Quantitative identification method for water invasion volume based on semi-ellipsoid radial seepage model

Abstract

The invention relates to a water invasion volume quantitative identification method based on a semi-ellipsoid radial seepage model, and belongs to the technical field of oil reservoir engineering. The method comprises the following specific steps that dimensionless time tD and pressure increment delta pj of an oil well are calculated; calculating dynamic reserves without water invasion according to the dynamic data of the oil well and a flowing substance balance equation; calculating a water invasion coefficient; the water invasion volume is obtained. The invention relates to a novel method for calculating invasion volumes of different types of water bodies invaded into an oil reservoir by radial flow edge and bottom water by utilizing a semi-ellipsoid geometric model of a Van Everdex-Hust equation principle, which can solve the problem of quantification of the invasion volumes of the water bodies at any moment in the water invasion process of the edge and bottom water oil reservoir. The influence of unstable seepage on the water invasion process is considered, the basic law of fluid flowing in the water invasion process is met, meanwhile, the water invasion coefficient calculation method which does not need to estimate the size of an oil reservoir is provided, and the overall error is small.

Description

TECHNICAL FIELD

[0001] The present application relates to a water body invasion volume quantitative identification method based on a semi-ellipsoid radial seepage model, and belongs to the technical field of oil reservoir engineering. BACKGROUND

[0002] Most oil reservoirs are connected with external natural water areas, including open water with external recharge, or limited edge water and bottom water. The area of the natural water body of some oil reservoirs is large and the energy is high, which has a significant impact on the development dynamics of the oil reservoir, so it is very important to accurately quantify the water body invasion volume. For oil reservoirs with active edge water and bottom water, as crude oil is continuously produced during the development of the oil reservoir, the decrease in formation pressure in the oil reservoir will gradually be transmitted to the external natural water in an elastic manner, causing the elastic expansion of formation water and formation rock in the natural water body. The pressure difference between the natural water body and the oil reservoir can cause the natural water to continuously flow into the oil reservoir. Under the driving of the pressure difference, the water body will continuously flow to the bottom of the well to offset or delay the pressure drop, thereby causing water invasion in the oil reservoir. Due to the different geometric shapes of the oil-water interface in different reservoirs and the different flow directions of the water body, the pressure drop between the natural water body and different reservoirs is different, and the water inflow of different reservoirs is quite different. However, during the development of the oil reservoir, the main reason affecting the development effect is the invasion of the water body. Once the oil well encounters water, the water content of the straight well continuously increases. In general, the formation with a larger water body invasion volume may result in a higher liquid production rate of the oil reservoir, while the oil production of the oil well continuously decreases. The continuous increase in water production leads to water flooding of the oil well, which faces shut-in, seriously affecting the development effect and the ultimate recovery of the oil reservoir.

[0003] In order to determine the effect of aquifer on oil production, the amount of water entering the reservoir from the aquifer must be estimated, so the water body invasion volume analysis is the preliminary work of reservoir dynamic analysis, water injection production plan determination and water control measure implementation. At present, many scholars have proposed different models to estimate the water inflow, these models are suitable for different flow states, the commonly used water body invasion volume calculation models include steady state (Schilthuis model), pseudo steady state (Fetkovich model) and non steady state (van Everdingen-Hust model), and when the Schilthuis model is used to calculate the steady state water invasion, the model describes the water invasion of the water layer to the reservoir with constant outer boundary pressure; when the Fetkovich model is used to calculate the non steady state water invasion, it is assumed that the oil production index is constant during the entire reservoir production period, which means that the water flow state in the water layer is always stable, so any transient effect caused by the pressure change in the oil and gas reservoir is ignored; when the Van Everdingen-Hust model is used to calculate the water body invasion volume, the method is based on the solution of the plane radial flow diffusion equation, and the solutions can be used to calculate the water body invasion volume at different times for all flow states occurring in the water layer. The Darcy equation is used to describe the relevant flow rate of the aquifer, and when calculating the water invasion coefficient, the size of the water body and the reservoir must be estimated, the water body may be an infinite water body with external supply, or a finite water body with a boundary, so there is a certain error in the estimation of the size of the reservoir, thereby causing some errors in the calculated water body invasion volume result.

[0004] At present, these calculation models always assume that the reservoir boundary is approximately circular in shape. However, when the fluid moves in multiple directions towards the wellbore perforation in the reservoir, radial flow occurs, thereby generating equipotential lines, which are not consistent with the approximate circular geometry, and the actual reservoir can be simulated by a semi-ellipsoidal body, and the actual reservoir area shape can be better approximated by an elliptical boundary. SUMMARY

[0005] In order to solve the problem that the Van Everdingen-Hust equation in the background art adopts the plane radial flow model and it is difficult to accurately estimate the size of the water body and the reservoir, thereby causing some errors in the calculated water body invasion volume result, the application provides a water body invasion volume quantitative identification method based on a semi-ellipsoidal radial seepage model, which uses a model more consistent with the natural water flow state of the reservoir to describe the edge and bottom water inflow state, and avoids predicting the size of the reservoir when calculating the water invasion coefficient parameter, so that the water body invasion volume of the edge and bottom water reservoir can be more accurately calculated.

[0006] The technical scheme adopted by the application is a water body invasion volume quantitative identification method based on a semi-ellipsoidal radial seepage model, and the specific steps are as follows:

[0007] S1, calculate the dimensionless time t of the oil well. D and pressure increment Δp j ;

[0008] S2, calculate the dynamic reserves without water intrusion based on oil well dynamic data and the flow material balance equation;

[0009] S3, calculate the water intrusion coefficient k';

[0010] S4 yields the volume of water intrusion.

[0011] Furthermore, the dimensionless time is calculated using formula (1);

[0012]

[0013] In the formula r w The outer radius of the oil well; Porosity; k is permeability; t is time; c t The overall compression factor is μ. w This refers to the viscosity of water.

[0014] Furthermore, the pressure increment Δp j During the calculation process, when j = 0 or 1, When j>2 Where j is the j-th time and i is any time other than j.

[0015] Furthermore, the fluid balance equation is as follows: in, The average pressure at a reservoir radius of R, expressed in MPa; p wf B is the bottom hole flowing pressure, in MPa. o B is the crude oil volume coefficient; oi b is the initial volume coefficient of crude oil; pss N is the epidermal coefficient. p Cumulative oil production, in tons; c t q is the overall compression ratio; N is the oil production rate; q is the oil yield. o This refers to the dynamic storage capacity before water intrusion.

[0016] Furthermore, the water intrusion coefficient k' is calculated using formula (2);

[0017] k′=2N o c t (2)

[0018] In the formula c t N is the overall compression coefficient. oThe dynamic reserves without water invasion.

[0019] Further, the water invasion volume W e (t j ) is calculated by formula (3).

[0020] W e (t j ) = k' Δp j Q D (t D ) (3)

[0021] Wherein, k' is the water invasion coefficient, Δp j is the pressure increment, Q D (t D ) is the annular water layer function, t D is the dimensionless time.

[0022] Further, the comprehensive compression coefficient, the crude oil volume coefficient, the crude oil initial volume coefficient, the bottom hole flowing pressure, and the skin factor are obtained from the geological basic parameters; the cumulative oil production is obtained from the daily production data of the oil reservoir.

[0023] Further, the oil well outer radius, the porosity, the permeability, the comprehensive compression coefficient, and the viscosity of water are obtained from the geological basic parameters.

[0024] Further, the water invasion coefficient k' = 2N o c t is according to the definition of Van Everdingen-Hurst Using the principle of Van Everdingen-Hust equation, the water invasion coefficient when the oil reservoir is regarded as a uniform compressible fluid and the oil well flows radially is expressed as Therefore, based on the principle of spherical radial flow, when the oil reservoir is regarded as a semi-ellipsoidal model, the water invasion coefficient can be expressed as: Using the flow material balance equation when , the dynamic reserves without water invasion at the initial stage of oil well production can be obtained That is, the water invasion coefficient expression k' = 2N o c t can be derived.

[0025] Further, the water invasion volume W e (t j ) = k' Δp j Q D (t D ) is derived as follows: first, according to the definition of Van Everdingen-Hust dimensionless radius ratio r D , dimensionless time tD and dimensionless pressure P D Neglecting the elastic release of lithology and water, fluid-structure coupling and interwell interference, the basic differential equation of the spherical radial seepage reservoir system of constant compressibility fluid is established:

[0026]

[0027]

[0028]

[0029]

[0030] wherein: r D is the dimensionless radius ratio; r w is the outer radius of the oil well; t D is the dimensionless time; r0 is the outer radius of the oil reservoir; is the porosity; k is the permeability; c t is the comprehensive compressibility coefficient; μ w is the viscosity of water; P D is the dimensionless pressure; P wf is the bottom-hole flowing pressure; the basic differential equation of the dimensionless form of the oil reservoir system with spherical symmetry is obtained by substituting formula (1, 5, 6) into formula (4):

[0031]

[0032] Subsequently, Van Everdingen-Hust applies Laplace transform to take constant pressure as the boundary condition, which assumes that water flows into the oil reservoir at the boundary of the oil reservoir and the water layer with the flow rate of e w , and the pressure drop at t=0 at the boundary is Δp, then the dimensionless variable q D of the semi-ellipsoidal model can be written as formula (8), wherein h is the effective thickness of the oil reservoir:

[0033]

[0034] Therefore, the water body invasion volume at different times can be expressed as:

[0035]

[0036] Van Everdingen-Hust definition has proved that P D (t D ) and Q D (t D ) are equal to t D in the convolution integral from 0 to t D , which can be expressed as follows:

[0037]

[0038] Thus the water body invasion volume can be obtained.

[0039] The application provides a water body invasion volume quantitative identification method based on a semi-ellipsoid radial seepage model. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0041] Figure 1 is a semi-ellipsoid reservoir schematic diagram surrounded by uniform concentric water layers;

[0042] Figure 2 is a semi-ellipsoid radial seepage model schematic side view and top view;

[0043] Figure 3 is an oil well P1 well production initial stage normalized production fitting straight line relationship diagram;

[0044] Figure 4 is an oil well P2 well production initial stage normalized production fitting straight line relationship diagram. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the following will combine the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. The following description of at least one exemplary embodiment is actually only illustrative, but not as any limitation on the present application and its application or use. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0046] In order to further understand the inventive content of the present application, the technical solution is further described below in combination with specific embodiments.

[0047] Embodiment 1: In order to solve the technical problem that there is a certain error in the planar radial flow model for the commonly used van Everdingen-Hust equation in the prior art, a differential equation based on spherical radial seepage theory is provided, a semi-ellipsoidal radial seepage model more consistent with the actual production changes of the oil reservoir is used, and a flow material balance equation is used to analyze the change process of water invasion of the oil well from the oil reservoir engineering meaning, so that the water invasion volume of the oil reservoir at any moment can be more accurately determined, the size of the oil reservoir does not need to be predicted, and the water invasion volume of the oil reservoir invaded by the edge and bottom water at any moment can be more accurately calculated.

[0048] The present application adopts the solution based on the spherical radial flow equation of the normal compressible fluid, the position of the external boundary depends on the distance moment when the obvious pressure response occurs, that is, the external boundary can change position with time, which is consistent with the oil reservoir system, so the solution is suitable for finite or infinite water layer. The initial condition of the equation is that the internal boundary pressure is constant, that is, the pressure at the interface between the oil and gas reservoir and the water layer is constant, that is, the flow rate is a function of time; the rate of the inflow terminal of the internal boundary is constant, that is, the pressure drop is a function of time, and the water invasion coefficient is determined from the oil reservoir engineering meaning, and the method for calculating the water invasion volume of the oil reservoir without edge and bottom water is as follows:

[0049] According to the dimensionless radius ratio r D , the dimensionless time t D , and the dimensionless pressure P D , without considering the lithology and elastic release of water, without considering the fluid-solid coupling, without considering the well interference; the basic differential equation of the spherical radial seepage reservoir system of the normal compressible fluid is given:

[0050]

[0051]

[0052]

[0053]

[0054] Wherein: r D is the dimensionless radius ratio; r w is the outer radius of the oil well; t D is the dimensionless time; r0 is the outer radius of the oil layer; is the porosity; k is the permeability; c t is the comprehensive compression coefficient; μ w is the viscosity of water; P D is the dimensionless pressure; Pwf The basic differential equation for the bottom hole flowing pressure, i.e. the dimensionless form of the reservoir system with spherical symmetry, is:

[0055]

[0056] Van Everdingen-Hust applied the Laplace transform with constant pressure as the boundary condition, which assumes that water flows downstream through the boundary of the reservoir and water layer with e w = 0 at t = 0, the dimensionless variable q D of the semi-ellipsoidal model can be written as:

[0057]

[0058] Therefore, the water body invasion volume at different times can be expressed as:

[0059]

[0060]

[0061] Van Everdingen-Hust has proved that P D (t D ) and Q D (t D ) are equal to t D in the convolution integral from 0 to t D , which can be expressed as:

[0062]

[0063] The expression of the water body invasion volume can be obtained as follows, using the following formula to calculate the water body invasion volume according to the annular water layer function, dimensionless time, outer radius of the oil layer, porosity, comprehensive compression coefficient, and viscosity of water:

[0064] W e (t j ) = k' ΔPQ D (t D ) (3)

[0065] In the formula, k' is the water invasion coefficient, Δp j is the pressure increment, p j is the formation pressure at time t j , when j = 0 or 1, when j > 2, where j is the jth time, i is any time other than the jth time; Q D (t D ) is the annular water layer function, tD Dimensionless time.

[0066] where k' is calculated by formula (2):

[0067] k' = 2N o c t (2)

[0068] When the reservoir type is a complex fault block edge-bottom water reservoir, the heterogeneity is strong, the fluid connectivity is different, and the size and effective thickness of the oil layer are also difficult to obtain. According to the water invasion coefficient defined by Hurst It can be understood as the invasion amount of edge-bottom water per unit pressure drop in the oilfield development process. Using the principle of VanEverdingen-Hust equation, the water invasion coefficient when the oil well flows radially can be expressed as It can be seen from the formula that its size is mainly related to the cross-sectional area of the oil and gas accumulation area and the effective thickness of the reservoir, and secondly related to the viscosity of water, the permeability and porosity of the rock in the water-bearing layer. In addition to the viscosity ratio of oil and water and the elastic expansion coefficient of the water body, the water invasion coefficient can be expressed as: The water invasion in the reservoir can be understood as the elastic expansion of the rock pores and the fluid, including the primary water and the primary oil. When the reservoir is in the elastic stage and the oil well produces initially without water invasion, the dynamic reserves can be expressed as The normalized production fitted by the flow material balance equation and the normalized cumulative oil production are in a linear relationship, and when , the dynamic reserves N of the oil well at the initial production without water invasion can be obtained o , that is, the water invasion coefficient expression k' = 2N o c t , which avoids the prediction of the radius of the oil layer in the edge-bottom water reservoir.

[0069] The expression of the flow material balance equation is as follows:

[0070]

[0071] where, is the average pressure at the reservoir radius R, MPa; p wf is the bottom hole flowing pressure, MPa; B o is the volume coefficient of crude oil; B oi is the initial volume coefficient of crude oil; b pss is the skin factor; N p is the cumulative oil production, tons; c tis the compressibility factor; q is the oil production; N is the dynamic reserve o is the dynamic reserve without water invasion.

[0072] Taking the P1 well in the study area as an example, combined with the static and dynamic data of the oil well P1 such as permeability, porosity, viscosity of water and compressibility factor, the dimensionless time t is calculated according to formula (1), and t = 8.117 is obtained. The pressure difference table is calculated by superimposing each pressure drop effect, as shown in Table 1. On this basis, the dynamic reserve N0 of the P1 well at the initial stage of production without water invasion is calculated according to the rearranged expression of the flow material balance equation, and N0 = 116*10 D t is obtained, as shown in Table 1. On this basis, the dynamic reserve N0 of the P1 well at the initial stage of production without water invasion is calculated according to the rearranged expression of the flow material balance equation, and N0 = 116*10 4 t is obtained, as shown in Table 1. On this basis, the dynamic reserve N0 of the P1 well at the initial stage of production without water invasion is calculated according to the rearranged expression of the flow material balance equation, and N0 = 116*10 Figure 3 t is obtained, as shown in Table 1. On this basis, the dynamic reserve N0 of the P1 well at the initial stage of production without water invasion is calculated according to the rearranged expression of the flow material balance equation, and N0 = 116*10

[0073] Table 1 Pressure difference table of P1 well

[0074] Time (years) Δp (Mpa) Time (years) Δp (Mpa) 0 2.574 9 0.279 1 5.975 10 0.381 2 7.219 11 3.738 3 5.427 12 4.193 4 2.050 13 1.027 5 0.791 14 1.171 6 0.568 15 1.028 7 0.363 16 0.313 8 0.269 17

[0075] Table 2 Water body invasion volume calculation table of P1 well

[0076] n j jt D ]]> Q D (j△t D )]]> △p ∑ Cumulative We(t) 1 0 0.000 0.000 2.574 0.000 0.000 2 1 8.117 5.230 5.975 13.463 8841.531 3 2 16.234 8.920 7.219 54.209 35601.652 4 3 24.351 10.390 5.427 117.795 77361.082 5 4 32.468 11.210 2.050 183.708 120649.647 6 5 40.585 11.490 0.791 230.688 151503.188 7 6 48.702 11.520 0.568 258.037 169464.414 8 7 56.819 11.890 0.363 274.545 180306.048 9 8 64.936 11.910 0.269 285.384 187424.707 10 9 73.053 11.920 0.279 293.171 192538.718 11 10 81.170 11.940 0.381 299.173 196480.805 12 11 89.287 11.960 3.738 304.182 199770.004 13 12 97.404 11.980 4.193 326.589 214485.741 14 13 105.521 12.000 1.027 363.856 238960.700 15 14 113.638 12.000 1.171 391.159 256891.866 16 15 121.755 12.000 1.028 410.840 269817.599 17 16 129.872 12.000 0.313 426.835 280322.075 18 17 137.989 12.000 436.339 286563.901

[0077] Example 2: Taking the P2 well in the study area as an example, combined with the data of the oil well P2, the dimensionless time t is calculated according to formula (1), and t = 117.517 is obtained. The pressure difference table is calculated by superimposing each pressure drop effect, as shown in Table 3. On this basis, the dynamic reserve N0 of the P2 well at the initial stage of production without water invasion is calculated according to the rearranged expression of the flow material balance equation, and N0 = 56*10 D t is obtained, as shown in Table 3. On this basis, the dynamic reserve N0 of the P2 well at the initial stage of production without water invasion is calculated according to the rearranged expression of the flow material balance equation, and N0 = 56*10 4 t is obtained, as shown in Table 3. On this basis, the dynamic reserve N0 of the P2 well at the initial stage of production without water invasion is calculated according to the rearranged expression of the flow material balance equation, and N0 = 56*10 Figure 4 t is obtained, as shown in Table 3. On this basis, the dynamic reserve N0 of the P2 well at the initial stage of production without water invasion is calculated according to the rearranged expression of the flow material balance equation, and N0 = 56*10

[0078] Table 3 Pressure difference table of P2 well

[0079] Time (years) Δp (Mpa) Time (years) Δp (Mpa) 0 0.845 8 0.578 1 3.856 9 1.366 2 4.499 10 3.044 3 1.642 11 3.060 4 0.429 12 2.235 5 0.877 13 1.081 6 1.811 14 0.164 7 1.068 15

[0080] Table 4 Water body invasion volume calculation table of P2 well

[0081] n j jt D ]]> QD(j△t D )]]> △p ∑ Cumulative We(t) 1 0 0.000 0.000 0.845 0.000 0.000 2 1 117.517 12.000 3.856 10.140 12859.248 3 2 235.034 12.000 4.499 56.413 71543.007 4 3 352.551 12.000 1.642 110.400 140008.713 5 4 470.068 12.000 0.429 130.104 164997.846 6 5 587.586 12.000 0.877 135.251 171525.033 7 6 705.103 12.000 1.181 145.779 184876.917 8 7 822.620 12.000 1.068 159.955 202854.423 9 8 940.137 12.000 0.578 172.766 219101.759 10 9 1057.654 12.000 1.366 179.705 227901.510 11 10 1175.171 12.000 3.044 196.094 248686.088 12 11 1292.688 12.000 3.060 232.627 295017.118 13 12 1410.205 12.000 2.235 269.344 341581.069 14 13 1527.722 12.000 1.081 296.165 375596.379 15 14 1645.240 12.000 0.164 309.134 392042.689 16 15 1762.757 12.000 311.099 394535.645

[0082] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for quantitatively identifying the volume of water intrusion based on a semi-ellipsoidal radial seepage model, characterized in that, The specific steps are as follows: S1, calculate the dimensionless time t of the oil well. D and pressure increment Δp j ; S2, calculate the dynamic reserves without water intrusion based on oil well dynamic data and the flow material balance equation; S3, calculate the water intrusion coefficient k'; S4 yields the volume of water intrusion.

2. The method for quantitative identification of water intrusion volume based on a semi-ellipsoidal radial seepage model according to claim 1, characterized in that, Dimensionless time is calculated using formula (1); In the formula r w The outer radius of the oil well; Porosity; k is permeability; t is time; c t The overall compression factor is μ. w This refers to the viscosity of water.

3. The method for quantitative identification of water intrusion volume based on a semi-ellipsoidal radial seepage model according to claim 2, characterized in that, The outer radius of the oil well, porosity, permeability, overall compressibility coefficient, and water viscosity are obtained from basic geological parameters.

4. The method for quantitative identification of water intrusion volume based on a semi-ellipsoidal radial seepage model according to claim 1, characterized in that, Pressure increment Δp j During the calculation process, when j = 0 or 1, When j>2 Where j is the j-th time and i is any time other than j.

5. The method for quantitative identification of water intrusion volume based on a semi-ellipsoidal radial seepage model according to claim 1, characterized in that, The mass balance equation for flow is in, The average pressure at a reservoir radius of R, expressed in MPa; p wf B is the bottom hole flowing pressure, in MPa. o B is the crude oil volume coefficient; oi b is the initial volume coefficient of crude oil; pss N is the epidermal coefficient. p Cumulative oil production, in tons; c t q is the overall compression ratio; N is the oil production rate; q is the oil yield. o This refers to the dynamic storage capacity before water intrusion.

6. The method for quantitative identification of water intrusion volume based on a semi-ellipsoidal radial seepage model according to claim 5, characterized in that, The comprehensive compressibility factor, crude oil volume factor, crude oil initial volume factor, bottom hole flowing pressure, and skin factor are obtained from basic geological parameters; the cumulative oil production is obtained from the reservoir's daily production data.

7. The method for quantitative identification of water intrusion volume based on a semi-ellipsoidal radial seepage model according to claim 5, characterized in that, The water intrusion coefficient k' is calculated using formula (2); k'=2N o c t (2) In the formula c t N is the overall compression coefficient. o This refers to the dynamic storage capacity before water intrusion.

8. The method for quantitative identification of water intrusion volume based on a semi-ellipsoidal radial seepage model according to claim 7, characterized in that, Water intrusion volume W e (t j It is calculated from formula (3); W e (t j )=k'Δp j Q D (t D ) (3) In the formula, k' is the water erosion coefficient, Δp j For pressure increment, Q D (t D ) is the annular water layer function, t D It is dimensionless time.

9. The method for quantitative identification of water intrusion volume based on a semi-ellipsoidal radial seepage model according to claim 7, characterized in that, Water intrusion coefficient k'=2N0c t It is defined according to Van Everdingen-Hurst. Using the Van Everdingen-Hust equation, the reservoir is considered as a homogeneous compressible fluid, and the water intrusion coefficient during radial flow in the well is expressed as: Therefore, based on the principle of spherical radial flow, when the reservoir is considered as a semi-ellipsoidal model, the water intrusion coefficient can be expressed as: Using the fluid balance equation when At that time, the dynamic reserves during the initial stage of oil well production without water intrusion can be obtained. The expression for the water intrusion coefficient k' = 2N can then be derived. o c t .

10. The method for quantitative identification of water intrusion volume based on a semi-ellipsoidal radial seepage model according to claim 8, characterized in that, Water intrusion volume W e (t j )=k'Δp j Q D (t D The derivation process is as follows: First, based on the dimensionless radius ratio r defined by Van Everdingen-Hust... D Dimensionless time t D and dimensionless pressure P D Ignoring lithology and the release of elastic energy of water, fluid-structure interaction, and inter-well interference, the basic differential equations for a normally compressible fluid spherical radial flow reservoir system are established: Where: r D The ratio of dimensionless radii; r w t is the outer radius of the oil well; D The time is dimensionless; r0 is the outer radius of the oil layer; Porosity; k is permeability; c t The overall compression factor is μ. w P is the viscosity of water. D P is a dimensionless pressure. wf Let be the bottom hole flowing pressure; substituting equations (1, 5, 6) into equation (4), we obtain the dimensionless basic differential equation of the reservoir system with spherical symmetry: Van Everdingen-Hust then applied the Laplace transform, using constant pressure as the boundary condition, assuming that water moves at an et... w The flow rate crosses the boundary between the oil reservoir and the water layer and enters the oil reservoir. At this boundary, the pressure drop at t=0 is Δp. Then, the dimensionless variable q of the semi-ellipsoidal model... D According to Darcy's law, it can be written as formula (8), where h is the effective thickness of the reservoir: Therefore, the volume of water intrusion at different times can be expressed as: The Van Everdingen-Hust definition has proven that P D (t D ) and Q D (t D ) from 0 to t D The convolution integral is equal to t D It can be expressed as follows: Therefore, the volume of water intrusion can be obtained.

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