A method for analyzing oil and gas well testing based on production data

Abstract

The present invention discloses a method for analyzing oil and gas well tests based on production data, comprising the following steps: establishing a normalized pressure equation according to a variable production convolution formula; acquiring long-term production data on site; performing rapid deconvolution calculation on the long-term production data based on the normalized pressure equation to obtain a pressure response function and its logarithmic time derivative, and preliminarily identifying characteristic flow segments based on the pressure response function and its logarithmic time derivative; establishing an accurate identification model for the characteristic flow segments based on the normalized pressure equation, accurately identifying the characteristic flow segments of the long-term production data based on the accurate identification model, and then performing parameter inversion using the characteristic flow segments to obtain formation parameters or dynamic reserves; and realizing rapid convolution inversion of pressure and pressure derivatives based on the production data based on the equation, thereby unifying traditional PTA and RTA methods to form a new method for analyzing production data well tests.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas development, and in particular to an oil and gas well testing analysis method based on production data. Background Art

[0002] In the petroleum industry, transient pressure analysis (PTA) and transient 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 analyzing short-term production and pressure test data, such as pressure drawdown and pressure buildup data. These data points are dense and highly accurate, often measured in seconds but with short durations, often measured in hours. During long-term oil and gas well production, wellhead pressure data must be converted to bottomhole flowing pressure data. Furthermore, due to wellhead measurement errors, the bottomhole pressure and wellhead production used in the calculations often contain significant noise, limiting the application of PTA in long-term production data analysis.

[0004] RTA was created to address the shortcomings of PTA in long-term production data analysis. RTA is primarily used for long-term production data analysis of oil and gas wells. The data source is wellhead pressure and production data, which are large in volume and long in duration, often measured in months and years. Within the RTA theoretical framework, the material balance time proposed by Blasingame plays a key role. Its introduction enables the transition from variable-rate production to fixed-rate production. Throughout RTA's decades of development, numerous scholars have identified the following challenges in its application:

[0005] (1) Material balance time lacks a clear physical meaning. Under fluctuations in production, material balance time will jump back and forth, losing its time series characteristics and even violating physical laws. At the same time, changes in production will cause characteristic flow segments in the material balance time coordinate system to exhibit "advance" or "lag" phenomena, such as an unsteady flow period appearing as a quasi-steady flow period. Therefore, theoretical diagrams with material balance time as the horizontal axis lack physical meaning.

[0006] (2) The theoretical system established by Blasingame is only strictly valid in the quasi-steady-state phase and has not yet been rigorously theoretically proven in the unsteady flow phase, resulting in a lack of rigorous theoretical support for RTA. This is particularly true for unconventional reservoirs, where oil and gas wells remain in the unsteady flow phase for extended periods, making RTA 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 the material balance time, which is not the time-pressure and pressure derivative in the traditional well test chart. Therefore, the chart cannot be used to accurately identify the characteristic flow section, which limits the application of this method.

[0008] In summary, the RTA method lacks a rigorous theoretical foundation for production data analysis during unstable flow phases, cannot obtain pressure and pressure derivative curves, and has difficulty accurately identifying characteristic flow segments, making it unsuitable for production evaluation in unconventional oil and gas reservoirs. While PTA theory is comprehensive, it is primarily used for analyzing short-term, low-noise test data and cannot be applied to long-term, noisy production data. Summary of the Invention

[0009] The purpose of the present invention is to provide an oil and gas well test analysis method based on production data to solve the technical problem that the RTA method and the PTA method in the prior art each have defects and cannot meet the production data analysis requirements.

[0010] In order to solve the above technical problems, the present invention specifically provides the following technical solutions:

[0011] A method for analyzing oil and gas well testing based on production data comprises the following steps:

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

[0013] Obtain long-term production data on 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, and the characteristic flow segment is preliminarily identified based on the pressure response function and its logarithmic time derivative;

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

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

[0017] Starting from the basic convolution formula under variable production / variable pressure, the present invention establishes an explicit normalized pressure equation applicable to the entire flow stage. Based on this equation, rapid convolution inversion of pressure and pressure derivatives based on production data can be achieved, thereby unifying the traditional PTA method and RTA method to form a new production data well test analysis method.

[0018] This analysis method overcomes the defects of the existing PTA method and RTA method, 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 very conveniently implement fast deconvolution calculations and obtain pressure and pressure derivative values, making it suitable for characteristic flow segment analysis of all flow segments, organically combining the advantages of the RTA and PTA models. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other implementation drawings based on the provided drawings without inventive effort.

[0020] Figure 1 A schematic diagram of a process flow provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0021] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0022] like Figure 1 As shown, the present invention provides an oil and gas well test analysis method 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 of identifying characteristic flow sections and obtaining reservoir parameters is performed using well test interpretation charts (time-pressure and time-pressure logarithmic time derivative).

[0023] The specific steps are as follows.

[0024] (1) Establishment of theoretical model:

[0025] Starting from the basic variable yield convolution formula, an explicit normalized pressure formula is established. This formula can explicitly represent the normalized pressure, time variable, the derivative of the pressure response function, and the normalized pressure equation of the material balance time relationship.

[0026] (2) Data acquisition:

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

[0028] (3) Fast deconvolution calculation:

[0029] Through the established normalized pressure formula, the production data is quickly deconvolved to obtain the pressure response function p u and its logarithmic time derivative dp u / dlnt.

[0030] (4) Carry out characteristic flow segment analysis:

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

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

[0033] Parameter inversion is performed using characteristic flow sections and well test analysis methods and steps.

[0034] In the present invention, the traditional PTA method is used for stress analysis of short-term test data, and the traditional RTA method is used for yield 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.

[0035] Secondly, compared to test data, production data is characterized by lower precision and greater measurement errors, resulting in high data noise. While traditional deconvolution methods have been explored for decades and occasionally used for short-term test data, mature algorithms suitable for field production data remain elusive. Our proposed displayed normalized pressure model allows for rapid deconvolution calculations to easily obtain pressure and pressure derivative values.

[0036] Furthermore, the PTA model has a rigorous theoretical basis and its greatest advantage is its ability to identify characteristic flow segments. However, it is currently only applicable to short-term test data analysis and cannot be used for production data analysis, limiting its application. RTA is theoretically incomplete and, strictly speaking, can only be used to analyze pseudo-steady-state flow segments. It cannot obtain pressure and pressure derivative curves, making it imperfect in identifying characteristic flow segments. The theoretical model proposed in this paper 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 the RTA and PTA models.

[0037] Finally, the concept of production data well test analysis is proposed, which applies the traditional short-term test well test analysis method to long-term production data analysis, thereby borrowing the entire set of mature characteristic flow segment identification and parameter inversion in well test analysis.

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

[0039] The present invention provides a new explicit calculation method for convolution equations. This method enables the convolution equation to be explicitly expressed using functions and can intuitively display the relationship between various functions. At the same time, it can greatly improve the computational efficiency of convolution and deconvolution, and can be widely used for fast calculations under large amounts of data.

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

[0041] Its expression is:

[0042]

[0043] Here, h(t)=df(t) / dt(2) is defined.

[0044] Substituting equation (2) into equation (1) yields:

[0045]

[0046] Integrating equation (3) by parts yields

[0047]

[0048] Where:

[0049]

[0050] Equation (4) can be further expressed as:

[0051]

[0052] Where y(t) is the response of the system, which is the convolution of the functions f(t) and g(t).

[0053] The convolution time function is defined as:

[0054]

[0055] And the convolution time function and its derivative satisfy:

[0056] Γ(0)=0,Γ'(0)=1(8);

[0057] Substituting equation (7) into equation (6) yields:

[0058]

[0059] Integrating equation (9) by parts yields:

[0060]

[0061] Integrating equation (10) again by parts and using the initial condition equation (8) yields:

[0062]

[0063] In practical applications, we can select a suitable convolution time function, such as a linear function, a quadratic function, an exponential function, a polynomial, etc., according to the changing characteristics of the g(t) function to further simplify Equation (11).

[0064] If a linear convolution time function is used, the convolution time function satisfies:

[0065] Γ(τ)=τ (12)

[0066] Substituting equation (12) into equation (11), we get the simplified explicit convolution equation:

[0067]

[0068] The method proposed in the present invention is based on the convolution integral equation. Through rigorous mathematical derivation, a general convolution expression is obtained. On this basis, a simplified explicit convolution expression based on the assumption of a linear convolution time function is derived. Similarly, when the convolution time function selects other functions, such as quadratic functions, exponential functions, polynomials, etc., other types of simplified explicit convolution expressions can also be obtained. For other fields that satisfy 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 determine the three functions, namely y(t), g(t) and f(t), according to the process of this patent.

[0069] In the oil industry, the observed pressure drop is the convolution of the input flow function and the derivative of the constant flow pressure response. In the prior art, at the initial moment, assuming the system is in equilibrium, the pressure drop corresponding to time t can be expressed as:

[0070]

[0071] Its discrete form is:

[0072]

[0073] Where p u is the pressure response function, q w is the oil and gas well production. w and the pressure response function p u When the bottom hole pressure drop Δp is known, the above equation can be used to forward calculate w When the output qw and bottomhole pressure drop Δp w When known, the pressure response function p is obtained by inverting the above equation u .

[0074] However, the above equation has the following two problems in engineering applications:

[0075] First, calculating the pressure drop at time t requires multiplication and addition operations, and the calculation requires the use of all discrete flow segments before time t. Therefore, the computational cost is proportional to the number of discrete segments. With the advent of the big data era and the increasing density of production data, especially with the application and promotion of intelligent production systems in recent years, the amount of production data is increasing, and the time required for dynamic prediction calculations using convolution methods is increasing.

[0076] Second, when the above equation is used for deconvolution operation, the data errors and calculation errors before time t will accumulate; therefore, in addition to the problem of large amount of calculation, there is also a stability problem in performing deconvolution operation.

[0077] In order to solve the above problems, the present invention adopts the above explicit convolution expression, which requires few parameters and small amount of calculation, can greatly improve the operational efficiency of convolution and deconvolution, and can be widely used for fast calculation under huge data volumes.

[0078] Assume that the bottom hole pressure of single-phase, slightly compressible fluid seepage satisfies the superposition principle, and the bottom hole pressure drop satisfies,

[0079]

[0080] Where t is the time variable; τ is the integral variable; p i is the initial reservoir pressure; Δp w is the bottom hole pressure drop; p w is the bottom hole pressure.

[0081] According to the above equation and equation (3), we can know that:

[0082] y(t)=Δp w (t) = p i -p w (t);

[0083] g(t)=q w (t);

[0084] f(t)=p u (t);

[0085] According to the calculation equation of the cumulative output G(t) at time t, the material balance time t is defined as mb ,in:

[0086]

[0087] Substituting the above equation into the simplified explicit convolution expression (Equation 13) yields:

[0088]

[0089] 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, the pressure response function, and its derivatives. This equation enables forward and inverse convolution modeling. Further refinement of the equation yields the normalized pressure equation:

[0090]

[0091] In this embodiment, convolution inversion is taken as an example for description.

[0092] Convolution inversion: According to the yield (q w ) and pressure drop (Δp w )Inversion reservoir pressure response function (p u ).

[0093] In the convolution inversion calculation, production and bottomhole pressure drop are used as known parameters, and the pressure response function is obtained through inversion. The calculation process is as follows:

[0094] (1) Collect production well data; Collect production data w and bottom hole pressure data p wf According to the original formation pressure p i , calculate the production pressure difference Δp w =p i -p wf .

[0095] (2) Calculate the cumulative output G at a certain moment q , i=1,2,…,N

[0096]

[0097] (3) Calculate material balance time t mb ;

[0098] (4) Calculation of Δp w / q w Assuming that the pressure response function near time t can be approximated linearly, the following formula is used to approximate the pressure response function derivative dp u / dt and logarithmic time derivative dp u / dlnt

[0099]

[0100] (5) with t, △p w / q w 、dp u / dt and t mb Substitute the following formula to calculate the pressure response function p u ;

[0101]

[0102] Comprehensive analysis based on long-term production data to accurately identify characteristic flow segments includes the following three steps:

[0103] (1) Preliminary identification of characteristic flow segments based on the pressure response function and its logarithmic time derivative

[0104] Under fixed production conditions, the pressure response function p of the characteristic flow section at time t u (t) is a linear function of the power function of the time variable t, expressed as:

[0105] p u (t) = a u +b u ·t n ;

[0106] Where a u and b u is the characteristic flow constant; n is the characteristic flow index;

[0107] In particular, the pressure response function for radial flow (n=0) is expressed as follows:

[0108] p u (t) = a u +b u lnt

[0109] The logarithmic time derivative of the characteristic flow segment is but:

[0110]

[0111] In double logarithmic coordinates, the straight line with a slope n of the logarithmic time derivative is the characteristic flow segment.

[0112] Draw tp u and The double logarithmic chart is used to obtain the slope n through segmented fitting of the chart morphology, and to preliminarily identify possible characteristic flow segments.

[0113] (2) Accurate identification of characteristic flow segments

[0114] The possible characteristic flow segments are analyzed to establish an accurate identification model of the characteristic flow segments.

[0115] When the output changes relatively slowly, establish t mbe The -RNP equation is:

[0116] RNP(t)=a u +b u ·t mbe ;

[0117] Where, t mbe is the effective material balance time, where:

[0118]

[0119] 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 of the time variable t, while viewing t mbe -RNP equation straight line segment and characteristic flow parameter a u and b u The constant segment of the curve with time variable t is used to determine whether a specified characteristic flow segment occurs and the duration range of the characteristic flow segment (t min ,t max ). In the time range (t min ,t max ), when t mbe -RNP curve shows a linear relationship, and ta u and tb u When the curve is constant within this time period, it is considered that there is a characteristic flow segment within this time range, and its characteristic flow index is n.

[0120] (3) Reconstruct characteristic flow segment curves and invert reservoir parameters.

[0121] In the time range (t min ,t max ), according to the characteristic flow parameter a u and b u , the characteristic flow segment curve is reconstructed using the following formula, where the pressure response function and logarithmic time derivative of the characteristic flow segment are:

[0122]

[0123] After completing the preliminary analysis, accurate identification, and reconstruction of the characteristic flow segments through (1)-(3), the conventional well test analysis model can be used to perform parameter inversion. For example, in the case of pseudo-steady-state flow analysis, it is possible to determine whether production has entered the boundary flow stage and calculate the original geological reserves. The constructed smooth pressure response function and derivative curve can be directly used for chart fitting, which can greatly improve the chart fitting effect.

[0124] It should be pointed out that when constructing the characteristic flow, it is not necessary to accurately obtain the complete characteristic flow segment, but only to determine a segment with more significant characteristics.

[0125] The method proposed in this paper makes no assumptions about the pressure response function during equation derivation. Therefore, the universal equation proposed in this paper can be used for convolution forward and inversion modeling at different production stages for any reservoir and production well combination. The differences in calculations for different reservoir and production well combinations primarily lie in the differences in the pressure response function. Simply select the corresponding pressure response function for your specific reservoir and production well combination and follow the aforementioned process for calculations.

[0126] The method proposed in the present invention is derived based on the oil well convolution integral equation. By replacing the pressure with the pseudo-pressure of the gas reservoir, the method can be extended to be applied in the calculation of gas reservoirs.

[0127] The concept of production data well test analysis proposed in the present invention applies the traditional short-term test well test analysis method to long-term production data analysis, thereby borrowing the entire set of mature characteristic flow segment identification and parameter inversion in well test analysis.

[0128] The above embodiments are merely exemplary embodiments of the present application and are not intended to limit the scope of the present application. The scope of protection of the present application is defined by the claims. Those skilled in the art may make various modifications or equivalent substitutions to the present application within the essence and scope of protection of the present application, and such modifications or equivalent substitutions shall also be deemed to fall within the scope of protection of the present application.

Claims

1. A method for analyzing oil and gas well testing based on production data, characterized in that: The steps include: Define the variable yield convolution formula, and establish the normalized pressure equation based on the variable yield convolution formula to explicitly characterize the normalized pressure, time variable, the derivative of the pressure response function and the material balance time relationship; Normalized pressure equation: Where RNP is the abbreviation of normalized pressure, Δp w (t) is the pressure drop at time t; q w (t) is the output at time t; p u (t) is the pressure response function at time t; p u is the pressure response function; t mb is the material balance time, t is the time variable; Obtain long-term production data on 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, and the characteristic flow segment is preliminarily identified based on the pressure response function and its logarithmic time derivative; Based on the normalized pressure equation, a fast deconvolution calculation is performed on long-term production data to obtain the pressure response function as follows: Based on the long-term production data obtained, 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: Where i = 1, 2, ..., N, where N is the number of production data points up to time t; q i is the output corresponding to the i-th data point; Calculate the material balance time t corresponding to time t mb : Assume that the pressure response function at time t is approximated by a linear function, and calculate the time derivative of the pressure response function and the logarithmic time derivative of the pressure response function: Where, is the derivative of the pressure response function with respect to the production time, and the logarithmic time derivative of the pressure response function can be obtained: Calculate the pressure response function p at time t u (t): The time variable t and output q w and bottom hole pressure data p wf Substitute in, and the production pressure difference Δp can be calculated in sequence w , normalized pressure Δp w / q w , cumulative output G q , material balance time t mb , pressure response function derivative Logarithmic time derivative of the pressure response function and the pressure response function p u ; Draw tp u and Plate, preliminarily identify possible characteristic flow segments through plate morphology; An accurate identification model of the characteristic flow segment is established based on the normalized pressure equation, and the characteristic flow segment of long-term production data is accurately identified according to the accurate identification model. The characteristic flow segment is then used to perform parameter inversion to obtain formation parameters or dynamic reserves.

2. The oil and gas well testing analysis method based on production data according to claim 1, characterized in that: Assume that the two variable functions are h(t) and g(t), and generate a third function y(t) by receiving the two variable functions h(t) and g(t) through convolution. Then the convolution formula of the two variable functions h(t) and g(t) is defined as: Among them, t is the time variable; τ is the integral variable.

3. The oil and gas well testing analysis method 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: Where G q (t) is the cumulative output at time t; G q (t-τ) is the cumulative output at time t-τ; q w (t) is the output at time t; And the convolution time function and its derivative satisfy Γ(τ)=0, Γ'(τ)=1; Assume that the bottom hole pressure of the single-phase, slightly compressible fluid seepage satisfies the superposition principle, where the bottom hole pressure drop Δp at time t is w (t) Satisfy: Where t is the time variable; τ is the integral variable; p i is the initial pressure; p w (t) is the bottom hole pressure; q w (t-τ) is the output at time t-τ; p u is the pressure response function, defined as the pressure drop per unit production; When the production changes relatively slowly, the production curve shape is set to be approximated by a linear function. Then, the convolution time function satisfies Γ(τ) = τ, and the normalized pressure equation of explicit convolution is obtained: Where RNP is the abbreviation of normalized pressure, Δp w (t) is the pressure drop at time t; q w (t) is the output at time t; p u (t) is the pressure response function at time t; p u is the pressure response function; t mb is the material balance time, and t is the time variable.

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

5. According to the oil and gas well testing analysis method based on production data of claim 1, the specific method of establishing the accurate identification model of the characteristic flow segment based on the normalized pressure equation is: Under fixed production conditions, the pressure response function p of the characteristic flow section at time t 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 ; Where a u and b u is the characteristic flow constant; n is the characteristic flow index, and 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 segment is but: In the double logarithmic coordinates, the straight line with the slope n of the logarithmic time derivative is the characteristic flow segment; when the output changes relatively slowly, the t of the characteristic flow segment when the output changes mbe The -RNP equation is: RNP(t)=a u +b u ·t mbe ; Where RNP(t) is the normalized pressure at time t; mbe is the effective material balance time; in:

6. The oil and gas well testing analysis method based on production data according to claim 5, characterized in that: The method for accurately identifying the characteristic flow segments of long-term production data according to the accurate identification model is as follows: According to the initially identified characteristic flow segment, the t mbe -RNP equation; The characteristic flow constant a of the characteristic flow segment is calculated using the moving window method u and b u The curve of the time variable t, while viewing t mbe -RNP equation straight line segment and characteristic flow parameter a u and b u The constant segment of the curve with time variable t is used to determine whether a specified characteristic flow segment occurs and the duration range of the characteristic flow segment (t min ,t max ); In the time range (t min ,t max ) through t mbe -RNP equation straight line segment linear fitting to obtain characteristic flow parameter a u and b u , calculate the pressure response function and logarithmic time derivative of the characteristic flow segment.

7. The oil and gas well testing analysis method based on production data according to claim 6, characterized in that: The pressure response function and logarithmic time derivative of the characteristic flow section are:

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