservoir well test model may be simplified to be shown in fig. 2 (taking the existence of 2 karst cave in the stratum as an example), where the distance from the first karst cave 202 to the well 201 is L 1 The second karst cave 203 is a distance L from the borehole 201 2 . The method provided by the invention is to determine the number of karst cave in stratum and the distance L between each karst cave and shaft by using well test analysis and oil reservoir engineering method i 。
In this embodiment, the fracture-cavity reservoir well test model may preferably be represented by the following expression:
wherein r is D Represents a dimensionless radius, d is a derivative symbol,representing the dimensionless pressure, p, of a first type of medium in Laplace space 1D Expressed as dimensionless pressure in the first type of medium; u represents the Laplace variable,/->Representing the dimensionless pressure, p, of a second type of medium in Laplace space 2D Represented as dimensionless pressure in the second type of medium.Representing dimensionless bottom hole pressure, s, in Laplace space w Represents the skin coefficient of the wellbore, s v Represents the skin coefficient of karst cave,/->Represents the dimensionless karst cave pressure in the Laplace space, r vD Represents the radius of the dimensionless karst cave, C wD The method is characterized by expressing a dimensionless wellbore storage constant, lambda expressing a dimensionless height, alpha expressing an equation correction coefficient, beta expressing a dimensionless fluctuation coefficient, and gamma expressing a dimensionless damping coefficient.
Dimensionless pressure p jD Can be calculated using the following expression:
wherein k represents the external medium permeability, h 1 Representing formations associated with a wellboreThickness h 2 Representing the thickness of the stratum connected with the karst cave, p i Representing the original formation pressure, p v Represents karst cave pressure, p f Represents fracture pressure, Q represents production, B represents volume coefficient, μ represents fluid viscosity.
Dimensionless time t D Can be calculated according to the following expression:
wherein phi represents the porosity of the external medium, C t Represents the external medium compression coefficient, t represents time, r w Representing the wellbore radius.
Dimensionless radius r D Can be calculated according to the following expression:
where r represents the detection radius.
Dimensionless wellbore reservoir coefficient C wD Can be calculated according to the following expression:
wherein C is w Representing wellbore reservoir coefficient, C t Represents the external medium compression coefficient, r v Indicating the karst cave radius.
Dimensionless karst cave reservoir coefficient C vD Can be calculated according to the following expression:
wherein C is v Representing the karst cave reservoir coefficient.
The dimensionless height λ may be calculated according to the following expression:
the dimensionless fluctuation coefficient beta can be calculated according to the following expression:
wherein ρ represents the fluid density, D represents the wellbore diameter, v 0 Indicating the initial velocity (which can be calculated from the flow).
The dimensionless damping coefficient γ can be calculated according to the following expression:
the mathematical function Γ (x) may be expressed as:
wherein, the subscript f in the above description indicates a fracture, the subscript v indicates a karst cave, and the subscript w indicates an oil well.
In the fracture-cavity reservoir well test model shown in expression (1), the last equation is a dimensionless equation established based on the conservation of energy law.
The fluid flows into the shaft from the karst cave and flows out of the ground from the shaft, and the continuity equation, the momentum conservation equation and the energy conservation equation to be satisfied by the fluid flow in the process can be expressed as follows:
wherein ρ represents fluid density, t represents time, v represents fluid flow velocity, x-axis represents one-dimensional coordinate axis established downward from center of wellbore, p represents pressure, f represents friction resistance coefficient of fluid, D represents wellbore diameter, p wf And p v Representing the pressure in the well bore and karst cave, respectively, v wf Indicating the velocity of the fluid at the junction of the wellbore and the karst cave.
Taking a fluid element in the wellbore as in fig. 3, the mass conservation can be achieved by:
wherein A represents the cross-sectional area of the infinitesimal.
Under high pressure conditions, where the fluid is compressible, the tubing is also an elastomer, the deformation of which is determined by the tubing diameter, wall thickness and young's modulus of the tubing material, the expansion expression (14) can be obtained:
from the relationship between the total derivative and the partial derivative in the fluid mechanics, it is possible to obtain:
the above expression may be modified as:
considering the compressibility of a fluid, the density term in expression (18) can be expressed as a function of pressure, i.e., there is:
where G represents the volumetric flow rate of the fluid.
Assuming that the tubing is elastically deformed, for a thin walled tube, when the pressure increases dp, the relationship of its radial deformation dD to dp can be expressed as:
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:
joint expression (19) and expression (20), expression (18) can be changed to:
for wave speed C in pipes and fluid systems, there is:
specifically, using the full derivative formula, expression (22) may become:
it can be seen that the pressure conduction in the x-axis direction is in the form of waves, the wave velocity of which is C.
If the karst cave is also considered as a cylinder, the continuity equation is as in expression (24), but the speed of pressure propagation C can be expressed as:
combining the continuity equation with conservation of momentum, one can obtain:
observing the flow of fluid in the karst cave, neglecting gravity and fluid friction due to the small speed v, and considering the storage constant C of the karst cave v Since the friction is a quadratic term of the velocity v, a second order small amount can be omitted, and there are:
the solution of expression (27) is the fluid flow rate in karst cave:
wherein v is 0 Representing the velocity at the initial moment, which can be determined from the ground production. Due to the radius r of the large karst cave v The value of (2) is large, and thereforeThe term is larger and is a constant and can be added to the additional pressure drop. By modifying the equation, the second term to the right in expression (28) can also be ignored, i.e., there is:
the yield Q provided by the karst cave can be obtained, namely:
the velocity v of the fluid flowing into the wellbore wf And can be calculated according to the following expression:
according to the energy conservation equation at the shaft and the karst cave, there are:
the expression (32) can also be converted to the last equation in the fracture-cavity reservoir well test model according to dimensionless definition.
In the embodiment, as shown in fig. 1, in step S102, according to the established fracture-cavity oil reservoir well test model, the method adopts the superposition principle to obtain the true space bottom hole pressure solution when a plurality of karst cavities exist in the stratum at the same time.
Fig. 4 shows a schematic implementation flow chart of obtaining a true space bottom hole pressure solution when multiple karst holes exist in a stratum simultaneously by using a superposition principle in the embodiment.
In this embodiment, as shown in fig. 4, the method performs laplace transformation on the fracture-cavity reservoir well test 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:
wherein,representing a first laplace space bottom-hole pressure solution function, u representing a laplace variable.
The volume coefficient B is calculated according to the following expression:
wherein M is 1 、M 2 、M 3 、M 4 T represents an intermediate parameter, and the specific meaning is as above. K (K) 0 Representing zero-order Bessel functions of the second class, s v Represents the skin coefficient of karst cave, r vD Represents the radius of the dimensionless karst cave, K 1 Representing a first order Bessel function of a second class, C wD Represents the dimensionless wellbore reservoir coefficient, lambda represents the dimensionless height, C vD Represents the dimensionless karst cave storage coefficient, alpha represents the correction coefficient, and beta representsThe coefficient of fluctuation, γ, represents the damping coefficient.
Of course, in other embodiments of the present invention, the method may also use other reasonable ways to perform laplace transformation on the fracture-cavity reservoir well test model according to actual needs, so as to obtain the first laplace space bottom hole pressure solution function.
In this embodiment, as shown in fig. 4, the method uses the superposition principle to determine the dimensionless pressure function of the source sink at the wellbore in step S402. Specifically, referring to the fractured reservoir test simplified model shown in FIG. 2, when multiple karst cave (2 karst cave are examples) exist in the formation, the first karst cave 202 provides the production Q for the wellbore 201 1 The second karst cave 203 provides the production Q for the wellbore 201 2 。
During the flow to the wellbore, the pressure of the first and second karst caves 202, 203 may decrease. Thus, for the wellbore 201, the first and second karst caverns 202, 203 are present in an amount corresponding to 2 separate production rates Q in the formation 1 And Q 2 Is being produced at the same time. The superposition principle can be utilized to obtain the true space bottom hole pressure solution when the first karst cave 202 and the second karst cave 203 exist simultaneously.
If the first karst cave 202 and the second karst cave 203 are considered as point sources, then, according to the source sink theory, the continuity equation of the multi-source sink in the formation is considered as follows:
wherein q i (i=1, 2,.) represents the intensity of the ith sink source (i.e., the ith karst cave), M 1 And M 2 The positions of the first and second point sources in space are represented by M, the positions of any points in space, and δ, the physical quantities (e.g., particles, point charges, point heat, concentration forces, etc.) that are distributed in a concentrated manner.
The delta function is a mathematical tool describing a centrally distributed physical quantity. If the centrally distributed physical quantities are to be described mathematically by a delta function, it fulfils the following two requirements:
an important property of the delta function is: for any continuous function f (x, y, z), there is:
another important property of the delta function is symmetry, i.e. presence:
δ(M-M O )＝δ(M O -M) (44)
using the microcompression assumption and substituting darcy's law into expression (40), one can obtain:
the dimensionless quantity is defined and a dimensionless source-sink equation is solved, so that the dimensionless pressure of the source-sink at the shaft can be obtained, namely that:
wherein P is DwfL Representing dimensionless pressure of a source sink at a wellbore, t D Represent dimensionless time, E i Represents an exponential integral function, L 1D Represents the dimensionless distance of the 1 st karst cave from the shaft, Q 1D Represents the flow ratio provided by the 1 st karst cave, L 2D Represents the dimensionless distance of the 2 nd karst cave from the shaft, Q 2D Indicating the flow ratio provided by the 2 nd karst cave.
If there are multiple karst holes in the fracture-cave reservoir well test model, then expression (45) may be written as:
wherein Q is jD Represents the flow ratio provided by the jth karst cave, L jD The dimensionless distance of the jth karst cave from the wellbore is represented, and J represents the total number of karst cave.
Dimensionless pressure P of a source sink at a wellbore DwfL Can be expressed as:
dimensionless time t D Can be expressed as:
dimensionless distance L of 1 st karst cave from wellbore 1D Can be expressed as:
dimensionless distance L of 2 nd karst cave from wellbore 2D Can be expressed as:
exponential integral function E i Can be expressed as:
the 1 st karst cave (i.e. first karst cave) provides a flow ratio Q 1D Can be expressed as:
the flow ratio Q provided by the 2 nd karst cave (second karst cave) 2D Can be expressed as:
as shown in fig. 4, in this embodiment, after obtaining the dimensionless pressure function of the source sink at the wellbore, the method performs laplace transformation on the dimensionless pressure function of the source sink at the wellbore in step S403, thereby obtaining a second laplace space bottom hole pressure solution function
The method then proceeds to step S404 according to the first Laplace space bottom hole pressure solution function determined in step S401And the second Laplace space bottom hole pressure solution function determined in step S403 +.>To determine a solution function of the bottom hole pressure in the laplace space taking into account the point source function.
Specifically, in this embodiment, the solution function of the bottom hole pressure in the laplace space after considering the point source function can be expressed as:
wherein,representing the solution function of the bottom hole pressure in the laplace space after considering the point source function. />
At the point of considerationBottom hole pressure solution function on Laplace space after source functionThe method may preferably be based on the solution function +_in step S405 for the bottom hole pressure in Laplace space after considering the point source function>And inverting to obtain a true space bottom hole pressure solution when a plurality of karst caves exist in the stratum at the same time.
Specifically, in this embodiment, the method preferably uses the Stehfest numerical inversion technique in step S405 to determine the true space bottom hole pressure solution when multiple karst holes exist in the formation at the same time. For example, a true space bottom hole pressure solution when multiple karsts are present in the formation at the same time may be determined according to the following expression:
wherein p is wD Representing the real space bottom hole pressure solution when a plurality of karst cave exist in stratum at the same time, t D Represents the dimensionless time, N represents a constant,representing the solution function of the bottom hole pressure in the 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 be configured to other reasonable values according to actual needs, and the present invention is not limited to the specific value of the constant N.
It should be noted that, in other embodiments of the present invention, the method may also use other reasonable ways to obtain the true space bottom hole pressure solution when multiple karst holes exist in the stratum at the same time according to practical needs.
In this embodiment, after obtaining the real-space bottom-hole pressure solutions when the plurality of karst cave exist simultaneously, the method fits the real-space bottom-hole pressure solutions obtained in step S102 and the actually 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 the true space bottom hole pressure solution when a plurality of karst cave exist simultaneously, and then obtains the dimensionless distance L from each karst cave to the shaft by fitting the double logarithmic pressure and derivative of the actual pressure recovery curve D . The method will then be based on the resulting dimensionless distance L D And a wellbore radius r w And determining the distance L from each karst cave to the shaft.
In this embodiment, the method preferably determines the karst cave to wellbore distance according to the following expression:
L＝L D ×r w (57)
wherein L represents the distance from the karst cave to the well bore.
It should be noted that, in the embodiment, when curve fitting is performed, the number of karst cave included in the stratum may also be determined according to the number of upturned sections (for example, the number of sections with a slope equal to 1 in the curve) of the curve corresponding to the true space bottom hole pressure solution obtained in the step S102.
To more clearly illustrate the reliability and advantages of the method for determining the hole distance in the stratum provided by the embodiment, taking a certain stratum as an example, bottom hole pressure and derivative double logarithmic curves of different dimensionless distances when a karst cave exists in the stratum as shown in fig. 5 can be obtained. The calculation parameters in fig. 5 are respectively: c (C) D e 2S =100, dimensionless distance L D 200, 300 and 400 respectively.
When multiple karst cavities are present in the formation, the resulting typical curve will also change, and FIG. 6 shows a schematic diagram of a typical curve when multiple karst cavities are present in the formation. Wherein the calculated parameters in FIG. 6 are C respectively D e 2S =100, dimensionless distanceFrom L 1D 100 dimensionless distance L 2D 600.
As can be seen from fig. 5 and fig. 6, when a karst cave exists in the stratum, the pressure derivative curve will be tilted up, the number of karst cave can be determined from the number of tilted up derivative curves, and the dimensionless distance can be obtained through curve fitting values.
By deriving the actual pressure recovery curve, a pressure derivative double logarithmic curve can be plotted, fitting to the plate shown in FIG. 5. Table 1 shows the basic parameters of the well case and fig. 7 shows the log-log pressure and derivative fitting map of the well case. Wherein, the calculation parameter C of the plate D e 2S ＝3.28×10 16 ，L D ＝1290.6。
TABLE 1
According to the dimensionless distance L from karst cave to shaft D The distance from the karst cave to the shaft can be obtained, namely:
L＝L D ×r w ＝1290.6×0.67＝86.47 (58)
meanwhile, the number of the upturned sections of the actual measurement curve can be seen, and only one karst cave exists in the stratum.
From the above description, the method and the system for determining the hole distance in the stratum provided by the invention provide a matched interpretation method for calculation of fracture-cavity type oil reservoir parameters and calculation of reserves, can directly interpret the number and the distance of karst cavities in the fracture-cavity type oil reservoir, and provide technical support for formulation of an oil field development scheme.
The fracture-cavity oil reservoir well test model used by the method has the advantages of simple model result, convenient solution, capability of giving an analytical solution in the Laplace space, no relation to the calculation of complex functions, and high calculation speed. Meanwhile, the method can conveniently give the number and the distance of karst cave according to the interpretation result of curve fitting.
It is to be understood that the disclosed embodiments are not limited to the specific structures or process steps disclosed herein, but are intended to extend to equivalents of these features as would be understood by one of ordinary skill in the relevant arts. 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 intended to illustrate the principles of the invention in one or more applications, it will be apparent to those skilled in the art that various modifications in form, use and details of implementation may be made without departing from the principles and concepts of the invention. Accordingly, the invention is defined by the appended claims.
Claims (5)
1. A method of determining a hole distance in a formation, the method comprising:
step one, establishing a fracture-cavity type oil reservoir well test model, and taking a karst cavity in a stratum as a point source;
obtaining a true space bottom hole pressure solution when a plurality of karst caves exist in a stratum at the same time by adopting a superposition principle according to the fracture-cave type oil reservoir well test model, wherein the second step comprises the following steps:
step a, carrying out Laplace transformation on the fracture-cavity oil reservoir well test model to obtain a first Laplace space bottom hole pressure solution function, wherein in the step a, the first Laplace space bottom hole pressure solution function is expressed as:
wherein,represents a first Laplace space bottom hole pressure solution function, u represents a Laplace variable, M 1 And B represent intermediate parameters, respectively, wherein the intermediate parameters are calculated according to the following expression:
wherein M is 1 、M 2 、M 3 、M 4 T represents an intermediate parameter, K 0 Representing zero-order Bessel functions of the second class, s w Represents the skin coefficient of the wellbore, s v Represents the skin coefficient of karst cave, r vD Represents the radius of the dimensionless karst cave, K 1 Representing a first order Bessel function of a second class, C wD Representing dimensionlessWellbore reservoir coefficient, λ represents dimensionless height, C vD The method is characterized in that the method comprises the steps of expressing a dimensionless karst cave storage coefficient, wherein alpha represents a correction coefficient, beta represents a fluctuation coefficient, and gamma represents a damping coefficient;
step b, determining a dimensionless pressure function of the source sink at the well bore by adopting a superposition principle, wherein in the step b, the dimensionless pressure function of the source sink at the well bore is determined according to the following expression:
wherein P is DwfL Representing dimensionless pressure of a source sink at a wellbore, t D Represent dimensionless time, E i Represents an exponential integral function, Q jD Represents the flow ratio provided by the jth karst cave, L jD The dimensionless distance between the jth karst cave and the shaft is represented, and J represents the total number of karst cave;
step c, carrying out Laplace transformation according to the dimensionless pressure function of the source sink at the shaft to obtain a second Laplace space bottom hole pressure solution function;
step d, determining a bottom hole pressure solution function in the Laplace space after the point source function is considered according to the first and second Laplace space bottom hole pressure solution functions, wherein in the step d, the bottom hole pressure solution function in the Laplace space after the point source function is considered is determined according to the following expression:
wherein,representing the solution function of the bottom hole pressure in Laplace space after considering the point source function, +.>Representing a first Laplace space bottom hole pressure solution function,/->Representing a second laplace space bottom hole pressure solution function;
step e, inverting according to a bottom hole pressure solution function on the Laplace space after the point source function is considered to obtain a real space bottom hole pressure solution when a plurality of karst holes in the stratum exist at the same time;
fitting the real space bottom hole pressure solution and the actually measured bottom hole pressure data when a plurality of karst cave exist simultaneously, and determining the distance from the karst cave to the shaft according to the fitting result.
2. The method of claim 1, wherein in step e, a true space bottom hole pressure solution for the simultaneous presence of multiple karst cave in the formation is determined according to the following expression:
wherein p is wD Representing the real space bottom hole pressure solution when a plurality of karst cave exist in stratum at the same time, t D Represents the dimensionless time, N represents a constant,representing the solution function of the bottom hole pressure in the laplace space after considering the point source function.
3. The method according to claim 1 or 2, wherein in said step three,
fitting by utilizing real space bottom hole pressure solutions when a plurality of karst caves exist simultaneously and actually measured bottom hole pressure data to obtain dimensionless distances from each karst cave to a shaft;
and determining the distance from each karst cave to the shaft according to the dimensionless distance and the shaft radius.
4. The method of claim 3, wherein the karst cave to wellbore distance is determined according to the following expression:
L＝L D ×r w
wherein L represents the distance from the karst cave to the shaft, L D Representing the dimensionless distance from the karst cave to the shaft, r w Representing the wellbore radius.
5. A system for determining the hole distance in a formation, wherein the system uses the method of any one of claims 1 to 4 to determine the hole-to-wellbore distance in the formation.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106599449A (en) * | 2016-12-12 | 2017-04-26 | 中国石油化工股份有限公司 | Well test explanation method for cave volume calculation |
| CN107563027A (en) * | 2017-08-21 | 2018-01-09 | 西南石油大学 | For analyzing the WELL TEST INTERPRETATION MODEL and method of more fracture-cavity units cascaded structures |
| CN108798634A (en) * | 2018-07-09 | 2018-11-13 | 合肥辰工科技有限公司 | A kind of fractured-vuggy reservoir list hole-mean value of single layer Well Test Data Analysis Method |
| CN108920849A (en) * | 2018-07-09 | 2018-11-30 | 合肥辰工科技有限公司 | A kind of fractured-vuggy reservoir well testing determines hole method of flow in stratum |
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106599449A (en) * | 2016-12-12 | 2017-04-26 | 中国石油化工股份有限公司 | Well test explanation method for cave volume calculation |
| CN107563027A (en) * | 2017-08-21 | 2018-01-09 | 西南石油大学 | For analyzing the WELL TEST INTERPRETATION MODEL and method of more fracture-cavity units cascaded structures |
| CN108798634A (en) * | 2018-07-09 | 2018-11-13 | 合肥辰工科技有限公司 | A kind of fractured-vuggy reservoir list hole-mean value of single layer Well Test Data Analysis Method |
| CN108920849A (en) * | 2018-07-09 | 2018-11-30 | 合肥辰工科技有限公司 | A kind of fractured-vuggy reservoir well testing determines hole method of flow in stratum |
Non-Patent Citations (1)
| Title |
|---|
| 流线干扰数值试井解释模型及矿场应用;吴明录等;《西安石油大学学报(自然科学版)》;20131125(第06期);第67-71 * |
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