Production-data-based well test analysis method for oil and gas well

Abstract

Disclosed in the present invention is a production-data-based well test analysis method for an oil and gas well. The method comprises the following steps: on the basis of a variable-rate convolution formula, establishing a normalized pressure equation; acquiring field long-term production data; on the basis of the normalized pressure equation, performing rapid deconvolution calculation on the long-term production data to obtain a pressure response function and a logarithmic time derivative thereof, and on the basis of the pressure response function and the logarithmic time derivative thereof, preliminarily identifying characteristic flow regimes; and on the basis of the normalized pressure equation, establishing an accurate identification model for the characteristic flow regimes, and on the basis of the accurate identification model, accurately identifying the characteristic flow regimes in the long-term production data, and then using the characteristic flow regimes to perform parameter inversion to acquire formation parameters or dynamic reserves. On the basis of the equation, rapid production-data-based deconvolution of pressure and pressure derivatives can be achieved, thereby unifying conventional PTA and RTA methods to form a new well test analysis method based on production data.

Description

A well test analysis method for oil and gas wells based on production data Technical Field

[0001] This invention relates to the field of oil and gas development technology, and more specifically to a well test analysis method for oil and gas wells based on production data. Background Technology

[0002] In the petroleum industry, unsteady pressure analysis (PTA) and unsteady production analysis (RTA) are two core technologies for production data analysis. By analyzing production and pressure data, PTA and RTA methods can obtain reservoir parameters and dynamic reserves of oil and gas wells.

[0003] PTA is primarily used for short-term production and pressure test data analysis, such as pressure drop and pressure recovery data. These data points are dense and highly accurate, often measured in seconds, but the duration is short, typically measured in hours. However, during long-term oil and gas well production, wellhead pressure data needs to be converted to bottomhole flowing pressure data, and the influence of wellhead measurement errors often results in significant noise in the calculated bottomhole pressure and wellhead production figures. This limits the application of PTA in long-term production data analysis.

[0004] The development of Remote Temperature Analyzer (RTA) aimed to address the shortcomings of PTA in long-term production data analysis. RTA is primarily used for analyzing long-term production data from oil and gas wells, with data sources including wellhead pressure and production figures. This data is large in volume and spans a long period, often measured in months or years. In the RTA theoretical framework, the material equilibrium time proposed by Blasingame plays a crucial role, enabling the transformation from variable-yield production to constant-yield production. However, over the decades of RTA development, many scholars have also identified the following problems in its application:

[0005] (1) The material equilibrium time lacks a clear physical meaning. With fluctuations in output, the material equilibrium time jumps back and forth, losing its time series characteristics and even exhibiting phenomena that violate physical laws. At the same time, changes in output can cause characteristic flow segments in the material equilibrium time coordinate system to exhibit "leading" or "lagging" phenomena, such as the unsteady flow period appearing as a quasi-steady flow segment. Therefore, theoretical charts with material equilibrium time as the horizontal axis lack physical meaning.

[0006] (2) Blasingame's theoretical framework is only strictly valid in the quasi-steady-state stage, and has not yet been rigorously proven in the unsteady flow stage, resulting in a lack of rigorous theoretical support for RTA. Especially for unconventional reservoirs, where oil and gas wells are in an unstable flow stage for extended periods, RTA is unusable. Currently, RTA is widely misused in the field for unconventional reservoirs.

[0007] (3) The vertical axis of the RTA theoretical chart uses normalized pressure and the horizontal axis is material equilibrium time, which is not the time-pressure and pressure derivative in the traditional well test chart. Therefore, the chart cannot be used for accurate identification of characteristic flow sections, which limits the application of this method.

[0008] In summary, in production data analysis, the RTA method lacks a rigorous theoretical foundation in the unstable flow stage, cannot obtain pressure and pressure derivative curves, and struggles to accurately identify characteristic flow segments, making it unsuitable for production evaluation of unconventional oil and gas reservoirs. While the PTA method has a complete theoretical framework, it is primarily used for short-term, low-noise test data analysis and cannot be applied to long-term production data analysis with significant noise levels. Summary of the Invention

[0009] The purpose of this invention is to provide a well test analysis method for oil and gas wells based on production data, so as to solve the technical problem that the existing RTA method and PTA method have their own defects and cannot meet the needs of production data analysis.

[0010] To solve the above-mentioned technical problems, the present invention specifically provides the following technical solution:

[0011] A well test analysis method for oil and gas wells based on production data includes the following steps:

[0012] Define the variable yield convolution formula, and establish a normalized pressure equation based on the variable yield convolution formula to explicitly characterize the normalized pressure, time variable, derivative of pressure response function and material equilibrium time relationship.

[0013] Obtain long-term production data from the site;

[0014] Based on the normalized pressure equation, a fast deconvolution calculation is performed on long-term production data to obtain the pressure response function and its logarithmic time derivative. Based on the pressure response function and its logarithmic time derivative, characteristic flow sections are preliminarily identified.

[0015] An accurate identification model for the characteristic flow segment is established based on the normalized pressure equation. The characteristic flow segment of long-term production data is accurately identified based on the accurate identification model. Then, the characteristic flow segment is used to perform parameter inversion to obtain formation parameters or dynamic reserves.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] This invention starts from the basic formula of convolution under variable production / pressure and establishes an explicit normalized pressure equation applicable to the entire flow stage. Based on this equation, it is possible to achieve rapid convolution inversion of pressure and pressure derivative based on production data, thereby unifying the traditional PTA method and RTA method to form a new production data well test analysis method.

[0018] This analytical method overcomes the shortcomings of existing PTA and RTA methods, and can be used for the analysis of both short-term test data and long-term production data. Based on the explicit normalized pressure equation, it can easily achieve rapid deconvolution calculation to obtain pressure and pressure derivative values, making it applicable to the analysis of characteristic flow sections in all flow sections, and organically combining the advantages of RTA and PTA models. Attached Figure Description

[0019] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0020] Figure 1 is a schematic diagram of the process provided in an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] As shown in Figure 1, this invention provides a well test analysis method for oil and gas wells based on production data. First, the concept of production well test is defined: based on long-term production data of oil and gas wells, such as daily production data, a method is used to identify characteristic flow sections and obtain reservoir parameters by using well test interpretation charts (time-pressure and time-pressure logarithmic time derivative).

[0023] Specifically, the steps are as follows.

[0024] (1) Theoretical model establishment:

[0025] Starting with the basic variable yield convolution formula, an explicit normalized pressure formula is established. This formula can explicitly characterize the normalized pressure, time variable, derivative of the pressure response function, and normalized pressure equation relating mass equilibrium time.

[0026] (2) Data Acquisition:

[0027] Long-term production data: mainly includes production and pressure data during the continuous production process of oil and gas wells, with the time period measured in days.

[0028] (3) Fast deconvolution calculation:

[0029] By establishing a normalized pressure formula, a rapid deconvolution calculation is performed on the production data to obtain the pressure response function p. u and its logarithmic time derivative dp u / dlnt.

[0030] (4) Conduct characteristic flow segment analysis:

[0031] Based on the pressure response function and its logarithmic time derivative, characteristic flow segments are initially identified. Based on the normalized pressure equation, an accurate identification model for characteristic flow segments is established to precisely identify production data flow segments.

[0032] (5) Obtain formation parameters or dynamic reserves.

[0033] Using the characteristic flow section, parameter inversion is performed using well test analysis methods and procedures.

[0034] In this invention, the traditional PTA method is used for stress analysis of short-term test data, and the traditional RTA method is used for output and stress analysis of long-term production data. This method unifies the traditional RTA and PTA, and can be used for analysis of both short-term test data and long-term production data at the same time.

[0035] Secondly, compared to test data, production data is characterized by low precision and large measurement errors, resulting in significant data noise. While traditional deconvolution methods have been explored for decades and occasionally used for short-term test data, a mature algorithm suitable for actual field production data has yet to be found. Based on our proposed explicit normalized pressure model, we can easily and quickly perform deconvolution calculations to obtain pressure and pressure derivative values.

[0036] Furthermore, while the PTA model has a rigorous theoretical foundation and its greatest advantage lies in its ability to identify characteristic flow segments, it is currently only applicable to short-term test data analysis and cannot be used for production data analysis, thus limiting its application. RTA, on the other hand, is theoretically incomplete; strictly speaking, it can only be used for quasi-steady-state flow segment analysis and cannot obtain pressure and pressure derivative curves, exhibiting flaws in characteristic flow segment identification. The theoretical model proposed in this invention is based on rigorous mathematical derivation, is applicable to all flow segments, and can be used for characteristic flow segment analysis, organically combining the advantages of both RTA and PTA models.

[0037] Finally, the concept of production data well test analysis is proposed, which applies the traditional short-term well test analysis method to long-term production data analysis, thereby enabling the use of a complete set of mature characteristic flow section identification and parameter inversion methods from well test analysis.

[0038] The following will be described in conjunction with specific embodiments.

[0039] This invention provides a novel explicit computation method for convolution equations, which enables the convolution equations to be explicitly represented by functions and can intuitively display the relationships between the functions. At the same time, it can greatly improve the computational efficiency of convolution and deconvolution, and can be widely used for fast computation with massive amounts of data.

[0040] In mathematics, convolution is defined as a mathematical operator that takes two functions, h and g, and generates a third function, y, which represents the amount of overlap between g and its inverted form h. In other words, convolution is defined as the integral of the product of one function (inverted and translated) and another function.

[0041] Its expression is:

[0042] Wherein, h(t) is defined as df(t) / dt(2);

[0043] Substituting equation (2) into equation (1) yields:

[0044] Integrating equation (3) by parts yields

[0045] In the formula:

[0046] Equation (4) can be further expressed as:

[0047] Where y(t) is the system response, which is the convolution of functions f(t) and g(t).

[0048] Define the convolution time function as:

[0049] Furthermore, the convolution time function and its derivative satisfy: Γ(0)=0,Γ'(0)=1 (8);

[0050] Substituting equation (7) into equation (6), we get:

[0051] Integrating equation (9) by parts yields:

[0052] Integrating equation (10) by parts again and using the initial condition equation (8), we obtain:

[0053] In practical applications, appropriate convolution time functions, such as linear functions, quadratic functions, exponential functions, polynomials, etc., can be selected based on the changing characteristics of the g(t) function to further simplify the equation (11).

[0054] When a linear convolution time function is used, the convolution time function satisfies: Γ(τ)=τ (12)

[0055] Substituting equation (12) into equation (11), we obtain the simplified explicit convolution equation:

[0056] The method proposed in this invention is based on the convolution integral equation. Through rigorous mathematical derivation, a general convolution expression is obtained. Based on this, a simplified explicit convolution expression under the assumption of a linear convolution time function is derived. Similarly, when other functions are chosen for the convolution time function, such as quadratic functions, exponential functions, or polynomials, other types of simplified explicit convolution expressions can be obtained. For other fields satisfying the convolution integral equation (1), the general convolution expression (Equation 11) and the simplified explicit convolution expression (Equation 13) proposed in this patent are still applicable. It is only necessary to follow the process of this patent to determine three functions, namely y(t), g(t), and f(t).

[0057] In petroleum industry production, the observed pressure drop is the convolution of the input flow function and the derivative of the constant flow pressure response. In existing technology, assuming the system is in equilibrium at the initial moment, the pressure drop at time t can be expressed as:

[0058] Its discrete form is:

[0059] In the formula, p u Let q be the pressure response function. w This represents the production rate of an oil and gas well. When the production rate is q... w and pressure response function p u When the information is known, the bottom hole pressure drop Δp can be calculated using the above equations through forward modeling. w When the output q w and bottom hole pressure drop Δp w When the given information is available, the pressure response function p can be obtained through inversion calculation using the above equations. u .

[0060] However, the above equation has the following two problems in engineering applications:

[0061] First, calculating the pressure drop at time t requires multiplication and addition operations, and the calculation needs to use all discrete segments of flow before time t. Therefore, the computational cost is directly proportional to the number of discrete segments. With the advent of the big data era, and with the increasing density of production data, especially in recent years with the application and promotion of intelligent manufacturing systems, the amount of production data is growing larger and larger, and the time required for dynamic prediction calculations using the convolution method is also increasing.

[0062] Secondly, when performing deconvolution using the above equations, data errors and calculation errors before time t will accumulate; therefore, in addition to the problem of large computational load, deconvolution also presents stability issues.

[0063] To address the aforementioned issues, this invention employs the explicit convolution expression described above. This equation requires fewer parameters and involves less computation, which can significantly improve the operational efficiency of convolution and deconvolution, and can be widely applied to rapid computation with massive amounts of data.

[0064] The bottom-hole pressure of a single-phase, slightly compressible fluid seepage flow is assumed to satisfy the superposition principle, and the bottom-hole pressure drop is assumed to satisfy the following conditions.

[0065] In the formula, t is the time variable; τ is the integration variable; p i Δp represents the initial pressure of the reservoir. w For the pressure drop at the bottom of the well; p w This refers to the bottom hole pressure.

[0066] According to the above equation and equation (3), we know that: y(t)=Δp w (t)=p i -p w g(t); g(t)=q w (t); f(t) = p u (t);

[0067] Based on the aforementioned equation for calculating the cumulative output G(t) at time t, and defining the material equilibrium time t... mb ,in:

[0068] Substituting the above equation into the simplified explicit convolution expression (Equation 13) yields:

[0069] The above equation is a simplified explicit pressure response convolution equation for oil production. This equation significantly improves computational efficiency. It intuitively reveals the relationship between pressure differential, production rate, pressure response function, and their derivatives. This equation enables both forward and inverse convolution modeling. Further simplification yields the normalized pressure equation:

[0070] In this embodiment, convolution inversion is used as an example for explanation.

[0071] Convolution inversion: based on output (q) w ) and pressure drop (Δp) w Inverted reservoir pressure response function (p) u ).

[0072] In convolution inversion calculations, production rate and bottom hole pressure drop are used as known parameters, and the pressure response function is obtained through inversion. The calculation process is as follows:

[0073] (1) Collect production well data; collect production data q w and bottom hole flowing pressure data p wf According to the original formation pressure p i Calculate the production pressure difference Δp w =p i -p wf .

[0074] (2) Calculate the cumulative output G at a certain moment. q i = 1, 2, ..., N

[0075] (3) Calculate the equilibrium time t mb ;

[0076] (4) Calculate Δp w / q w Assuming the pressure response function near time t can be approximated linearly, the derivative dp of the pressure response function can be approximated using the following formula. u / dt and logarithmic time derivative dp u / dlnt

[0077] (5) with t and △p w / q w dp u / dt and t mb Calculate the pressure response function p using the following formula. u ;

[0078] The comprehensive analysis for accurate identification of characteristic flow segments based on long-term production data includes the following three steps:

[0079] (1) Identify the characteristic flow section based on the pressure response function and its logarithmic time derivative.

[0080] Under constant production conditions, the pressure response function p at time t in the characteristic flow section. u (t) is a linear function of the power function of the time variable t, expressed as: p u (t)=a u +b u ·t n ;

[0081] In the formula, a u and b u is the characteristic flow constant; n is the characteristic flow index;

[0082] Specifically, the pressure response function for radial flow (n=0) is expressed as follows: p u (t)=a u +b u ·ln t

[0083] The logarithmic time derivative of the characteristic flow section is but:

[0084] In a double logarithmic coordinate system, the characteristic flow segment is represented by a straight line with a slope of n, which is the logarithmic time derivative.

[0085] Drawing tp u and The double logarithmic chart is used to obtain the slope n by segmenting the chart shape, and to initially identify the characteristic flow segments that may appear.

[0086] (2) Accurate identification of characteristic flow segments

[0087] Analyze the possible characteristic flow segments and establish an accurate identification model for the characteristic flow segments.

[0088] When the output changes relatively slowly, t is established for each of the characteristic flow segments initially identified in step (1). mbe The RNP equation is: RNP(t) = a u +b u ·t mbe ;

[0089] In the formula, t mbe The effective material equilibrium time, where:

[0090] Given a characteristic flow index n, the characteristic flow constant a of the characteristic flow segment is calculated using the moving window method. u and b u The curve is plotted against the time variable t, and t is viewed simultaneously. mbe -RNP equation straight segment and characteristic flow parameter a u and b u The constant segment of the curve versus the time variable t is used to determine whether a specified characteristic flow segment occurs and the duration range of said characteristic flow segment (t). min ,t max Within the time range (t) min ,t max Within ) when t mbe - The RNP curve shows a linear relationship, and ta u and tb u When the curve is constant within this time period, it is assumed that there is a characteristic flow segment within this time range, and its characteristic flow index is n.

[0091] (3) Reconstruct the characteristic flow section curve and invert the reservoir parameters.

[0092] Within the time range (t) min ,t max Within ), based on the characteristic flow parameter a u and b u The characteristic flow section curve is reconstructed using the following formulas, where the pressure response function and logarithmic time derivative of the characteristic flow section are respectively:

[0093] After completing the preliminary analysis, accurate identification and reconstruction of the characteristic flow section in steps (1)-(3), the conventional well test analysis model can be used to perform parameter inversion. For example, in the pseudo-steady-state flow analysis, it is determined whether production has entered the boundary flow stage and the original geological reserves are calculated; the constructed smooth pressure response function and derivative curve can be directly used for chart fitting, which can greatly improve the chart fitting effect.

[0094] It should be noted that when constructing a feature flow, it is not necessary to obtain the complete feature flow segment precisely; it is only necessary to determine the segment with the most significant features.

[0095] The method proposed in this invention makes no assumptions about the pressure response function during the equation derivation process. Therefore, the general equation proposed in this invention can be used for convolution forward and inverse models of different production stages under any reservoir and production well combination. The main difference in calculations for different reservoir and production well combinations lies in the different pressure response functions. It is only necessary to select the corresponding pressure response function based on the specific reservoir and production well combination and perform the calculation according to the aforementioned process.

[0096] The method proposed in this invention is derived from the oil well convolution integral equation. It replaces the actual pressure with the pressure in the gas reservoir, and this method can be extended to the calculation of gas reservoirs.

[0097] The concept of well test analysis of production data proposed in this invention applies the traditional short-term well test analysis method to long-term production data analysis, thereby enabling the use of a complete set of mature characteristic flow section identification and parameter inversion methods in well test analysis.

[0098] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. The scope of protection of this application is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to this application within its substance and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A method for analyzing oil and gas well tests based on production data, characterized in that, Includes the following steps: Define the variable yield convolution formula, and establish a normalized pressure equation based on the variable yield convolution formula to explicitly characterize the normalized pressure, time variable, derivative of pressure response function and material equilibrium time relationship. Obtain long-term production data from the site; Based on the normalized pressure equation, a fast deconvolution calculation is performed on long-term production data to obtain the pressure response function and its logarithmic time derivative. Based on the pressure response function and its logarithmic time derivative, characteristic flow sections are preliminarily identified. An accurate identification model for the characteristic flow segment is established based on the normalized pressure equation. The characteristic flow segment of long-term production data is accurately identified based on the accurate identification model. Then, the characteristic flow segment is used to perform parameter inversion to obtain formation parameters or dynamic reserves.

2. The method for oil and gas well testing analysis based on production data according to claim 1, characterized in that, Let h(t) and g(t) be two variable functions. A third function y(t) is generated by convolution of h(t) and g(t). The convolution formula for h(t) and g(t) is defined as follows: Where t is the time variable and τ is the integration variable.

3. The method for oil and gas well testing analysis based on production data according to claim 2, characterized in that, The normalized pressure equation is established as follows: Define the convolution time function as Γ(τ), then: In the formula, G q (t) represents the cumulative output at time t; G q (t-τ) represents the cumulative output at time t-τ; q w (t) represents the output at time t; Furthermore, the convolution time function and its derivative satisfy Γ(τ)=0, Γ'(τ)=1; Assume that the bottom pressure of a single-phase, slightly compressible fluid seepage well satisfies the superposition principle, where the pressure drop Δp at time t at the bottom of the well is... w (t) satisfies: In the formula, t is the time variable; τ is the integration variable; p i p is the initial pressure; w (t) represents the bottom hole pressure; q w (t-τ) is t- Production at time τ; p u The pressure response function is defined as the pressure drop per unit output. When output changes relatively slowly, and the shape of the output curve is approximated by a linear function, then the convolution time function satisfies Γ(τ)=τ, yielding the normalized pressure equation for explicit convolution: In the formula, RNP is the abbreviation for normalized pressure, and Δp w (t) represents the pressure drop at time t; q w (t) represents the output at time t; p u (t) is the pressure response function at time t; p u The pressure response function; t mb Let t be the time to material equilibrium, where t is the time variable.

4. The method for oil and gas well testing analysis based on production data according to claim 3, characterized in that, Convolutional time functions include linear functions, quadratic functions, exponential functions, and polynomial functions; Wherein, when Γ(τ)=τ, it is a linear convolution time function.

5. The method for oil and gas well testing analysis based on production data according to claim 4, characterized in that, The specific method for obtaining the pressure response function by performing fast deconvolution calculation on long-term production data based on the normalized pressure equation is as follows: Based on the acquired long-term production data, including the output q at time t. w (t), bottom hole pressure p wf Initial pressure p i Calculate the production pressure difference Δp w =p i -p wf And calculate the normalized pressure Δp w / q w (t); Calculate the cumulative output G at time t q (t), then: In the formula, i = 1, 2, ..., N, where N is the number of production data points up to time t; q i This represents the output corresponding to the i-th data point; Calculate the material equilibrium time t corresponding to time t. mb : Assuming the pressure response function at time t is approximated by a linear function, calculate the time derivative and the logarithmic time derivative of the pressure response function: In the formula, Given the derivative of the pressure response function with respect to production time, we can then obtain the logarithmic time derivative of the pressure response function: Calculate the pressure response function p at time t u (t): Let time variable t and output q be used. w and bottom hole pressure data p wf By substituting the values, the production pressure difference Δp can be calculated sequentially. w Normalized pressure Δp w / q w Cumulative output G q Material equilibrium time t mb Derivative of pressure response function Logarithmic time derivative of pressure response function and pressure response function p u ; Drawing tp u and The chart can be used to initially identify potential characteristic flow segments based on its shape.

6. The specific method for establishing an accurate identification model of the characteristic flow section based on the normalized pressure equation in the oil and gas well test analysis method based on production data according to claim 1 is as follows: Under constant production conditions, the pressure response function p at time t in the characteristic flow section. u (t) is a linear function of the power function of the time variable t, expressed as: p u (t)=a u +b u ·t n ; In the formula, a u and b u is the characteristic flow constant; n is the characteristic flow index; t is the time variable; When the flow is radial, the pressure response function p of the characteristic flow section at time t is... u (t) is a linear function of the power function of the time variable t, expressed as: p u (t)=a u +b u ·lnt The logarithmic time derivative of the characteristic flow section is but: In a logarithmic coordinate system, the characteristic flow segment is represented by a straight line with a slope of 'n' representing the logarithmic time derivative. When the output changes relatively slowly, the characteristic flow segment at variable output has a t-value of 'n'. mbe The RNP equation is: RNP(t)=a u +b u ·t mbe ; In the formula, RNP(t) is the normalized pressure at time t; t mbe For effective material balance time; in:

7. The method for analyzing oil and gas well tests based on production data according to claim 6, characterized in that, The method for accurately identifying the characteristic flow segments of long-term production data based on the aforementioned accurate identification model is as follows: Based on the initially identified characteristic flow segments, establish the t-value for the specified characteristic flow segments. mbe -RNP equation; The characteristic flow constant α of the characteristic flow section is calculated using the moving window method. u and b u The curve is plotted against the time variable t, and t is viewed simultaneously. mbe -RNP equation straight segment and characteristic flow parameter a u and b u The constant segment of the curve versus the time variable t is used to determine whether a specified characteristic flow segment occurs and the duration range of said characteristic flow segment (t). min ,t max ); Within the time range (t) min ,t max Within ) through t mbe - Linear fitting of the RNP equation straight line segment yields the characteristic flow parameter a u and b u Calculate the pressure response function and logarithmic time derivative of the characteristic flow section.

8. The method for well testing analysis of oil and gas wells based on production data according to claim 7, characterized in that, The pressure response function and logarithmic time derivative of the characteristic flow section are as follows:

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