Application of improved variable production analysis method in evaluating reservoir physical properties

Abstract

The present 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. The method comprises the following steps: first, simplifying the change in production in actual production into a step-by-step change, and calculating the bottom hole flow pressure at each moment according to the superposition principle; second, treating each production section as a homogeneous reservoir, solving the bottom hole flow pressure equation obtained at each moment, obtaining the change in reservoir permeability, and establishing a minimum objective function for each flow pressure; finally, recording the permeability when the minimum M is achieved at each production rate, and obtaining the average permeability of the pressure-affected area at that production rate. The method can analyze the continuous changes in reservoir parameters around the production well, is simple, and has accurate analysis results. It is applicable to both homogeneous reservoirs and heterogeneous reservoirs for averaging processing, and can be extended to production analysis of other reservoir types, with 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 seepage theory, changes in reservoir physical parameters cause changes in oil well production. Once the production changes, it will cause the redistribution of formation pressure and the change of bottom hole pressure. The reasons for the change in production are, on the one hand, the exhaustion of formation energy and the increase of water content, and secondly, the artificial change of working system. Generally, the pressure drop superposition principle is used to deal with the change in production. The superposition principle generally considers homogeneous reservoirs. Even if it is considered to be 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 does not change, it can cause changes in production. Since the reservoir and fluid are regarded as continuous medium fields 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 unstable flow, and the back part is quasi-stable flow. It still cannot explain the continuous changes in reservoir properties. Summary of the Invention

[0005] In response to the above-mentioned problems of the prior art, the present invention provides an improved variable production analysis method for application in evaluating reservoir physical properties. This method can analyze the continuous changes in 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 solutions adopted in the present invention are as follows:

[0007] A method for improving variable yield analysis in evaluating reservoir physical properties comprises 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 based on the superposition principle;

[0009] S2. Consider each production section as a homogeneous reservoir, solve the bottom hole pressure equation at each moment obtained in step S1, obtain the change in reservoir permeability, and establish the minimum objective function for each flow pressure;

[0010] S3. Calculate the permeability when the minimum objective function M is achieved at each production rate, and obtain the average permeability of the pressure-affected area at that production rate.

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

[0012] S11 calculates the bottom hole pressure at t1 when the well is producing at q1. Its expression is:

[0013]

[0014] Where q0 is the output before production (q0=0), t0 is the start time before production (t0=0), and q1 is the output within t1 (unit: 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, the unit is mPa.s, B o is the crude oil volume coefficient, h is the effective reservoir thickness, the unit is m, r w is the well radius, in m, C t is the total compression coefficient, the unit is MPa -1 , φ is the reservoir porosity, the unit is decimal, E i (x) is the power integral function, η1 is the pressure conduction coefficient in time t1, unit is m 2 / ks;

[0015] S12 calculates the bottom hole pressure at t2 when the well is producing at q2. Its expression is:

[0016]

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

[0018] S13 calculation well q n During production, t n The bottom hole pressure at , 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, unit is 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 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, a minimum objective function for each flow pressure is established, and the expression is as follows:

[0022]

[0023] Where k1 is the average permeability of the time period t1, k2 is the average permeability of the time period t2, and k n t n The average permeability of the time period, the subscript indicates that the fitting error in this time period is minimized, and the overall fitting error is minimized by changing the permeability fitting of each period. is the actual bottom hole pressure at time i, MPa, p wfi is the theoretical bottom hole pressure at time i, MPa.

[0024] Preferably, the theoretical bottom hole pressure p at time i in step S2 is wfi Obtained by the expression calculated in step S13.

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

[0026] S21 assumes a range of permeability variations,

[0027] S22k increases by 0.01 steps. Each time a step is added, 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 errors between the actual flow pressure and the calculated flow pressure, and record the permeability and flow pressure values ​​with the smallest error;

[0028] S23 returns to step S21 and repeats steps S21-S22 to calculate the reservoir permeability at the next production moment until the last production stage.

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

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

[0031] Where r w is the wellbore radius, m, r we 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 an 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 block diagram of parameter optimization calculation;

[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 same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

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

[0045] (1) Simplify the change of output in actual production into a step-by-step change, and 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] 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 pressure at time t, in MPa, p i is the original formation pressure, in MPa, μ o is the viscosity of crude oil, the unit is mPa.s, B o is the crude oil volume coefficient, h is the effective reservoir thickness, 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 conduction coefficient, unit is m 2 / ks;

[0048] 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

[0049] r we =r w e -s (3)

[0050] Where s is the pollution coefficient;

[0051] (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:

[0052] Where, is the actual bottom hole pressure at time i, MPa, p wfi is the theoretical bottom hole pressure at time i, calculated by formula (1), MPa.

[0053] Calculation of variable production and permeability analysis of the production data of this well:

[0054] The original formation pressure of an oil well is 95 MPa, the reservoir porosity is 0.06, the effective reservoir thickness is 5.5 m, the crude oil viscosity is 0.7 mPa.s, the crude oil volume coefficient at the original formation pressure is 1.59, and the total compressibility coefficient is 0.002226 MPa. -1 , its production curve is as follows Figure 2 As shown, the production changes greatly. The variable production optimization method can be used to obtain reservoir physical properties. 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.

[0055] Disadvantages of variable production analysis: (1) As the production data increases, the fitting time is very long; (2) The constant permeability fitting effect is very poor.

[0056] The improvement of variable yield analysis of production data of oil well formations includes the following steps:

[0057] S1. Simplify the change of production in actual production into a step-by-step change, and calculate the bottom hole pressure at each moment based on the superposition principle;

[0058] S2. Consider each production section as a homogeneous reservoir, solve the bottom hole pressure equation at each moment obtained in step S1, obtain the change in reservoir permeability, and establish the minimum objective function for each flow pressure;

[0059] S3. Calculate the permeability when the minimum objective function M is achieved at each production rate, and obtain the average permeability of the pressure-affected area at that production rate.

[0060] like Figure 4 As shown, step S1 obtains the bottom hole flowing pressure at each moment, including the following steps:

[0061] S11 calculates the bottom hole pressure at t1 when the well is producing at q1. Its expression is:

[0062]

[0063] Where q0 is the output before production (q0=0), t0 is the start time before production (t0=0), and q1 is the output within t1 (unit: 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, μo is the viscosity of crude oil, the unit is mPa.s, B o is the crude oil volume coefficient, h is the effective reservoir thickness, the unit is m, r w is the well radius, in m, C t is the total compression coefficient, the unit is MPa -1 , φ is the reservoir porosity, the unit is decimal, E i (x) is the power integral function, η1 is the pressure conduction coefficient in time t1, unit is m 2 / ks;

[0064] S12 calculates the bottom hole pressure at t2 when the well is producing at q2. Its expression is:

[0065]

[0066] 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, the unit is μm 2 , is the bottom hole pressure at time t2, in MPa, η2 is the pressure conductivity coefficient within time t2, in m 2 / ks;

[0067] S13 calculation well q n During production, t n The bottom hole pressure at , is expressed as:

[0068]

[0069] 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, unit is 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 Bottom hole pressure at the moment, in MPa, η n is time t n The pressure conductivity coefficient in m 2 / ks.

[0070] In step S2, the minimum objective function of each flow pressure is established, and the expression is as follows:

[0071]

[0072] Where k1 is the square sum of the pressure fitting errors under the average permeability of the time period t1, k2 is the square sum of the pressure fitting errors under the average permeability of the time period t2, and k n t n The sum of squares of the flow pressure fitting error under the average permeability of the time period. The subscript indicates that the fitting error in this time period is minimized. By changing the permeability fitting of each section, the overall fitting error is minimized. is the actual bottom hole pressure at time i, in MPa, p wfi is the theoretical bottom hole pressure at time i, in MPa, calculated by expression (9).

[0073] like Figure 5 As shown, obtaining the optimal permeability and flow pressure values ​​in step S2 includes the following steps:

[0074] S21 assumes a range of permeability variations,

[0075] S22k increases by 0.01 steps. Each time a step is added, 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 errors between the actual flow pressure and the calculated flow pressure, and record the permeability and flow pressure values ​​with the smallest error;

[0076] S23 returns to step S21 and repeats steps S21-S22 to calculate the reservoir permeability at the next production moment until the last production stage.

[0077] 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 in the figure, 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 the constant permeability analysis. The improved variable production analysis is more consistent with the actual production, which is in line with the continuous medium field.

[0078] 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 applicable to 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.

[0079] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for improving the yield analysis in evaluating the physical properties of oil well formation reservoirs, 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 based on the superposition principle; S2. Consider each production section as a homogeneous reservoir, solve the bottom hole pressure equation at each moment obtained in step S1, obtain the change in reservoir permeability, and establish the minimum objective function for each flow pressure; S3. Calculate the minimum objective function for each output The permeability at that time is calculated to obtain the average permeability of the pressure affected area under that production rate.

2. The method for improving the yield analysis in evaluating the physical properties of oil well formations according to claim 1, characterized in that: The step S1 obtains the bottom hole flowing pressure at each moment, including the following steps: S11 calculates the bottom hole pressure at t1 when the well is producing at q1. Its expression is: Where q0 is the output before production q0=0, t0 is the start time before production t0=0, 1 is the output in time t1, the unit is m 3 / ks, 1 is the average permeability of the reservoir during the propagation of the pressure wave in time t1, in µm 2 , is the bottom hole pressure at time t1, in MPa. is the original formation pressure, in MPa, is the viscosity of crude oil, in mPa·s, is the crude oil volume coefficient, is the effective thickness of the reservoir, in m, is the well radius, in m, is the total compression coefficient, the unit is MPa -1 , is the reservoir porosity, a decimal number. is the power integral function, is the pressure conductivity coefficient in time t1, unit is m 2 / ks; S12 calculates the bottom hole pressure at t2 when the well is producing at q2. Its expression is: Where, 2 is the output in time t2, m 3 / ks, 2 is the average reservoir permeability of the pressure wave during the propagation time t2, μm 2 , is the bottom hole pressure at time t2, in MPa, is the pressure conductivity coefficient in time t2, unit is m 2 / ks; S13 calculation well q n During production, t n The bottom hole flowing pressure at time , its expression is: Where, is the production stage, j=1,...,n, is the output, the unit is m 3 / ks, t is the production time, the unit is ks, n t n Output in time, unit is m 3 / ks, 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, is time t n The pressure conductivity coefficient in m 2 / ks.

3. The method for improving the yield analysis in evaluating the physical properties of oil well formations according to claim 1, characterized in that: In step S2, the minimum objective function of each flow pressure is established, and the expression is as follows: Where, Represents the value of each permeability, is the actual bottom hole pressure at time i, in MPa. is the theoretical bottom hole pressure at time i, in MPa.

4. The method for improving the yield analysis in evaluating the physical properties of oil well formations according to claim 2, characterized in that: The theoretical bottom hole flowing pressure at time i in step S2 Obtained by the expression calculated in step S13.

5. The method for improving the yield analysis in evaluating the physical properties of oil well formations according to claim 2, characterized in that: Obtaining the optimal permeability and flow pressure values ​​in step S2 includes the following steps: S21 assumes a range of permeability variations, ; S22 The step size is increased by 0.

01. Each time the step size is increased, the bottom hole pressure at time t1 is calculated by the expression in step S13. , compared with the actual bottom hole pressure , calculate the sum of squares of the errors 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 repeats steps S21-S22 to calculate the reservoir permeability at the next production moment until the last production stage.

6. The method for improving the yield analysis in evaluating the physical properties of oil well formations according to claim 1, characterized in that: In step S1, when obtaining the bottom hole pressure at each moment, if the contamination near the bottom hole is taken into consideration, the well radius is replaced by the effective well radius, and the expression is: ， Where, is the effective well radius, is the pollution coefficient.

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