CN110362931B - Oil and gas reservoir well testing interpretation model and method based on karst cave point source equivalent principle - Google Patents

Oil and gas reservoir well testing interpretation model and method based on karst cave point source equivalent principle Download PDF

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CN110362931B
CN110362931B CN201910646964.6A CN201910646964A CN110362931B CN 110362931 B CN110362931 B CN 110362931B CN 201910646964 A CN201910646964 A CN 201910646964A CN 110362931 B CN110362931 B CN 110362931B
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karst cave
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刘建仪
刘治彬
刘学利
邹宁
黄知娟
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Southwest Petroleum University
Sinopec Northwest Oil Field Co
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Sinopec Northwest Oil Field Co
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Abstract

The invention discloses an oil and gas reservoir well testing explanation model and method based on a karst cave point source equivalent principle, which comprises the following steps: s1, establishing a karst cave point source equivalent radial oil and gas reservoir well testing physical model; s2, establishing a mathematical model of seepage of the production well in the dual-medium stratum and solving the mathematical model; s3, establishing a mathematical model with karst cave equivalence as an injection well; s4, simultaneously solving the equivalent injection well and production well mathematical models, and drawing a log-log typical well testing curve of bottom pressure and pressure derivative; and S5, fitting the bottom hole pressure and pressure derivative typical well test curve with the measured bottom hole pressure and pressure derivative curve, and explaining the formation parameters. The invention establishes a karst cave point source equivalent radial well testing model aiming at a radial oil and gas reservoir with large karst caves in discrete distribution, takes continuously-developed natural microcracks and erosion and dissolution holes in the oil and gas reservoir as double continuous media, and equates the large karst caves as discrete distribution variable strength point sources to establish the radial oil and gas reservoir karst cave point source equivalent radial well testing model.

Description

Oil and gas reservoir well testing interpretation model and method based on karst cave point source equivalent principle
Technical Field
The invention relates to the technical field of geological exploration, in particular to an oil and gas reservoir well testing interpretation model and method based on a karst cave point source equivalent principle.
Background
The carbonate reservoir fracture-cave is unbalanced in development, extremely strong in heterogeneity, complex in reservoir type and diverse in reservoir space. There are four types that can be distinguished by reservoir type: fractured, fractured-vuggy, and vuggy-fractured-vuggy reservoirs. The fracture-cave type oil reservoir with the simultaneously developed fracture and karst cave is an important oil reservoir type, the fracture-cave type oil reservoir represented by the oil field of the Taliman basin and the Tahe in China accounts for more than 30% of the total quantity of carbonate rock oil reservoirs, and the fracture-cave type oil reservoir is also an important branch field of the increasing storage and the increasing production of the carbonate rock oil reservoirs.
A large number of natural cracks and corrosion and dissolution holes develop in the fracture-cavity type oil reservoir, and a plurality of large dissolution holes are distributed in the oil reservoir in a scattered manner, and the three media are good oil and gas storage spaces. For the well testing model of the oil deposit, because of the existence of the discrete big karst cave, the seepage flow model can not be established based on the continuous medium theory, therefore, the oil deposit is mostly calculated by adopting an equivalent model or a numerical simulation method at present, and the defects are that the error of the former is large, the modeling of the latter is difficult and the calculation amount is large. For example, the classical continuous dual medium model proposed by Warren, Root [2] and the scholars at home and abroad propose various well testing models and draw corresponding well testing theory charts after decades of researches, but most of the well testing theories are based on continuous medium assumptions, the continuity assumption of the well testing models is not completely applicable to fracture-cavity type oil reservoirs with large fracture-cavity development scale and discrete distribution, and the continuous medium model well testing charts are often difficult to fit to actual measurement curves of the fracture-cavity oil reservoir mines and cannot release large-scale fractures and large karst-cavity parameters. In recent years, students establish a well drilling solution cavity well testing model, a fracture cavity series-parallel combination well testing model and other well testing models based on a non-continuous medium to successfully solve fracture cavity parameters, but the fracture cavity combination modes of the models are simple, the application range is limited, and the models cannot be applied to oil reservoirs with more fracture cavity combination types. Therefore, the method and the model for testing the fracture-cavity oil reservoir based on the discontinuous medium and establishing different fracture-cavity combination relations have important significance in further knowing the multi-scale flow rule of the fracture-cavity oil reservoir.
Disclosure of Invention
Aiming at the problems, the invention provides an oil and gas reservoir well testing explanation model and a method based on a karst cave point source equivalent principle, wherein a karst cave point source equivalent radial well testing model is established for a radial oil reservoir with large karst cave discrete distribution, natural micro-cracks and corrosion dissolving holes which continuously develop in the oil reservoir are regarded as double continuous media, the large karst cave is equivalent to a discrete distribution variable strength point source, a karst cave point source equivalent thought theory is provided, and the karst cave point source equivalent radial well testing model is established.
The invention adopts the following technical scheme:
an oil and gas reservoir well testing explanation model and method based on karst cave point source equivalent principle comprises the following steps:
s1, establishing a karst cave point source equivalent radial oil and gas reservoir well testing physical model;
s2, establishing a dimensionless mathematical model of seepage of the production well in the dual-medium stratum, and solving an expression of pressure drop caused by the production well at any point in the stratum;
s3, establishing a dimensionless mathematical model with karst cave equivalent as an injection well;
s4, solving the equivalent injection well and production well dimensionless mathematical model in a simultaneous mode, calculating to obtain a Laplace bottom flowing pressure expression through a stratum pressure drop superposition principle, and obtaining a pressure and pressure derivative typical well testing curve in a real space by adopting Stehfest numerical inversion calculation;
and S5, fitting a typical well testing curve of the bottom hole pressure and the pressure derivative with an in-situ measured bottom hole pressure and pressure derivative curve through an optimization algorithm to explain the formation parameters.
Preferably, in step S1, the physical model of the karst cave point source equivalent radial well test is: in a radial oil and gas reservoir, large karst caves which are not drilled in production wells distributed in a scattered mode are equivalent to injection wells with variable well diameter and injection amount.
Preferably, the mathematical model of the production well seepage in the dual medium formation is established in step S2 as follows:
differential control equation:
Figure GDA0003469021700000031
Figure GDA0003469021700000032
inner boundary conditions:
Figure GDA0003469021700000033
outer boundary conditions:
infinite formation:
p0fD(∞,tD)＝0 (4)
closing the boundary stratum:
Figure GDA0003469021700000034
and (3) constant pressure boundary stratum:
p0fD(reD,tD)＝0 (6)
initial conditions:
p0fD(rD,0)＝0 (7)
the dimensionless bottom hole flow pressure produced by the production well is:
Figure GDA0003469021700000035
in the formula, p0fDThe dimensionless pressure of the fracture system is only considered when the production well produces, and the dimensions are not needed; p is a radical of0vDThe dimensionless pressure and dimension of a dissolved hole system are considered only when the production well is produced; r isDDimensionless radial distance, dimensionless; t is tDDimensionless time and dimension are not included; omega is the elastic storage-capacity ratio of the crack and has no dimension; lambda is a channeling coefficient and is dimensionless; cDThe method is dimensionless and dimensionless for dimensionless well bore storage coefficients; r iseDDimensionless radial distance, dimensionless; p is a radical of0wDDimensionless bottom hole flow pressure for production well production is dimensionless; s is an epidermal coefficient and has no dimension;
the bottom hole pressure expression of any point in the stratum caused by a production well is as follows:
Figure GDA0003469021700000041
wherein:
Figure GDA0003469021700000042
definite solution parameter A0、B0The values of (A) are as follows:
1) infinite boundary:
Figure GDA0003469021700000043
2) and (3) closing the boundary:
Figure GDA0003469021700000044
3) and (3) constant pressure boundary:
Figure GDA0003469021700000045
in the formula, sigma is an intermediate variable,
Figure GDA0003469021700000046
the dimensionless bottom hole flowing pressure in Laplace is MPa; s is a Laplace variable, dimensionless; a. the0、B0Undetermined parameters related to the boundary conditions of the model are dimensionless; i is1A first class of modified Bessel function that is zero first order; k1A second type modified Bessel function of zero first order; f(s) is a characteristic function, dimensionless; cDThe method is dimensionless and dimensionless for dimensionless well bore storage coefficients; r iseIs the reservoir radius, m; omega is the elastic storage-capacity ratio of the crack and has no dimension; lambda is a channeling coefficient and is dimensionless; r iswDIs the dimensionless production well bore radius, m; i is0A first type of modified Bessel function of zero order; k0A modified Bessel function of the second type of zero order; s is the epidermis coefficient and has no dimension.
Preferably, the dimensionless mathematical model for the cavern equivalent injection well in step S3 is:
Figure GDA0003469021700000051
inner boundary conditions:
Figure GDA0003469021700000052
wherein, the pressure at any point in the stratum is the sum of the pressure drops generated by the production well and all equivalent wells, namely:
pD＝p0D+p1D+p2D+...+pND (16)
outer boundary conditions:
1) infinite:
pjD(∞,tD)＝0 (17)
2) and (3) closing the boundary:
Figure GDA0003469021700000053
3) and (3) constant pressure boundary:
pjD(re,tD)＝0 (19)
in the formula, pDDimensionless actual formation pressure, MPa; p is a radical ofjDThe dimensionless pressure, MPa, generated when the equivalent injection well at the jth opening is independently injected; r isDDimensionless radial distance, dimensionless; t is tDDimensionless time and dimension are not included; p is a radical ofDThe actual formation pressure is dimensionless pressure; h isDDimensionless formation thickness, dimensionless; vjDThe dimensionless volume and dimension of the jth karst cave are eliminated; r iswjDThe injection well of the jth opening has dimensionless radius and no dimension; r iseDDimensionless radial distance, dimensionless; r iseIs the reservoir radius, m; p is a radical ofNDThe dimensionless pressure generated by the equivalent well of the Nth hole is dimensionless.
Preferably, all pressure parameters p of the mathematical model in the well testing interpretation model of the oil and gas reservoir are replaced by the gas reservoir simulated pressure psi, and the fluid physical property parameters adopt corresponding gas reservoir gas parameters, so that the gas reservoir karst cave point source equivalent well testing model is obtained.
Preferably, the optimization algorithm in step S5 is a genetic algorithm, the in-situ measured bottom hole pressure and derivative curve are compared with the curve calculated by the established well testing interpretation model, and the error is used as an objective function:
Figure GDA0003469021700000061
in the formula: p is a radical ofcCalculating the obtained bottom hole pressure of the model in MPa; p is a radical oft *The bottom hole pressure is measured in situ in MPa; n is the number of experimental data.
The invention has the beneficial effects that:
1. a karst cave point source equivalent radial well testing model is established for a radial oil and gas reservoir with large karst caves in discrete distribution, natural microcracks and erosion karst caves which continuously develop in the oil and gas reservoir are regarded as double continuous media, the large karst caves are equivalent to discrete distribution variable strength point sources, the thought theory of the karst cave point source equivalent is provided, and the karst cave point source equivalent radial well testing model is established.
2. And carrying out dimensionless calculation on the established mathematical model, carrying out Laplace transformation solving, obtaining a dimensionless pressure and pressure derivative well testing typical chart through numerical inversion, and compiling corresponding well testing interpretation software to carry out fitting interpretation on the field measured data.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly described below, and it is apparent that the drawings in the following description only relate to some embodiments of the present invention and are not limiting on the present invention.
FIG. 1 is a schematic diagram of a fracture-cavity radial reservoir physical model according to the present invention;
FIG. 2 is a schematic diagram of a physical model of a karst cave point source equivalent radial stratum according to the present invention;
FIG. 3 is a schematic diagram of a typical well testing plate (single karst cave) of the karst cave point source equivalent model of the present invention;
FIG. 4 is a schematic diagram of a typical well testing plate (without erosion holes) of the cave point source equivalent model of the present invention;
FIG. 5 is a schematic view of the main flow of the well testing interpretation procedure of the present invention;
FIG. 6 is a well testing fitting graph of a target well of the present invention;
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the drawings of the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention without any inventive step, are within the scope of protection of the invention.
Unless otherwise defined, technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this disclosure belongs. The use of the word "comprising" or "comprises", and the like, in this disclosure is intended to mean that the elements or items listed before that word, include the elements or items listed after that word, and their equivalents, without excluding other elements or items. "upper", "lower", "left", "right", and the like are used merely to indicate relative positional relationships, and when the absolute position of the object being described is changed, the relative positional relationships may also be changed accordingly.
The invention is further illustrated with reference to the following figures and examples.
As shown in fig. 1 to 6, a hydrocarbon reservoir well testing interpretation model and method based on karst cave point source equivalence principle includes the following steps:
s1, establishing a karst cave point source equivalent radial oil and gas reservoir well testing physical model;
as shown in figure 1, considering that in a radial reservoir, a plurality of large karsts distributed discretely develop, and a production well does not drill and meet the karsts. The reservoir outside the large cavern is a continuously developed natural fracture and erosion hole dual continuous medium reservoir;
the volume of the discretely distributed large karst caves is smaller than the whole oil reservoir range, the influence of the boundaries on the pressure distribution of the whole oil reservoir is small and can be ignored, the action of the large karst caves on the oil reservoir can be described as energy supply, a behavior model is similar to a point source, and the supply intensity depends on the pressure gradient of the position. Thus, a large cavern can be equivalent to a point source of varying strength (or a production well with a well diameter), with an equivalent model as shown in fig. 2; the basic assumptions of its physical model are as follows:
(1) the reservoir is developed with a matrix, continuously distributed natural fractures, continuously distributed erosion holes and discretely distributed karst caves, the reservoir matrix is compact, and has no storage and seepage capacity, and the natural fractures and the karst caves are continuous media. A plurality of large karsts are randomly distributed in the oil reservoir, and the distance between each karst cave and the well shaft of the production well is r1,r2,r3...rNVolume is V1,V2,V3...VNAnd the big cavern is a discrete medium. The karst cave is connected with the stratum through the natural cracks to form a channel, and the scattered large karst cave is equivalent to a variable strength point source.
(2) The vertical well produces with fixed yield, the reservoir fluid is single-phase crude oil, and the karst cave is completely filled with the crude oil;
(3) the cracks are channels for fluid to flow, and in the flowing process, the channeling only occurs in the flow of the erosion holes and the karst caves to the cracks.
(4) The flow of the crude oil in the crack and the pore-dissolving system is Darcy isothermal flow, and capillary force and gravity are ignored;
(5) the stratum pressure at the initial moment is equal everywhere and is the original stratum pressure;
(6) the karst cave, the cracks and the fluid are all slightly compressible, and the compression coefficient is constant;
(7) consider wellbore reservoir effects and skin effects.
S2, establishing a dimensionless mathematical model of seepage of the production well in the dual-medium stratum, and solving an expression of pressure drop caused by the production well at any point in the stratum;
dimensionless variables are defined as follows:
only the dimensionless pressure of the fracture system at production of the production well is considered:
Figure GDA0003469021700000081
only the dimensionless pressure of the solution pore system when producing the production well is considered:
Figure GDA0003469021700000082
dimensionless time tD：
Figure GDA0003469021700000091
Dimensionless radial distance rD：
Figure GDA0003469021700000092
Dimensionless radial distance rD：
Figure GDA0003469021700000093
Dimensionless wellbore reservoir coefficient CD：
Figure GDA0003469021700000094
Elastic storage capacity ratio ω:
Figure GDA0003469021700000095
the blow-by coefficient λ:
Figure GDA0003469021700000096
in the formula: kfPermeability of the fracture System, μm2；KvPermeability of the pore system, μm2；
Figure GDA0003469021700000097
The porosity of a crack system and a pore dissolving system is dimensionless; cft、CvtThe comprehensive compression coefficients of a crack system and a pore-dissolving system are respectively MPa-1；p0f、p0vRespectively causing the pressure of a fracture system and a pore dissolving system for a production well, wherein the pressure is MPa; p is a radical ofiIs the original pressure of the stratum, MPa; q is the production well yield, m3D; mu is the viscosity of the crude oil, mPa & s; b isoIs the volume coefficient of crude oil, m3/m3(ii) a r is a radial coordinate, m; r iswIs the radius of the production well bore, m; r iseIs the reservoir radius, m; c is the wellbore storage coefficient, MPa-1(ii) a h is the formation thickness, m; omega is the elastic storage-capacity ratio of the crack and has no dimension; lambda is a channeling coefficient and is dimensionless; α is a shape factor, m-2(ii) a r is a radial coordinate, m; t is well productionProduction time h;
the formation seepage differential equation is:
Figure GDA0003469021700000101
Figure GDA0003469021700000102
inner boundary conditions:
Figure GDA0003469021700000103
outer boundary conditions:
infinite formation:
p0fD(∞,tD)＝0 (4)
closing the boundary stratum:
Figure GDA0003469021700000104
and (3) constant pressure boundary stratum:
p0fD(reD,tD)＝0 (6)
initial conditions:
p0fD(rD,0)＝0 (7)
the dimensionless bottom hole flow pressure produced by the production well is:
Figure GDA0003469021700000105
in the formula, p0fDThe dimensionless pressure of the fracture system is only considered when the production well produces, and the dimensions are not needed; p is a radical of0vDThe dimensionless pressure and dimension of a dissolved hole system are considered only when the production well is produced; r isDDimensionless radial distance, dimensionless; t is tDDimensionless time and dimension are not included; omega is the elasticity of crackThe storage volume ratio is dimensionless; lambda is a channeling coefficient and is dimensionless; cDThe method is dimensionless and dimensionless for dimensionless well bore storage coefficients; r iseDDimensionless radial distance, dimensionless; p is a radical of0wDDimensionless bottom hole flow pressure for production well production is dimensionless; s is an epidermal coefficient and has no dimension;
performing a Rayleigh transform on the dimensionless mathematical models (formula (1) to formula (8)) and eliminating
Figure GDA0003469021700000106
The following can be obtained:
Figure GDA0003469021700000111
wherein:
Figure GDA0003469021700000112
inner boundary conditions:
Figure GDA0003469021700000113
outer boundary conditions:
infinite:
Figure GDA0003469021700000114
and (3) closing the boundary:
Figure GDA0003469021700000115
and (3) constant pressure boundary:
Figure GDA0003469021700000116
bottom hole flowing pressure:
Figure GDA0003469021700000117
then, equation (29) is solved as follows:
Figure GDA0003469021700000118
in the formula, A0、B0Undetermined parameters related to the boundary conditions of the model are dimensionless; f(s) is a characteristic function, dimensionless; i is0Is as follows; k0Is as follows; s is;
equation (29) is derived:
Figure GDA0003469021700000121
in the formula I1The first kind of modified Bessel function is zero-order and has no dimension; sigma is an intermediate variable and is dimensionless;
equations (36) through (37) can be substituted for equation (35) to obtain the bottom hole flow pressure:
Figure GDA0003469021700000122
substituting the formula (37) into the inner boundary condition formula (31) and the outer boundary condition formulas (32), (33), (34) can obtain the waiting coefficient A under three outer boundary conditions0、B0The value of (c):
infinite boundary:
Figure GDA0003469021700000123
and (3) closing the boundary:
Figure GDA0003469021700000124
and (3) constant pressure boundary:
Figure GDA0003469021700000125
in the formula (I), the compound is shown in the specification,
Figure GDA0003469021700000126
dimensionless bottom hole flow pressure in Laplace; s is a laplace variable; a. the0、B0Undetermined parameters related to boundary conditions for the model; i is0A first type of modified Bessel function of zero order; k0A modified Bessel function of the second type of zero order; i is1A first order modified Bessel function; k1A modified Bessel function of a first order and a second kind; f(s) is a characteristic function.
S3, establishing a dimensionless mathematical model with karst cave equivalent as an injection well;
after the karst cave is equivalent to an injection well, according to the pressure superposition principle, the pressure drop of the jth karst cave is the algebraic sum of the pressure drops formed by all the karst cave equivalent injection wells and the production wells at the jth cave. At this time, the flow rate of the jth cavern is the elastic change amount of the cavern. The Darcy's law and the elastic law can be written as:
Figure GDA0003469021700000131
wherein p is the actual formation pressure in the reservoir:
p＝pi-(Δp0+Δp1+Δp2+...+ΔpN) (39)
wherein p is the actual formation pressure in the reservoir; mu is the viscosity of the crude oil, mPa & s; h is the formation thickness, m; r is a radial coordinate, m; vjVolume of the jth karst cave, m3(ii) a Cvj is comprehensive compression coefficient of karst cave, MPa-1；Δp0The pressure drop created for the production well (j ═ 1,2,3, …, N), MPa; Δ pjCreating a pressure drop (j ═ 1,2,3, …, N), MPa, for the jth equivalent injection well; Δ pNCreating a pressure drop for the nth equivalent injection well.
rwjThe equivalent injection well radius of the jth karst cave is equivalent to the following by volume:
Figure GDA0003469021700000132
the dimensionless quantity is redefined on the basis of step S2:
dimensionless pressure P generated by independent injection of the equivalent injection well at the jth openingjD(j ═ 1,2,3 … N, the same applies below):
Figure GDA0003469021700000133
dimensionless pressure actual formation pressure PD：
Figure GDA0003469021700000134
Is dimensionless formation thickness hD：
Figure GDA0003469021700000135
The ratio of the compressive coefficient of cracks to the compressive coefficient of pores is (a):
Figure GDA0003469021700000136
dimensionless volume V of jth cavernjD:
Figure GDA0003469021700000141
Defining a dimensionless radius r for the jth injection wellwjD：
Figure GDA0003469021700000142
In the formula, PjfThe pressure generated when the equivalent injection well of the jth opening is injected independently (j is 1,2,3 … N, the same below), wherein, the pressure is Mpa, and the pressure is the actual pressure of the stratum; vjVolume of the jth karst cave, m3 rwjIs the jth injection well radius, m.
The dimensionless mathematical model for the injection well is:
dimensionless differential equation of seepage:
Figure GDA0003469021700000143
inner boundary conditions:
Figure GDA0003469021700000144
wherein the pressure at any point in the formation gives rise to the sum of the pressure drops for the production well and all equivalent wells, i.e.:
pD＝p0D+p1D+p2D+...+pND (16)
outer boundary conditions:
1) infinite:
pjD(∞,tD)＝0 (17)
2) and (3) closing the boundary:
Figure GDA0003469021700000145
3) and (3) constant pressure boundary:
pjD(re,tD)＝0 (19)
in the formula, pDDimensionless actual formation pressure, MPa; p is a radical ofjDThe dimensionless pressure, MPa, generated when the equivalent injection well at the jth opening is independently injected; r isDDimensionless radial distance, dimensionless; t is tDDimensionless time and dimension are not included; p is a radical ofDIs dimensionless pressure actual formation pressure, and has no volumeA head line; h isDDimensionless formation thickness, dimensionless; vjDThe dimensionless volume and dimension of the jth karst cave are eliminated; r iswjDThe injection well of the jth opening has dimensionless radius and no dimension; r iseDDimensionless radial distance, dimensionless; r iseIs the reservoir radius, m;
s4, performing Laplace transformation on the equivalent injection well and production well dimensionless mathematical models (formulas (14) - (19)), performing simultaneous solution, calculating by using a stratum pressure drop superposition principle to obtain a Laplace bottom flowing pressure expression, and performing inversion calculation by using a Stehfest numerical value to obtain a typical well testing curve of pressure and pressure derivative in a real space;
the lagrange transform of each karst cave equivalent injection well (point source) model is:
Figure GDA0003469021700000151
Figure GDA0003469021700000152
outer boundary conditions:
infinite:
Figure GDA0003469021700000153
and (3) closing the boundary:
Figure GDA0003469021700000154
and (3) constant pressure boundary:
Figure GDA0003469021700000155
the general solution of equation (39) is:
Figure GDA0003469021700000156
the derivation of equation (45) can be:
Figure GDA0003469021700000157
substituting equation (47) into the inner boundary condition equation (42) yields N equations:
when j is 1,2,3.. N, i.e. represents the inner boundary condition of the flow at the jth cavern, N equations can be obtained:
Figure GDA0003469021700000161
taking the closed outer boundary as an example, substituting equation (47) into the outer boundary condition (44), the outer boundary condition at the jth karst cave can obtain N equation sets:
Figure GDA0003469021700000162
2N equations can be formed by the 2N equivalent injection wells, and 2N undetermined parameters (A)1,A2,A3...AN-1,AN),(B1,B2,B3...BN-1,BN) Therefore, the values of the 2N parameters can be solved by adopting a linear elimination method, and the equivalent solution of each karst cave can be obtained. Finally, the total pressure drop of the stratum is obtained through the pressure drop superposition principle:
Figure GDA0003469021700000163
if production well skin and well reservoir effects are considered, the bottom hole flow pressure can be expressed as:
Figure GDA0003469021700000164
in the formula (I), the compound is shown in the specification,Ajand BjUndetermined parameters of a model solution of the equivalent injection well of the jth karst cave; r isjThe distance between the jth well and the wellhead of the production well (j is 1,2,3 …, N), m; r is(i,j)The distance between the equivalent injection well of the ith opening and the equivalent injection well of the jth opening is (i is 1,2,3 …, N; j is 1,2,3 …, N); r is(i,j)DThe distance between the equivalent injection well of the ith opening and the equivalent injection well of the jth opening is defined as the distance between the equivalent injection well of the ith opening and the equivalent injection well of the jth opening.
When N is 1, i.e. there is only one isolated cavern in the formation, the laguerre bottom hole flow pressure is expressed as follows:
Figure GDA0003469021700000165
(1) an infinite boundary:
Figure GDA0003469021700000171
(2) and a closed boundary:
Figure GDA0003469021700000172
(3) and a constant pressure boundary:
Figure GDA0003469021700000173
taking a single karst cave model as an example, adopting a Stehfest numerical inversion method to express the dimensionless bottom hole flow pressure in the Las space as follows: performing inversion calculation by using the formula (51) to obtain a typical well testing curve of pressure and pressure derivative in a real space, as shown in fig. 3;
in fig. 3, the radial reservoir karst cave point source equivalent model well testing curve is divided into seven flowing stages:
stage I: in the shaft storage effect stage, the dimensionless pressure and pressure derivative curves are all straight lines with the slope of 1;
stage II: in the stage of skin effect, a curve of pressure and pressure derivative is bent downwards;
stage III: erosion hole channeling stage. The pressure derivative curve is concave, forming a concavity. There may also be a fracture radial flow phase before this phase, characterized by a pressure derivative of "0.5 line".
And IV stage: fracture radial flow phase, the pressure derivative exhibits a "0.5 line".
And a V stage: and in the large cavern channeling stage, the pressure derivative curve is concave downwards to form a second concave. The big cavern forming pits are different from the cavern forming pits in that: after the corrosion hole is sunken, the pressure derivative line is directly transited to a '0.5 line', the pressure derivative line value in the whole process cannot exceed 0.5, and the pressure derivative line of the large cavern channeling transits to the next flow stage can exceed the '0.5 line'. The reasons for this phenomenon are: the flow of the large cavern is determined according to the pressure change, and the pressure change value is negative in the liquid supply process of the cavern, so that the fluid flows back to the cavern.
If the formation has no erosion holes, the model degenerates to a continuous fracture-discrete karst model, and a typical well test curve is shown in fig. 4. Compared with a stratum model with erosion and dissolution holes, the well testing typical curve has no hole channeling section, and other flowing stages and flowing characteristics are the same.
And S5, fitting the typical well testing curve of the bottom hole pressure and the pressure derivative obtained in the step S4 with the curve of the bottom hole pressure and the pressure derivative measured in the field through an optimization algorithm so as to explain the formation parameters.
And fitting a field actual measurement produced tracer concentration curve by adopting an optimization algorithm so as to explain the stratum parameters. Obtaining an optimal solution meeting requirements through a genetic algorithm, comparing a field actual measurement bottom hole pressure curve and a derivative curve with a curve calculated by an established well testing interpretation model, and taking the error of the curve as a target function:
Figure GDA0003469021700000181
in the formula: p is a radical ofcCalculating the obtained bottom hole pressure of the model in MPa; p is a radical oft *The bottom hole pressure is measured in situ in MPa; n is the number of experimental data.
The main flow of the well testing interpretation program is shown in FIG. 5;
examples
The target well is a exploration well in a certain block of the northwest oil field. And (3) in 2010, the drilling is started at 27 months, and the conditions of emptying, leakage and overflow are avoided in the drilling process. And 3, 6 days after 2011, completing drilling, wherein the drilling depth is 7110m, and the drilling layer position is O2 yj.
Acid fracturing construction is carried out on a well section of Otto series one-room group (O2yj)6950-3Min, injection into wellbore 897m3Squeeze into the ground layer 897m3. By 3 months, 24 days 9: 3mm liquid discharge of 00 oil nozzle and 4.1m liquid discharge3H, generating gas of 11085m3D, gas-oil ratio 114m3/m3No water, 189.5m of accumulated effluent3Wherein the oil is 123.4m3. And closing the well and measuring the pressure from 4 months 8 days to 4 months 14 days, wherein the test horizon O2yj and the test well section 6950-. The maximum daily oil yield in the initial period of well opening is 107.8t, the accumulative oil yield is 149976t from 3 months and 24 days in 2011 to 6 months and 11 days in 2016, and the accumulative oil yield is 149955 t.
The target well logging curve shows that the near well zone cracks are relatively developed; the acid fracturing curve shows that the acid fracturing communicates with a certain reservoir body; the seismic data have chaotic response characteristics, and the reservoir heterogeneity is obvious; the well drilling shows that the test well section has no emptying and no loss. And selecting a well storage + surface skin + radial single karst cave + closed boundary model for explanation and analysis by combining the static data characteristics and the dynamic pressure recovery bi-logarithmic graph response characteristics.
A graph of the fit of measured data from the target well to a typical plate of the well test is shown in fig. 6. The flow of a well can be divided into five phases: a well storage effect stage; an epidermal effect stage; a large karst cave equivalent point source channeling stage; a fracture radial flow stage; closing the boundary response segment; the interpretation results are shown in Table 1.
Figure GDA0003469021700000191
TABLE 1 interpretation of target well pressure recovery well test results
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. An oil and gas reservoir well testing explanation model and method based on a karst cave point source equivalent principle are characterized by comprising the following steps:
s1, establishing a karst cave point source equivalent radial oil and gas reservoir well testing physical model;
the basic assumptions of the physical model are as follows:
(1) the reservoir is developed with a matrix, continuously distributed natural fractures, continuously distributed erosion holes and discretely distributed karst caves, the reservoir matrix is compact and has no storage and seepage capability, and the natural fractures and the karst caves are continuous media; a plurality of large karsts are randomly distributed in the oil reservoir, and the distance between each karst cave and the well shaft of the production well is r1,r2,r3...rNVolume is V1,V2,V3...VNThe big karst cave is a discrete medium; the karst cave is connected with the stratum through the natural cracks to form a channel, and the scattered large karst cave is equivalent to a variable strength point source;
(2) the vertical well produces with fixed yield, the reservoir fluid is single-phase crude oil, and the karst cave is completely filled with the crude oil;
(3) the cracks are channels for fluid to flow, and in the flowing process, the channeling only occurs in the flow from the erosion and dissolution holes and the solution cavity to the cracks;
(4) the flow of the crude oil in the crack and the pore-dissolving system is Darcy isothermal flow, and capillary force and gravity are ignored;
(5) the stratum pressure at the initial moment is equal everywhere and is the original stratum pressure;
(6) the karst cave, the cracks and the fluid are all slightly compressible, and the compression coefficient is constant;
(7) considering wellbore reservoir effect and skin effect;
s2, establishing a dimensionless mathematical model of seepage of the production well in the dual-medium stratum, and solving an expression of pressure drop caused by the production well at any point in the stratum;
s3, establishing a dimensionless mathematical model with the karst cave equivalent as an injection well:
Figure FDA0003469021690000011
inner boundary conditions:
Figure FDA0003469021690000021
wherein, the pressure at any point in the stratum is the sum of the pressure drops generated by the production well and all equivalent wells, namely:
pD＝p0D+p1D+p2D+...+pND (16)
outer boundary conditions:
1) infinite:
pjD(∞,tD)＝0 (17)
2) and (3) closing the boundary:
Figure FDA0003469021690000022
3) and (3) constant pressure boundary:
pjD(re,tD)＝0 (19)
in the formula, pDDimensionless actual formation pressure, MPa; p is a radical ofjDThe dimensionless pressure, MPa, generated when the equivalent injection well at the jth opening is independently injected; r isDDimensionless radial distance, dimensionless; t is tDIs dimensionlessMeta, dimensionless; p is a radical ofDThe actual formation pressure is dimensionless pressure; h isDDimensionless formation thickness, dimensionless; vjDThe dimensionless volume and dimension of the jth karst cave are eliminated; r iswjDThe injection well of the jth opening has dimensionless radius and no dimension; r iseDDimensionless radial distance, dimensionless; r iseIs the reservoir radius, m; p is a radical ofNDDimensionless pressure is generated for the equivalent well of the Nth hole;
s4, solving the equivalent injection well and production well dimensionless mathematical model in a simultaneous mode, calculating to obtain a Laplace bottom flowing pressure expression through a stratum pressure drop superposition principle, and obtaining a pressure and pressure derivative typical well testing curve in a real space by adopting Stehfest numerical inversion calculation;
and S5, fitting the calculated bottom hole pressure and pressure derivative typical well test curve with the in-situ measured bottom hole pressure and pressure derivative curve through an optimization algorithm to explain the formation parameters.
2. The hydrocarbon reservoir well testing interpretation model and method based on karst cave point source equivalence principle as claimed in claim 1, wherein in step S1, the karst cave point source equivalent radial well testing physical model is: in a radial oil and gas reservoir, large karst caves which are not drilled in production wells distributed in a scattered mode are equivalent to injection wells with variable well diameter and injection amount.
3. The hydrocarbon reservoir well testing interpretation model and method based on karst cave point source equivalence principle as claimed in claim 1, wherein the mathematical model of seepage of the production well in the dual medium stratum established in step S2 is as follows:
differential control equation:
Figure FDA0003469021690000031
Figure FDA0003469021690000032
inner boundary conditions:
Figure FDA0003469021690000033
outer boundary conditions:
infinite formation:
p0fD(∞,tD)＝0 (4)
closing the boundary stratum:
Figure FDA0003469021690000034
and (3) constant pressure boundary stratum:
p0fD(reD,tD)＝0 (6)
initial conditions:
p0fD(rD,0)＝0 (7)
the dimensionless bottom hole flow pressure produced by the production well is:
Figure FDA0003469021690000041
in the formula, p0fDThe dimensionless pressure of the fracture system is only considered when the production well produces, and the dimensions are not needed; p is a radical of0vDThe dimensionless pressure and dimension of a dissolved hole system are considered only when the production well is produced; r isDDimensionless radial distance, dimensionless; t is tDDimensionless time and dimension are not included; omega is the elastic storage-capacity ratio of the crack and has no dimension; lambda is a channeling coefficient and is dimensionless; cDThe method is dimensionless and dimensionless for dimensionless well bore storage coefficients; r iseDDimensionless radial distance, dimensionless; p is a radical of0wDDimensionless bottom hole flow pressure for production well production is dimensionless; s is the epidermis coefficient and is dimensionless;
the bottom hole pressure expression of any point in the stratum caused by a production well is as follows:
Figure FDA0003469021690000042
wherein:
Figure FDA0003469021690000043
definite solution parameter A0、B0The values of (A) are as follows:
1) infinite boundary:
Figure FDA0003469021690000044
2) and (3) closing the boundary:
Figure FDA0003469021690000045
3) and (3) constant pressure boundary:
Figure FDA0003469021690000051
in the formula, sigma is an intermediate variable,
Figure FDA0003469021690000052
Figure FDA0003469021690000053
the dimensionless bottom hole flowing pressure in Laplace is MPa; s is a Laplace variable, dimensionless; a. the0、B0Undetermined parameters related to the boundary conditions of the model are dimensionless; i is1A first class of modified Bessel function that is zero first order; k1A second type modified Bessel function of zero first order; f(s) is a characteristic function, dimensionless; cDThe method is dimensionless and dimensionless for dimensionless well bore storage coefficients; r iseIs the reservoir radius, m; omega is the elasticity of crackThe storage volume ratio is dimensionless; lambda is a channeling coefficient and is dimensionless; r iswDIs the dimensionless production well bore radius, m; i is0A first type of modified Bessel function of zero order; k0A modified Bessel function of the second type of zero order; s is the epidermis coefficient and has no dimension.
4. The hydrocarbon reservoir well testing interpretation model and method based on the karst cave point source equivalence principle as claimed in claim 1, characterized in that all pressure parameters p in the mathematical model are replaced by a gas reservoir simulated pressure psi, and the gas reservoir point source equivalent well testing model is obtained after the fluid physical property parameters adopt corresponding gas reservoir gas parameters.
5. The model and method for explaining well testing of oil and gas reservoir based on karst cave point source equivalence principle as claimed in claim 1, wherein the optimization algorithm in step S5 is a genetic algorithm, comparing the measured bottom hole pressure and derivative curve on site with the curve calculated by the established model for explaining well testing, and the error is used as the objective function:
Figure FDA0003469021690000054
in the formula: p is a radical ofcCalculating the obtained bottom hole pressure of the model in MPa; p is a radical oft *The bottom hole pressure is measured in situ in MPa; n is the number of experimental data.
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