A method for predicting the activity degree of water in a heterogeneous edge water gas reservoir

Abstract

The application discloses a method for predicting the activity degree of water in a heterogeneous edge water gas reservoir, and utilizes the percolation theory of the oil and gas reservoir, establishes the percolation mathematical model and equation of the heterogeneous edge water gas reservoir according to the invasion mode of the peripheral water body, and carries out numerical solution, so that the recovery degree of the gas reservoir under different permeability difference and peripheral water body size conditions can be predicted and analyzed, and the influence of the reservoir heterogeneity on the water activity of the water-bearing gas reservoir can be quickly and conveniently predicted.

Description

Technical Field

[0001] This invention belongs to the field of water-bearing gas reservoir development technology, specifically, it is a method for predicting the water activity level of heterogeneous edge-water gas reservoirs. Background Technology

[0002] Water-bearing gas reservoirs are widely distributed and numerous in China, accounting for 40% to 50% of the gas reservoirs currently under development, making them a key target for natural gas development. These reservoirs are primarily edge-water reservoirs, with the main reservoir space consisting of various dissolution pores. Fractures and high-porosity sections are the main channels for gas and water flow, and these reservoirs are characterized by either overall connectivity with water bodies or the presence of edge water in certain areas. Differences in the development of reservoir fractures and high-porosity sections result in reservoir heterogeneity. As production progresses, when pressure waves propagate to the surrounding water bodies, formation water irregularly intrudes into the gas reservoir along fracture zones or high-porosity sections, leading to two-phase gas-water flow within the formation. This impacts gas reservoir development, and severe formation water intrusion can cause well flooding and production shutdowns, reducing the gas recovery rate. Statistical analysis shows that the recovery rate of water-intruded active gas reservoirs in the Sichuan Basin during the self-flowing stage is mostly below 30%. Therefore, accurately understanding the impact of reservoir heterogeneity on water activity in edge-water gas reservoirs and formulating corresponding countermeasures in a timely manner plays a positive role in improving the development effect of water-bearing gas reservoirs. Currently, the evaluation of the impact of reservoir heterogeneity on water activity is mainly based on core displacement experiments and other methods. However, these methods have limitations. This is mainly because core displacement experiments simulate the process of formation water intrusion, which is a microscopic mechanism study. The experimental conclusions cannot be extended to the macroscopic level and cannot fully and effectively guide the prediction and analysis of water activity levels.

[0003] In the prior art, for quantitative prediction of water activity levels, invention patent CN111507537A discloses a method and device for predicting the reserves and water intrusion of water-driven gas reservoirs. This patent, based on the principle of mass balance, uses production dynamic data and reservoir physical parameters to predict the reserves and water intrusion of water-driven gas reservoirs or the reserves of a constant-volume, closed, abnormally high-pressure water-producing gas reservoir. It also considers the elastic expansion effect of bound water and rock particles, making the prediction results more accurate and applicable to abnormally high-pressure water-driven gas reservoirs where general mass balance methods are not applicable. Invention patent CN111927411A discloses an intelligent method for tracking and early warning of water intrusion in water-bearing gas reservoirs. Based on the gas-water two-phase flow equation, combined with the gas-water two-phase inter-permeability expression and the water intrusion mass balance method, it calculates the water intrusion constant and water drive index, enabling real-time tracking and early warning of water intrusion direction and intensity. It shows good fitting results and strong generalizability. However, the aforementioned patents only consider homogeneous gas reservoirs with water, and do not address the impact of reservoir heterogeneity, nor establish corresponding theoretical models and derive seepage equations. Therefore, they cannot be used for quantitative prediction of the water activity level in heterogeneous edge-water gas reservoirs. Summary of the Invention

[0004] To quickly and conveniently predict the impact of reservoir heterogeneity on the water activity of water-bearing gas reservoirs, this invention provides a method for predicting the water activity level of heterogeneous edge-water gas reservoirs. Utilizing oil and gas reservoir seepage theory, a mathematical model and equation for seepage in heterogeneous edge-water gas reservoirs are established based on the intrusion mode of the surrounding water body, and numerical solutions are performed. This method can predict and analyze the recovery degree of gas reservoirs under different permeability ranges and the size of the surrounding water body, enabling a quantitative evaluation of the impact of reservoir heterogeneity on the water activity of water-bearing gas reservoirs.

[0005] This invention is achieved through the following technical solution: a method for predicting the water activity level of heterogeneous edge water gas reservoirs, comprising the following steps:

[0006] A. Based on the circular mean gas reservoir model, a seepage mathematical model and seepage mathematical equations are established according to the intrusion mode of the water body surrounding the gas reservoir.

[0007] B. Based on the above seepage mathematical model and seepage mathematical equation, establish analytical equations for gas reservoir production volume and gas reservoir stage production degree;

[0008] C. Collect the physical properties of the gas reservoir, and predict the dynamic changes of heterogeneous edge water gas reservoirs based on the established seepage mathematical equations, gas production volume, and gas production stage analysis equations.

[0009] In step A, the intrusion modes of the water surrounding the gas reservoir are defined as radial intrusion along the plane and unidirectional intrusion along the high-permeability strip, and the corresponding seepage mathematical models and seepage mathematical equations are established for different intrusion modes.

[0010] The mathematical model for the seepage of peripheral water bodies radially intruding into the gas reservoir along a plane is as follows:

[0011]

[0012] Where dp / dr is the derivative of formation pressure along radial distance; dp / dt is the derivative of formation pressure over time; Ф0 is formation porosity; μ is the viscosity of the fluid in the formation; C t denoted as the formation compressibility coefficient; r as the radial flow radius of the gas reservoir; k as the gas reservoir permeability; and t as the production time.

[0013] The mathematical equation for the seepage of peripheral water bodies into the gas reservoir radially along the plane is:

[0014]

[0015] Where, q w1 p represents the radial water intrusion front flow rate of the gas reservoir. i p represents the original formation pressure of the gas reservoir. e1 R is the radial flow stability pressure of the gas reservoir; R is the radius of the surrounding water body; rf The radius of the radial water intrusion front of the gas reservoir; μ w denoted as ρ, where ρ is the viscosity of formation water; k is the permeability of the gas reservoir; and h is the reservoir thickness.

[0016] The mathematical model for the seepage of the surrounding water body unidirectionally intruding into the gas reservoir along the high-permeability strip is as follows:

[0017]

[0018] in, Find the derivative of formation pressure along the high-permeability strip; Calculate the derivative of formation pressure over time; Ф0 is formation porosity; μ is the viscosity of the fluid in the formation; C t denoted as the formation's overall compressibility coefficient; L is the length of the high-permeability strip; k is the gas reservoir permeability; and t is the production time.

[0019] The mathematical equation for the seepage of the surrounding water body unidirectionally intruding into the gas reservoir along the high-permeability strip is:

[0020]

[0021] Where, q w2 p represents the radial water intrusion front flow rate of the gas reservoir. i p represents the original formation pressure of the gas reservoir. e2 R is the radial flow stability pressure of the gas reservoir; R is the radius of the surrounding water body; L f The radius of the radial water intrusion front of the gas reservoir; μ w k is the viscosity of formation water. f denoted as permeability of the high-permeability strip; w represents the width of the high-permeability strip; and h represents the reservoir thickness.

[0022] In step B, during the radial intrusion of the surrounding water body into the gas reservoir, the analytical equation for the gas production of the reservoir is as follows:

[0023]

[0024] Where, q g1 Φ represents the radial flow rate of gas production from the gas reservoir; h represents the reservoir thickness; and Ф represents the porosity. Find the derivative of the radial gas content of the gas reservoir with time; r f S is the radius of the radial water intrusion front of the gas reservoir; wi S represents the bound water saturation. gr Residual gas saturation; r e B is the gas reservoir radius; t is the production time. g This is the volume coefficient for natural gas.

[0025] In step B, during the radial intrusion of the surrounding water body into the gas reservoir, the analytical equation for the gas production of the reservoir is as follows:

[0026]

[0027] Where, q g1 denoted as radial gas production rate of the gas reservoir; w is the width of the high-permeability strip; h is the reservoir thickness; Ф is the porosity. Find the derivative of the gas content in the high-permeability strip of the gas reservoir over time; L f S is the radius of the radial water intrusion front of the gas reservoir; wi S represents the bound water saturation. gr Residual gas saturation; r e B is the gas reservoir radius; t is the production time. g This is the volume coefficient for natural gas.

[0028] In step B, the gas reservoir stage recovery degree analysis equation is:

[0029]

[0030] Among them, R g B represents the degree of recovery during the gas reservoir stage. gi B is the volume factor of natural gas under its original conditions; g r is the natural gas volume coefficient; f S is the radius of the radial water intrusion front of the gas reservoir; wi S represents the bound water saturation. gr Residual gas saturation; r e L is the gas reservoir radius; w is the width of the high-permeability strip; L f r is the radial water intrusion front radius of the gas reservoir; e The radius of the gas reservoir is given.

[0031] In step C, an explicit iterative method is used to solve the problem and obtain a prediction and analysis chart of the gas reservoir's recovery degree, so as to realize the prediction and analysis of the dynamic changes of heterogeneous edge water gas reservoirs.

[0032] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0033] Currently, determining the impact of heterogeneity on water activity primarily relies on methods such as core displacement experiments and numerical simulations, but both have limitations. Core displacement experiments, which simulate formation water intrusion, fall under the category of microscopic mechanism research, and their conclusions cannot be fully extended to the macroscopic development of gas reservoirs. Numerical simulations can quantitatively evaluate the impact of heterogeneity, but they rely heavily on detailed geological modeling, analysis, and prediction, which is time-consuming and labor-intensive. Therefore, to address the aforementioned problems with existing methods for analyzing water activity in heterogeneous edge-water gas reservoirs, this invention proposes a method for predicting water activity in heterogeneous edge-water gas reservoirs.

[0034] This invention combines the classification and evaluation of water intrusion in gas reservoirs, clarifies the characterization parameters of reservoir heterogeneity and their impact on the development of water-bearing gas reservoirs, and utilizes the seepage theory of oil and gas reservoirs to establish a mathematical model and numerical solution method for seepage in heterogeneous edge water gas reservoirs with locally existing high-permeability channels (microfractures or high-porosity sections). This solves the problem of water intrusion model description, and uses this to draw a predictive analysis chart of gas reservoir recovery degree under different permeability ranges and peripheral water body sizes. It can be used for quantitative analysis and prediction of water body activity, solving many problems in the analysis and prediction of the influence of water body activity on heterogeneous edge water gas reservoirs. Attached Figure Description

[0035] Figure 1 This is a physical model diagram of seepage in a heterogeneous edge water gas reservoir.

[0036] Figure 2 Charts for predicting and analyzing the extent of water recovery when water is encountered under different permeability ranges and water volume ratios. Detailed Implementation

[0037] The present invention will be further described in detail below with reference to embodiments, but the implementation of the present invention is not limited thereto.

[0038] Example 1:

[0039] This embodiment presents a method for predicting the water activity level of heterogeneous edge-water gas reservoirs. Based on the established mathematical equations for seepage into the gas reservoir by peripheral water bodies along radial and high-permeability strips, as well as the gas reservoir recovery prediction equations, numerical solutions are obtained to predict and analyze the dynamic changes of heterogeneous edge-water gas reservoirs.

[0040] First, based on the circular mean gas reservoir model, consider the existence of a high-permeability band, which could be a micro-fractured or high-porosity section, capable of connecting with the surrounding natural water body, forming a heterogeneous edge-water gas reservoir seepage physical model, such as... Figure 1 As shown.

[0041] Gas reservoir physical properties: The radius of the edge water gas reservoir is r e The reservoir thickness is h, the permeability is k, the porosity is Ф, and the original pressure of the gas reservoir is p. i The bottom pressure is p wf Water saturation S w The bound water saturation is S wi Gas saturation S g The residual gas saturation is S gr The fluid density is ρ, and the overall compressibility coefficient is C. t The original geological reserves of the gas reservoir are G; the width of the high-permeability strip is w, and the permeability is k. f Its height is also h; the radius of the outer water body is R, and the ratio of the water volume to the pore volume of the air zone is N times the water volume. num .

[0042] Assuming a constant gas production rate q g Production, with a cumulative gas production of G per stage. p The formation pressures of the surrounding formation water intruding into the gas reservoir along the radial direction and the high-permeability strips are respectively p e1 p e2 .

[0043] In the above assumptions: r e ρ is the reservoir radius, m; h is the reservoir thickness, m; k is the reservoir permeability, mD; Ф is the reservoir porosity, dimensionless; p i The original formation pressure of the gas reservoir is MPa; p wf The bottom hole flowing pressure is measured in MPa and S. w Water saturation, %; S wi Water saturation, %; S g Gas saturation, %; S gr Residual gas saturation, %; fluid density, g / cm³. 3 C t G represents the overall compressibility coefficient, 1 / MPa; G represents the original geological reserves of the gas reservoir, in m³. 3 w represents the width of the high-permeability strip, in meters; k represents the width of the strip. f The permeability of the high-permeability strip is expressed in mD; R is the radius of the surrounding water body in m; N num q is a multiple of the water volume, dimensionless; g The daily gas production of the gas reservoir is expressed in m. 3 / d;G p For the cumulative gas production during the gas reservoir stage, m 3 ;p e1 p represents the formation pressure (MPa) at which formation water radially intrudes into the gas reservoir. e2 This represents the formation pressure, expressed in MPa, at which formation water intrudes into the gas reservoir along a high-permeability strip.

[0044] During the gas reservoir production process, the internal pressure of the gas reservoir gradually decreases, and surrounding water continuously intrudes into the gas reservoir. There are two main ways in which the surrounding water intrudes into the gas reservoir: one is to intrude radially along the circular boundary, and the other is to intrude into the gas reservoir along high-permeability strips.

[0045] according to Figure 1 The corresponding mathematical model and equations are established based on the seepage physical model, and mathematical solutions are obtained to determine the relationship between gas production, water volume and time in the gas reservoir, thereby realizing the prediction and analysis of dynamic changes in heterogeneous edge water gas reservoirs.

[0046] The derivation process of the specific steps and methods in this embodiment is as follows:

[0047] S1: Based on the two modes of water intrusion around the gas reservoir: radial intrusion along the plane and unidirectional intrusion along the high-permeability strip, mathematical models and mathematical equations of seepage are established for different intrusion modes based on the theory of unsteady flow.

[0048] a) Peripheral water bodies intrude radially into the gas reservoir.

[0049] The seepage process of gas and elastic liquid follows a linear seepage law. Ignoring the influence of gravity and keeping the temperature constant, the gas reservoir pore medium is homogeneous with constant porosity and permeability, and its flow law can still be represented by Darcy's law.

[0050]

[0051] In equation (1), ρ is the seepage velocity, cm / s; μ is the fluid viscosity in the formation, MPa·s.

[0052] Considering the unstable seepage as a porous medium and a liquid that can be compressed, the equations of state for the porous medium and the elastic liquid need to be taken into account, where ρ0 and Ф0 are the fluid density and porosity under standard pressure p0, respectively.

[0053] Φ=Φ0[1+C Φ (p-p0)] (2)

[0054] ρ=ρ0[1+Cp(p-p0)] (3)

[0055] The seepage of gases and elastic fluids in formations follows the principle of mass conservation (the principle of continuity). The equations of motion and the equations of state can be linked together on the basis of mass conservation to describe the entire seepage process, which can be expressed by differential equations.

[0056]

[0057] Combine equations (2) and (3):

[0058] Фρ=Ф0ρ0+(p-p0)(C Φ -Cp) (5)

[0059] Define the overall compression factor C t =(C Ф Substitute -Cp) into equation (5) and take the partial derivative with respect to time t:

[0060]

[0061] Expanding the seepage differential equation (4) along the x, y, and z directions, and combining it with equation (6), we get:

[0062]

[0063] Further coordinate transformation according to the radial flow r direction in the plane, equation (7) can be transformed into:

[0064]

[0065] Considering the presence of a large water body surrounding the gas reservoir, the edge-water gas reservoir model can be simplified to a single well at the center of a constant-pressure boundary formation, producing at a constant rate. The initial conditions of the gas reservoir are considered as p(r, 0) = p i At the bottom of the well, r = r w Internal boundary conditions at the location Gas reservoir isobaric boundary r = r e External boundary condition p(r) e ,0)=p e1 Based on the above conditions, the mathematical model is solved.

[0066] Using the method of separation of variables, the image function is transformed into an ordinary differential equation, which is then solved under the corresponding boundary conditions. Laplace inversion is then performed to obtain the solution. The pressure expression at any point in the formation at any time is then obtained as follows:

[0067]

[0068] In the formula, β n (n = 1, 2, ...) — J0(r) D β n )Y(r D β n )-Y0(r D β n )J0(β n The nth root of ∑∞β; J0(x) and J1(x) are the first-order and first-order Bessel functions of the zero and first order, respectively; Y0(x) and Y1(x) are the second-order and first-order Bessel functions of the zero and first order, respectively. n 2 ηt

[0069] When the gas reservoir production time is very long, i.e. t→∞, the series terms in equation (9) tend to zero, and the fluid flow exhibits steady seepage. The pressure at each point in the formation stabilizes and no longer changes. The formulas for steady seepage pressure and production are:

[0070]

[0071]

[0072] In equations (10) and (11), p e The stable flow pressure of the gas reservoir is expressed in MPa; r e Let be the stable flow radius of the gas reservoir, in meters (m).

[0073] For the water body surrounding the gas reservoir, the intrusion process during production conforms to Schilthuis' steady-state theory and the steady-state displacement of gas. The water intrusion along the radial front r... f The flow rate can be expressed as:

[0074]

[0075] In equation (12), q w1 The radial water intrusion front flow rate of the gas reservoir is m. 3 / d;p e1 The radial flow stability pressure of the gas reservoir is given in MPa; r f Radius of the radial water intrusion front of the gas reservoir, in meters (m); μ w ν is the viscosity of formation water, mPa·s.

[0076] Assuming the peripheral water intrusion process is similar to the piston-driven water gas displacement process, the gas saturation of the reservoir at the formation water intrusion front is S of residual gas. gr Water intrusion radial leading edge r f The flow rate can also be expressed as:

[0077]

[0078] Formation water advances to the radial water front r f Cumulative gas production at the stage G p1 The mass balance expression is:

[0079]

[0080] In equation (14), G p1 The cumulative gas production during the radial flow stage of the gas reservoir is expressed in m. 3 B g B is the volume factor for natural gas, dimensionless; gi It is the volume factor of natural gas under its original conditions, and is dimensionless.

[0081] During the radial intrusion of peripheral formation water, the gas production rate q g1 It can be represented as

[0082]

[0083] In equation (15), q g1 —Radial flow rate of gas production from the gas reservoir, in m 3 / d.

[0084] b) Surrounding water unidirectionally intrudes into the gas reservoir along a high-permeability strip.

[0085] As the formation pressure of the gas reservoir decreases, the surrounding water preferentially intrudes into the gas reservoir unidirectionally along the high-permeability strip. Its seepage differential equation can be expressed by Equation (7), only considering the relationship between pressure and time in the x direction.

[0086]

[0087] Further, following the unidirectional flow L direction, a coordinate transformation is performed, and equation (16) can be transformed into:

[0088]

[0089] Considering the initial conditions of the gas reservoir, p(L, 0) = p i Well bottom L = r w Internal boundary conditions at the location Gas reservoir isobaric boundary L = r e External boundary condition p(r) e ,0)=p e2 Based on the above conditions, a mathematical model is solved. When the gas reservoir has a long production time, the fluid flow exhibits steady-state seepage. The formulas for steady-state seepage pressure and production rate are:

[0090]

[0091]

[0092] As formation pressure decreases, peripheral water preferentially intrudes into the gas reservoir along high-permeability strips. This intrusion process also conforms to Schilthuis' steady-state theory and the steady-state displacement of gas. The water intrusion radial front L... f The flow rate can be expressed as:

[0093]

[0094] In equation (20), q w2 —Flow rate at the water front of the high-permeability strip in the gas reservoir, m 3 / d;L f — Distance at the water intrusion front of the high-permeability strip, in meters.

[0095] Assuming the intrusion of peripheral edge water along high-permeability strips is similar to the piston-water gas-drive process, and the gas saturation of the reservoir at the formation water intrusion front is S (residual gas S), then... gr Water intrusion radial leading edge L f The flow rate can also be expressed as:

[0096]

[0097] Formation water advances along the high-permeability strip to the water front L f Cumulative gas production at the stage G p2 The mass balance expression is:

[0098]

[0099] In equation (22), G p2 —Cumulative gas production during the high-permeability stripe flow stage of the gas reservoir, in m 3 .

[0100] During the intrusion of peripheral formation water along high-permeability strips, the gas production rate q g2 It can be represented as:

[0101]

[0102] In equation (23), q g2 —Gas production in high-permeability zones of gas reservoirs, m 3 / d.

[0103] S2: Based on the previously established physical model and mathematical equations of seepage in heterogeneous edge water gas reservoirs, the concept of stage recovery degree of gas reservoirs is introduced, and the analytical equations for stage recovery degree of heterogeneous edge water gas reservoirs are determined.

[0104] The formation water flow rate at the outer edge of the intrusion front at any given time can be expressed as:

[0105] q w =q w1 +q w2 (twenty four)

[0106] In equation (24), q w — Formation water inrush flow, m 3 / d.

[0107] Substituting equations (13) and (21) into equation (24), we obtain the equation relating formation water intrusion flow rate and distance from the water intrusion front:

[0108]

[0109]

[0110]

[0111] To more intuitively represent the water-gas replacement relationship in the formation, based on the expansion theory, the formation water intrusion flow can also be expressed as:

[0112]

[0113] In formula (28), the water volume ratio N is... num It is incorporated into the water pressure drop equation.

[0114] Substituting equations (12) and (20) into equation (28), we obtain the total pressure drop equation at the formation water front:

[0115]

[0116] Total gas production q at the formation water front g It can be represented as:

[0117] q g =q g1 +q g2 (30)

[0118] In equation (30), q g —Gas reservoir production, m 3 / d.

[0119] Substituting equations (15) and (23) into equation (24), we obtain the total production equation at the formation water front:

[0120]

[0121] At the corresponding production time t, the total cumulative gas production G at the formation water front is... p It can be represented as:

[0122] G p =G p1 +G p2 (32)

[0123] In equation (30), G p —Cumulative gas production during the gas reservoir stage, m 3 .

[0124] Substituting equations (14) and (22) into equation (26), we can obtain the total cumulative gas production equation at the formation water front:

[0125]

[0126] For example Figure 1 The original geological reserves G of the heterogeneous edge-water gas reservoir physical model shown can be expressed by the following formula:

[0127]

[0128] Degree of gas recovery at the formation water front gas reservoir stage R g It can be represented as:

[0129]

[0130] Substituting equations (27) and (28) into equation (29), the gas reservoir stage recovery rate R g This can be further expressed as:

[0131]

[0132] In equation (36), R g —Degree of recovery during the gas reservoir stage, %.

[0133] S3: Based on the established mathematical equations for seepage of the peripheral water bodies of heterogeneous edge water gas reservoirs along the radial plane and high-permeability strips invading the gas reservoir, as well as the gas reservoir recovery prediction and analysis equations, numerical solutions are performed to carry out dynamic change prediction and analysis of heterogeneous edge water gas reservoirs.

[0134] Equations (26) to (30) constitute a set of production equations for heterogeneous edge-water gas reservoirs. By employing iterative methods and combined numerical solutions, dynamic production data and predicted water breakthrough times for heterogeneous edge-water gas reservoirs can be obtained. The permeability range (k...) f / k) is defined as the ratio of the permeability of the high-permeability strip to the formation permeability, and is dimensionless.

[0135] First, collect parameters of the gas reservoir and gas wells, including: reservoir permeability k, and permeability k of high-permeability zones. f Porosity Ф, Formation water viscosity μ w Bound water saturation S wi Residual gas saturation S gr Water pressure p l Average pressure p of the gas reservoir, gas reservoir temperature T, reservoir thickness h, width of high-permeability strip w, gas reservoir radius r e Gas well production q g wait.

[0136] Second, the model is solved using explicit iteration. The specific solution steps are as follows:

[0137] 1) Take the time step as t i t is calculated according to equations (25) to (27). i The stage water intrusion volume; at the same time, the gas production volume at this time step is calculated; using the volumetric method, the stage recovery degree R at this time step is calculated using equation (35). g (t i ).

[0138] 2) Solve for the natural gas volume coefficient B at this moment using the mass balance equation (31). gi Further according to B gi Find t at this time i gas reservoir mean pressure p e (t i ).

[0139] 3) Calculate the water inrush volume based on the water inrush flow rate obtained in step 1, and calculate the water pressure drop at one time step using the water pressure drop equation (28); then calculate the water pressure drop at one time step t by combining equations (26) and (27). i+1 d belowrf d Lf .

[0140] 4) Using the initial time L f =0, to obtain L at a time step f(i+1) =L fi +d Lf ; and obtain the propagation distance L of the formation water intrusion along the high-permeability strip, L = r e -L fi .

[0141] 5) Determine whether L is greater than or equal to the reservoir radius r. e If not, proceed to the next long iteration, repeating steps 1 to 5 until the discrimination condition is met, and obtain the permeability range and the water volume ratio N. num The degree of water production at the moment when the gas well encounters water.

[0142] 6) Change the permeability range (k) f / k), water volume ratio N num Below, we plotted a chart predicting the extent of recovery when water is seen under different permeability ranges and water volume ratios.

[0143] Third, use charts to predict and analyze the dynamic changes of heterogeneous edge water gas reservoirs.

[0144] Example 2:

[0145] This embodiment is a specific implementation process of predictive analysis using the prediction method described in Embodiment 1.

[0146] First, using the aforementioned prediction method, collect specific parameter values ​​for the gas reservoir and gas well, including: reservoir matrix permeability k, and high-permeability strip permeability k. f Gas reservoir with extremely poor permeability (k) f / k, the water volume ratio surrounding the gas reservoir (N) num ...and so on, as well as various parameter values ​​of the gas reservoir and gas well when water is encountered in the gas reservoir.

[0147] Secondly, based on the above prediction method, plotted prediction and analysis charts of the recovery rate under different permeability ranges and water volume ratios when water is seen, such as... Figure 2 .Depend on Figure 2 It can be seen that the permeability difference of the gas reservoir and the size of the water body are important factors affecting the recovery rate. For example, the greater the difference in permeability between the high-permeability zone and the matrix in the gas reservoir, that is, the greater the permeability difference (k... f The larger the / k), the faster the formation water invades the gas reservoir, and the lower the recovery rate when the gas well (reservoir) encounters water; the larger the water body surrounding the gas reservoir, that is, the larger the water volume ratio (N) num The larger the value, the greater the expansion energy. Under the same reservoir conditions, the faster the formation water invades the gas reservoir, and the lower the recovery rate when the gas well (reservoir) encounters water.

[0148] Based on the statistical analysis of the recovery rate when water breaks in typical well areas of the Sichuan Basin, as shown in Table 1, for well areas such as TD29, the permeability is extremely poor (k f / k) is mainly distributed in the range of 2 to 10, and the water volume multiple (N) num )1~10, when water is encountered, the recovery rate is generally greater than 50%, and the formation water is not active; for well areas such as HL001-X1, the permeability is extremely poor (k f / k) is mainly distributed in the range of 2 to 15, and the water volume multiple (N) num )2~15, with a recovery rate of 30%~50% upon water exposure, indicating relatively active formation water; for well areas such as ZB19, permeability is extremely poor (k f / k) is mainly distributed in the range of 5 to 20, and the water volume multiple (N) num )10~50, when water is encountered, the extraction rate is generally less than 30%, and the formation water is active.

[0149] Table 1. Statistics on the degree of recovery when water is encountered in typical gas wells (reservoirs)

[0150]

[0151] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for predicting the water activity level of heterogeneous edge water gas reservoirs, characterized in that: Includes the following steps: A. Based on the circular mean gas reservoir model, the intrusion modes of the water surrounding the gas reservoir are set as radial intrusion along the plane and unidirectional intrusion along the high-permeability strip, and the corresponding seepage mathematical models and seepage mathematical equations are established under different intrusion modes. B. Based on the above seepage mathematical model and seepage mathematical equation: (a) During the radial intrusion of the surrounding water body into the gas reservoir, the analytical equation for the gas production of the reservoir is established as follows: in, q g1 This represents the radial flow gas production rate of the gas reservoir. h Reservoir thickness; Ф Porosity; Find the derivative of the radial gas content of the gas reservoir as a function of time; r f The radius of the radial water intrusion front of the gas reservoir; S wi To bind water saturation; S gr Residual gas saturation; r e The radius of the gas reservoir; t For production time, B g This is the volume factor for natural gas. (b) During the process of the surrounding water body unidirectionally intruding into the gas reservoir along the high-permeability strip, the analytical equation for the gas production of the gas reservoir is established as follows: in, q g2 This refers to the gas production of high-permeability zones in gas reservoirs; w The width of the high-permeability strip; h Reservoir thickness; Ф Porosity; Find the derivative of the gas content in the high-permeability strip of the gas reservoir as a function of time; L f The radius of the radial water intrusion front of the gas reservoir; S wi To bind water saturation; S gr Residual gas saturation; r e The radius of the gas reservoir; t For production time, B g This is the natural gas volume factor; C. Based on the above seepage mathematical model and seepage mathematical equation, determine the analysis equation for the degree of recovery in the gas reservoir stage; D. Collect the physical properties of the gas reservoir, and predict the dynamic changes of heterogeneous edge water gas reservoirs based on the established seepage mathematical equations, gas production and stage recovery analysis equations.

2. The method for predicting the water activity level of a heterogeneous edge water gas reservoir according to claim 1, characterized in that: The mathematical model for the seepage of peripheral water bodies radially intruding into the gas reservoir along a plane is as follows: in, dp / dr Find the derivative of formation pressure along radial distance; dp / dt Find the derivative of formation pressure as a function of time; Ф 0 represents formation porosity; μ The viscosity of the fluid in the formation; C t The overall compressibility coefficient of the formation; r The radial flow radius of the gas reservoir; k This represents the permeability of the gas reservoir.

3. The method for predicting the water activity level of a heterogeneous edge water gas reservoir according to claim 1, characterized in that: The mathematical equation for the seepage of peripheral water bodies into the gas reservoir radially along the plane is: in, q w1 This represents the radial water intrusion front flow rate of the gas reservoir. p i This represents the original formation pressure of the gas reservoir. p e1 The radial flow stabilization pressure of the gas reservoir; R The radius of the outer water body; r f The radius of the radial water intrusion front of the gas reservoir; μ w Formation water viscosity; k This represents the permeability of the gas reservoir.

4. The method for predicting the water activity level of a heterogeneous edge-water gas reservoir according to claim 1, characterized in that: The mathematical model for the seepage of the surrounding water body unidirectionally intruding into the gas reservoir along the high-permeability strip is as follows: in, Find the derivative of formation pressure along the high-permeability strip; Find the derivative of formation pressure as a function of time; Ф 0 represents formation porosity; μ The viscosity of the fluid in the formation; C t The overall compressibility coefficient of the formation; L The length of the high-permeability strip; k This represents the permeability of the gas reservoir.

5. The method for predicting the water activity level of a heterogeneous edge-water gas reservoir according to claim 1, characterized in that: The mathematical equation for the seepage of the surrounding water body unidirectionally intruding into the gas reservoir along the high-permeability strip is: in, q w2 This represents the flow rate at the water front of the high-permeability strip in the gas reservoir. p i This represents the original formation pressure of the gas reservoir. p e2 The radial flow stabilization pressure of the gas reservoir; R The radius of the outer water body; L f The radius of the radial water intrusion front of the gas reservoir; μ w Formation water viscosity; k f For high-permeability strips; w For high-permeability strip width.

6. The method for predicting the water activity level of a heterogeneous edge-water gas reservoir according to claim 1, characterized in that: In step C, based on the seepage physical model and seepage mathematical equation, the concept of gas reservoir stage recovery degree is introduced, and the gas reservoir stage recovery degree analysis equation is determined.

7. The method for predicting the water activity level of a heterogeneous edge-water gas reservoir according to claim 6, characterized in that: The analytical equation for the degree of recovery during the gas reservoir stage is as follows: in, R g This refers to the degree of recovery during the gas reservoir stage; B gi The volume factor of natural gas under its original conditions; r f The radius of the radial water intrusion front of the gas reservoir; w The width of the high-permeability strip; L f The radius of the radial water intrusion front of the gas reservoir is denoted as .

8. The method for predicting the water activity level of a heterogeneous edge-water gas reservoir according to claim 1, characterized in that: In step D, the physical properties of the gas reservoir include the reservoir permeability. k High-permeability strip permeability k f Porosity Ф Formation water viscosity Bound water saturation S wi Residual gas saturation S gr Water pressure p l Mean pressure of gas reservoir, gas reservoir temperature T reservoir thickness h High-permeability strip width w Gas reservoir radius r e Gas well production q g。 9. The method for predicting the water activity level of a heterogeneous edge-water gas reservoir according to claim 8, characterized in that: In step D, based on the preset gas reservoir physical property parameters, an explicit iterative method is used to solve the problem and obtain a gas reservoir recovery degree prediction and analysis chart, so as to realize the prediction and analysis of the dynamic changes of heterogeneous edge water gas reservoirs.

10. The method for predicting the water activity level of a heterogeneous edge-water gas reservoir according to claim 9, characterized in that: The steps for solving the problem using the explicit iterative method are as follows: (1) Take the time step, calculate the water intrusion volume in this stage according to the relationship equation between the formation water intrusion flow and the distance of the water intrusion front, calculate the gas production volume in this time step, and use the volumetric method to calculate the stage production degree in this time step. (2) Solve for the natural gas volume factor at this moment based on the mass balance equation, and further calculate the average reservoir pressure at this time step based on the natural gas volume factor; (3) Calculate the water intrusion volume based on the water intrusion flow rate obtained in step (1), calculate the water pressure drop at one time step using the water pressure drop equation, and then calculate the change in the water intrusion front distance of the high permeability strip at the next time step by combining the relationship equation between the formation water intrusion flow rate and the distance of the water intrusion front. (4) Using the initial time step where the distance of the high-permeability strip water intrusion front is zero, the distance of the high-permeability strip water intrusion front in the next time step is accumulated, and the advance distance of the formation water intrusion along the high-permeability strip is calculated; (5) Determine whether the advance distance of formation water along the high-permeability strip is greater than or equal to the gas reservoir radius. If not, proceed to the next long iteration and repeat steps (1) to (5) until the discrimination condition is met, and obtain the production degree at the time of water breakthrough in the gas well under the conditions of extremely poor permeability and water volume ratio. The permeability range is the ratio of the permeability of the high-permeability strip to the formation permeability; (6) By changing the permeability range, draw prediction and analysis charts of the extent of water production when water is seen under different permeability ranges and water volume ratios.

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