Application of improved variable yield analysis method in evaluation of reservoir physical properties

Abstract

The invention relates to the technical field of reservoir physical properties, and particularly discloses application of an improved variable yield analysis method in evaluation of reservoir physical properties. Comprising the following steps that firstly, the change of the yield in actual production is simplified into stepped change, and the flowing bottomhole pressure at each moment is calculated according to the superposition principle; secondly, regarding each production section as a homogeneous reservoir, solving the obtained flowing bottomhole pressure equation at each moment to obtain the change of the permeability of the reservoir, and establishing a minimum objective function of each flowing pressure; and finally, recording the permeability when the minimum M is obtained under each yield to obtain the average permeability of the pressure wave and the area under the yield. The method can analyze the continuous change of the parameters of the reservoir around the production well, is simple, accurate in analysis effect, suitable for homogenizing oil reservoirs and homogenizing heterogeneous oil reservoirs, can be popularized to production analysis of other reservoir types, and has great application prospects.

Description

Technical Field

[0001] The invention relates to the technical field of reservoir physical properties, and specifically discloses the application of an improved variable production analysis method in evaluating reservoir physical properties. Background Art

[0002] According to the seepage theory, changes in reservoir physical parameters cause changes in oil well production. Once the production changes, it will cause redistribution of formation pressure and change of bottom hole pressure. The reasons for the change in production are, on the one hand, formation energy exhaustion and water content increase, and secondly, artificial changes in the working system. Generally, the change in production is handled by the pressure drop superposition principle, and the superposition principle generally considers homogeneous reservoirs. Even if it is considered as a heterogeneous reservoir, it is often considered as a limited multi-zone composite reservoir, using Laplace space superposition.

[0003] However, people have not considered that even if the working system has not changed, it can also cause changes in production. Since the reservoir and the fluid are regarded as a continuous medium field during the seepage process, the changes in reservoir properties are also continuous. In fact, in the analysis process, the reservoir properties are considered to have limited changes. Therefore, it is difficult to achieve ideal results when using the variable yield method to analyze production data in the actual production process, and the fitting effect is very poor.

[0004] Currently, the only method that can use production data to evaluate reservoir parameters is the modern production decline method. This method does not use the variable production analysis method. It uses the material balance time combined with the quasi-stable flow to fit the chart. The front part of the chart is the unstable flow, and the back part is the quasi-stable flow. It still cannot explain the continuous changes in reservoir properties. Summary of the invention

[0005] In view of the above-mentioned problems in the prior art, the present invention provides an improved variable production analysis method for application in evaluating reservoir physical properties. The method can analyze the continuous changes of reservoir parameters around production wells. The method is simple and the analysis effect is accurate. It can be extended to production analysis of other reservoir types and has great application prospects.

[0006] The technical solution adopted by the present invention is as follows:

[0007] The application of the improved variable production analysis method in evaluating reservoir physical properties includes the following steps:

[0008] S1. Simplify the change of production in actual production into a step-by-step change, and calculate the bottom hole pressure at each moment according to the superposition principle;

[0009] S2, treating each production section as a homogeneous reservoir, solving the bottom hole pressure equation at each moment obtained in step S1, obtaining the change of reservoir permeability, and establishing the minimum objective function of each flow pressure;

[0010] S3. Record the permeability when the minimum M is obtained at each production rate, and obtain the average permeability of the pressure affected area at the production rate.

[0011] Preferably, the step S1 of obtaining the bottom hole flow pressure at each moment includes the following steps:

[0012] S11 calculates the bottom hole pressure at t1 when the well is producing at q1, and its expression is:

[0013]

[0014] Where q1 is the output in time t1, the unit is m 3 / ks, k1 is the average permeability of the reservoir during the propagation of the pressure wave in time t1, the unit is μm 2 , is the bottom hole pressure at time t1, in MPa, p i is the original formation pressure, in MPa, μ o is the viscosity of crude oil, in mPa.s, B o is the crude oil volume coefficient, h is the effective thickness of the reservoir, the unit is m, r w is the well radius, in m, C t is the total compression coefficient, in MPa -1 , φ is the reservoir porosity, the unit is decimal, E i (x) is the power integral function, η1 is the pressure conductivity coefficient in time t1, unit is m 2 / ks;

[0015] When the S12 calculation well produces at q2, the bottom hole flowing pressure at t2 is expressed as:

[0016]

[0017] In the formula, q2 is the output in time t2, m 3 / ks, k2 is the average reservoir permeability of the pressure wave during the propagation of time t2, μm 2 , is the bottom hole pressure at time t1, in MPa, η2 is the pressure conductivity coefficient at time t2, in m 2 / ks;

[0018] S13 calculation well q n During production, t n The bottom hole flowing pressure at time is expressed as:

[0019]

[0020] Where j is the production stage, j = 1,...,n, q is the output, the unit is m 3 / ks, t is the production time, the unit is ks, q n t n Output in time, in m 3 / ks,k n is the pressure wave at t n The average value of reservoir permeability propagated over time, in μm 2 , t n The bottom hole pressure at the moment, in MPa, η n is time t n The pressure conductivity coefficient in m 2 / ks.

[0021] Preferably, in step S2, each flow pressure minimum objective function is established, and the expression is as follows:

[0022]

[0023] In the formula, k represents the value of each permeability, is the actual bottom hole pressure at time i, MPa, p wfi is the theoretical bottom hole flowing pressure at time i, MPa.

[0024] Preferably, the p in step S2 wfi Obtained by calculation of the expression in step S13.

[0025] Preferably, obtaining the optimal permeability and flow pressure value in step S2 includes the following steps:

[0026] S21 assumes a range of permeability changes,

[0027] S22k increases in steps of 0.01. Each time the step increases, the bottom hole pressure at time t1 is calculated by the expression in step S13. Compare actual bottom hole flowing pressure Calculate the sum of squares of the error between the actual flow pressure and the calculated flow pressure, and record the permeability and flow pressure values ​​when the error is the smallest;

[0028] S23 returns to step S21 and continues the above operations to calculate the reservoir permeability at the next production moment until the last production stage.

[0029] Preferably, when obtaining the bottom hole flow pressure at each moment in step S1, if the pollution near the bottom hole is considered, the well radius is replaced by the effective well radius, and the expression is:

[0030] r we =r w e -s ,

[0031] In the formula, rwe is the effective well radius, and s is the pollution coefficient.

[0032] The present invention has the following characteristics and advantages:

[0033] (1) It can analyze the continuous changes of reservoir parameters around production wells with simple methods, accurate analysis results and fast calculation speed;

[0034] (2) It is applicable to both homogeneous reservoirs and heterogeneous reservoirs for averaging treatment;

[0035] (3) This method can be extended to other reservoir types and has great application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of variable output production;

[0037] Figure 2 It is a production curve chart of historical production data of a certain oil well;

[0038] Figure 3 It is the variable output production fitting curve diagram;

[0039] Figure 4 It is a schematic diagram of improved variable output;

[0040] Figure 5 It is a parameter optimization calculation block diagram;

[0041] Figure 6 It is an improved flow pressure fitting curve diagram for variable production analysis. DETAILED DESCRIPTION

[0042] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments.

[0043] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0044] The process of calculating the permeability of the variable production and analyzing the production data of the well includes the following steps:

[0045] (1) Simplify the change of output in actual production into a step-by-step change. The diagram of variable output production is as follows: Figure 1 As shown, the reservoir permeability around the well is Kum 2 At the initial moment, t0=0, q0=0, according to the superposition principle, the bottom hole pressure of the oil well at time t is calculated as:

[0046]

[0047]

[0048] Where q is the output in time t, and the unit is m 3 / ks, k is the reservoir permeability, the unit is μm 2 , j is the production stage, j = 1,...,n, t is the production time, the unit is ks, p wf(t) is the bottom hole flowing pressure at time t, in MPa, p i is the original formation pressure, in MPa, μ o is the viscosity of crude oil, in mPa.s, B o is the crude oil volume coefficient, h is the effective thickness of the reservoir, the unit is m, r w is the well radius, in m, C t is the total compression coefficient, in MPa -1 , φ is the reservoir porosity and is a decimal, E i (x) is the power integral function, η is the pressure conductivity coefficient, unit is m 2 / ks;

[0049] If the pollution near the bottom of the well is considered, the effective well radius is used instead of the well radius, that is, r we Instead of r w ,Right now

[0050] r we =r w e -s (3)

[0051] Where s is the pollution coefficient;

[0052] (2) Taking the permeability k and the contamination coefficient s as the parameters to be determined, the production data flow pressure fitting objective function is established, namely:

[0053] In the formula, is the actual bottom hole pressure at time i, MPa, p wfi is the theoretical bottom hole flowing pressure at time i, calculated by formula (1), MPa.

[0054] Calculation of variable production permeability analysis Specific example analysis of the production data of this well:

[0055] The original formation pressure of an oil well is 95MPa, the reservoir porosity is 0.06, the effective reservoir thickness is 5.5m, the crude oil viscosity is 0.7mPa.s, the crude oil volume coefficient under the original formation pressure is 1.59, and the total compression coefficient is 0.002226MPa -1 , its production curve is as follows Figure 2As shown, the production changes greatly. The variable production optimization method can be used to obtain reservoir physical property parameters. The variable production optimization iteration takes a very long time. If there are n data points, one cycle requires n(n+1) / 2 iterations. The fitted permeability is 0.00433547μm 2 , the skin coefficient is 2.18846321, and the fitting effect is as follows Figure 3 As shown, the fitting effect is very poor, indicating that the production data of this well cannot be analyzed using a single permeability.

[0056] Disadvantages of variable production analysis: (1) As the production data increases, the fitting time becomes very long; (2) The constant permeability fitting effect is very poor.

[0057] How to improve the variable yield analysis method so that the analysis results are more in line with production reality. The improved variable yield analysis method is introduced below.

[0058] The application of the improved variable production analysis method in evaluating reservoir physical properties includes the following steps:

[0059] S1. Simplify the change of production in actual production into a step-by-step change, and calculate the bottom hole pressure at each moment according to the superposition principle;

[0060] S2, treating each production section as a homogeneous reservoir, solving the bottom hole pressure equation at each moment obtained in step S1, obtaining the change of reservoir permeability, and establishing the minimum objective function of each flow pressure;

[0061] S3. Record the permeability when the minimum M is obtained at each production rate, and obtain the average permeability of the pressure affected area at the production rate.

[0062] like Figure 4 As shown, step S1 obtains the bottom hole flow pressure at each moment, including the following steps:

[0063] S11 calculates the bottom hole pressure at t1 when the well is producing at q1, and its expression is:

[0064]

[0065] Where q1 is the output in time t1, the unit is m 3 / ks, k1 is the average permeability of the reservoir during the propagation of the pressure wave in time t1, the unit is μm 2 , is the bottom hole pressure at time t1, in MPa, p i is the original formation pressure, in MPa, μ o is the viscosity of crude oil, in mPa.s, B o is the crude oil volume coefficient, h is the effective thickness of the reservoir, the unit is m, r w is the well radius, in m, Ct is the total compression coefficient, in MPa -1 , φ is the reservoir porosity, the unit is decimal, E i (x) is the power integral function, η1 is the pressure conductivity coefficient in time t1, unit is m 2 / ks;

[0066] When the S12 calculation well produces at q2, the bottom hole flowing pressure at t2 is expressed as:

[0067]

[0068] Where q2 is the output in time t2, the unit is m 3 / ks, k2 is the average reservoir permeability of the pressure wave propagating during time t2, in μm 2 , is the bottom hole pressure at time t1, in MPa, η2 is the pressure conductivity coefficient at time t2, in m 2 / ks;

[0069] S13 calculation well q n During production, t n The bottom hole flowing pressure at time is expressed as:

[0070]

[0071] Where j is the production stage, j = 1,...,n, q is the output, the unit is m 3 / ks, t is the production time, the unit is ks, q n t n Output in time, in m 3 / ks,k n is the pressure wave at t n The average value of reservoir permeability propagated over time, in μm 2 , t n The bottom hole pressure at the moment, in MPa, η n is time t n The pressure conductivity coefficient in m 2 / ks.

[0072] In step S2, the minimum objective function of each flow pressure is established, and the expression is as follows:

[0073]

[0074] In the formula, k represents the value of each permeability, is the actual bottom hole pressure at time i, in MPa, p wfi is the theoretical bottom hole flowing pressure at time i, in MPa, calculated by expression (9).

[0075] like Figure 5 As shown, obtaining the optimal permeability and flow pressure value in step S2 includes the following steps:

[0076] S21 assumes a range of permeability changes,

[0077] S22k increases in steps of 0.01. Each time the step increases, the bottom hole pressure at time t1 is calculated by the expression in step S13. Compare actual bottom hole flowing pressure Calculate the sum of squares of the error between the actual flow pressure and the calculated flow pressure, and record the permeability and flow pressure values ​​when the error is the smallest;

[0078] S23 returns to step S21 and continues the above operations to calculate the reservoir permeability at the next production moment until the last production stage.

[0079] The following is an analysis of the same example. According to the above analysis steps, the flow pressure fitting curve in the production process is obtained as follows: Figure 6 As shown, the change of permeability is a continuous process. The drastic change of permeability will cause a very drastic change in production. The permeability of conventional variable production analysis is only one value in the continuous permeability. Therefore, the variable production analysis cannot use constant permeability analysis. The improved variable production analysis is more consistent with actual production, which is in line with the continuous medium field.

[0080] In summary, this method can analyze the continuous changes of reservoir parameters around production wells. The method is simple, the analysis effect is accurate, and the calculation speed is fast. It is suitable for both homogeneous reservoirs and heterogeneous reservoirs for averaging processing. It can be extended to production analysis of other reservoir types and has great application prospects.

[0081] The embodiments described above are only descriptions of the preferred modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. Application of improved variable yield analysis method in evaluating reservoir properties, It is characterized in that The following steps are involved: S1. Simplify the change of production in actual production into a step-by-step change, and calculate the bottom hole pressure at each moment according to the superposition principle; S2, treating each production section as a homogeneous reservoir, solving the bottom hole pressure equation at each moment obtained in step S1, obtaining the change of reservoir permeability, and establishing the minimum objective function of each flow pressure; S3. Record the permeability when the minimum M is obtained at each production rate, and obtain the average permeability of the pressure affected area at the production rate.

2. The method according to claim 1, It is characterized in that The step S1 obtains the bottom hole flow pressure at each moment, comprising the following steps: S11 calculation well q 1 During production, t 1 The bottom hole flowing pressure at time is expressed as: In the formula, q 1 t 1 Output in time, in m 3 / ks,k 1 is the pressure wave at t 1 The average permeability of the reservoir propagated over time, in μm 2 , t 1 The bottom hole pressure at the moment, in MPa, p i is the original formation pressure, in MPa, μ o is the viscosity of crude oil, in mPa.s, B o is the crude oil volume coefficient, h is the effective thickness of the reservoir, the unit is m, r w is the well radius, in m, C t is the total compression coefficient, in MPa -1 , φ is the reservoir porosity, single digit decimal, E i (x) is the power integral function, η 1 is time t 1 The pressure conductivity coefficient in m 2 / ks; S12 calculation well q 2 During production, t 2 The bottom hole flowing pressure at time is expressed as: In the formula, q 2 t 2 Output in time, m 3 / ks,k 2 is the pressure wave at t 2 Average reservoir permeability over time, μm 2 , t 1 The bottom hole pressure at the moment, in MPa, η 2 is time t 2 The pressure conductivity coefficient in m 2 / ks; S13 calculation well q n During production, t n The bottom hole flowing pressure at , is expressed as: Where j is the production stage, j = 1,...,n, q is the output, the unit is m 3 / ks, t is the production time, the unit is ks, q n t n Output in time, in m 3 / ks,k n is the pressure wave at t n The average value of reservoir permeability propagated over time, in μm 2 , t n The bottom hole pressure at the moment, in MPa, η n is time t n The pressure conductivity coefficient in m 2 / ks.

3. The method according to claim 1, It is characterized in that In step S2, each flow pressure minimum objective function is established, and the expression is as follows: In the formula, k represents the value of each permeability, is the actual bottom hole pressure at time i, in MPa, p wfi is the theoretical bottom hole flowing pressure at time i, in MPa.

4. The method according to claim 3, It is characterized in that The p in step S2 wfi Obtained by calculation of the expression in step S13.

5. The method according to claim 1, It is characterized in that The step S2 of obtaining the optimal permeability and flow pressure value includes the following steps: S21 assumes a range of permeability changes, S22k increases in steps of 0.

01. Each time the step increases, t is calculated by the expression in step S13. 1 Bottom hole pressure Compare actual bottom hole flowing pressure Calculate the sum of squares of the error between the actual flow pressure and the calculated flow pressure, and record the permeability and flow pressure values ​​when the error is the smallest; S23 returns to step S21 and continues the above operations to calculate the reservoir permeability at the next production moment until the last production stage.

6. The method according to claim 1, It is characterized in that When obtaining the bottom hole flow pressure at each moment in step S1, if the pollution near the bottom hole is considered, the well radius is replaced by the effective well radius, and the expression is: r we ＝r w e -s ， In the formula, r we is the effective well radius, and s is the pollution coefficient.

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