CN113294147B - Single-hole type broken solution reservoir well testing interpretation method considering gravity factor influence - Google Patents
Single-hole type broken solution reservoir well testing interpretation method considering gravity factor influence Download PDFInfo
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Abstract
The invention discloses a single-hole type broken solution reservoir well testing interpretation method considering the influence of gravity factors, which comprises the following steps: step 1, establishing a single-hole type broken solution reservoir well test mathematical model considering gravity factors, and regarding a karst cave and crack combination system as a combined cylindrical area; step 2, performing dimensionless treatment on the well test mathematical model to obtain dimensionless gravity coefficient definition; step 3, solving in Laplace space after Laplace transformation to obtain an expression of time variation of pressure in the stratum cavity under the influence of gravity factors; and 4, obtaining curve parameters and time and pressure fitting values by adopting a well testing method, and obtaining the influence of gravity factors on interpretation of a well testing curve. By the method, the technical problem that the well testing interpretation method in the prior art cannot determine some parameters for directly servicing the development of the oil field is solved, and meanwhile, the influence of gravity on a well testing curve is analyzed, so that technical support is provided for the development of the oil field.
Description
Technical Field
The invention belongs to the technical field of oil reservoir engineering, and particularly relates to a well testing interpretation method of a carbonate broken solution oil reservoir.
Background
"Miscibility" broadly refers to the reservoir formed by the erosion of surrounding rock by atmospheric water or buried fluids along a fracture. Fracture serves as an important fluid pathway and plays an important role in both the surface and buried phases. The fluid can generate a series of erosion-filling actions in the process of flowing through the fracture, the local erosion actions can lead to the formation of a new reservoir space or the expansion of erosion to preexisting cracks and pores, and the development distribution of the finally formed reservoir body shows a characteristic of being closely related to the fracture, so the fluid is called as a broken solution. The North-oriented broken solution oil reservoir has extremely strong heterogeneity, has the characteristics of large burial depth and high temperature and pressure, is influenced by the limitation of a monitoring process, and has the technical problems that the broken solution presents the characteristic of one broken solution and one oil reservoir in reservoir recognition and evaluation, the conventional well test interpretation technology has poor adaptability, and the fracture and karst cave are difficult to describe.
The carbonate broken solution reservoir matrix is basically free of oil, the reservoir space is mainly a crack and a karst cave, and the flow of crude oil in the crack and the karst cave has pipe flow and seepage. Because the local corrosion effect is mainly formed by the expansion of corrosion under the action of gravity, the reservoir often shows a vertical bead-shaped characteristic, and when crude oil flows in deep fracture cracks and karst cave, the vertical flow is obvious. This is essentially different from the reservoir characteristics of conventional sandstones, which flow is primarily concentrated in radial flow, while flow of a broken solution reservoir is primarily concentrated in vertical flow, where the effects of gravity are not negligible. The existing well test analysis method is mainly based on triple medium and equipotential body theory, and based on the two theories, whether a karst cave exists in a stratum or not cannot be judged, and well test interpretation parameters such as the distance, the size, the combination form and the like of the karst cave cannot be given under the condition that gravity factors are taken as variables.
The triple medium adopts a macroscopic statistical theory to divide the oil storage space of a reservoir into three types of medium (holes, slits and matrixes) with permeability and porosity, wherein the matrixes are main oil storage spaces; the fracture is directly communicated with the shaft, and the karst cave supplies liquid to the fracture and the matrix supplies liquid to the fracture and the karst cave. However, the Darcy law is still adopted in each medium to express the flow therein, and a set of more complete well testing theoretical system is established based on the seepage theory.
Equipotential body theory assumes: 1) the reservoir space has only karst cave, but no consideration is given to the flow of fluid in karst cave, pressure wave propagates instantaneously in cave, 2) the crack is not the oil storage space but only seepage channel, 3) the matrix is neither the oil storage space nor seepage channel.
CN106599449a discloses a well testing interpretation method for karst cave volume calculation, which comprises the following steps: step 1, establishing a well testing model according to the combination relation of cracks, karst cave and shaft of a fracture-cave type oil reservoir and the measurement parameters of the three; step 2, obtaining a real space bottom hole pressure solution according to the well test model; and step 3, fitting the real space bottom hole pressure solution and the actually measured bottom hole pressure data to obtain parameters of the crack permeability, the wellbore reservoir coefficient, the crack length, the crack sectional area and the karst cave volume. The well testing interpretation method for calculating the karst cave volume can establish corresponding well testing interpretation models aiming at different fracture-cave combination relations, can interpret the volumes of all karst cave and can give out the information of the lengths, the cross sectional areas and the like of cracks or seepage channels. The effect of gravity on the seepage is likewise not taken into account in this technique.
However, the theory of the existing interpretation method is based on the conventional well testing interpretation theory, and the results based on the conventional well testing interpretation are parameters such as permeability, storage capacity ratio, fluid channeling coefficient and the like, wherein the parameters are just average values of fracture, matrix and karst cave parameters in the stratum, the characteristics of the fracture and cave cannot be known by using the parameters, and the parameters for directly serving the development of the karst-fluid oilfield such as the size, number and distance of the fracture and cave cannot be determined. Meanwhile, at present, both theories take gravity as a constant, the influence of gravity as a variable is ignored, and under the condition of considering the longitudinal flow of a broken solution reservoir, the influence of gravity on seepage is an important factor and is reflected as a sensitive factor.
Disclosure of Invention
In order to solve the technical problems, the invention provides a single-hole type broken solution reservoir well test interpretation method based on the combination of energy conservation law and karst cave fluctuation and considering the influence of gravity factors, wherein the single-hole type broken solution reservoir well test interpretation parameters are obtained through pressure recovery well test curve interpretation, and the sensitivity analysis of gravity coefficients is carried out.
A single-hole type broken solution reservoir well testing interpretation method considering the influence of gravity factors comprises the following steps:
step 1, establishing a single-hole type broken solution reservoir well test mathematical model considering gravity factors, and regarding a karst cave and crack combination system as a combined cylindrical area;
Step 2, performing dimensionless treatment on the well test mathematical model to obtain a dimensionless gravity coefficient;
step 3, solving in Laplace space after Laplace transformation to obtain an expression of time variation of pressure in the stratum cavity under the influence of gravity factors;
And 4, obtaining well testing interpretation curve parameters and time and pressure fitting values by adopting a well testing method, and obtaining the influence of gravity factors on the well testing interpretation curve form.
Preferably, the building of the single-hole type disconnected solution reservoir well test mathematical model considers the influence of gravity factors in the longitudinal direction.
Preferably, the mathematical model is specifically that karst cave are connected through cracks, each karst cave is a cylinder, a crack system between karst cave is equivalent to a cylindrical area, and the mathematical model can be expressed by the following formula:
A one-dimensional cartesian coordinate system is employed, wherein: : indicating that the karst cave cracks are all cylindrical with the radius of the cylinder; h: karst cave height; h 1: crack 1 height; h 2: the sum of the heights of the crack 1 and the karst cave 1; and p: pressure, p 1: crack 1 pressure, p 2: crack 2 pressure, p v: karst cave pressure, p i: the original formation pressure at which the pressure wave did not begin to propagate; ρ: a fluid density; mu: viscosity of the fluid; c t: synthesizing compression coefficients; k: permeability of the material; g: acceleration of gravity; c f: a fluid compression coefficient; t: pressure wave transmission time; and z: radius length; z e: boundary distance; q: a flow rate; b: volume coefficient; c v: karst cave storage constants.
Preferably, the dimensionless treatment process is as follows:
Wherein:
dimensionless pressure: 。
Dimensionless time: ; wherein the method comprises the steps of Is of porosity
Dimensionless distance:；
Dimensionless wellbore coefficients: Wherein C is a wellbore storage constant, (phi C t)1 represents the product of the porosity of the gap 1 and the comprehensive compression coefficient;
dimensionless karst cave storage coefficient: ；
The resulting dimensionless gravity coefficients were: 。
Preferably, the expression of the pressure over time under the influence of gravity is:
Wherein:
fluidity ratio: ；
storage ratio: Is that;
S is a t time item after Laplace transformation;
Alpha is the shape factor of the hole, and the closer alpha is to 1, which means that the closer the karst hole is to a cylinder shape, the parameters can be manually input;
And obtain the corresponding under three boundary conditions Is a value of (2).
(1) Infinite boundary condition:
(2) Closed boundary conditions
(3) Constant pressure boundary condition
。
Preferably, the well test curve parameters obtained by calculation are:
Wellbore storage constant: ；
Equivalent radius of karst cave: ；
equivalent permeability of crack 1: ；
Karst cave storage constant: ；
The calculated time and pressure fitting values are as follows: ；。
Preferably, the gravity factor has an influence on the interpretation of the well test curve, in particular, that in the boundary flow phase, the gravity effect causes an equivalent constant pressure boundary reduction.
Compared with the prior art, the invention has the beneficial effects that: according to the invention, under the influence of gravity factors, a single-hole type broken solution reservoir well test mathematical model is established, fitting values of parameters, time and pressure of a well test curve are obtained according to the established mathematical model, the influence of gravity on the well test curve is analyzed, the characteristics of the fracture holes are recognized through the parameters, the parameters of the fracture holes for directly serving broken solution oilfield development such as size, number and distance of the fracture holes are determined, and technical support is provided for the establishment of oilfield development schemes. The invention has three advantages: (1) The model is simple, the solution is convenient, an analytic solution can be given in the Laplace space, the analytic solution does not relate to the calculation of complex functions, and the calculation speed is high; (2) The fitted interpretation result can directly give out parameters of karst cave and crack; (3) vertically taking into account gravity influence factors.
Drawings
FIG. 1 is a simplified schematic diagram of a fracture-karst cave-fracture model;
FIG. 2 is a graph of gravity coefficient sensitivity analysis.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the accompanying drawings.
The following detailed description of the present invention is further described in terms of examples, with reference to the accompanying drawings, in order to facilitate a more complete, accurate and thorough understanding of the concepts, aspects, and the like of the present invention by those skilled in the art. The following examples are only for more clearly illustrating the technical aspects of the present invention, and thus are merely examples, and are not intended to limit the scope of the present invention. Throughout the drawings, identical elements or portions are identified by identical reference numerals, and the elements or portions are not necessarily drawn to actual scale.
The single-hole type broken solution reservoir well test interpretation method considering the influence of gravity in the invention determines formation interpretation parameters such as the size, the distance and the like of holes and slits in a stratum when the influence of gravity is considered in the vertical direction by using well test analysis and an oil reservoir engineering method, and the method specifically comprises the following steps:
Step 1, establishing a single-hole type broken solution reservoir well test mathematical model which is shown in the figure 1 and takes the gravity factor into consideration, and regarding a karst cave and crack combination system as a simultaneous cylindrical area; as shown in fig. 1, the well bore is connected with a crack 1, a karst cave 1 and a crack 2 in sequence. The actual complex well-seam-hole-seam structure is simplified: assuming that n karst cave are arranged in the stratum, the karst cave is connected through cracks, and the property of the karst cave is kept unchanged; each karst cave is a cylinder, and the equivalent radius of the karst cave is The upper boundary of the karst cave isThe lower boundary is; The cracks are all cracks with limited flow conductivity, and the matrix permeability is negligible compared with the crack permeability, namely the cracks are the only channels among karst caves; the fracture system between karst cave is equivalent to cylindrical area, and the permeability in the area is equivalent to the fracture permeability in the area.
The above model can be formulated as:
A one-dimensional cartesian coordinate system is employed, wherein: : indicating that the karst cave cracks are all cylindrical with the radius of the cylinder; h: karst cave height; h 1: crack 1 height; h 2: the sum of the heights of the crack 1 and the karst cave 1; and p: pressure, p 1: crack 1 pressure, p 2: crack 2 pressure, p v: karst cave pressure, p i: the original formation pressure at which the pressure wave did not begin to propagate; ρ: a fluid density; mu: viscosity of the fluid; c t: synthesizing compression coefficients; k: permeability of the material; g: acceleration of gravity; c f: a fluid compression coefficient; t: pressure wave transmission time; and z: radius length; z e: boundary distance; q: a flow rate; b: volume coefficient; c v: karst cave storage constants.
Step 2, performing dimensionless treatment on the well test mathematical model:
Wherein:
dimensionless pressure: B is the volume coefficient.
Dimensionless time:
Dimensionless distance:
Dimensionless wellbore coefficients: where C is the wellbore storage constant.
Dimensionless karst cave storage coefficient: c v is a karst cave storage constant.
After dimensionless treatment, the obtained dimensionless gravity coefficient is as follows:。
step 3, adopting Laplace transformation and solving in Laplace space to obtain an expression of time variation of the pressure in the stratum cavity under the influence of gravity;
And carrying out Laplace transformation on the well test model, wherein the transformed equation is generally solved as follows:
Wherein:
under the three boundary conditions, respectively, the corresponding is obtained Is a value of (2).
(1) Infinite boundary condition:
(2) Closed boundary conditions
(3) Constant pressure boundary condition
Step 4, solving through a matrix solver to obtain a dimensionless bottom hole pressure solution in a pull-type space:
Considering well storage and skin effects, the dimensionless bottom hole pressure solution on the pull space can be written as:
The relationship between bottom hole pressure and time is obtained through Laplace numerical inversion, the relationship is drawn in a double-logarithmic coordinate axis, and a bottom hole pressure and derivative dimensionless double-logarithmic graph when a karst cave exists in a stratum is obtained, as shown in fig. 2, and calculation parameters in fig. 2 are respectively: karst cave storage constant: c v1D=5,Cv2D =100; dimensionless length: z D1=1,zD2=2,zD3=10,zD4 = 50; fluidity ratio: m 12=1,M13 =1, storage ratio: 12=1， 13 Dimensionless wellbore coefficients =1: c D =0.01, skin factor: s kin = 0.5.
In the figure, G D is the gravity coefficient, and a smaller G D means that the gravity effect is less obvious, and that G D =0 is to be taken into consideration. The greater the coefficient of gravity, the greater the resistance to longitudinal flow.
It can be seen from fig. 2 that the gravity factor has a certain influence on the later stage of the curve, and in the boundary flow stage, the gravity effect is equivalent to a constant pressure boundary, so that the smaller the equivalent constant pressure boundary is. In the early stages of flow, the gravitational effect does not have an effect on the curve characteristics. In the boundary flow stage, in order to ensure smooth production, the bottom hole pressure is greater than the gravity effect caused by the hydraulic pressure generated by the height of the liquid column in the shaft.
And (3) using the double-logarithmic pressure and derivative fitting of the actual pressure recovery curve, and combining the bottom hole pressure and derivative dimensionless double-logarithmic graph to obtain a time fitting value and a pressure fitting value:
；
deriving desired formation parameters based on dimensionless definitions of the parameters:
Wellbore storage constant:
Equivalent radius of karst cave:
equivalent permeability of crack 1:
Karst cave storage constant: 。
The invention is described above by way of example with reference to the accompanying drawings. It will be clear that the invention is not limited to the embodiments described above. As long as various insubstantial improvements are made using the method concepts and technical solutions of the present invention; or the invention is not improved, and the conception and the technical scheme are directly applied to other occasions and are all within the protection scope of the invention.
Claims (4)
1. A single-hole type broken solution reservoir well testing interpretation method considering the influence of gravity is characterized by comprising the following steps:
step 1, establishing a single-hole type broken solution reservoir well test mathematical model considering gravity factors, and regarding a karst cave and crack combination system as a combined cylindrical area;
Step 2, performing dimensionless treatment on the well test mathematical model to obtain a dimensionless gravity coefficient;
step 3, solving in Laplace space after Laplace transformation to obtain an expression of time variation of pressure in the stratum cavity under the influence of gravity factors;
Step 4, obtaining well testing interpretation curve parameters and time and pressure fitting values by adopting a well testing method, and obtaining the influence of gravity factors on the well testing interpretation curve form;
In the boundary flow stage, in order to ensure smooth production, the bottom hole pressure is required to be larger than the gravity effect caused by the hydraulic pressure generated by the height of a liquid column in a shaft;
fitting the double logarithmic pressure and the derivative of the actual pressure recovery curve, and combining the bottom hole pressure and the derivative dimensionless double-logarithmic graph to obtain a time fitting value and a pressure fitting value;
taking the influence of gravity in the longitudinal direction into consideration in the single-hole type broken solution reservoir well test mathematical model;
The mathematical model is specifically that karst cave are connected through cracks, each karst cave is a cylinder, a crack system between karst cave is equivalent to a cylindrical area, and the mathematical model can be expressed by the following formula:
A one-dimensional cartesian coordinate system is employed, wherein: : indicating that karst cave cracks are all cylindrical radii; h: karst cave height; h 1: crack 1 height; h 2: the sum of the heights of the crack 1 and the karst cave 1; and p: pressure, p 1: crack 1 pressure, p 2: crack 2 pressure, p v: karst cave pressure, p i: the original formation pressure at which the pressure wave did not begin to propagate; ρ: a fluid density; mu: viscosity of the fluid; c t: synthesizing compression coefficients; k: permeability of the material; g: acceleration of gravity; c f: a fluid compression coefficient; t: pressure wave transmission time; and z: radius length; z e: boundary distance; q: a flow rate; b: volume coefficient; c v: karst cave storage constants;
The dimensionless treatment process comprises the following steps:
Wherein:
dimensionless pressure: the subscript 1 indicates the parameter corresponding to the crack 1;
Dimensionless time: subscript 1 denotes the parameter corresponding to crack 1, wherein Is porosity;
Dimensionless distance: ；
Dimensionless wellbore coefficients: Wherein C is a wellbore storage constant, (phi C t)1 represents the product of the porosity of the fracture 1 and the comprehensive compression coefficient;
dimensionless karst cave storage coefficient: (phi c t)1 represents the product of the porosity of the fracture 1 and the integrated compression coefficient;
The resulting dimensionless gravity coefficients were: 。
2. the single hole, solution reservoir well test interpretation method of claim 1, wherein the expression of the pressure over time taking into account the influence of gravity is:
Wherein:
fluidity ratio: ；
storage ratio: ；
S is a t time item after Laplace transformation;
α is the shape factor of the hole;
And obtain the corresponding under three boundary conditions Is the value of (1):
(1) Infinite boundary condition:
(2) Closed boundary conditions
(3) Constant pressure boundary condition
。
3. The single hole type solution reservoir well test interpretation method of claim 2, wherein the calculated well test interpretation curve parameters are:
Wellbore storage constant: ；
Equivalent radius of karst cave: ；
equivalent permeability of crack 1: ；
Karst cave storage constant: ；
The calculated time and pressure fitting values are as follows: ； 。
4. A single hole, broken solution reservoir well test interpretation method according to any of claims 1-3, characterized in that the influence of gravity factors on the interpretation of the well test curve is in particular that in the boundary flow phase the effect of gravity results in an equivalent constant pressure boundary reduction.
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| CN106599449B (en) * | 2016-12-12 | 2020-04-17 | 中国石油化工股份有限公司 | Well test interpretation method for karst cave volume calculation |
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| CN110532592B (en) * | 2019-07-15 | 2022-04-22 | 西南石油大学 | A well test interpretation method in large caverns for fracturing wells in fractured-cave oil and gas reservoirs |
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