Method for predicting form of water cone of oil reservoir of fault control body and application

Abstract

The invention provides a fault control body oil reservoir water cone form prediction method and application, and relates to the technical field of oilfield development. The method comprises the following steps that on the basis of a water cone interface differential equation and a seepage velocity calculation formula, the fault control body oil reservoir is regarded as one-way linear flow, and a water cone height differential equation is established; determining a water cone height nonlinear equation through a material balance method; and solving and predicting the heights of water cones with different yields in different production stages by adopting a Newton method. By means of the method, water cone height prediction, water breakthrough time prediction and reasonable production system optimization are achieved, and a theoretical basis is provided for development scheme compilation and development technology policy making of the fault control body oil reservoir.

Description

Technical Field

[0001] This invention relates to the field of oilfield development technology, specifically to a method and application for predicting the water cone morphology of fault-controlled reservoirs. Background Technology

[0002] Bottom-water reservoirs constitute a large proportion of my country's oil reservoirs, with substantial reserves. Besides numerous natural bottom-water reservoirs, as oil fields enter secondary and tertiary production phases, the development characteristics of more and more oil fields are increasingly trending towards bottom-water type reservoirs. Bottom-water reservoirs are characterized by their entire oil-bearing area being in contact with bottom water. This is both an advantage and a challenge in developing bottom-water reservoirs. On the one hand, the large contact area between the reservoir and bottom water greatly enhances the ability of bottom water to infiltrate the reservoir, allowing the formation energy consumed in crude oil extraction to be replenished promptly from the bottom water. Most bottom-water reservoirs exhibit abundant energy during development. However, on the other hand, the presence of bottom water brings serious water production problems to oil wells. During production, they often exhibit characteristics such as early water breakthrough, short waterless production periods, rapid rise in water cut after water breakthrough, and even sudden water flooding, leading to reduced oil recovery and increased oilfield development risks. In order to rationally develop bottom water reservoirs, reduce extraction costs and risks, and strengthen the control of bottom water coning, it is necessary to deepen the research on the laws governing bottom water coning.

[0003] Chinese patent CN107989598A provides a method for predicting the water cone fallback height of a vertical well in a bottom-water reservoir, comprising: Step 1, establishing a numerical simulation conceptual model of a vertical well in a bottom-water reservoir using reservoir numerical simulation software; Step 2, calculating the quantitative relationship between the water cone fallback height and shut-in time under each single influencing factor using the established numerical simulation conceptual model of a vertical well in a bottom-water reservoir; Step 3, establishing a prediction model for the water cone fallback height of a vertical well in a bottom-water reservoir under multiple influencing factors using multivariate nonlinear regression based on the calculated relationship between the water cone fallback height and shut-in time under each single influencing factor; Step 4, calculating the water cone fallback height using the established prediction model for the water cone fallback height of a vertical well in a bottom-water reservoir. However, this technical solution is designed for determining the water cone fallback height after shut-in of a vertical well with high water cut in a bottom-water reservoir, and is not suitable for dynamic prediction of the water cone height in real time.

[0004] Exploration and development results indicate that the Shunbei oil and gas field in the Tarim Basin of my country develops deep fault-controlled carbonate reservoirs. These reservoirs are mainly influenced by fault zones, and seepage primarily reflects narrow, linear flow characteristics. Water cone morphology prediction for bottom-water development reservoirs plays a crucial role in predicting the dynamics of development and determining development technology policies for this type of reservoir. However, existing water cone morphology prediction models for bottom-water development reservoirs still have significant limitations when applied to fault-controlled reservoirs.

[0005] Existing methods for predicting water cone height and shape mainly fall into three categories: The first category is based on the water cone interface pressure balance equation, comprehensively considering theories such as planar radial flow, spherical flow, and combinations of radial and spherical flow to establish water cone height prediction models for different production rates. This type of method does not consider the impact of previous accumulated production leading to water cone surface rise, and planar radial flow, spherical flow, and combinations of radial and spherical flow are not suitable for fault-controlled reservoirs. The second category is the material balance equation method, which calculates the static oil-water interface position by calculating water intrusion. The resulting water cone is an average interface, which is not suitable for real-time water cone height prediction and production regime optimization in bottom-water development reservoirs. The third category is statistical methods, such as field statistics and big data model prediction. These methods require a large amount of data, and since there are relatively few bottom-water development wells in fault-controlled reservoirs, it is difficult to establish models that meet the requirements of field statistics and big data prediction.

[0006] Therefore, developing a new method suitable for predicting the water cone morphology of fault-controlled reservoirs is of great significance to researchers in this field. Summary of the Invention

[0007] To address the aforementioned problems, this invention provides a method for predicting the water cone morphology of fault-controlled reservoirs, enabling prediction of water cone height, water break-in time, and optimization of rational production systems, thus providing a theoretical basis for the formulation of development plans and development technology policies for fault-controlled reservoirs.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] On the one hand, the present invention provides a method for predicting the water cone morphology of fault-controlled reservoirs, comprising the following steps:

[0010] S1: Based on the differential equation of the water cone interface and the formula for calculating the seepage velocity, the fault-controlled reservoir is regarded as a unidirectional linear flow, and the differential equation of the water cone height is established.

[0011] S2: Determine the nonlinear equation for the height of the water cone using the mass balance method;

[0012] S3: The Newton-Raphson method is used to predict the height of the water cone at different production stages and with different outputs.

[0013] Preferably, in step S1, the differential equation of the water cone interface is:

[0014]

[0015] Where r is the distance from the well, in meters;

[0016] p is the oil-water interface pressure at point r, in MPa;

[0017] ρ w Density of formation water, g / cm³ 3 ;

[0018] ρ o Density of formation crude oil, g / cm³ 3 ;

[0019] g is the acceleration due to gravity, 9.8 m / s². 2 ;

[0020] f(r) is the height of the water cone at point r.

[0021] Preferably, in step S1, the fault-controlled reservoir is a narrow strip-type reservoir.

[0022] Preferably, in step S1, the formula for calculating the seepage velocity is:

[0023]

[0024] Where: v is the seepage velocity at point r, m / s;

[0025] K o The crude oil permeability under bound water conditions in the reservoir is expressed in μm. 2 ;

[0026] μ o The viscosity of the formation crude oil is expressed in mPa·s.

[0027] g is the acceleration due to gravity, 9.8 m / s². 2 ;

[0028] f(r) is the height of the water cone at point r, in meters.

[0029] B o The volume factor of crude oil is 1;

[0030] Q o For Japanese oil production, m 3 / D;

[0031] D is the width of the fault zone, in meters;

[0032] h is the height of the oil column at the edge of the water cone, in meters.

[0033] Preferably, in step S1, the differential equation for the height of the water cone is:

[0034]

[0035] We obtain the result by substituting formula (2) into formula (1).

[0036] Preferably, after rearranging formula (3), a differential equation for f(r) is obtained:

[0037]

[0038] This is a separable differential equation, which can be solved using the method of separation of variables:

[0039]

[0040] Where: C is an undetermined constant, and a is an intermediate variable;

[0041]

[0042] Preferably, C is determined by a mass balance method, and is handled in two cases: one is the water cone leading edge r i Less than the oil well control radius r e Another type is the leading edge of the water cone. i Reaching the control radius r of the oil well e .

[0043] Preferably, in the first case: the leading edge r of the water cone i Less than the oil well control radius r e .

[0044] Well shaft location:

[0045]

[0046] At the leading edge of the water cone:

[0047]

[0048] Because the height of the water cone at the leading edge is 0, that is:

[0049] f(r i )=0 (9)

[0050] Substituting into formula (8) will determine C:

[0051] C = ar i (10)

[0052] Substituting into formula (5), the height of the water cone at point r can be determined:

[0053]

[0054] Formula (11) is a quadratic equation in one variable. Solving the equation yields f(r). Considering that f(r) should be less than h:

[0055]

[0056] Formula (12) establishes the relationship between the water cone height f(r) and the water cone leading edge position r. i The relational expression.

[0057] Calculate r based on the bottom water drive mass balance equation. i In bottom-water development reservoirs, pressure changes are stable, and the water cone intrusion volume equals the crude oil production volume.

[0058]

[0059] Where: N p For cumulative oil production, m 3 ; 1 represents reservoir porosity.

[0060] Calculate the integral and rearrange to obtain information about r. i Nonlinear equations:

[0061]

[0062] Preferably, in the second case: the leading edge r of the water cone i Reaching the control radius r of the oil well e .

[0063] Well shaft location:

[0064]

[0065] At the leading edge of the water cone:

[0066]

[0067] Let H be the height of the water cone at the leading edge, then:

[0068] f(r e )=H(20)

[0069] Substitute formula (20) into (19) to determine C:

[0070]

[0071] Substitute into formula (5) to determine the height of the water cone at point r:

[0072]

[0073] Similarly, we can solve for f(r):

[0074]

[0075] Similarly, the volume of water cone intrusion is equal to the volume of crude oil produced:

[0076]

[0077] Integrating yields a nonlinear equation for H:

[0078]

[0079] Preferably, formula (14) can be solved iteratively using Newton's method, given r iInitial value, calculate the iteration value r according to formula (15-17) i * .

[0080]

[0081]

[0082]

[0083] Preferably, when the iteration value r i * With r i If the error is less than 0.1, the iteration value r i * That is, the desired r i Otherwise, the iteration value r will be... i * As r i The initial value continues to iterate until the iteration value r is reached. i * With r i Until the error is less than 0.1.

[0084] Preferably, in the first case, r i Greater than r e They believed that the leading edge had reached the reservoir boundary and treated it as the second scenario.

[0085] Preferably, formula (25) is solved iteratively using Newton's method:

[0086]

[0087]

[0088]

[0089] Preferably, in the second case, if H is negative, it is considered that the leading edge has not reached the reservoir boundary, and it is treated as the first case.

[0090] Furthermore, this invention provides the application of the above method in the prediction of water cone morphology in fault-controlled reservoirs.

[0091] Compared with the prior art, the present invention has the following beneficial effects:

[0092] This invention fully integrates actual mining data to predict the water cone morphology of bottom-water development reservoirs. It comprehensively considers the seepage characteristics of fault-controlled bodies and the material balance equation, and intuitively shows the water cone morphology of bottom-water development reservoirs to geologists. It can better serve the dynamic prediction of bottom-water development reservoirs and also provide a reference for the preparation of development plans and the formulation of development technology policies for fault-controlled carbonate reservoirs. Attached Figure Description

[0093] Figure 1 This is a schematic diagram when the leading edge of the water cone is smaller than the control radius of the oil well.

[0094] Figure 2 This is a schematic diagram showing the water cone tip reaching the control radius of the oil well. Detailed Implementation

[0095] To make the technical means, creative features, achieved objectives, and effects of this invention readily understandable, the invention is further illustrated below with specific embodiments. However, these embodiments are merely preferred embodiments and not all embodiments. Other embodiments obtained by those skilled in the art based on the embodiments described herein without creative effort are all within the scope of protection of this invention. It is worth noting that the raw materials used in this invention are all common commercially available products, and their sources are not specifically limited. The technical and scientific terms used in the embodiments have the meanings commonly understood by those skilled in the art to which this invention pertains.

[0096] Example 1

[0097] 1. Differential equation of the control volume water cone

[0098] Differential equation of water cone interface in bottom water development reservoirs:

[0099]

[0100] Where r is the distance from the well, in meters;

[0101] p is the oil-water interface pressure at point r, in MPa;

[0102] ρ w Density of formation water, g / cm³ 3 ;

[0103] ρ o Density of formation crude oil, g / cm³ 3 ;

[0104] g is the acceleration due to gravity, 9.8 m / s². 2 ;

[0105] f(r) is the height of the water cone at point r.

[0106] The fault-controlled reservoir is a narrow strip-shaped reservoir, and its seepage characteristics exhibit linear flow along the fault direction. The formula for calculating the seepage velocity is:

[0107]

[0108] Where: v is the seepage velocity at point r, m / s;

[0109] K oThe crude oil permeability under bound water conditions in the reservoir is expressed in μm. 2 ;

[0110] μ o The viscosity of the formation crude oil is expressed in mPa·s.

[0111] g is the acceleration due to gravity, 9.8 m / s². 2 ;

[0112] f(r) is the height of the water cone at point r, in meters.

[0113] B o The volume factor of crude oil is 1;

[0114] Q o For Japanese oil production, m 3 / D;

[0115] D is the width of the fault zone, in meters;

[0116] h is the height of the oil column at the edge of the water cone, in meters.

[0117] Substituting equation (2) into equation (1) establishes the differential equation for the height of the water cone:

[0118]

[0119] 2. Prediction model for water cone in the control volume

[0120] After rearranging formula (3), we obtain the differential equation for f(r):

[0121]

[0122] This is a separable differential equation, which can be solved using the method of separation of variables:

[0123]

[0124] Where C is an undetermined constant and a is an intermediate variable.

[0125]

[0126] Variable C is determined using the mass balance method and handled in two scenarios.

[0127] First scenario: Water cone leading edge r i Less than the oil well control radius r e ,like Figure 1 As shown.

[0128] Well shaft location:

[0129]

[0130] At the leading edge of the water cone:

[0131]

[0132] Because the height of the water cone at the leading edge is 0, that is:

[0133] f(r i )=0 (9)

[0134] Substituting into formula (8) will determine C:

[0135] C = ar i (10)

[0136] Substituting into formula (5), the height of the water cone at point r can be determined:

[0137]

[0138] Formula (11) is a quadratic equation in one variable. Solving the equation yields f(r). Considering that f(r) should be less than h:

[0139]

[0140] Formula (12) establishes the relationship between the water cone height f(r) and the water cone leading edge position r. i The relational expression.

[0141] Calculate r based on the bottom water drive mass balance equation. i In bottom-water development reservoirs, pressure changes are stable, and the water cone intrusion volume equals the crude oil production volume.

[0142]

[0143] Where: N p For cumulative oil production, m 3 Φ represents reservoir porosity, 1.

[0144] Calculate the integral and rearrange to obtain information about r. i Nonlinear equations:

[0145]

[0146] Formula (14) can be solved iteratively using Newton's method, given r i Initial value, calculate the iteration value r according to formula (15-17) i * .

[0147]

[0148]

[0149]

[0150] When the iteration value r i * With r i If the error is less than 0.1, the iteration value r i * That is, the desired r i Otherwise, the iteration value r will be... i * As r i The initial value continues to iterate until the iteration value r is reached. i * With r i Until the error is less than 0.1.

[0151] Second scenario: Water cone leading edge r i Reaching the control radius r of the oil well e ,like Figure 2 As shown.

[0152] Well shaft location:

[0153]

[0154] At the leading edge of the water cone:

[0155]

[0156] Let H be the height of the water cone at the leading edge, then:

[0157] f(r e )=H (20)

[0158] Substitute formula (20) into (19) to determine C:

[0159]

[0160] Substitute into formula (5) to determine the height of the water cone at point r:

[0161]

[0162] Similarly, we can solve for f(r):

[0163]

[0164] Similarly, the volume of water cone intrusion is equal to the volume of crude oil produced:

[0165]

[0166] Integrating yields a nonlinear equation for H:

[0167]

[0168] Formula (25) is solved iteratively using Newton's method:

[0169]

[0170]

[0171]

[0172] Note: The first case is as r i Greater than r e If H is negative, it is considered that the leading edge has reached the reservoir boundary and is treated as the second case; if H is negative, it is considered that the leading edge has not reached the reservoir boundary and is treated as the first case.

[0173] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention do not depart from the essence and scope of the technical solution of the present invention.

Claims

1. A method for predicting the water cone morphology of fault-controlled reservoirs, characterized in that, Includes the following steps: S1: Based on the differential equation of the water cone interface and the formula for calculating the seepage velocity, the fault-controlled reservoir is regarded as a unidirectional linear flow, and the differential equation of the water cone height is established. S2: Determine the nonlinear equation for the height of the water cone using the mass balance method; S3: The Newton-Raphson method is used to predict the height of the water cone at different production stages and with different outputs.

2. The method according to claim 1, characterized in that, In step S1, the differential equation of the water cone interface is: Where r is the distance from the well, in meters; p is the oil-water interface pressure at point r, in MPa; ρ w Density of formation water, g / cm³ 3 ; ρ o Density of formation crude oil, g / cm³ 3 ; g is the acceleration due to gravity, 9.8 m / s². 2 ; f(r) is the height of the water cone at point r.

3. The method according to claim 1, characterized in that, In step S1, the fault-controlled reservoir is a narrow strip-type reservoir.

4. The method according to claim 1, characterized in that, In step S1, the formula for calculating the seepage velocity is: Where: v is the seepage velocity at point r, m / s; K o The crude oil permeability under bound water conditions in the reservoir is expressed in μm. 2 ; μ o The viscosity of the formation crude oil is expressed in mPa·s. g is the acceleration due to gravity, 9.8 m / s². 2 ; f(r) is the height of the water cone at point r, in meters. B o The volume factor of crude oil is 1; Q o For Japanese oil production, m 3 / D; D is the width of the fault zone, in meters; h is the height of the oil column at the edge of the water cone, in meters.

5. The method according to claim 1, characterized in that, In step S1, the differential equation for the height of the water cone is: We obtain the result by substituting formula (2) into formula (1).

6. The method according to claim 5, characterized in that, After rearranging formula (3), we obtain the differential equation for f(r):

7. The method according to claim 6, characterized in that, Formula (4) is a separable differential equation, which can be solved using the method of separation of variables: Where: C is an undetermined constant, and a is an intermediate variable; 8. The method according to claim 7, characterized in that, The value of C is determined by a mass balance method, and is handled in two cases: one is the water cone leading edge r. i Less than the oil well control radius r e Another type is the leading edge of the water cone. i Reaching the control radius r of the oil well e .

9. The method according to claim 8, characterized in that, First scenario: Water cone leading edge r i Less than the oil well control radius r e : Well shaft location: At the leading edge of the water cone: Because the height of the water cone at the leading edge is 0, that is: f(r i )＝0 (9) Substituting into formula (8) will determine C: C=on i (10) Substituting into formula (5), the height of the water cone at point r can be determined: Formula (11) is a quadratic equation in one variable. Solving the equation yields f(r). Considering that f(r) should be less than h: Formula (12) establishes the relationship between the water cone height f(r) and the water cone leading edge position r. i Relationship; Calculate r based on the bottom water drive mass balance equation. i In bottom-water development reservoirs, pressure changes are stable, and the water cone intrusion volume equals the crude oil production volume. Where: N p For cumulative oil production, m 3 ; For reservoir porosity, 1; Calculate the integral and rearrange to obtain information about r. i Nonlinear equations:

10. The method according to claim 8, characterized in that, Second scenario: Water cone leading edge r i Reaching the control radius r of the oil well e : Well shaft location: At the leading edge of the water cone: Let H be the height of the water cone at the leading edge, then: f(r e )=H(20) Substitute formula (20) into (19) to determine C: Substitute into formula (5) to determine the height of the water cone at point r: Similarly, we can solve for f(r): Similarly, the volume of water cone intrusion is equal to the volume of crude oil produced: Integrating yields a nonlinear equation for H:

11. The method according to claim 9, characterized in that, Formula (14) can be solved iteratively using Newton's method, given r i Initial value, calculate the iteration value r according to formula (15-17) i * :

12. The method according to claim 11, characterized in that, When the iteration value r i * With r i If the error is less than 0.1, the iteration value r i * That is, the desired r i Otherwise, the iteration value r will be... i * As r i The initial value continues to iterate until the iteration value r is reached. i * With r i Until the error is less than 0.

1.

13. The method according to claim 9, characterized in that, The first case is as follows: i Greater than r e They believed that the leading edge had reached the reservoir boundary and treated it as the second scenario.

14. The method according to claim 10, characterized in that, Formula (25) is solved iteratively using Newton's method:

15. The method according to claim 10, characterized in that, In the second case, if H is negative, it is assumed that the leading edge has not reached the reservoir boundary, and it is treated as the first case.

16. The application of the method according to any one of claims 1-15 in the prediction of water cone morphology in fault-controlled reservoirs.

Images