A well test interpretation method for high-sulfur carbonate bioherm gas reservoirs

Abstract

The present invention relates to a method for well test interpretation of a high-sulfur carbonate bioherm gas reservoir. The well test interpretation method includes: the physical model includes vertically: reef cap, reef core, reef base, and fracturing well from top to bottom; the bottom of the fracturing well is placed in the reef cap and the reservoir forms a double-wing seam after fracturing; the reef cap includes natural fractures, dissolved pores and natural gas; the reef core includes dissolved pores and natural gas; the reef base includes dissolved pores and bottom water; and there is crossflow between the natural fractures and dissolved pores in the reef cap, between the reef cap and the reef core, and between the reef core and the reef base; and then a mathematical model of this type of gas reservoir is established; after the mathematical model is dimensionless, a double logarithmic curve is drawn after transformation and solution; and the well test interpretation is performed according to the double logarithmic curve. The present invention fully considers the physical property differences of the structural characteristics of the reef base, reef core, and reef cap, and combined with the physical property characteristics of acid fracturing fracture creation, it can well evaluate the conductivity, pollution status and gas supply capacity of the reservoir after acid fracturing.

Description

Technical Field

[0001] The invention relates to a well test interpretation method for a high-sulfur carbonate bioherm gas reservoir, belonging to the technical field of gas field exploration and development. Background Art

[0002] Well testing is an important part of oil and gas field exploration and development. It mainly tests oil wells, gas wells or water wells, including production, pressure, temperature and sampling. It is a method based on the theory of seepage mechanics, constructs and solves the mathematical model of well testing, establishes the logarithmic curve chart of well testing, and uses steel wires, cables, etc. to lower the pressure gauge to the bottom of the well to measure the pressure and temperature. Then, according to the chart, the various physical parameters of oil, gas and water wells (formation pressure, flow coefficient, pollution status, boundary conditions, edge and bottom water activity), production capacity, and the connectivity between oil, gas and water layers corresponding to the pressure and temperature changes are inversely calculated, which provides support for the rational development of oil and gas fields. Well testing mainly includes testing technology and testing interpretation methods. At present, a variety of well testing interpretation methods have been formed for different types of oil and gas reservoirs.

[0003] For high-sulfur carbonate bioherm gas reservoirs, conventional methods such as Figure 1 The multi-layer model shown in Figure 2The dual medium model shown in the figure is used for well test interpretation, but there are several problems: 1. The conventional multi-layer model divides the production layer into multiple layers and assumes that the reservoir space of each layer is homogeneous and the fluid is single-phase flow. The thickness, permeability, porosity, fluid saturation and other parameters between layers are different. The main parameters obtained from its interpretation are the single-layer fluid permeability k, the interlayer crossflow coefficient λ (characterizing the flow ability of the fluid from the low permeability layer to the high permeability layer), and the formation coefficient ratio κ (characterizing the permeability difference between different layers); although the bioherm gas reservoir meets the characteristics of the multi-layer model, its reef base contains bottom water, and the reef cap and reef core contain high-sulfur gas, which is a multiphase fluid. At the same time, the reef base and reef cap reservoir space are heterogeneous (including pore and fracture systems), bottom water crossflow, bottom water and gas The flow characteristics in the reef cap and reef core (heterogeneous space) cannot be described by conventional multi-layer models; 2. The conventional dual-medium model simplifies the production layer into two systems, one is a high-conductivity fracture system, and the other is a low-conductivity bedrock system. Assuming that the fluid is a single-phase flow, the fluid flows from the bedrock system to the fracture system, and then from the fracture system to the wellbore. The main parameters obtained are the elastic energy storage ratio ω (the ratio of the fluid stored in the fracture system to the amount of fluid stored in the entire system) and the crossflow coefficient λ (characterizing the flow capacity of the fluid from the dissolved pore to the natural fracture system). The bottom water reaction of the high-sulfur carbonate bioherm gas reservoir, the vertical crossflow reaction of the fluid between the reef base and the reef core, the reef core and the reef cap, and the artificial acid fracturing fractures are not considered, resulting in a low accuracy of the well test interpretation. The low accuracy of the well test interpretation will affect the provision of a reasonable production basis for gas wells in the later stage, and the judgment of the influence of the water body on the development of gas reservoirs in the later stage.

[0004] In view of the defects of the conventional dual-medium model, some people have proposed to use the triple-medium model to interpret well tests for this type of gas reservoir. For example, a journal article entitled "Study on Well Test Model of Fracture Wells in Carbonate Reef Phase Gas Reservoirs with Weak Bottom Water" published in the journal "Special Oil and Gas Reservoirs" with the journal number of 2020, No. 3, established the following Figure 3 The new physical model and well test interpretation method shown in the figure mainly regard the exterior of the reef-facies gas reservoir as a whole, and use triple media (matrix system pores, fracture system, and cave system) to describe the interior. It is assumed that the fluid flows from natural fractures to artificial fractures, and then from artificial fractures to the wellbore. Both matrix pores and caves are used as replenishment sources for natural fractures. The elastic energy storage ratio ω and crossflow coefficient λ between different systems are then obtained.

[0005] However, the physical model established in the above article did not take into account the vertical cross-flow characteristics of bottom water and gas between the reef base and reef core, and between the reef core and the reef cap. At the same time, on the double logarithmic curve chart established after the model was solved, the derivative characteristics of weak bottom water and strong bottom water were both downward, and there was no obvious difference between the two, resulting in low accuracy in the interpretation of well test data, and thus a low degree of consistency in the depicted gas reservoir structure and weak bottom water identification characteristics, which affected the understanding of this type of gas reservoir. Summary of the invention

[0006] The purpose of this application is to provide a method for interpreting a well test in a high-sulfur carbonate bioherm gas reservoir, so as to solve the problem that the accuracy of the well test interpretation in the prior art is low, resulting in a large deviation in the understanding of the high-sulfur carbonate bioherm gas reservoir.

[0007] To achieve the above purpose, the present application proposes a technical solution for a well test interpretation method for a high-sulfur carbonate bioherm gas reservoir, comprising the following steps:

[0008] 1) Establishing a physical model of a high-sulfur carbonate bioherm gas reservoir; the physical model includes vertically: a reef cap, a reef core, a reef base, and a fracturing well from top to bottom; the bottom of the fracturing well is placed in the reef cap and the reservoir forms a double-wing seam after fracturing; the reef cap includes natural fractures, dissolved pores and natural gas; the reef core includes dissolved pores and natural gas; the reef base includes dissolved pores and bottom water; and there is crossflow between the natural fractures and dissolved pores in the reef cap, between the reef cap and the reef core, and between the reef core and the reef base;

[0009] 2) On the basis of the physical model, the mathematical model of this type of gas reservoir is established by using the mass conservation, Darcy's law and the equation of state;

[0010] 3) Non-dimensionalizing the mathematical model to obtain a dimensionless mathematical model;

[0011] 4) Using Laplace transform to solve the dimensionless mathematical model, the dimensionless bottom hole pressure of the fractured well is obtained;

[0012] 5) Draw a double logarithmic curve of dimensionless bottom hole pressure, pressure derivative and dimensionless time based on the dimensionless bottom hole pressure;

[0013] 6) Conduct sensitivity analysis based on the double logarithmic curve to characterize the internal structure and bottom water characteristics of this type of gas reservoir and complete the well test interpretation of this type of gas reservoir.

[0014] The technical solution of the method for interpreting well testing of high-sulfur carbonate bioherm gas reservoirs of the present invention has the following beneficial effects: the present invention studies the geological characteristics of high-sulfur carbonate bioherm gas reservoirs, takes into account the structural characteristics of the reef base, reef core, and reef cap, the fluid seepage characteristics, and the influence of weak bottom water, and combines the working conditions of acid fracturing and fracture creation in the development wells during the development of gas reservoirs, couples the acid fracturing fracture characteristics, and then establishes a physical model and a mathematical model that finely describes the vertical distribution characteristics, fluid seepage characteristics, and the influence of weak bottom water in the bioherm gas reservoir. The established mathematical model is solved, a double logarithmic curve is drawn, and then a sensitivity analysis is performed on this type of gas reservoir, and the well testing interpretation is completed, which effectively improves the understanding of this type of gas reservoir. The present invention fully considers the differences in physical properties of the reef base, reef core and reef cap structures, and combined with the physical properties of acid fracturing fracture creation, can well evaluate the reservoir conductivity, pollution status and gas supply capacity after acid fracturing, and provide a theoretical basis for reasonable well layout and process technology optimization. At the same time, the present invention well integrates weak bottom water into the mathematical model, so that the weak bottom water characteristics can be well identified on the double logarithmic curve, which is consistent with the understanding of the geological static data of this type of gas reservoir, and can help technical personnel fully understand the bottom water characteristics, and provide guidance for the formulation of reasonable working system of gas wells and water treatment.

[0015] Furthermore, the mathematical model includes the seepage equations of natural fractures in the reef cap, the seepage equations of dissolved pores in the reef cap, the seepage equations of the reef core, the seepage equations of the reef base, as well as initial conditions, internal boundary conditions, and external boundary conditions:

[0016] The seepage equation of the natural fracture in the reef cap is:

[0017]

[0018] The seepage equation of the solution pores in the reef cap is:

[0019]

[0020] The seepage equation of the reef core is:

[0021]

[0022] The seepage equation of the reef foundation is:

[0023]

[0024] The initial conditions are:

[0025] p f1 =p m1 =p2=p3=p i ;

[0026] The outer boundary conditions are:

[0027]

[0028] The inner boundary conditions are:

[0029]

[0030] Among them, φ f is the porosity of natural fractures in the reef cap, dimensionless; k f is the permeability of natural fractures in the reef cap, μm 2 ; C tf is the comprehensive compression coefficient of natural fractures in the reef cap, atm -1 ;p f1 is the pressure of natural fractures in the reef cap, atm; φ m is the porosity of the solution pores in the reef cap, dimensionless; k m is the permeability of the dissolved pores in the reef cap, μm 2 ; C tm is the comprehensive compressibility coefficient of the dissolved pores in the reef cap, atm -1 ;p m1 is the pressure of the solution pores in the reef cap, atm; h1 is the thickness of the reef cap, cm; (k v ) 1-2 is the vertical permeability of the interface between the reef cap and the reef core, μm 2 ; φ a is the porosity of the reef core, dimensionless; C ta is the comprehensive compression coefficient of the reef core, atm -1 ; p2 is the pressure of the reef core, atm; h2 is the thickness of the reef core, cm; (k v ) 2-3 is the vertical permeability of the interface between the reef core and the reef base, μm 2 ; φ b is the porosity of the reef foundation, dimensionless; C tb is the comprehensive compression coefficient of the reef base, atm -1 ; p3 is the pressure of the reef foundation; h3 is the thickness of the reef foundation, cm; μ w is the viscosity of the bottom water, mPa.s; μ g is the natural gas viscosity under average formation conditions, mPa.s; p i is the original formation pressure, atm; q sc Gas well surface volume flow, cm 3 / s; is the line sink ground volume flow, B g is the natural gas volume coefficient under average formation conditions, dimensionless; t is the production time, s; r is the radial distance, cm; r e is the outer boundary radius, cm; α is the shape factor, cm -2 .

[0031] Furthermore, in order to improve the accuracy of well test interpretation, a dimensionless mathematical model is solved based on the Duhamel principle, combining the well reservoir coefficient and the skin coefficient.

[0032] Furthermore, in order to draw the double logarithmic curve more accurately, the double logarithmic curve is drawn according to the Stehfest numerical inversion method in step 5).

[0033] Furthermore, in order to comprehensively conduct sensitivity analysis on the gas reservoir, the sensitivity analysis is conducted through the storage capacity ratio and the crossflow coefficient in the step 6), wherein the storage capacity ratio includes the storage capacity ratio of the storage capacity coefficient of natural fractures in the reef cap to the storage capacity coefficient of the reef cap, the storage capacity ratio of the storage capacity coefficient of the reef cap to the total storage capacity coefficient, and the storage capacity ratio of the storage capacity coefficient of the reef core to the total storage capacity coefficient; the crossflow coefficient includes the crossflow coefficient between the natural fractures and the dissolved pores in the reef cap, the crossflow coefficient between the reef cap and the reef core, and the crossflow coefficient between the reef core and the reef base. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a schematic diagram of a conventional multi-layer model in the prior art;

[0035] Figure 2 It is a schematic diagram of a conventional dual medium model in the prior art;

[0036] Figure 3 It is a schematic diagram of a triple medium model in the prior art;

[0037] Figure 4 It is a flow chart of the well test interpretation method of the high sulfur carbonate bioherm gas reservoir of the present invention;

[0038] Figure 5 It is a schematic diagram of the physical model of the high-sulfur carbonate bioherm gas reservoir of the present invention;

[0039] Figure 6 It is a double logarithmic well test curve diagram of pressure and pressure derivative of a fractured well in a reef-facies weak bottom water gas reservoir of the present invention;

[0040] Figure 7 The double logarithmic well test curve of pressure and pressure derivative under the storage capacity ratio of the storage capacity coefficient of natural fractures in different reef caps to the storage capacity coefficient of the reef cap according to the present invention;

[0041] Figure 8 It is a double logarithmic well test curve diagram of pressure and pressure derivative under the storage capacity ratio of the storage capacity coefficient of different reef caps and the total storage capacity coefficient of the present invention;

[0042] Fig. 9 It is a double logarithmic well test curve diagram of pressure and pressure derivative under the storage capacity ratio of the storage capacity coefficient of different reef cores and the total storage capacity coefficient of the present invention;

[0043] Fig.10 It is a double logarithmic well test curve diagram of pressure and pressure derivative under the cross-flow coefficient between natural fractures and dissolved pores in different reef caps of the present invention;

[0044] Fig.11 It is a double logarithmic well test curve diagram of pressure and pressure derivative under different cross-flow coefficients between the reef cap and the reef core of the present invention;

[0045] Fig.12 It is a double logarithmic well test curve diagram of pressure and pressure derivative under different cross-flow coefficients between the reef core and the reef base of the present invention;

[0046] In the figure: 1 is the reef cap, 2 is the reef core, 3 is the reef base, and 4 is the hydraulic fracture. DETAILED DESCRIPTION

[0047] Example of well test interpretation method for high sulfur carbonate bioherm gas reservoir:

[0048] In recent years, geological studies on high-sulfur carbonate bioherm gas reservoirs have found that: from the perspective of pore structure, the storage space of this type of gas reservoir is mainly porous, with locally developed fractures, among which: intergranular dissolved pores, intragranular dissolved pores, and dissolved pores are the main storage spaces; from the perspective of sedimentary characteristics, its exterior can be considered as a whole layer, but its interior is mainly composed of reef base, reef core, and reef cap from bottom to top, among which the reef base stores bottom water, and the reef cap and reef core store high-sulfur gas, and there are multiphase fluids; and bottom water rises, and bottom water and gas seep in the reef cap and reef core (heterogeneous space), the plane and vertical heterogeneity are extremely strong, and it shows abnormalities during the pressure dynamic test. This abnormal phenomenon may be related to the characteristics of the gas reservoir structure and the degree of bottom water activity.

[0049] To this end, the main idea of ​​the well test interpretation method proposed in the present invention is to take into account the structural characteristics of the reef base, reef core and reef cap, while taking into account the influence of weak bottom water, combining the common acid fracturing and fracture creation conditions of gas reservoirs during development, coupling the acid fracturing fracture characteristics, and establishing a physical model and a mathematical model that accurately describe the high-sulfur carbonate bioherm gas reservoir. The Laplace transform is used to solve the mathematical model and the inverse transform is used to draw a typical curve chart. Through sensitivity analysis, the internal structural characteristics and bottom water characteristics of the high-sulfur carbonate bioherm gas reservoir are characterized, which effectively improves the understanding of this type of gas reservoir.

[0050] The following is a detailed description of the well test interpretation method of the present invention by taking a gas field reef phase reservoir as an example. Figure 4 As shown, the following steps are included:

[0051] 1) Based on the study of geological characteristics, a physical model of high-sulfur carbonate bioherm gas reservoirs was established.

[0052] The reef-facies reservoir of a gas field generally follows the Wilson sedimentary model. The physical model established is as follows: Figure 5 ( Figure 5 As shown in the figure, the upward arrow in the figure indicates that the gas production is fixed and put into production. In the vertical direction, it is divided into three microfacies: reef cap 1, reef core 2 and reef base 3. The lower part of the reef gas reservoir is connected to the bottom water. A well (i.e., a fracturing well) is drilled in the middle of the reef body, and only the upper reef cap 1 is opened. After fracturing, the reservoir forms a double-wing fracture 4 (i.e., a double-wing fracture). The basic assumptions are as follows:

[0053] a. The reef cap 1 is composed of two media: natural fractures and dissolved pores, and the reef core 2 is composed of dissolved pores;

[0054] b. The reef foundation 3 is composed of dissolved pores;

[0055] c. Natural gas is mainly stored in reef cap 1 and reef core 2;

[0056] d. Bottom water is mainly stored in the reef foundation 3 and is limited bottom water (limited means that the amount of bottom water is small);

[0057] e. In order to avoid the fracture 4 directly connecting to the bottom water and causing the gas well to be flooded too quickly, only the upper part of the reef cap 1 is opened;

[0058] f. Gas flow satisfies Darcy's law;

[0059] g. There is crossflow between the solution pores and natural fractures of reef cap 1;

[0060] h. As production proceeds, the pressure drops, the gas in the reef core 2 can flow to the reef cap 1 for replenishment, and the bottom water in the reef base 3 can replenish energy to the reef core 2.

[0061] 2) Based on the physical model established in step 1), a mathematical model of high-sulfur carbonate bioherm gas reservoir is established by using the law of conservation of mass, Darcy's law and equation of state.

[0062] High-sulfur carbonate bioherm gas reservoirs generally have high pressures, so the gas reservoir seepage equation can be expressed in pressure form. Therefore, the mathematical model includes the seepage equations of natural fractures in reef cap 1, the seepage equations of dissolved pores in reef cap 1, the seepage equations of reef core 2, the seepage equations of reef base 3, as well as initial conditions, internal boundary conditions, and external boundary conditions:

[0063] The seepage equation of the natural fracture in reef cap 1 is:

[0064]

[0065] The seepage equation of the dissolved pores in reef cap 1 is:

[0066]

[0067] The seepage equation of reef core 2 is:

[0068]

[0069] The seepage equation of reef foundation 3 is:

[0070]

[0071] The initial condition is that the pressure distribution is uniform, all p i , that is: p f1 =p m1 =p2=p3=p i ;

[0072] The outer boundary conditions are:

[0073] The inner boundary condition is (fixed production ):

[0074] Among them, φ f is the porosity of natural fractures in reef cap 1, dimensionless; k f is the permeability of natural fractures in reef cap 1, μm 2 ; C tf is the comprehensive compression coefficient of natural fractures in reef cap 1, atm -1 ;p f1 is the pressure of the natural fracture in the reef cap 1, atm; φ m is the porosity of the solution pores in reef cap 1, dimensionless; k m is the permeability of the solution pores in reef cap 1, μm 2 ; C tm is the comprehensive compressibility coefficient of the dissolved pores in reef cap 1, atm -1 ;p m1 is the pressure of the solution pores in the reef cap 1, atm; h1 is the thickness of the reef cap 1, cm; (k v ) 1-2 is the vertical permeability of the interface between reef cap 1 and reef core 2, μm 2 ; φ a is the porosity of reef core 2, dimensionless; C ta is the comprehensive compression coefficient of reef core 2, atm -1 ; p2 is the pressure of the reef core 2, atm; h2 is the thickness of the reef core 2, cm; (k v ) 2-3 is the vertical permeability of the interface between reef core 2 and reef base 3, μm 2 ; φ b is the porosity of reef foundation 3, dimensionless; C tb is the comprehensive compression coefficient of reef base 3, atm -1 ; p3 is the pressure of the reef foundation 3; h3 is the thickness of the reef foundation 3, cm; μw is the viscosity of the bottom water, mPa.s; μ g is the natural gas viscosity under average formation conditions, mPa.s; p i is the original formation pressure, atm; q sc Gas well surface volume flow, cm 3 / s; is the line sink ground volume flow, B g is the natural gas volume coefficient under average formation conditions, dimensionless; t is the production time, s; r is the radial distance, cm; r e is the outer boundary radius, cm; α is the shape factor, cm -2 .

[0075] 3) The mathematical model in step 2) is dimensionless to obtain a dimensionless mathematical model.

[0076] The purpose of this step is to reduce the interference of different physical dimensions on the model solution. The specific process of dimensionless transformation is:

[0077] Dimensionless pressure p of natural fractures in reef cap 1 f1D :

[0078]

[0079] The dimensionless pressure p of the solution pores in reef cap 1 m1D :

[0080]

[0081] The dimensionless pressure p of reef core 2 2D :

[0082]

[0083] Dimensionless pressure p of reef foundation 3 3D :

[0084]

[0085] Dimensionless time t D : r w is the well radius, cm;

[0086] Dimensionless well radius r D :

[0087] Since the formation coefficient of natural fractures in reef cap 1 is much larger than that of dissolved pores, the formation coefficient of dissolved pores can be ignored in actual calculations. Therefore, the formation coefficient of natural fractures is used to represent the formation coefficient of reef cap 1.

[0088] Therefore, the total formation coefficient = k f h1+k m h1+k a h2+k b h3, simplified as total formation coefficient = k f h1+k a h2+k b h3;

[0089] Total storage capacity factor = φ f C tf h1+φ m C tm h1+φ a C ta h2+φ b C tb h3;

[0090] Among them, k f h1 is the formation coefficient of the natural fracture in reef cap 1; k m h1 is the formation coefficient of the dissolved pores in reef cap 1; k a h2 is the formation coefficient of reef core 2; k b h3 is the formation coefficient of reef base 3; φ f C tf h1 is the storage capacity coefficient of natural fractures in reef cap 1; φ m C tm h1 is the storage coefficient of the dissolved pores in reef cap 1; φ a C ta h2 formation coefficient of reef core 2; φ b C tb h3 is the formation coefficient of reef base 3; k a is the permeability of reef core 2, μm 2 ;k b is the permeability of reef foundation 3, μm 2 .

[0091] The ratio of the formation coefficient of reef cap 1 to the total formation coefficient χ1:

[0092] The ratio of the formation coefficient of reef core 2 to the formation coefficient of the total system is χ2:

[0093] The storage capacity ratio of the natural fractures in reef cap 1 to the storage capacity coefficient of reef cap 1 is ω m-f :

[0094]

[0095] The storage capacity ratio of the storage capacity coefficient of reef cap 1 to the total storage capacity coefficient ω1:

[0096] The storage capacity ratio of the storage capacity coefficient of reef core 2 to the total storage capacity coefficient ω2:

[0097] The storage capacity ratio of the storage capacity coefficient of reef foundation 3 to the total storage capacity coefficient ω3:

[0098] The cross-flow coefficient λ between natural fractures and solution pores in reef cap 1 m-f :

[0099]

[0100] The crossflow coefficient λ′ between reef cap 1 and reef core 2 is:

[0101] The cross-flow coefficient λ″ between the reef core 2 and the reef base 3 is:

[0102] Viscosity ratio of bottom water to natural gas μ R :

[0103] Under the above definition of dimensionless quantity, the dimensionless mathematical model is:

[0104] The dimensionless equation of natural fractures in reef cap 1 is:

[0105]

[0106] The dimensionless equation of solution pores in reef cap 1 is:

[0107] The dimensionless equation of reef core 2 is:

[0108] The dimensionless equation of reef base 3:

[0109] Dimensionless initialization condition: p f1D =p m1D =p 2D =p 3D =0;

[0110] Dimensionless external boundary conditions: r eD is the dimensionless outer boundary radius, dimensionless;

[0111] Dimensionless internal boundary conditions: It is the dimensionless production of the line well.

[0112] 4) Using Laplace transform, the dimensionless mathematical model obtained in step 3) is converted from nonlinear to linear, and the solution of the model in Laplace space is obtained, and then the relationship expression between dimensionless pressure and formation parameters is obtained using Laplace inverse transform.

[0113] Specifically, the dimensionless mathematical model is subjected to Laplace transformation to obtain:

[0114] The transformation equation of natural fractures in reef cap 1 is:

[0115] s is the Laplace variable; is the dimensionless pressure of the natural fracture in reef cap 1 after Laplace transformation; is the dimensionless pressure of reef core 2 after Laplace transformation; is the dimensionless pressure of the solution pores in reef cap 1 after Laplace transformation.

[0116] Solution pore transformation equation in reef cap 1:

[0117] Reef Kernel 2 Transformation Equation:

[0118] Reef base 3 transformation equation: is the dimensionless pressure of reef foundation 3 after Laplace transformation;

[0119] External boundary condition transformation equation:

[0120] Internal boundary condition transformation equation: is the dimensionless line sink output after Laplace transformation;

[0121] According to the solution pore transformation equation in reef cap 1, we get Therefore

[0122]

[0123] By transforming the equation of reef base 3, we get Therefore

[0124] Substitute into the reef core 2 transformation equation, and we get:

[0125] Therefore is the dimensionless pressure of the natural fracture in reef cap 1 in Laplace space;

[0126] By transforming the equation based on the external boundary conditions, we can obtain:

[0127]

[0128] Where F is F = ω m-f ω1s-λm-f χ1(a1-1)-λ'(a3-1); K1 is the first-order second-kind deformed Bessel function; A is the undetermined coefficient; B is the undetermined coefficient; I1 is the first-order first-kind deformed Bessel function.

[0129] By transforming the equation based on the internal boundary conditions, we can obtain:

[0130]

[0131] Equations ① and ② form a second-order linear algebraic equation system, which can determine the two unknown coefficients A and B. After the unknown coefficients are determined, the dimensionless pressure of the natural fracture in the reef cap 1 after Laplace transformation caused by the line sink is It is determined, and its expression is as follows:

[0132]

[0133] The dimensionless pressure response of the natural fracture in reef cap 1 after Laplace transformation caused by the line sink only represents the one caused by the line sink, while the hydraulic fracture 4 can be regarded as two symmetric planes. According to the superposition principle, the pressure response caused by the line sink is calculated along the length direction of the fracture (from -x f to x f ) integral, x f is the half length of the fracture 4 (unit, cm), and the pressure response caused by the fracture 4 (i.e., the symmetry plane) can be obtained. After dimensionless conversion, the dimensionless pressure response of the fractured well (i.e., the fracture 4) can be obtained.

[0134]

[0135] In the above formula, I0 is the zero-order first-kind deformed Bessel function; K0 is the zero-order second-kind deformed Bessel function; β is the integral variable; is the dimensionless pressure distribution in Laplace space, which represents the dimensionless pressure response of the fractured well at any point in the gas reservoir. According to the coordinate relationship According to the conclusions obtained by Gringarten and other scholars in studying other problems, when r in the above formula D The parameter x in D When the specific value of 0.732 is taken, it can be used to equivalently calculate the dimensionless bottom hole pressure response of the fractured well under infinite conductivity; when r in the above formula D The parameter x in D When the specific value is 0, the dimensionless bottom hole pressure response of the fractured well under uniform flow can be obtained. Therefore, the dimensionless bottom hole pressure response (or pressure solution) of the fractured well in the reef-facies gas reservoir under the conditions of reef cap 1, reef core 2, reef base 3, and weak bottom water is Obtained immediately.

[0136] above The calculation does not take into account the skin factor S and the well reservoir factor C D When there is skin effect and wellbore reservoir effect, it can be considered by the following formula, of course, this is not a process that must be considered. This formula is mainly given by the Duhamel principle combined with the definition of wellbore reservoir coefficient and skin coefficient:

[0137]

[0138] in, is the bottom hole pressure response when the skin and well reservoir are not considered, that is, when x D When the specific value is 0.732 or 0 It is the dimensionless bottom hole pressure response (or pressure solution) of a fractured well in a reef-facies gas reservoir under the conditions of reef cap 1, reef core 2, reef base 3 and weak bottom water when considering the well reservoir and skin effect.

[0139] Whether to consider the skin factor S and well storage factor C D The bottom hole pressure can be obtained to carry out the subsequent well test interpretation, and the present invention does not impose any limitation on this.

[0140] 5) Based on the dimensionless bottom hole pressure solution obtained in step 4), a typical well test double logarithmic curve of a high-sulfur carbonate bioherm gas reservoir is drawn.

[0141] The dimensionless bottom hole pressure p of a fractured well in a reef-facies weak bottom water gas reservoir can be plotted using the Stehfest numerical inversion method. wD , pressure derivative p wD ′·(t D / C D ) and dimensionless time t D / C D The double logarithmic curve is Figure 6 As shown, Figure 6 The gentle curve corresponds to the dimensionless bottom hole pressure, and the uneven curve corresponds to the pressure derivative. For a fractured gas well in a weak bottom water reef phase gas reservoir, its typical curve may show 8 seepage stages:

[0142] ① Early pure wellbore reservoir section. The pressure and pressure derivative of this section are straight lines with a slope of 1 on the double logarithmic graph;

[0143] ② The transition section after well storage is manifested as a "hump";

[0144] ③ In the linear flow stage of the formation to the fracture 4, the derivative curve is a straight line with a slope of 1 / 2;

[0145] ④ The section where the matrix pore fluid flows to the natural fractures. At this stage, the pressure difference between the matrix pores and the natural fractures in the reef cap 1 has been established, and the matrix pores flow to the natural fractures. The pressure derivative of this section presents a downward "concave";

[0146] ⑤ Fracture-bedrock system (i.e. dissolved pores) radial flow section. In this stage, the flow from matrix dissolved pores to fractures reaches equilibrium, the pressure of fractures and bedrock decreases synchronously, and the pressure derivative curve tends to the 0.5 horizontal line;

[0147] ⑥ The natural gas in the reef core 2 is replenished to the reef cover 1. In this stage, the pressure difference between the reef core 2 and the reef cover 1 has been established, and the natural gas in the reef core 2 is replenished to the reef cover 1. The pressure derivative of this section shows a downward "concave";

[0148] ⑦ The reflection period of the energy replenishment from the bottom water in the reef base 3 to the reef core 2. In this stage, the pressure difference between the reef base 3 and the reef core 2 has been established, and the bottom water in the reef base 3 replenishes energy to the reef core 2. The pressure derivative of this section shows a downward "concave";

[0149] ⑧ Radial flow section of the total system.

[0150] 6) According to the characteristics of the double logarithmic curve, the storage capacity ratio of the natural cracks in the reef cap 1 to the storage capacity coefficient of the reef cap 1 is ω m-f , the storage capacity ratio of the storage capacity coefficient of reef cap 1 to the total storage capacity coefficient ω1, the storage capacity ratio of the storage capacity coefficient of reef core 2 to the total storage capacity coefficient ω2, the cross-flow coefficient λ between the natural cracks in reef cap 1 and the matrix pores m-f , the crossflow coefficient λ′ between the reef cap 1 and the reef core 2, the crossflow coefficient λ″ between the reef core 2 and the reef base 3, etc., to characterize the internal structural characteristics and bottom water characteristics of the high-sulfur carbonate bioherm gas reservoir and complete the well test interpretation.

[0151] Change the storage capacity ratio of the natural fractures in reef cap 1 to the storage capacity coefficient of reef cap 1 ω m-f , get different ω m-f The comparison curve of dimensionless bottom hole pressure and pressure derivative under Figure 7 As shown, Figure 7 The two gentle curves correspond to different ω m-f The dimensionless bottom hole pressure under the condition is not clearly distinguished, and the two uneven curves correspond to different ω m-f The derivative curve of the pressure is more able to distinguish the reservoir characteristics. Figure 7 It can be concluded that: m-f The smaller it is, the wider and deeper the first "dent" on the pressure derivative curve will be.

[0152] By changing the storage ratio ω1 of the storage coefficient of reef cap 1 and the total storage coefficient, the comparison curve of dimensionless bottom hole pressure and pressure derivative under different ω1 is obtained, as shown in Figure 8As shown, Figure 8 The two gentle curves in the figure correspond to dimensionless bottom hole pressures at different ω1, and the distinction is not obvious. The two uneven curves correspond to pressure derivatives at different ω1. The derivative curves are more able to distinguish reservoir characteristics. Figure 8 It can be concluded that there are more stages affected by ω1. The smaller ω1 is, the higher the position of the linear flow segment is, and the wider and deeper the (second) depression reflecting the segment where the natural gas in reef core 2 supplies energy to reef cap 1 and the (third) depression reflecting the segment where the bottom water in reef base 3 supplies energy to reef core 2 is.

[0153] By changing the storage ratio ω2 of the storage coefficient of reef core 2 and the total storage coefficient, the comparison curve of dimensionless bottom hole pressure and pressure derivative under different ω2 is obtained, as shown in Fig. 9 As shown, Fig. 9 The two gentle curves correspond to the dimensionless bottom hole pressure under different ω2, and the distinction is not obvious. The two uneven curves correspond to the pressure derivatives under different ω2. The derivative curves can better distinguish the reservoir characteristics. Fig. 9 It can be concluded that ω2 mainly affects the second and third dimples. The larger ω2 is (ω1 remains unchanged, ω3 decreases), the first "dimple" on the derivative curve remains basically unchanged, the second dimple becomes wider and deeper, and the third dimple becomes shallower and narrower.

[0154] Since the sum of the storage ratio ω1 of the storage coefficient of reef cap 1 and the total storage coefficient, ω2 of the storage coefficient of reef core 2 and the total storage coefficient, and ω3 of the storage coefficient of reef base 3 and the total storage coefficient is equal to 1, when ω1 and ω2 change, ω3 changes accordingly. The situation when ω3 is changed is not analyzed separately here.

[0155] Changing the cross-flow coefficient λ between natural fractures and matrix pores in reef cap 1 m-f , get different λ m-f The comparison curve of dimensionless bottom hole pressure and pressure derivative under Fig.10 As shown, Fig.10 The two gentle curves in the figure correspond to different λ m-f The dimensionless bottom hole pressure under the condition is not clearly distinguished. The two uneven curves correspond to different λ m-f The derivative curve of the pressure is more able to distinguish the reservoir characteristics. Fig.10 It can be concluded that: m-f Mainly affects the early or late appearance of the first concave, λ m-f The smaller it is, the later the first dent will appear.

[0156] By changing the crossflow coefficient λ′ between the reef cap 1 and the reef core 2, the comparison curves of dimensionless pressure and pressure derivative under different λ′ are obtained, as shown in Fig.11 As shown, Fig.11The two gentle curves in the figure correspond to dimensionless bottom hole pressures under different λ′, which are not clearly distinguishable. The two uneven curves correspond to pressure derivatives under different λ′. The derivative curves are more capable of distinguishing reservoir characteristics. Fig.11 It can be concluded that λ′ mainly affects the early or late appearance of the second concave. The smaller λ′ is, the later the second concave appears.

[0157] By changing the crossflow coefficient λ″ between the reef core 2 and the reef base 3, the comparison curves of dimensionless bottom hole pressure and pressure derivative under different λ″ are obtained, as shown in Fig.12 As shown, Fig.12 The two smooth curves correspond to dimensionless bottom hole pressures under different λ″, which are not clearly distinguished. The two uneven curves correspond to pressure derivatives under different λ″. The derivative curves are more able to distinguish reservoir characteristics. Fig.12 It can be concluded that λ″ mainly affects the early or late appearance of the third concave. The smaller λ″ is, the later the third concave appears.

[0158] The well test interpretation method of the present invention fully considers the differences in physical properties of the structural characteristics of the reef base 3 (dissolved pores and weak bottom water), the reef core 2 (dissolved pores), and the reef cap 1 (cracks, dissolved pores), as well as the working conditions of acid fracturing and fracture creation, and at the same time well integrates the weak bottom water boundary conditions into the interpretation model, which is in line with the understanding of static geological data of reef-phase gas reservoirs, and makes up for the shortcomings of conventional well test interpretation methods that cannot describe the structural characteristics of the reef base 3, the reef core 2, and the reef cap 1 of the bioherm gas reservoir and identify the weak bottom water, resulting in a small amount of formation information mining, low accuracy, and low data utilization. It can help test technicians fully understand the structure, bottom water characteristics, and development dynamics of the bioherm gas reservoir, provide guidance for the formulation of a reasonable working system for the gas reservoir and water treatment, and at the same time provide a new interpretation method for improving the exploration and development level of this type of gas reservoir.

Claims

1. A method for interpreting well testing of high-sulfur carbonate bioherm gas reservoirs, characterized in that: The following steps are involved: 1) Establishing a physical model of a high-sulfur carbonate bioherm gas reservoir; the physical model includes vertically: a reef cap, a reef core, a reef base, and a fracturing well from top to bottom; the bottom of the fracturing well is placed in the reef cap and the reservoir forms a double-wing seam after fracturing; the reef cap includes natural fractures, dissolved pores and natural gas; the reef core includes dissolved pores and natural gas; the reef base includes dissolved pores and bottom water; and there is crossflow between the natural fractures and dissolved pores in the reef cap, between the reef cap and the reef core, and between the reef core and the reef base; 2) On the basis of the physical model, the mathematical model of this type of gas reservoir is established by using the mass conservation, Darcy's law and the equation of state; 3) Non-dimensionalizing the mathematical model to obtain a dimensionless mathematical model; 4) Using Laplace transform to solve the dimensionless mathematical model, the dimensionless bottom hole pressure of the fractured well is obtained; 5) Draw a double logarithmic curve of dimensionless bottom hole pressure, pressure derivative and dimensionless time based on the dimensionless bottom hole pressure; 6) Conduct sensitivity analysis based on the double logarithmic curve to characterize the internal structure and bottom water characteristics of this type of gas reservoir and complete the well test interpretation of this type of gas reservoir; The mathematical model includes the seepage equations of natural fractures in the reef cap, the seepage equations of dissolved pores in the reef cap, the seepage equations of the reef core, the seepage equations of the reef base, as well as initial conditions, internal boundary conditions, and external boundary conditions: The seepage equation of the natural fracture in the reef cap is: The seepage equation of the solution pores in the reef cap is: The seepage equation of the reef core is: The seepage equation of the reef foundation is: The initial conditions are: pf1=p m1 =p2=p3=pi; The outer boundary conditions are: The inner boundary conditions are: Among them, φ f is the porosity of natural fractures in the reef cap, dimensionless; k f is the permeability of natural fractures in the reef cap, μm 2 ; C tf is the comprehensive compression coefficient of natural fractures in the reef cap, atm -1 ;p f1 is the pressure of natural fractures in the reef cap, atm; φ m is the porosity of the solution pores in the reef cap, dimensionless; k m is the permeability of the dissolved pores in the reef cap, μm 2 ; C tm is the comprehensive compressibility coefficient of the dissolved pores in the reef cap, atm -1 ;p m1 is the pressure of the solution pores in the reef cap, atm; h1 is the thickness of the reef cap, cm; (k v ) 1-2 is the vertical permeability of the interface between the reef cap and the reef core, μm 2 ; φ a is the porosity of the reef core, dimensionless; C ta is the comprehensive compression coefficient of the reef core, atm -1 ; p2 is the pressure of the reef core, atm; h2 is the thickness of the reef core, cm; (k v ) 2-3 is the vertical permeability of the interface between the reef core and the reef base, μm 2 ; φ b is the porosity of the reef foundation, dimensionless; C tb is the comprehensive compression coefficient of the reef base, atm -1 ; p3 is the pressure of the reef foundation; h3 is the thickness of the reef foundation, cm; μ w is the viscosity of the bottom water, mPa.s; μ g is the natural gas viscosity under average formation conditions, mPa.s; p i is the original formation pressure, atm; q sc Gas well surface volume flow, cm 3 / s; is the line sink ground volume flow, B g is the natural gas volume coefficient under average formation conditions, dimensionless; t is the production time, s; r is the radial distance, cm; r e is the outer boundary radius, cm; α is the shape factor, cm -2 .

2. The method for interpreting a high-sulfur carbonate bioherm gas reservoir according to claim 1, characterized in that: According to Duhamel's principle, the dimensionless mathematical model is solved by combining the well-reservoir coefficient and the skin coefficient.

3. The method for well testing interpretation of high-sulfur carbonate bioherm gas reservoir according to claim 1, characterized in that: In the step 5), a double logarithmic curve is drawn according to the Stehfest numerical inversion method.

4. The method for well testing interpretation of high-sulfur carbonate bioherm gas reservoir according to claim 1, characterized in that: In the step 6), a sensitivity analysis is performed through the storage capacity ratio and the crossflow coefficient, wherein the storage capacity ratio includes the storage capacity ratio of the storage capacity coefficient of natural fractures in the reef cover to the storage capacity coefficient of the reef cover, the storage capacity ratio of the storage capacity coefficient of the reef cover to the total storage capacity coefficient, and the storage capacity ratio of the storage capacity coefficient of the reef core to the total storage capacity coefficient; the crossflow coefficient includes the crossflow coefficient between the natural fractures and the dissolved pores in the reef cover, the crossflow coefficient between the reef cover and the reef core, and the crossflow coefficient between the reef core and the reef base.

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