Improved analysis method for conventional pressure recovery well testing

Abstract

The invention provides an improved analysis method for conventional pressure recovery well testing. The improved analysis method comprises the steps that 1, improved conventional pressure recovery well testing analysis is conducted; and step 2, analyzing and solving the improved conventional well test. According to the method, a conventional pressure recovery well testing analysis theory explanation method is improved, continuous changes of reservoir parameters are analyzed through a nonlinear segment analysis method, and more reliable parameters are provided for meeting actual production requirements.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas exploration, and in particular relates to an improved analysis method for conventional pressure recovery well testing. Background Art

[0002] Conventional well testing often starts from a homogeneous reservoir. Its assumption is that a well produces at a certain rate in an infinite, homogeneous, and equal-thickness reservoir. According to its seepage theory, no matter it is a pressure drop test or a pressure recovery test, a straight line segment must appear between the bottom hole pressure and the semi-logarithm of the shut-in time. This is the theoretical basis of the conventional pressure recovery test. However, the actual reservoir is assumed to be a continuous medium during the seepage process. Therefore, under actual geological conditions, the reservoir cannot be homogeneous and may not appear in a straight line segment, which brings difficulties to the conventional pressure recovery test analysis. As a result, many pressure recovery test interpretations cannot be explained by conventional well testing. In particular, it is very difficult to produce a straight line segment in low permeability reservoir testing. Therefore, modern well testing interpretation can only be used for analysis. However, with the increase of interpretation parameters, modern well testing interpretation cannot overcome the existence of multiple solutions.

[0003] Application number CN202410363863.9, invention name A method for interpreting the productivity of a low-permeability heterogeneous water-bearing gas reservoir, comprising: constructing a binary function between the starting pressure gradient and the permeability and water saturation, collecting gas well productivity test data, and calculating the production pressure difference at different measuring points; determining the leakage radius of the gas well; calculating the starting pressure of different small layers; judging whether each small layer under each measuring point participates in the flow according to the size of the production pressure difference and the starting pressure, and calculating the thickness of the producing layer, the formation coefficient and the average permeability; calculating the laminar and turbulent comparison coefficients of the productivity equation at each measuring point, drawing the productivity indication curve, determining the productivity equation coefficient, and calculating the unobstructed flow.

[0004] The above invention has the following disadvantages: (1) The invention is not a pressure recovery test in an unstable test at all, but a productivity test in a stable test. Its test conditions are very harsh and must meet stable flow conditions. (2) The method is calculated based on the production pressure difference. Therefore, before the productivity test, the formation pressure must be obtained by the pressure recovery test. The production pressure difference can be obtained by using the formation pressure to calculate the reservoir permeability. The method still regards the permeability as homogeneous, while the actual reservoir may be heterogeneous. Summary of the invention

[0005] The purpose of the present invention is to solve the defects of the above-mentioned prior art and provide an improved analysis method for conventional pressure recovery well testing. The present invention belongs to an unstable test, which tests the relationship between the flow pressure and time and solves it according to the unstable flow theory of the flow pressure.

[0006] The present invention adopts the following technical solution:

[0007] The improved analysis method of conventional pressure buildup well test includes the following steps:

[0008] Step 1. Improved conventional pressure buildup test analysis

[0009] First, the flow stage is subjected to differential homogenization. The wellbore reservoir stage 0-Δt1 is regarded as a homogeneous flow with a permeability of k1. At this time, the bottom hole flow pressure is:

[0010]

[0011] Where:

[0012] p wf - Bottom hole flowing pressure during production before shutting in, MPa;

[0013] q-production before shut-in, m 3 / ks;

[0014] μ-fluid viscosity, mPa.s;

[0015] B-fluid volume coefficient, dimensionless;

[0016] k1-reservoir permeability, μm 2 ;

[0017] h-effective reservoir thickness, m;

[0018] φ-porosity, decimal;

[0019] c t -Total compression factor, MPa -1 ;

[0020] Δt1-shut-in time, ks;

[0021] p ws1 — Bottom hole test pressure corresponding to the shut-in time Δt1, MPa;

[0022] t p - Production time before shut-in, ks;

[0023] r w -well radius, m;

[0024] γ-constant, 1.78…;

[0025] Pressure conductivity coefficient within η1-Δt1 time, m 2 / ks.

[0026] The skin effect flow stage Δt1-Δt2 near the wellbore is regarded as a homogeneous flow with a permeability of k2. At this time, the bottom hole flow pressure is:

[0027]

[0028] Where:

[0029] Δt2-shut-in time, ks;

[0030] p ws2 — Bottom hole test pressure corresponding to the shut-in time Δt2, MPa;

[0031] k2-reservoir permeability, μm 2 ;

[0032] Pressure conductivity coefficient in η2-Δt2 time, m 2 / ks.

[0033] The radial flow stage in the formation plane Δt1-Δt n , the permeability is considered to be k n Homogeneous flow, at this time, the bottom hole pressure is:

[0034]

[0035] Where:

[0036] Δt n - Shut-in time, ks;

[0037] k n - Reservoir permeability, m 2 / ks;

[0038] η n -Δt n Pressure conductivity coefficient in time, m 2 / ks;

[0039] p wsn —Shut-in time Δt n Corresponding bottom hole test pressure, MPa.

[0040] Theoretically, the pressure drop model is established by Δt1-Δt n In the moment flow stage, if k2=k3…k n-1 =k n , formulas (6)-(11) are simplified to formulas (1)-(3), and the time Δt0-Δt1 describes the wellbore storage effect.

[0041] Step 2. Improved conventional well test analysis solution

[0042] The iterative method is used to solve the change of permeability. The specific calculation steps are as follows:

[0043] s101. Input the number of test data num and the range of reservoir permeability, assuming that the logarithm of permeability is [-5,1]μm 2Interval change, i.e. lgk∈[-5,1] (i.e. the permeability range is [0.0001,10]μm 2 , suitable for all reservoirs of low, medium and high levels), assuming the number of cycles is n;

[0044] s102. Assume that the permeability step size pow(10.0, 0.001) increases (the step size can be set according to the permeability of the reservoir. If the permeability is high, the step size can be set larger, and vice versa, if the reservoir permeability is low, the step size can be set smaller), and increase logarithmically. Calculate η and the flow pressure p wf , and record |pwf-pwf * The minimum value of | corresponds to k until k>10.0μm 2 (Reservoirs exceeding 10 darcy are very rare);

[0045] s103. Determine whether the data calculation is completed. If n>num, complete the calculation of the permeability corresponding to each data point; if n<num, return to step s101 to calculate the next data point until all data are completed.

[0046] Furthermore, in formulas (1) to (3):

[0047] Conventional well test analysis: Assuming a well in a homogeneous, uniformly thick reservoir, produces at a certain rate p After that, the well was shut in for pressure recovery test. Without considering the influence of wellbore storage coefficient and skin coefficient, the bottom hole flowing pressure after shutting in Δt time was:

[0048]

[0049] Where:

[0050] p ws - Bottom hole recovery pressure, MPa;

[0051] p wf - Bottom hole flowing pressure during production before shutting in, MPa;

[0052] q-production before shut-in, m 3 / ks;

[0053] μ-fluid viscosity, mPa.s;

[0054] B-fluid volume coefficient, dimensionless;

[0055] k- reservoir permeability, μm 2 ;

[0056] h-effective reservoir thickness, m;

[0057] η-pressure conductivity, m 2 / ks;

[0058] φ-porosity, decimal;

[0059] c t -Total compression factor, MPa -1 ;

[0060] Δt-shut-in time, ks;

[0061] t p - Production time before shut-in, ks;

[0062] r w -well radius, m;

[0063] γ-constant, 1.78…….

[0064] After the skin factor s is introduced:

[0065] The above formula (1) is the most basic pressure recovery formula. On this basis, the influence of the skin coefficient s is introduced to consider the pollution or improvement of the reservoir around the wellbore. At this time, the bottom hole flowing pressure is rewritten as:

[0066]

[0067] Beneficial effects of the present invention:

[0068] (1) This method can explain the conventional pressure buildup test interpretation without straight line segments.

[0069] (2) It can avoid the ambiguity of modern well test interpretation; (3) This method can explain the changes in reservoir physical properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is a schematic diagram of conventional pressure recovery analysis;

[0071] Figure 2 Schematic diagram of improved conventional pressure recovery well test analysis;

[0072] Figure 3 To improve the conventional well test solution schematic diagram;

[0073] Figure 4 Recover test data for a well pressure;

[0074] Figure 5 This is the semi-logarithmic analysis curve of a certain well;

[0075] Figure 6 This is the double logarithmic fitting curve of a well Ⅰ;

[0076] Figure 7 This is the double logarithmic fitting curve of a well Ⅱ;

[0077] Figure 8Improved the permeability curve of the pressure recovery analysis method for a certain well;

[0078] Fig. 9 Improved semi-logarithmic fitting curve of pressure buildup analysis method for a certain well. DETAILED DESCRIPTION

[0079] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are 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 creative work are within the scope of protection of the present invention.

[0080] The improved analysis method of conventional pressure buildup well testing of the present invention comprises the following steps:

[0081] Step 1. Analysis of factors affecting conventional pressure buildup testing

[0082] Conventional well test analysis theory is based on the pressure drop test theory in homogeneous reservoirs. Assuming that a production well in a homogeneous and uniformly thick reservoir produces t at a certain rate q p After that, the well was shut in for pressure recovery test. Without considering the influence of wellbore storage coefficient and skin coefficient, the bottom hole flowing pressure after shutting in Δt time was:

[0083]

[0084] Where:

[0085] p ws - Bottom hole recovery pressure, MPa;

[0086] p wf - Bottom hole flowing pressure during production before shutting in, MPa;

[0087] q-production before shut-in, m 3 / ks;

[0088] μ-fluid viscosity, mPa.s;

[0089] B-fluid volume coefficient, dimensionless;

[0090] k- reservoir permeability, μm 2 ;

[0091] h-effective reservoir thickness, m;

[0092] η-pressure conductivity, m 2 / ks;

[0093] φ-porosity, decimal;

[0094] ct -Total compression factor, MPa -1 ;

[0095] Δt-shut-in time, ks;

[0096] t p - Production time before shut-in, ks;

[0097] r w -well radius, m;

[0098] γ-constant, 1.78…….

[0099] S101. Introduction of skin factor s

[0100] The above formula (1) is the most basic pressure recovery formula. On this basis, the influence of the skin coefficient s is introduced to consider the pollution or improvement of the reservoir around the wellbore. At this time, the bottom hole flowing pressure is rewritten as:

[0101]

[0102] make:

[0103] The essence of the skin coefficient s is also the change in the physical properties of the reservoir around the well, that is, the change in permeability, that is:

[0104]

[0105] Where:

[0106] k s - Reservoir permeability near the well, μm 2 ;

[0107] r s - Reservoir permeability near the well k s Range radius, m;

[0108] Since it is difficult to determine the size and range of reservoir changes near the well in actual production, the concept of skin coefficient is introduced. The number of parameters increases, which also increases the difficulty of the problem.

[0109] S102. Effect of straight line segments on permeability

[0110] From equation (3), we know that by using the straight line segment analysis method, we can plot the bottom hole pressure and time t in different coordinate systems. A The corresponding straight line segment of Figure 1The straight line segment analysis method is simple and convenient in operation; the intercept and slope of the straight line segment can be found according to the linear relationship diagram in the coordinate system, and the corresponding s and k values ​​can be calculated. When using the straight line segment analysis method, if the division of the straight line segment is correct, then the obtained formation parameters are correct and unique, and there will be no multiple solutions.

[0111] There are also some shortcomings in the analysis using the straight line segment method: (1) No straight line segment appears, or no radial flow stage appears, and conventional well testing cannot be completed.

[0112] According to the above assumptions: homogeneous and equal-thickness reservoirs, after fixed-rate production, the pressure recovery test will definitely result in the appearance of a straight line segment; according to the principle of proposition and inverse proposition, the absence of a straight line segment in the pressure recovery test leads to either heterogeneity, unequal thickness, or no fixed production. Assuming that reservoir equal thickness and fixed-rate production are easy to meet, only reservoir homogeneity is difficult to meet, so the absence of a straight line segment is mainly caused by reservoir heterogeneity.

[0113] The change of permeability is used to describe the change of reservoir physical properties, so the skin coefficient parameter can be ignored. The introduction of the wellbore reservoir system makes the conventional pressure recovery test have a great influence on the selection time of the straight line segment. According to Professor Li Chuanliang’s theory: the pipe flow in the wellbore can be equivalent to seepage, but it is a flow with extremely high permeability.

[0114] Therefore, the following is an improved conventional pressure buildup well test analysis method:

[0115] S103. Influence on skin factor

[0116] From formula (3), we can get that when t A =1ks, we get:

[0117]

[0118] From formula (5), we know that once the slope of the straight line is determined, the size of the skin coefficient depends on whether the flow pressure before the well is shut in is correct. If the flow pressure is too low, the calculated skin coefficient will be too large. On the contrary, if the flow pressure is too high, the skin coefficient will be too small. If the slope of the straight line cannot be determined, there will be a multi-solution problem.

[0119] Step 2. Improved conventional pressure buildup test analysis method

[0120] First, the flow stage is subjected to differential homogenization, such as Figure 2 As shown, the wellbore reservoir stage 0-Δt1 is regarded as a homogeneous flow with a permeability of k1. At this time, the bottom hole flowing pressure is:

[0121]

[0122] Pressure conductivity coefficient within η1-Δt1 time, m 2 / ks.

[0123] p ws1 - Bottom hole test pressure corresponding to the shut-in time Δt1, MPa;

[0124] The skin effect flow stage Δt1-Δt2 near the wellbore is regarded as a homogeneous flow with a permeability of k2. At this time, the bottom hole flow pressure is:

[0125]

[0126] Where:

[0127] Δt2-shut-in time, ks;

[0128] p ws2 — Bottom hole test pressure corresponding to the shut-in time Δt2, MPa;

[0129] Pressure conductivity coefficient in η2-Δt2 time, m 2 / ks.

[0130] The radial flow stage in the formation plane Δt1-Δt n , the permeability is considered to be k n Homogeneous flow, at this time, the bottom hole pressure is:

[0131]

[0132] Where:

[0133] Δt n - Shut-in time, ks;

[0134] k n - Reservoir permeability, m 2 / ks;

[0135] η n -Δt n Pressure conductivity coefficient in time, m 2 / ks;

[0136] p wsn —Shut-in time Δt n Corresponding bottom hole test pressure, MPa;

[0137] Theoretically, the pressure drop model is established by Δt1-Δt n In the moment flow stage, if k1=k2=k3…k n-1 =k n , formulas (6)-(11) are simplified to formulas (1) to (3). The time Δt0-Δt1 describes the wellbore reservoir effect.

[0138] Step 3. Improved conventional well test analysis solution method

[0139] If the reservoir heterogeneity makes it difficult to form a straight line segment for well test analysis, the relationship between flow pressure and time is nonlinear, and linear regression cannot be used to obtain reservoir physical parameters. In this case, an iterative method is used to solve the change in permeability. The calculation block diagram is as follows: Figure 3 As shown, the specific calculation steps are as follows:

[0140] (1). Input the number of test data num and the range of reservoir permeability, assuming that the logarithm of permeability is [-5,1]μm 2 Interval change, assuming the number of cycles is n;

[0141] (2) Assuming that the permeability step size pow(10.0, 0.001) increases logarithmically, calculate η and flow pressure pwf, and record |pwf-pwf * | corresponds to the minimum value of k, until k>10.0;

[0142] (3) Determine whether the data calculation is complete. If n>num, complete the calculation of the permeability corresponding to each data point; if n<num, return to step (1) to calculate the next data point until all data are completed.

[0143] Example

[0144] like Figure 4 The following is the pressure recovery test data of a production well in the early stage. The basic data of the well are shown in Table 1. The stable production time before shutting in is about 200 hours. According to formula (3), a semi-logarithmic analysis curve is drawn, as shown in Figure 5 As shown, there is no straight line segment, which is very difficult to analyze using conventional well testing. Therefore, people can only use modern well testing analysis. The fitting results are shown in Table 1.

[0145] Table 1 Basic data of a well

[0146]

[0147] The double logarithmic fitting curve is as follows Figure 6 As shown in Table 2, due to the large number of modern well testing parameters, multiple solutions are likely to occur. The double logarithmic fitting curve is shown in Table 2. Figure 7 As shown in Figure 1, the fitting curves of modern well testing interpretation show that the fitting effects are very good. From Table 1 and Table 2, the parameter results are quite different. Therefore, it is difficult for modern well testing to overcome the problem of multiple solutions.

[0148] Table 2 Modern well test interpretation results of a well

[0149]

[0150] According to the theory, there must be straight line segments in homogeneous reservoirs. In reality, there are no typical straight line segments. Therefore, the conventional pressure recovery interpretation method cannot be used to interpret the reservoir. Therefore, an improved method is used to interpret the reservoir without using the skin coefficient parameter. The skin coefficient is essentially the change in permeability. Its interpretation of permeability change is as follows: Figure 8 As shown, the fitting effect is Fig. 9 As shown, the initial permeability is high, indicating that there is no pollution near the bottom of the well. The permeability near the well is high, and the permeability in the periphery is low, which is consistent with the trend of modern well test interpretation.

[0151] in conclusion

[0152] Permeability is an important property of the reservoir, and its size directly affects the productivity of the oil well. The improved pressure recovery test analysis method can well reflect the changes in reservoir physical properties. The change of the contamination coefficient can be ignored, and the method is simple and applicable.

[0153] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An improved analysis method for conventional pressure buildup well testing, characterized in that: The steps include: Step 1. Improved conventional pressure buildup test analysis First, the flow stage is subjected to differential homogenization. The wellbore reservoir stage 0-Δt1 is regarded as a homogeneous flow with a permeability of k1. At this time, the bottom hole flow pressure is: Where: p wf - Bottom hole flowing pressure during production before shutting in, MPa; q-production before shut-in, m 3 / ks; μ-fluid viscosity, mPa.s; B-fluid volume coefficient, dimensionless; k1-reservoir permeability, μm 2 ; h-effective reservoir thickness, m; φ-porosity, decimal; c t -Total compression factor, MPa -1 ; Δt1-shut-in time, ks; p ws1 - Bottom hole test pressure corresponding to shut-in time Δt1, MPa; t p - Production time before shut-in, ks; r w -well radius, m; γ-constant, 1.78…; Pressure conductivity coefficient within η1-Δt1 time, m 2 / ks; The skin effect flow stage Δt1-Δt2 near the wellbore is regarded as a homogeneous flow with a permeability of k2. At this time, the bottom hole flow pressure is: Where: Δt2-shut-in time, ks; p ws2 - Bottom hole test pressure corresponding to the shut-in time Δt2, MPa; k2-reservoir permeability, μm 2 ; Pressure conductivity coefficient within η2-Δt2 time, m 2 / ks; The radial flow stage in the formation plane Δt1-Δt n , the permeability is considered to be k n Homogeneous flow, at this time, the bottom hole pressure is: Where: Δt n - Shut-in time, ks; p wsn - Shut-in time Δt n Corresponding bottom hole test pressure, MPa; k n - Reservoir permeability, m 2 / ks; η n -Δt n Pressure conductivity coefficient in time, m 2 / ks; Theoretically, the pressure drop model is established by Δt1-Δt n In the moment flow stage, if k2=k3…k n-1 =k n , formula (6)-(11) are simplified to formula (1)-(3), and the time Δt0-Δt1 describes the wellbore storage effect; Step 2. Improved conventional well test analysis solution The iterative method is used to solve the change of permeability. The specific calculation steps are as follows: s101. Input the number of test data num and the range of reservoir permeability, assuming that the logarithm of permeability is [-5,1]μm 2 Interval change, assuming the number of cycles is n; s102. Assume that the permeability step size pow(10.0, 0.001) increases logarithmically, calculate η and flow pressure pwf, and record |pwf-pwf * | corresponds to the minimum value of k, until k>10.0; s103. Determine whether the data calculation is completed. If n>num, complete the calculation of the permeability corresponding to each data point; if n<num, return to step s101 to calculate the next data point until all data are completed.

2. The method according to claim 1, characterized in that Formulas (1) to (3) are: Conventional well test analysis: Assuming a well in a homogeneous, uniformly thick reservoir, produces at a certain rate p After that, the well was shut in for pressure recovery test. Without considering the influence of wellbore storage coefficient and skin coefficient, the bottom hole flowing pressure after shutting in Δt time was: Where: p ws - Bottom hole recovery pressure, MPa; p wf - Bottom hole flowing pressure during production before shutting in, MPa; q-production before shut-in, m 3 / ks; μ-fluid viscosity, mPa.s; B-fluid volume coefficient, dimensionless; k- reservoir permeability, μm 2 ; h-effective reservoir thickness, m; η-pressure conductivity, m 2 / ks; φ-porosity, decimal; c t -Total compression factor, MPa -1 ; Δt-shut-in time, ks; t p - Production time before shut-in, ks; r w -well radius, m; γ-constant, 1.78…; After the skin factor s is introduced: The above formula (1) is the most basic pressure recovery formula. On this basis, the influence of the skin coefficient s is introduced to consider the pollution or improvement of the reservoir around the wellbore. At this time, the bottom hole flowing pressure is rewritten as:

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