Improved Analysis Method for Conventional Pressure Buildup Well Testing

Abstract

The present invention provides an improved analysis method for conventional pressure buildup well testing, including Step 1. Improved conventional pressure buildup well testing analysis; and Step 2. Solving for the improved conventional well testing analysis. The present invention improves the theoretical interpretation method of conventional pressure buildup well testing, and uses the analysis method of the non-linear segment to analyze the continuous change of reservoir parameters, so as to provide more reliable parameters for meeting the needs of actual production.

Description

Technical Field

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

[0002] Conventional well testing often starts from homogeneous reservoirs. Its assumption is that in an infinite, homogeneous, and isopachous reservoir, a well produces at a certain production rate. According to its seepage theory, whether it is drawdown well testing or pressure buildup well testing, a straight-line segment must appear between the bottom-hole pressure and the shut-in time on a semi-logarithmic scale. This is the theoretical basis for conventional pressure buildup well testing. However, in the actual reservoir during the seepage process, it is assumed to be a continuous medium. Therefore, in the actual geological conditions, the reservoir cannot be homogeneous, and a straight-line segment may not appear, which brings difficulties to the analysis of conventional pressure buildup well testing. As a result, many current pressure buildup well test interpretations cannot be explained by conventional well testing. Especially for low-permeability reservoir testing, it is very difficult to obtain a straight-line segment. Therefore, only modern well test interpretations can be used for analysis. However, with the increase in interpretation parameters in modern well test interpretations, it is impossible to overcome the problem of multiple solutions in the results.

[0003] Application No. CN202410363863.9, Invention Name: A Method for Interpreting the Productivity of a Well in a Low-Permeability Heterogeneous Water-Bearing Gas Reservoir, includes: constructing a binary function between the starting pressure gradient, permeability, and water saturation, collecting gas well productivity test data, and calculating the production pressure difference at different measuring points; determining the drainage radius of the gas well; calculating the starting pressure of different small layers; judging whether each small layer participates in flow under each measuring point according to the magnitude of the production pressure difference and the starting pressure, and calculating the thickness of the producing layer, formation factor, and average permeability; calculating the laminar and turbulent contrast coefficients of the productivity equation for each measuring point, drawing a productivity indicator curve, determining the productivity equation coefficients, and calculating the absolute open flow.

[0004] The disadvantages of the above invention are: (1) This invention is not a pressure buildup well test in unstable well testing at all. It is a productivity well test in stable well testing, and its test conditions are very harsh and must reach the stable flow condition. (2) This method is calculated based on the production pressure difference. Therefore, before conducting a productivity test, it is necessary to obtain the formation pressure through a pressure buildup test, and use the formation pressure to obtain the production pressure difference to calculate the reservoir permeability. This 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 existing in the above-mentioned prior art and provide an improved analysis method for conventional pressure buildup well testing. The present invention belongs to unstable testing, which tests the variation relationship of the flowing pressure with time and is solved according to the unstable flow theory of the flowing pressure.

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

[0007] Improved analysis method for conventional pressure buildup well testing, including the following steps:

[0008] Step 1. Improved analysis of conventional pressure buildup well testing

[0009] First, perform differential homogenization on the flow stage. For the wellbore storage stage from 0 to Δt 1 , consider it as a homogeneous flow with a permeability of k 1 . At this time, the bottom-hole flowing pressure is:

[0010]

[0011] In the formula:

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

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

[0014] μ - Fluid viscosity, mPa.s;

[0015] B - Fluid volume factor, dimensionless;

[0016] k 1 - Reservoir permeability, μm 2 ;

[0017] h - Effective thickness of the reservoir, m;

[0018] φ - Porosity, decimal;

[0019] c t - Total compressibility, MPa -1 ;

[0020] Δt 1 - Shut-in time, ks;

[0021] p ws1 — Bottom-hole test pressure corresponding to the shut-in time Δt 1 , MPa;

[0022] t p - Production time at a constant rate before shut-in, ks;

[0023] r w - Wellbore radius, m;

[0024] γ - Constant, 1.78……;

[0025] η 1 - Pressure conductivity coefficient within the time of Δt 1 , m 2 / ks.

[0026] Skin effect flow stage near the wellbore Δt 1 -Δt 2 , regarded as a homogeneous flow with permeability k 2 . At this time, the bottom-hole flowing pressure is:[[]]

[0027]

[0028] In the formula:

[0029] Δt 2 - Shut-in time, ks;

[0030] p ws2 — Bottom-hole test pressure corresponding to the shut-in time Δt 2 , MPa;

[0031] k 2 - Reservoir permeability, μm 2 ;

[0032] η 2 -Δt 2 The pressure conductivity coefficient within the time of, m 2 / ks.

[0033] Plane radial flow stage in the formation Δt 1 -Δt n , regarded as a homogeneous flow with permeability k n . At this time, the bottom-hole flowing pressure is:[[]]

[0034]

[0035] In the formula:

[0036] Δt n - Shut-in time, ks;

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

[0038] η n -Δt n The pressure conductivity coefficient within the time of, m 2 / ks;

[0039] p wsn — Bottom-hole test pressure corresponding to the shut-in time Δt n , MPa.

[0040] Theoretically, the pressure drop model is established for the flow stage at the moment of Δt 1 -Δt n . If k 2 = k 3 …k n-1 = k n, equations (6)-(11) are simplified to equations (1)-(3), Δt 0 -Δt 1 describes the wellbore storage effect at the moment.

[0041] Step 2. Solving by improved conventional well test analysis

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

[0043] s101. Input the number of test data num and the change range of reservoir permeability. Assume that the logarithm of permeability changes in the range of [-5,1] μm 2 interval change, that is, lgk ∈ [-5,1] (that is, the permeability range is [0.0001,10] μm 2 , suitable for all reservoirs of low, medium and high grades), and assume the number of cycles is n;

[0044] s102. Assume that the permeability step increases by pow(10.0, 0.001) (the step can be set according to the permeability of the reservoir. If the permeability is high, the step can be set larger; conversely, if the reservoir permeability is low, it can be set smaller), and increase in logarithmic scale. Calculate η and flowing pressure p wf , and record the k corresponding to the minimum value of |pwf - pwf * | until k > 10.0 μm 2 (reservoirs exceeding 10 darcies are very few);

[0045] s103. Judge whether the data calculation is completed. If n > num, complete the calculation and input 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 equations (1) to (3):

[0047] Conventional well test analysis: Assume a well in a homogeneous and isopachous reservoir, producing at a certain rate for t p and then shutting in for pressure build-up test. Without considering the effects of wellbore storage coefficient and skin factor, after shutting in for Δt time, the bottom-hole flowing pressure is:

[0048]

[0049] In the formula:

[0050] p ws - bottom-hole build-up pressure, MPa;

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

[0052] q - production rate before shutting in, m3 / ks;

[0053] μ - Fluid viscosity, mPa.s;

[0054] B - Fluid volume coefficient, dimensionless;

[0055] k - Reservoir permeability, μm 2 ;

[0056] h - Effective thickness of reservoir, m;

[0057] η - Pressure diffusivity, m 2 / ks;

[0058] φ - Porosity, fraction;

[0059] c t - Total compressibility, MPa -1 ;

[0060] Δt - Shut - in time, ks;

[0061] t p - Production time at a constant rate before shut - in, ks;

[0062] r w - Wellbore radius, m;

[0063] γ - Constant, 1.78…….

[0064] After introducing the skin factor s:

[0065] The above formula (1) is the most basic pressure buildup formula. On this basis, considering the influence of reservoir pollution or improvement around the wellbore and introducing the influence of the skin factor s, the bottom - hole flowing pressure is rewritten as:

[0066]

[0067] Advantages of the present invention:

[0068] (1) This method can interpret the conventional pressure buildup well test interpretation without a straight - line segment.

[0069] (2) It can avoid the multi - solution problem of modern well test interpretation; (3) This method can interpret the changes in reservoir physical property parameters. Brief description of the drawings

[0070] Figure 1 It is a schematic diagram of conventional pressure buildup analysis;

[0071] Figure 2 It is a schematic diagram of improved conventional pressure buildup well test analysis;

[0072] Figure 3 It is a schematic diagram of solving the improved well test;

[0073] Figure 4 For the pressure build-up test data of a certain well;

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

[0075] Figure 6 For the double-logarithmic fitting curve Ⅰ of a certain well;

[0076] Figure 7 For the double-logarithmic fitting curve Ⅱ of a certain well;

[0077] Figure 8 For the permeability change curve of the improved pressure build-up analysis method of a certain well;

[0078] Figure 9 For the semi-logarithmic fitting curve of the improved pressure build-up analysis method of a certain well. Specific implementation manner

[0079] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be described clearly and completely below. Apparently, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0080] The improved analysis method for the conventional pressure build-up well test of the present invention includes the following steps:

[0081] Step 1. Analysis of influencing factors of conventional pressure build-up well test

[0082] The theory of conventional well test analysis is based on the pressure drawdown well test theory in a homogeneous reservoir. Assume a production well in a homogeneous and isopachous reservoir, producing at a certain production rate q for t p After that, shut in the well for pressure build-up test. Without considering the influence of wellbore storage coefficient and skin factor, after shutting in for Δt time, the bottom-hole flowing pressure is:

[0083]

[0084] In the formula:

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

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

[0087] q - Production rate 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 thickness of reservoir, m;

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

[0093] φ - Porosity, decimal;

[0094] c t - Total compressibility, MPa -1 ;

[0095] Δt - Shut - in time, ks;

[0096] t p - Production time at a constant rate before shut - in, ks;

[0097] r w - Wellbore radius, m;

[0098] γ - Constant, 1.78…….

[0099] S101. Introduce the skin factor s

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

[0101]

[0102] Let:

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

[0104]

[0105] Wherein:

[0106] k s - Permeability of the reservoir near the well, μm 2 ;

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

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

[0109] S102. Influence of the straight-line segment on permeability

[0110] As known from equation (3), using the analysis method of the straight-line segment, in different coordinate systems, draw the bottom-hole pressure and time t A of the corresponding straight-line segment, as Figure 1 shown. The analysis method of the straight-line segment is simple and convenient in operation; the intercept and slope of the straight-line segment can be obtained from the linear relationship diagram in the coordinate system, and then the corresponding s and k values can be calculated. When using the analysis method of the straight-line segment, if the division of the straight-line segment is correct, the obtained formation parameters are correct and unique, and there will be no multiple-solution situation.

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

[0112] According to the above assumptions: homogeneous and isopachous reservoir, after constant-rate production, the pressure build-up test will definitely result in a straight-line segment; according to the principle of proposition and converse proposition, the non-appearance of a straight-line segment in the pressure build-up test indicates either inhomogeneity, or non-isopachous, or non-constant production. Assuming that the reservoir is isopachous and constant production are easy to meet, only the reservoir homogeneity is difficult to meet. Therefore, the non-appearance of a straight-line segment is mainly caused by reservoir inhomogeneity.

[0113] The change of reservoir physical properties is described by the change of permeability. Therefore, the skin factor parameter can be not considered, and the introduction of the wellbore storage system has a great impact on the selection time of the straight-line segment in conventional pressure build-up well testing. According to the theory of Professor Li Chuanliang: the fluid flow in the wellbore can be equivalent to seepage flow, only the flow with extremely high permeability.

[0114] Therefore, the following introduces the improved analysis method of conventional pressure build-up well testing:

[0115] S103. Influence on the skin factor

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

[0117]

[0118] As known from equation (5), once the straight-line slope is determined, the magnitude of the skin factor depends on whether the flowing pressure before shut-in before the test is correct. If the flowing pressure is too low, the calculated skin factor is too large; conversely, if the flowing pressure is too high, the skin factor is too small. If the straight-line slope cannot be determined, there will be a multiple-solution problem.

[0119] Step 2. Improved Conventional Pressure Buildup Well Test Analysis Method

[0120] First, perform differential homogenization on the flow stage, as Figure 2 shown. For the wellbore storage stage 0 - Δt 1 , consider it as a homogeneous flow with a permeability of k 1 . At this time, the bottom-hole flowing pressure is:

[0121]

[0122] η 1 -Δt 1 The pressure diffusivity within the time, m 2 / ks.

[0123] p ws1 - The bottom-hole test pressure corresponding to the shut-in time Δt 1 , MPa;

[0124] For the skin effect flow stage near the wellbore Δt 1 -Δt 2 , consider it as a homogeneous flow with a permeability of k 2 . At this time, the bottom-hole flowing pressure is:

[0125]

[0126] In the formula:

[0127] Δt 2 - The shut-in time, ks;

[0128] p ws2 — The bottom-hole test pressure corresponding to the shut-in time Δt 2 , MPa;

[0129] η 2 -Δt 2 The pressure diffusivity within the time, m 2 / ks.

[0130] For the planar radial flow stage in the formation Δt 1 -Δt n , consider it as a homogeneous flow with a permeability of k n . At this time, the bottom-hole flowing pressure is:

[0131]

[0132] In the formula:

[0133] Δt n - The shut-in time, ks;

[0134] k n - The reservoir permeability, m2 / ks;

[0135] η n -Δt n The pressure conductivity coefficient within the time, m 2 / ks;

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

[0137] Theoretically, the pressure drop model is established for Δt 1 -Δt n At the flowing stage at the moment, if k 1 = k 2 = k 3 …k n-1 = k n , Formulas (6)-(11) are simplified to Formulas (1) to (3). Δt 0 -Δt 1 Describe the wellbore storage effect at the moment.

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

[0139] If the heterogeneity of the reservoir makes it difficult to form a straight line segment in well test analysis, at this time the flowing pressure and time are non-linear relationships, and the reservoir physical property parameters cannot be obtained by linear regression. At this time, an iterative method is used to solve the change of permeability, and its calculation block diagram is as Figure 3 shown, and the specific calculation steps are as follows:

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

[0141] (2). Assume that the permeability step size increases by pow(10.0, 0.001), increasing in logarithmic order, calculate η and the flowing pressure pwf, and record the k corresponding to the minimum value of |pwf - pwf * | until k > 10.0;

[0142] (3). Judge whether the data calculation is completed. If n > num, complete the calculation and input 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] As Figure 4As shown, the pressure build-up well test data of a production well in the initial stage are presented. The basic data of the well are shown in Table 1. The stable production time before shut-in is approximately 200 hours. According to Equation (3), a semi-log analysis curve is plotted, as Figure 5 shown. There is no straight-line segment, making it very difficult to analyze using conventional well test analysis. Therefore, people can only use modern well test analysis for analysis. The fitting results are shown in Table 1.

[0145] Table 1 Basic data of a certain well

[0146]

[0147] The double-logarithmic fitting curve is as Figure 6 shown. Since there are many modern well test parameters, multi-solution problems are likely to occur. Also, the fitting results are shown in Table 2. The double-logarithmic fitting curve is as Figure 7 shown. From the perspective of the fitting curve of modern well test interpretation, the fitting effects are all very good. However, from Tables 1 and 2, the parameter results vary greatly. Therefore, it is very difficult for modern well test to overcome the multi-solution problem.

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

[0149]

[0150] According to the theory, a straight-line segment should definitely appear in a homogeneous reservoir. However, a typical straight-line segment does not appear in reality. Therefore, it cannot be interpreted using the conventional pressure build-up interpretation method. Thus, an improved method is adopted for interpretation without using the skin factor parameter because the skin factor essentially reflects the change in permeability. The interpreted permeability change is as Figure 8 shown, and the fitting effect is as Figure 9 shown. The initial permeability is relatively high, indicating that there is no pollution near the wellbore. The permeability near the well is relatively high, while the permeability in the outer area is relatively low, which is consistent with the trend of modern well test interpretation.

[0151] Conclusion

[0152] Permeability is an important property of the reservoir, and its magnitude directly affects the productivity of oil wells. The improved pressure build-up well test analysis method can well reflect the change in reservoir physical properties. The change in the pollution coefficient can be not considered, and this 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, not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate 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 the 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 in 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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