Method for judging full life cycle production stage of horizontal tight gas well

Abstract

The invention discloses a method for judging the full life cycle production stage of a horizontal tight gas well, and belongs to the field of gas reservoir engineering. For a horizontal tight gas well, a seepage mathematical model considering multiple sections of fracturing cracks is constructed, model solving is achieved through a semi-analytical method, a gas well full-life-cycle seepage law curve with pressure and a pressure derivative curve as reference is drawn, and a judgment method for dividing different life stages is established according to curve characteristics. According to the method, main control factors influencing occurrence and ending of life stages are defined, and a calculation method for occurrence time of each life stage is constructed, so that the life stage of the horizontal tight gas well and the future development life of the horizontal tight gas well are evaluated, and a theoretical reference is provided for efficient development of tight gas reservoirs.

Description

Technical Field

[0001] The invention belongs to the field of gas reservoir engineering and relates to a method for determining the production stage of a horizontal tight gas well during its entire life cycle. Background Art

[0002] For gas wells that are exploited in a depletion mode, the production will gradually decrease over time from the time they are put into production. The research on the production operation law of tight gas wells at home and abroad is mainly divided into two aspects: one is the empirical prediction method, which fits the actual production data through empirical formulas to obtain general laws; the other is the theoretical analysis method, which derives theoretical formulas such as the seepage equation and the material balance equation to obtain the equation for the change law of production or cumulative production, and finally fits the actual data in the form of a chart.

[0003] Regarding the empirical prediction method, in 1945, J. A. Arps, in "Analysis of Decline Curves", divided the decline law of oil and gas well production into three categories: exponential decline, hyperbolic decline, and harmonic decline based on the statistical research of mine data. At present, this method is most widely used in the dynamic analysis of oil and gas fields. In 2007, Rushing, in the article "Estimating Reserves in Tight Gas Sands at HP / HT Reservoir Conditions: Use and Misuse of an Arps Decline Curve Methodology", studied the application effect of the Arps decline model under different production stages, different reservoir and fracture parameters, different single well control ranges, and different formation pressure and temperature conditions. In 2008, Kupchenko summarized the change law of the decline exponent b under different flow stages in the document "Tight Gas Production Performance Using Decline Curves". In 2013, Fulford analyzed the changing characteristics of the decline index b of multi-stage fractured horizontal wells in tight shale gas reservoirs during the entire production stage in "Evaluation of Time-Rate Performance of Shale Wells using the Transient Hyperbolic Relation". Many scholars have conducted research based on the decline of Arps and derived many empirical prediction models for production decline, such as the Kopatov model, the Joshi model, and the Feng Wenguang FWG model.

[0004] Regarding theoretical analysis methods, Fetkovich found through research in "Decline Curve Analysis Using TypeCurves" in 1980 that Arps decline is theoretically the production characteristic of oil and gas wells after reaching quasi-steady state, and the exponential decline is actually the analytical solution of single-phase oil wells in the quasi-steady state period under the production conditions of fixed bottom hole pressure. In 1987, Fraim and Wattenbarger proposed a normalized time method in the paper "CharacterizeHeterogeneity in Reservoir Rock" to solve the problem of multiple solutions of Fetkovich curve fitting. He found that after converting the actual time into normalized time, the production data of gas wells in the quasi-steady state period will be consistent with the law of single-phase oil, that is, exponential decline. In 1991, Blasingame found in "Decline Curve Analysis for Variable Pressure Drop / Variable Flowrate Systems" that when oil and gas wells produce at variable production or variable bottom hole pressure, if the actual production time is replaced by the material balance time they defined, the decline curve at this time can be expressed by the solution under constant production conditions, that is, it becomes the harmonic decline form of Arps, so the Blasingame typical curve was proposed. In 1998, Agarwal and Gardner et al. considered in "Agarwal-Gardner Decline Curves Analysis" that the Blasingame typical curve is accurate for radial flow problems but inaccurate for vertical fracture wells, and it cannot clearly distinguish between the unsteady state stage and the quasi-steady state stage. Based on these two points, Agarwal and Gardner proposed a new decline typical curve. In 2013, Hao Mingqiang pointed out in "Establishment and Application of the Multi-Peak Forecasting Model" that the relationship between the production of oil and gas fields over time can be divided into: no peak, single peak, double peak and multi-peak. He analyzed the causes of double peak or multi-peak, and proposed a multi-peak production prediction model. The above decline analysis methods are all based on boundary control flow, requiring production data to reach the boundary control flow, and it is impossible to analyze only the data in the unstable flow stage. The transient decline analysis method is based on the dimensionless time and production relationship of the well test, and can also analyze data that is only in the unstable flow stage, reducing the multi-solution nature of the analysis results.

[0005] Although the current production seepage law analysis methods have many models and the prediction accuracy is constantly improving, the reservoir conditions and production data volume suitable for different models are still unclear. Although the production stage of tight gas wells can be divided into two stages: unstable flow and boundary control flow, it can only realize the judgment of the current production stage, and cannot realize the early prediction of the occurrence time of each life stage, so it is impossible to formulate preventive measures in advance. Summary of the invention

[0006] The purpose of the present invention is to provide a method for distinguishing the production stage of the entire life cycle of a horizontal tight gas well. By using gas reservoir engineering theory, reservoir seepage mechanics, and modern well testing analysis methods, a mathematical model of seepage for multi-stage fractured horizontal wells is established, a dynamic identification chart of seepage law is constructed, a method for distinguishing each life stage is formed, and the seepage mechanism of each life stage is revealed. Finally, a prediction method for the appearance time of each life stage is established. The present invention uses on-site single well production dynamic data to realize the prediction of the appearance time of the life cycle and the prediction of the decline law, providing a reference in advance for the formulation of the working system of tight gas wells and the adjustment of development countermeasures. The purpose of the present invention is achieved through the following specific technical solutions.

[0007] A method for determining the production stage of a horizontal tight gas well during its entire life cycle comprises the following steps:

[0008] S1 collects daily gas production, wellhead oil pressure and casing pressure data of horizontal tight gas wells, and draws and generates actual production history curves;

[0009] S2 establishes a horizontal tight gas well seepage model (including physical model and mathematical model) and inverts to obtain equivalent parameters of matrix permeability and fracture half-length;

[0010] S3 draws the logarithmic curve of the bottom hole pressure and its derivative during the whole life cycle of a horizontal tight gas well, and determines the life cycle based on the characteristics of the curve;

[0011] S4 calculates the occurrence time of each life cycle based on the matrix permeability and fracture half-length.

[0012] Specifically include the following:

[0013] (1) Physical model

[0014] Establish a physical model of seepage in a volumetric fractured horizontal well containing hydraulic main fractures, such as Figure 1 The basic assumptions of the model are as follows:

[0015] (1) A single-phase slightly compressible liquid undergoes radial flow in a plane in an infinite reservoir; (2) Gravity and capillary forces are ignored; (3) The fluid flow satisfies the linear Darcy flow, r D is the dimensionless pressure transmission radius; (4) The reformed area is a dual-porosity medium, consisting of a fracture system and a matrix system. The fracture system is the flow channel of the fluid (the permeability is ksf , unit is mD, porosity is φ sf , dimensionless), the matrix system is the reservoir space of the fluid (permeability is k m , unit is mD, porosity is φ m , unitless), the non-transformed area is a single homogeneous reservoir (permeability is k2, unit mD, porosity is φ2, dimensionless), the storage-volume ratio is ω, dimensionless, and the mobility ratio is λ, dimensionless; (5) The oil well produces at a fixed rate q, unit m 3 / d, wellbore flow considers the influence of wellbore reservoir C and skin coefficient S, the units are m 3 / MPa and dimensionless; (6) There is no pressure drop at the seepage interface between the inner and outer zones; (7) The pressure at all locations in the formation before the test is the original reservoir pressure p i , unit: MPa; (8) The formation fluid first flows from the outer single-porous medium system into the inner double-porous medium system, then flows from the inner double-porous medium system into the hydraulic main fracture, and then flows from the hydraulic main fracture into the vertical wellbore. There is a pressure drop along the fracture. (9) P sfD , P 2D is the dimensionless pressure of the cracks in the reformed area and the unreformed area, which is dimensionless. K0, I0, A, and B are the general solution coefficients of the Bessel function, which are dimensionless.

[0016] (2) Mathematical model and solution

[0017] ① Seepage model of the transformation area

[0018] Consider only one point sink in the infinite reservoir (to facilitate the calculation of the main fracture superposition, the dimensionless production of this point sink is defined as ), referring to the description of the dual medium by the Warren-Root model, the seepage control equation of the seepage system in the transformation area can be obtained as:

[0019]

[0020] The general solution to this equation is:

[0021]

[0022] In the formula,

[0023] ② Seepage model of non-reconstruction area

[0024] The seepage control equation of the external zone seepage system considering the reservoir stress sensitivity is:

[0025]

[0026] The perturbation technique is used to simplify equation (3), ignoring the minimum term γ D η 0DAfter Laplace transformation, we can get:

[0027]

[0028] The general solution of equation (4) is:

[0029]

[0030] In the formula,

[0031] ③Coupling solution of internal and external areas of the crack

[0032] According to the equal pressure and flow at the interface between the inner and outer zones, the coupling condition can be written as:

[0033]

[0034] The combined solution can be obtained to obtain the expression of the pressure of the point sink at any position in the reservoir in the Latten space:

[0035]

[0036] In the formula,

[0037] (3) Life cycle stage division method and time calculation

[0038] According to the solution of the tight gas seepage equation, the logarithmic curve of the bottom hole pressure and its derivative during the whole life cycle of a horizontal tight gas well can be drawn, such as Figure 2 As shown. According to the derivative curve, the horizontal tight gas well can be divided into three life cycle stages: the first stage is before the boundary control flow, the control boundary is not reached, at this time the boundary gradually expands outward, the pressure and production characteristics conform to the dynamic boundary characteristics, this is the unstable production stage; the second stage is the boundary control flow stage, the control boundary is reached, at this time the boundary distance remains unchanged, the pressure and production characteristics conform to the fixed boundary characteristics, this is the quasi-stable production stage, the production presents an exponential decreasing characteristic; the third stage is the end of the boundary control flow, the boundary distance remains unchanged, but due to the decrease in the pressure of the deficit formation, it drops to the abandonment pressure and stops, at this time it will enter the exhaustion development stage.

[0039] According to the above bottom hole pressure double logarithmic curve influencing factors, it can be seen that the boundary flow control flow occurrence time is a key parameter for dividing the life cycle stages of tight gas wells. Combined with the bottom hole pressure mathematical equation, the boundary control flow time formula can be derived as follows:

[0040] T1=-0.0067×R f ×ln(K)+0.2674 (8)

[0041] T2=-0.0471×R f×ln(K)+10.864 (9)

[0042] Where, T1 is the time to enter the quasi-steady state flow, in d (days); T2 is the time to enter the exhaustion stage, in d; R f is the fracture half-length, in m; K is the matrix permeability, in mD.

[0043] The present invention aims at horizontal tight gas wells, constructs a mathematical model of seepage that takes into account multi-stage fracturing cracks, draws the curve of pressure and its derivative changes in the whole life cycle of the gas well, establishes a discrimination method for dividing different life stages according to the characteristics of the curve, clarifies the main controlling factors that affect the occurrence and end of the life stage, and constructs a calculation method for the appearance time of each life stage, thereby evaluating the life stage of the horizontal tight gas well and its future development life, providing a theoretical reference for the efficient development of tight gas reservoirs. A mathematical model of seepage that takes into account multi-stage fracturing and tight gas seepage mechanism is constructed; a method for dividing the life cycle of horizontal tight gas wells based on pressure and its derivative curves is proposed; and a method for calculating the appearance time of life stages that takes into account the half-length of the fracture and the matrix permeability is established. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the physical model of seepage in a volume fracturing horizontal well;

[0045] Figure 2 A schematic diagram of the life cycle stages of a fractured horizontal well;

[0046] Figure 3 It is a schematic diagram of the process of the present invention;

[0047] Figure 4 This is a schematic diagram of production data for the implementation case Class I well X439;

[0048] Figure 5 This is a schematic diagram of the pressure and production history fitting of the X439 well, a Class I well in the implementation case;

[0049] Figure 6 This is a schematic diagram of production data for the implementation case II well X683;

[0050] Figure 7 This is a schematic diagram of the pressure and production history fitting of the Class II well X683 in the implementation case;

[0051] Figure 8 This is a schematic diagram of production data for the implementation case Class III well D21;

[0052] Fig. 9 This is a schematic diagram of the pressure and production history fitting diagram of the Class III well D21 in the implementation case. DETAILED DESCRIPTION

[0053] The technical solution of the present invention is described clearly and completely below in conjunction with the accompanying drawings of the specification. Obviously, the described implementation is only a part of the implementation of the present invention, not all of the implementations. Based on the implementation of the present invention, all other implementations obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] The Ordos Basin is located in the western part of the North China Platform. It is a large multi-cyclic cratonic superimposed basin with long-term stable development. It includes five primary tectonic units: Yimeng Uplift, Weibei Uplift, Jinxi Flexural Fold Belt, Tianhuan Depression, and Yishan Slope. The X gas field is located in the southeastern part of the basin. Structurally, it is located above the Yishan Slope tectonic unit of the Ordos Basin. It has a slope of less than 1° and a gentle structure. The reservoir porosity is between 4.0% and 12.0%, and the permeability is between 0.01mD and 3.0mD. It is a low-permeability and tight reservoir. The gas wells in this tight gas reservoir can be divided into three categories: I, II, and III according to the reservoir physical properties. The method of the present invention is used to determine the production stage of the gas wells in the tight gas reservoir throughout its life cycle. The process is as follows: Figure 3 shown.

[0055] Firstly, the production performance is fitted by using variable production and pressure, and the reservoir fractures and physical property parameters are inverted.

[0056] (1) Class I well - Well X439

[0057] Its entire historical production and bottom hole pressure are as follows Figure 4 shown.

[0058] Select the fixed well storage + limited diversion fracturing vertical well + radial composite reservoir + circular closed boundary model, enter the fitting parameters, and continue to adjust until the graph basically matches. The final fitting image is as follows: Figure 4 shown.

[0059] After continuous adjustments, the wellbore, fracture and reservoir parameters of Well X439 were finally obtained through inversion. The wellbore reservoir coefficient is 0.136m 3 / Mpa, skin coefficient is 0; the half-length of the fracture obtained by vertical well fracturing is 54m, and the fracture conductivity is 5000mD·cm; the extrapolated formation pressure in the reservoir is 25.11MPa, the radius of the inner zone is 150m, the drainage radius (control radius) is 500m, the permeability of the inner zone is 0.42mD, the mobility ratio of the reservoir is 3, and the permeability of the outer zone is 0.14mD, and the pressure conductivity ratio is adjusted to 3. The inverted parameters can be preliminarily calculated to control the reserves (surface) of about 7000×10 4 m 3 .

[0060] (2) Class II well X683

[0061] Taking the Class II well X683 as an example, its entire historical production and bottom hole pressure are as follows: Figure 5 shown.

[0062] Select the fixed well storage + limited diversion fracturing vertical well + radial composite reservoir + circular closed boundary model, enter the fitting parameters, and continue to adjust until the graph basically matches. The final fitting image is as follows: Figure 6 shown.

[0063] After continuous adjustments, the wellbore, fracture and reservoir parameters of Well X683 were finally obtained through inversion. The wellbore reservoir coefficient is 0.265m 3 / Mpa, skin coefficient is 0; the half-length of the fracture obtained by vertical well fracturing is 50m, and the fracture conductivity is 5000D·cm; the extrapolated formation pressure in the reservoir is 24.85MPa, the radius of the inner zone is 100m, the drainage radius (control radius) is 285m, and the permeability of the inner zone is 0.35mD, which is a typical tight reservoir. The mobility ratio of the reservoir is 5, and the permeability of the outer zone can be obtained to be 0.07mD. Based on the inversion parameters, it can be preliminarily calculated that the controlled reserves (surface) are about 3000×10 4 m 3 .

[0064] (3) Class III well D21

[0065] Take the Class III well D21 as an example. Its entire historical production and bottom hole pressure are as follows: Figure 7 shown.

[0066] Select the fixed well storage + limited diversion fracturing vertical well + radial composite reservoir + circular closed boundary model, enter the fitting parameters, and continue to adjust until the graph basically matches. The final fitting image is as follows: Figure 8 shown.

[0067] After continuous adjustments, the wellbore, fracture and reservoir parameters of Well D2 were finally obtained through inversion. The wellbore reservoir coefficient is 0.229m 3 / Mpa, skin coefficient is 0; the half-length of the fracture obtained by vertical well fracturing is 41m, and the fracture conductivity is 4000D·cm; the extrapolated formation pressure in the reservoir is 24.07MPa, the radius of the inner zone is 70m, the drainage radius (control radius) is 226m, and the permeability of the inner zone is 0.08mD, which is a typical tight reservoir. The mobility ratio of the reservoir is 5, and the permeability of the outer zone can be obtained to be 0.016mD. Based on the inversion parameters, it can be preliminarily calculated that the controlled reserves (surface) are about 1800×10 4 m 3 .

[0068] (4) Prediction of the emergence time of different life stages

[0069] Based on the determination of fracture half-length and matrix permeability, the occurrence time of each life stage of the gas well can be calculated by substituting the parameters into formula (8) and formula (9), as shown in Table 1.

[0070] Table 1 Prediction results of implementation cases

[0071]

[0072] As can be seen from Table 1, the reservoir properties of Class I wells are good, the pressure propagation speed is fast, the time to enter the quasi-steady flow is short, and due to the large gas leakage radius, it enters the exhaustion stage later, indicating that its main production stage lasts for a long time, and can obtain better development effect and recovery rate; Class III wells have poor reservoir properties, low pressure propagation speed, and enter the quasi-stable flow later. Due to the small gas leakage radius, it will soon enter the exhaustion development stage. Therefore, for Class III wells, the production dynamics should be analyzed in time, and repeated fracturing should be carried out in time to reduce the production exhaustion rate.

[0073] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention. The protection scope of the present invention is defined by the claims and their equivalent technical solutions.

Claims

1. A method for determining the production stage of a horizontal tight gas well during its entire life cycle, characterized in that: The following steps are involved: S1 collects daily gas production, wellhead oil pressure and casing pressure data of horizontal tight gas wells, and draws and generates actual production history curves; S2 establishes a horizontal tight gas well seepage model, including physical and mathematical models, and inverts to obtain matrix permeability and fracture half-length equivalent parameters; S3 draws the logarithmic curve of the bottom hole pressure and its derivative during the whole life cycle of a horizontal tight gas well, and determines the life cycle based on the characteristics of the curve; S4 calculates the occurrence time of each life cycle based on the matrix permeability and fracture half-length.

2. The method according to claim 1, characterized in that In step S2, the basic assumptions of the horizontal tight gas well seepage physical model are as follows: (1) Planar radial flow of a single-phase slightly compressible liquid in an infinite reservoir; (2) Ignore gravity and capillary force; (3) The fluid flow satisfies the linear Darcy flow, r D is the dimensionless pressure transmission radius; (4) The reformed area is a dual-porosity medium consisting of a fracture system and a matrix system. The fracture system is the flow channel of the fluid, and its permeability is k sf , unit is mD, porosity is φ sf , dimensionless; the matrix system is the reservoir space of the fluid, and the permeability is k m , unit is mD, porosity is φ m , unitless; the non-transformed area is a single homogeneous reservoir, the permeability is k2, unit mD, the porosity is φ2, dimensionless, the storage volume ratio is ω, dimensionless, and the mobility ratio is λ, dimensionless; (5) The oil well produces at a fixed rate of q, in m 3 / d, wellbore flow considers the influence of wellbore reservoir C and skin coefficient S, the units are m 3 / MPa and dimensionless; (6) There is no pressure drop at the seepage interface between the inner and outer zones; (7) The pressure at all locations in the formation before the test is the original reservoir pressure p i , unit: MPa; (8) The formation fluid first flows from the outer single-porous medium system into the inner double-porous medium system, then flows from the inner double-porous medium system into the hydraulic main fracture, and then flows from the hydraulic main fracture into the vertical horizontal wellbore, with a pressure drop along the fracture. (9)P sfD , P 2D is the dimensionless pressure of the cracks in the reformed area and the unreformed area, which is dimensionless. K0, I0, A, and B are the general solution coefficients of the Bessel function, which are dimensionless.

3. The method according to claim 2, characterized in that The mathematical model of seepage in horizontal tight gas wells and its solution process are as follows: ① Seepage model of the transformation area When only one point sink in an infinite reservoir is considered, in order to facilitate the calculation of the main fracture superposition, the dimensionless production of the point sink is defined as Based on the description of dual media by the Warren-Root model, the seepage control equation of the seepage system in the transformation area is obtained as follows: The general solution to this equation is: In the formula, ② Seepage model of non-reconstruction area The seepage control equation of the external zone seepage system considering the reservoir stress sensitivity is: The perturbation technique is used to simplify equation (3), ignoring the minimum term γ D η 0D After Laplace transformation, we can get: The general solution of equation (4) is: In the formula, ③Coupling solution of internal and external areas of the crack According to the equal pressure and flow at the interface between the inner and outer zones, the coupling condition can be written as: The combined solution can be obtained to obtain the expression of the pressure of the point sink at any position in the reservoir in the Latten space: In the formula, 4. The method according to claim 3, characterized in that The specific method of step S3 for determining the life cycle according to the curve characteristics is to divide the tight gas well into three life stages: the first stage is before the boundary control flow, which is the unstable production stage; the second stage is the boundary control flow stage, which is the quasi-stable production stage; the third stage is the end of the boundary control flow, which will enter the exhaustion development stage.

5. The method according to claim 4, characterized in that The occurrence time of each life cycle depends on the boundary control flow time, and the calculation formula is as follows: T1=-0.0067×R f ×ln(K)+0.2674 (8) T2=-0.0471×R f ×ln(K)+10.864 (9) Where, T1 is the time to enter the quasi-steady state flow, in d; T2 is the time to enter the exhaustion stage, in d; R f is the fracture half-length, in m; K is the matrix permeability, in mD.

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