Sensitive elastic parameter, parameter model and water saturation determination method and system

Abstract

The embodiment of the invention provides a sensitive elastic parameter, parameter model and water saturation determination method and system, and belongs to the field of seismic exploration. The determination method comprises the following steps: scanning a rock sample to obtain a three-dimensional digital rock core model which comprises a rock matrix model and a pore model of a three-dimensional digital rock core; according to the rock matrix model and the pore model of the three-dimensional digital core, constructing an elastic parameter model of the three-dimensional digital core under a plurality of water saturations; simulating the elastic parameter model of the three-dimensional digital core under the plurality of water saturations to obtain elastic simulation parameters; and determining an elastic parameter sensitive to the water saturation according to the elastic simulation parameter and a sensitivity threshold. According to the method, the problem of low sensitivity of conventional elastic parameters to the water saturation is solved, and the precision of calculating the water saturation is improved. In addition, by means of the water saturation prediction model, the water saturation of the target shaft can be effectively predicted.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic exploration, and in particular to a method and system for determining a sensitive elastic parameter, a parameter model, and water saturation. Background Art

[0002] Tight reservoirs are unconventional reservoirs with low porosity and low permeability. Studying the relationship between their elastic parameters and fluid saturation is of great significance for the exploration and development of oil and gas reservoirs.

[0003] In the prior art, the relationship between the elastic properties of rocks and water saturation is mainly studied through rock physics experiments. However, there have always been difficulties in using rock physics experiments to study the relationship between the elastic parameters and water saturation of tight reservoirs containing a certain amount of non-connected isolated pores, which are mainly manifested in two aspects: first, it is difficult to determine the original fluid type in the non-connected isolated pores, which makes it difficult to calculate the water saturation; second, due to the low porosity and low permeability characteristics of tight reservoirs, there are problems of insufficient saturation and high bound water saturation during saturation and dehydration, resulting in certain errors in the measured relationship between water saturation and elastic parameters.

[0004] The numerical simulation of three-dimensional digital core elastic parameters can quantitatively study the influence of rock matrix, pore structure and pore fluid on rock elastic parameters. The existing numerical simulation methods mainly use the finite element method to solve the stress-strain field under the minimum potential energy condition to infer the conventional elastic parameters.

[0005] From the current calculation methods of three-dimensional digital core elastic parameters, there are two main problems: on the one hand, the stress-strain method is difficult to stably and accurately calculate the elastic modulus of dry (pore-filled vacuum, that is, the longitudinal and transverse wave velocity values ​​are zero) rocks, which affects the calculation accuracy of water saturation; on the other hand, the stress-strain method cannot simulate the propagation of elastic wave fields in three-dimensional digital cores. Summary of the invention

[0006] The purpose of the embodiment of the present invention is to provide a method and system for determining sensitive elastic parameters, parameter models, and water saturation. The method uses sensitivity to determine elastic parameters that are sensitive to water saturation, while the prior art directly uses conventional elastic parameters, which have very low sensitivity to water saturation. Therefore, the method solves the problem of low sensitivity of conventional elastic parameters of tight reservoirs to water saturation in the prior art, thereby improving the accuracy of calculating water saturation. In addition, the elastic parameter model is further constructed using elastic parameters that are sensitive to water saturation, which can be effectively applied to the prediction of water saturation of the target wellbore.

[0007] In order to achieve the above-mentioned purpose, an embodiment of the present invention provides a method for determining elastic parameters that are sensitive to water saturation, the determination method comprising: scanning a rock sample to obtain a three-dimensional digital core model, wherein the three-dimensional digital core model comprises a rock matrix model and a pore model of the three-dimensional digital core; constructing an elastic parameter model of the three-dimensional digital core at multiple water saturations according to the rock matrix model and the pore model of the three-dimensional digital core; simulating the elastic parameter model of the three-dimensional digital core at multiple water saturations to obtain elastic simulation parameters; and determining the elastic parameters that are sensitive to water saturation according to the elastic simulation parameters and a sensitivity threshold.

[0008] Optionally, the elastic parameter model of the three-dimensional digital core at multiple water saturations includes an elastic parameter model of the pores of the three-dimensional digital core, and constructing the elastic parameter model of the pores at multiple water saturations of the three-dimensional digital core includes: based on the pore model of the three-dimensional digital core, obtaining multiple water saturations corresponding to the fluid type in the pore according to multiple preset water saturations, and according to the fluid type in the pore, obtaining elastic parameters of multiple water saturations corresponding to the fluid type in the pore, so as to construct the elastic parameter model of the pores at multiple water saturations of the three-dimensional digital core.

[0009] Optionally, the pore model based on the three-dimensional digital core, obtaining multiple water saturations corresponding to the fluid type in the pore according to multiple preset water saturations includes: determining a minimum value n of the number of water layers k to be filled according to the preset water saturation S and the following formula: in, is the porosity of the i-th layer, N is the number of pore layers, represents the pore ratio of water, k represents the number of water layers to be filled; according to the minimum value n and the pore ratio of water A plurality of water saturations corresponding to the fluid types in the pores are obtained.

[0010] Optionally, the elastic simulation parameters include longitudinal wave velocity, shear wave velocity and elastic parameters, and the elastic parameters include the ratio of longitudinal to shear wave velocity, bulk modulus, Poisson's ratio, Lamé constant and shear modulus; determining the elastic parameters sensitive to water saturation based on the elastic simulation parameters and the sensitivity threshold comprises: determining a sensitivity function of the elastic parameters and a sensitivity function of new elastic parameters based on the elastic simulation parameters; determining the sensitivity of the elastic parameters and / or the new elastic parameters in a specific water saturation range based on the sensitivity function of the elastic parameters and / or the sensitivity function of the new elastic parameters; and determining the elastic parameters and / or the new elastic parameters having a sensitivity greater than the sensitivity threshold as elastic parameters sensitive to water saturation.

[0011] Optionally, determining the sensitivity function of the new elastic parameter according to the elastic simulation parameter includes: determining the new elastic parameter according to the following formula, wherein the new elastic parameter includes the pore space modulus M and the pore fluid bulk modulus K f :M=(K sat -K dry ) / β 2 , And according to the new elastic parameter, determine the sensitivity function of the new elastic parameter, where K s represents the bulk modulus of the rock matrix, K dry represents the bulk modulus of dry rock, K s With K dry Determined according to the longitudinal wave velocity, shear wave velocity and elastic parameters; K sat represents the bulk modulus of fluid-saturated rock, K sat Determined according to the longitudinal wave velocity, the shear wave velocity and the elastic parameters; Represents the porosity of a rock sample.

[0012] Optionally, determining the sensitivity function of the elastic parameter or the new sensitivity function of the elastic parameter comprises: determining the sensitivity function of the elastic parameter according to y(S w ) and the following formula to determine y(S w )’s sensitivity function A w : Among them, S w represents water saturation, y(S w )) represents the elastic parameters or new elastic parameters at different water saturations.

[0013] On the other hand, the present invention also provides a method for predicting a saturation model of water saturation, the method comprising: determining an elastic parameter K sensitive to water saturation according to the method for determining an elastic parameter sensitive to water saturation f ; Based on the elastic parameter K that is sensitive to water saturation f And the following formula, construct the water saturation prediction model: S w =a*K f b , where S w Indicates water saturation, K f represents the bulk modulus of the saturated fluid, and a and b represent the unknown coefficients of the water saturation prediction model.

[0014] In another aspect, the present invention further provides a method for determining water saturation of a target wellbore, the method comprising: determining a bulk modulus K of a rock matrix in the target wellbore according to a plurality of parameter curves of the target wellbore; s, the bulk modulus K of dry rock dry and the bulk modulus K of the saturated fluid rock sat ; According to the bulk modulus K of the rock matrix in the target wellbore s , the bulk modulus K of dry rock dry , bulk modulus of saturated fluid rock K sat and the method for determining the elastic parameter sensitive to water saturation, determining the bulk modulus K of the pore fluid f ; and according to the water saturation prediction model and the pore fluid bulk modulus K f , determine the target wellbore water saturation.

[0015] Optionally, the multiple parameter curves include a longitudinal wave velocity curve, a shear wave velocity curve, a density curve and a saturation curve.

[0016] Correspondingly, the present invention also provides a system for determining elastic parameters sensitive to water saturation, the determination system comprising: a scanning device for scanning a rock sample to obtain a three-dimensional digital core model, wherein the three-dimensional digital core model comprises a rock matrix model and a pore model of the three-dimensional digital core; a construction device for constructing an elastic parameter model of the three-dimensional digital core at multiple water saturations according to the rock matrix model and the pore model of the three-dimensional digital core; an acquisition device for simulating the elastic parameter model of the three-dimensional digital core at multiple water saturations to obtain elastic simulation parameters; and a determination device for determining the elastic parameters sensitive to water saturation according to the elastic simulation parameters and a sensitivity threshold.

[0017] Accordingly, the present invention also provides a water saturation prediction model system, the system comprising: a construction device for determining the elastic parameter K sensitive to water saturation determined by the determination method; f ; Based on the elastic parameter K that is sensitive to water saturation f And the following formula, construct the water saturation prediction model: S w =a*K f b , where S w Indicates water saturation, K f represents the bulk modulus of the saturated fluid, and a and b represent the unknown coefficients of the water saturation prediction model.

[0018] Accordingly, the present invention also provides a system for determining the water saturation of a target wellbore, the system comprising: a first determining device for determining the bulk modulus K of the rock matrix in the target wellbore according to a plurality of parameter curves of the target wellbore; s , the bulk modulus K of dry rock dry and the bulk modulus K of the saturated fluid rocksat ; A second determining device for determining the bulk modulus K of the rock matrix in the target wellbore s , the bulk modulus K of dry rock dry , bulk modulus of saturated fluid rock K sat And the method for determining the elastic parameter sensitive to water saturation, determining the bulk modulus K of the pore fluid f ; and a third determining device for determining the water saturation prediction model and the pore fluid bulk modulus K f , determine the target wellbore water saturation.

[0019] Through the above technical solution, the rock sample is scanned to obtain a three-dimensional digital core model, wherein the three-dimensional digital core model includes a rock matrix model and a pore model of the three-dimensional digital core; based on the rock matrix model and the pore model of the three-dimensional digital core, an elastic parameter model of the three-dimensional digital core at multiple water saturations is constructed; the elastic parameter model of the three-dimensional digital core at multiple water saturations is simulated to obtain elastic simulation parameters, wherein the elastic model parameters include both conventional elastic parameters and new elastic parameters; and then the elastic parameters with a sensitivity greater than a sensitivity threshold and / or the new elastic parameters are determined as elastic parameters sensitive to water saturation. After the elastic parameters sensitive to water saturation are determined, a water saturation prediction model is constructed using the elastic parameters sensitive to water saturation, and the prediction model is used to predict the water saturation in the target wellbore or predict the water saturation in earthquakes.

[0020] Other features and advantages of the embodiments of the present invention will be described in detail in the subsequent detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The accompanying drawings are used to provide a further understanding of the embodiments of the present invention and constitute a part of the specification. Together with the following specific implementations, they are used to explain the embodiments of the present invention, but do not constitute a limitation on the embodiments of the present invention. In the accompanying drawings:

[0022] Figure 1 is a flow chart of a method for determining elastic parameters sensitive to water saturation provided by an embodiment of the present invention;

[0023] Figure 2 is a flow chart of constructing an elastic parameter model provided by an embodiment of the present invention;

[0024] Figure 3a It is a rock matrix model of a three-dimensional digital core provided by an embodiment of the present invention;

[0025] Figure 3b It is a rock pore model of a three-dimensional digital core provided by an embodiment of the present invention;

[0026] Figure 4 It is a saturated gas velocity model of a three-dimensional digital core provided by an embodiment of the present invention;

[0027] Figure 5a It is a dry rock longitudinal wave field map of a three-dimensional digital core provided by an embodiment of the present invention;

[0028] Figure 5b It is a dry rock shear wave field map of a three-dimensional digital core provided by an embodiment of the present invention;

[0029] Figure 6 is a flow chart of determining sensitive elastic parameters provided by an embodiment of the present invention;

[0030] Figure 7a is a sensitivity parameter of the elastic parameters of water and air provided by an embodiment of the present invention;

[0031] Figure 7b is a sensitivity parameter of the elastic parameters of water and oil provided by the embodiment of the present invention;

[0032] Figure 8a is a sensitivity parameter of the elastic simulation parameter of water and air provided in an embodiment of the present invention;

[0033] Figure 8b is a sensitivity parameter of the elastic simulation parameter of water and oil provided in an embodiment of the present invention;

[0034] Figure 9a It is a water and gas water saturation prediction model provided by an embodiment of the present invention;

[0035] Figure 9b It is a water and oil saturation prediction model provided by an embodiment of the present invention;

[0036] Fig.10 The invention provides a system for determining elastic parameters that are sensitive to water saturation. DETAILED DESCRIPTION

[0037] The specific implementation of the embodiment of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the embodiment of the present invention, and is not used to limit the embodiment of the present invention.

[0038] Figure 1 The flowchart of the method for determining elastic parameters sensitive to water saturation provided by the embodiment of the present invention includes the following steps S101-S104.

[0039] S 101. Scan the rock sample to obtain a three-dimensional digital core model.

[0040] The three-dimensional digital core model includes a rock matrix model and a pore model of the three-dimensional digital core.

[0041] Specifically, the rock sample is a core taken from a tight reservoir section, and the rock sample is scanned to obtain a three-dimensional digital core model. The rock sample can be scanned by CT using existing technical means such as X-rays, and then the CT scan image is subjected to image filtering, optimal threshold segmentation, and pore quantification analysis to obtain a three-dimensional digital core model. The three-dimensional digital core model includes a rock matrix model and a pore model of the three-dimensional digital core. In order to distinguish the rock matrix from the pores in the three-dimensional digital core model, the pores can be assigned a number such as 0, and according to the mineral type of the rock matrix, numbers such as 2, 3, 4, ..., N can be assigned respectively (the rock matrix is ​​composed of N kinds of mineral components, and the common ones are quartz, calcite, mud, clay, etc.). Different numbers are assigned to the pores and the rock matrix only for the convenience of distinguishing the specific positions of the rock matrix and the pores on the three-dimensional digital core model, which is convenient for viewing without actual physical meaning.

[0042] refer to Figure 3a This is the rock matrix model of the constructed three-dimensional digital core. There are two mineral components in the rock matrix, of which the black one is quartz, accounting for 86.691%, the white one is clay, accounting for 2.434%, and the rest is pores, accounting for 10.875%. The model size is 300*300*300 pixels, and the pixel size is 3μm. Figure 3b The pore model of the three-dimensional digital core constructed has a porosity of 10.875%. Both models are 300*300*300 pixels in size, and the pixel size is the same as the CT image scanning resolution, which is 3μm. In the three-dimensional digital core model, the number 0 can represent pores, 2 represents quartz, and 3 represents clay. The three-dimensional pore quantitative analysis obtained that in the three-dimensional digital core model of the rock sample of the dense sandstone, the number of pores in the three-dimensional digital core is 28054; the minimum equivalent diameter is 3.7221μm, the maximum equivalent diameter is 508.373μm, and the average equivalent diameter is 5.76969μm.

[0043] S102: constructing an elastic parameter model of the three-dimensional digital core at multiple water saturations according to the rock matrix model and the pore model of the three-dimensional digital core.

[0044] Based on the rock matrix model of the three-dimensional digital core in the above steps, the Rock Physics Handbook is consulted according to the mineral components of the rock matrix, and elastic parameters corresponding to the mineral components of the rock matrix are assigned respectively. For example, the mineral types of the rock matrix include quartz, calcite, clay and mud (the corresponding elastic parameters are consulted according to the actual mineral types), and the elastic parameters corresponding to quartz, calcite, clay and mud are consulted respectively to establish the elastic parameter model of the rock matrix of the three-dimensional digital core (i.e., the mapping relationship between the rock matrix and the value of the elastic parameter). For the rock matrix, whether its components are quartz, calcite or a mixture thereof, the method for establishing the elastic parameter model of the rock matrix of the three-dimensional digital core is the same, and the numerical values ​​corresponding to the elastic parameters corresponding to the mineral components of the rock matrix can be consulted according to the actual situation.

[0045] Based on the pore model of the three-dimensional digital core in the above steps, different fluid types are assigned to the pores (different fluid types can be assigned according to actual needs). The fluid types in the present invention mainly include water and gas and water and oil. Among them, two fluid types can be assigned to the pore model of the three-dimensional digital core. For the pore model of the three-dimensional digital core in which the fluid types in the pores are water and gas, the initial state of the pores is set to be all natural gas, which can be represented by the number 1. For the pore model of the three-dimensional digital core in which the fluid types in the pores are water and oil, the initial state of the pores is set to be all oil, which can also be represented by the number 1. According to the different fluid types and different water saturations, by referring to the "Handbook of Rock Physics", the elastic parameters of the fluid types in the pores at multiple water saturations are assigned respectively, thereby constructing multiple elastic parameter models of the pores at multiple water saturations of the three-dimensional digital cores (i.e., the mapping relationship between the values ​​of water saturation and elastic parameters). The embodiment of the present invention is described by taking the fluid types in the pores as water and gas as an example. For example, if the fluid types in the pores are water and gas, when the water saturation is 10%, the value corresponding to the elastic parameter is determined by consulting the Rock Physics Handbook; when the water saturation is 20%, another value corresponding to the elastic parameter is determined by consulting the Rock Physics Handbook; and so on, the elastic parameter model of the pores under multiple water saturations of the three-dimensional digital core can be obtained. When the fluid types in the pores are water and oil, the method for obtaining the elastic parameter model of the pores under multiple water saturations is the same as when the fluid types are water and gas, and will not be repeated here.

[0046] Among them, the elastic parameter model of the rock matrix and the elastic parameter model of the pores of the three-dimensional digital core constructed in the above manner constitute the elastic parameter model of the three-dimensional digital core at multiple water saturations, that is, the elastic parameter model of the three-dimensional digital core at multiple water saturations includes the elastic parameter model of the rock matrix and the elastic parameter model of the pores of the three-dimensional digital core.

[0047] Furthermore, the construction of the elastic parameter model of pores at multiple water saturations of the three-dimensional digital core specifically includes the following steps S1021-S1022.

[0048] S1021. Based on the pore model of the three-dimensional digital core, obtain multiple water saturations corresponding to the fluid types in the pores according to multiple preset water saturations.

[0049] In order to change the water saturation of the pores of the three-dimensional digital core, multiple preset water saturations may be set, thereby obtaining multiple water saturations corresponding to the fluid types in the pores.

[0050] S1022. According to the fluid type in the pore, obtain elastic parameters of multiple water saturations corresponding to the fluid type in the pore, so as to construct an elastic parameter model of the pores at multiple water saturations of the three-dimensional digital core.

[0051] Specifically, in order to construct the elastic parameter model of the three-dimensional digital core at multiple water saturations, the piston displacement principle can be used to change the water saturation of the pores under different fluid types in the manner of water-displacing oil or water-displacing gas. For example, when the fluid type is water and gas or water and oil, the water saturation of the three-dimensional digital core is changed by the piston displacement principle (for example, the preset water saturation is 10%, 20%, ..., 100%), and the elastic parameters under multiple water saturations are obtained by consulting the "Handbook of Rock Physics". At the same time, combined with the rock matrix elastic parameter model of the three-dimensional digital core established in step S102, the elastic parameter model of the pores under multiple water saturations of the three-dimensional digital core is constructed.

[0052] Further, the step of obtaining a plurality of water saturations corresponding to the fluid type in the pores according to a plurality of preset water saturations includes: determining a minimum value n of the number of water layers k to be filled according to the preset water saturation S and the following formula: in, is the porosity of the i-th layer, M represents the number of pore layers, represents the pore ratio of water, k represents the number of water layers to be filled; according to the minimum value n and the pore ratio of water Get multiple water saturations corresponding to the fluid types in the pores.

[0053] Specifically, taking the case where the fluid types in the pores are water and gas as an example, it is assumed that the three-dimensional digital core model is divided into several layers N along the Z-axis direction, and it is assumed that the initial filling state of the pores in each layer is natural gas. In order to change the water saturation of the pores, the piston displacement principle is used to change the water saturation in the pores in the form of water-driven gas. As the proportion of water in the water-driven gas pores increases, the water saturation of the pores increases. Considering that the pore proportion is not uniformly distributed in the Z-axis direction, the value k obtained to determine the number of layers of water that need to be filled is not necessarily an integer value or a fixed value (for example, it may be 2-3 layers). Preferably, the embodiment of the present invention takes the minimum value n of k as the actual number of layers of water that needs to be filled.

[0054] It can be calculated by the following formula: in, is the porosity of the i-th layer, N is the number of pore layers, represents the pore ratio of water, and k represents the number of water layers that need to be filled. Therefore, when the water saturation S is set to be known, the pore ratio of water can be determined. Then the value of k can be calculated (here it can be understood as the estimated number of water layers that need to be filled in the pores). By changing the minimum value n of the number of water layers k that need to be filled, the corresponding water pore ratio when the number of water layers is n can be calculated. Right now (When the exact minimum value n is calculated, the pore ratio of water corresponding to n can be calculated accordingly That is, the actual water saturation) obtains multiple water saturations corresponding to the fluid type in the pore.

[0055] S103, simulating the elastic parameter model of the three-dimensional digital core at multiple water saturations to obtain elastic simulation parameters.

[0056] After the elastic parameter model of the three-dimensional digital core at multiple water saturations is constructed in the above steps, the simulation is performed. The specific simulation method is as follows: the equivalent elastic modulus of the rock matrix of the three-dimensional digital core is calculated using existing technical means, such as the Voigt-Reuss-Hill formula (i.e., the brittleness index formula). Figure 4 This is a simulated 3D digital core saturated gas (gas content is 100%) velocity model. The white color in the figure represents gas-bearing pores, and the black color represents rock matrix. The bulk modulus of gas is set to 0.02GPa, the shear modulus is 0, and the density is 0.1g / cm3. The equivalent elastic modulus of the rock matrix has a bulk modulus of 38.04GPa, a shear modulus of 42.27GPa, and a density of 2.647g / cm3.

[0057] The embodiment of the present invention adopts the Voigt-Reuss-Hill formula to calculate the equivalent elastic modulus of the rock matrix of the three-dimensional digital core. Compared with the prior art that uses the finite element method to solve the stress-strain field under the minimum potential energy condition to reversely infer the equivalent elastic modulus, the accuracy is higher and the result obtained is more accurate.

[0058] In order to ensure the integrity of the experimental data, the elastic parameter model of the three-dimensional digital core at multiple water saturations is placed in the center of a larger uniform background model to establish a three-dimensional digital core test model, wherein the elastic parameters of the background model are the same as the equivalent elastic modulus of the rock matrix in the elastic parameter model of the three-dimensional digital core at multiple water saturations.

[0059] The longitudinal wave plane source and the shear wave plane source are used respectively, and the source is located at the top of the test model. Two sets of receiving detectors are located at the top (on the same center line as the source) and bottom of the elastic parameter model of the three-dimensional digital core at multiple water saturations. The three-dimensional elastic wave equation staggered grid finite difference numerical simulation method is used to simulate the elastic wave field of dry rock (i.e. rock matrix and pores, and the pores are in a vacuum state) and multiple water saturation cores of different fluid types.

[0060] The staggered grid finite difference numerical simulation method of three-dimensional elastic wave equation is used to solve the problem that the existing stress-strain method cannot simulate the elastic wave field propagation in three-dimensional digital rock cores. Figure 5a The snapshot of the P-wave field of the three-dimensional digital dry rock (vacuum) numerical simulation of the rock sample is a dense sandstone sample. Figure 5b It is a snapshot of the shear wave field. It can be seen that the method of the present invention can simulate the propagation of elastic wave fields of dry rock, water and gas, and water and oil stably and with high accuracy.

[0061] Preferably, the three-dimensional elastic wave equation is a three-dimensional first-order stress-degree elastic wave equation in an isotropic elastic medium, and the specific formula is as follows: Where, the seismic wave field vector Q = (ν x , ν y , ν z , σ xx , σ yy , σ zz , σ yz , σ xz , σ xy ) T A1, A2, A3 are

[0062]

[0063]

[0064]

[0065] Wherein, ρ represents the medium density, which is a known value; λ and μ are the Lame constants, which are known values; v represents the velocity, which is a known value; σ represents the stress, which is a known value.

[0066] The pore distribution of dense sandstone rock samples is highly non-uniform. The following three-dimensional digital core elastic wave field simulation results of these non-uniform pore dense sandstone rock samples at multiple water saturations are used to analyze the influence of pore fluid on rock elasticity, as well as the relationship between different fluid saturations of the three-dimensional digital core of dense sandstone samples and the longitudinal wave velocity and shear wave velocity.

[0067] S104: Determine elastic parameters that are sensitive to water saturation according to the elastic simulation parameters and the sensitivity threshold.

[0068] The elastic simulation parameters include longitudinal wave velocity, shear wave velocity and elastic parameters, and the elastic parameters include the ratio of longitudinal to shear wave velocity, bulk modulus, Poisson's ratio, Lamé constant and shear modulus.

[0069] refer to Figure 6 Flowchart, S104 specifically includes the following steps S1041-S1043.

[0070] S1041. Determine a sensitivity function of an elastic parameter and a new sensitivity function of an elastic parameter according to the elastic simulation parameter.

[0071] The elastic simulation parameters can be obtained by the above simulation method. The bulk modulus K of dry rock can be calculated by using the elastic simulation parameters and existing technical means such as equivalent medium theory and Gassmann equation. dry and the bulk modulus K of the fluid-saturated rock sat Wherein, the bulk modulus K of the rock matrix s That is, the equivalent elastic modulus of the rock matrix of the three-dimensional digital core calculated in the above step S103 using the existing technical means according to the Voigt-Reuss-Hill formula.

[0072] The new elastic parameters are determined according to the following formula, wherein the new elastic parameters include the pore space modulus M and the pore fluid bulk modulus K f :M=(K sat -K dry ) / β 2 , And according to the new elastic parameter, determine the sensitivity function of the new elastic parameter. Wherein, K s represents the bulk modulus of the rock matrix, K dry represents the bulk modulus of dry rock, K s With Kdry Determined according to the longitudinal wave velocity, shear wave velocity and elastic parameters; K sat represents the bulk modulus of fluid-saturated rock, K sat Determined according to the longitudinal wave velocity, the shear wave velocity and the elastic parameters; Represents the porosity of the rock sample, which is a known value obtained experimentally.

[0073] Specifically, the bulk modulus K of the rock matrix is ​​determined according to the elastic simulation parameters. s , the bulk modulus K of dry rock dry and the bulk modulus K of the fluid-saturated rock sat After that, two elastic parameters sensitive to different fluid (gas / water, oil / water) saturation can be constructed based on the Biot theory of saturated fluid porous media and its low-frequency approximation conditions, namely, the pore space modulus M and the pore fluid bulk modulus K. f .

[0074] After determining two new elastic parameters (i.e., new elastic parameters in addition to the conventional five elastic parameters), the elastic parameters (in this paper, conventional elastic parameters, i.e., longitudinal and transverse wave velocity ratio, bulk modulus, Poisson's ratio, Lamé constant and shear modulus) and the new elastic parameters M and K are used to calculate the elastic parameters of the composite material. f , respectively determine the sensitivity function of the elastic parameter and the sensitivity function of the new elastic parameter.

[0075] S1042: Determine the sensitivity of the elastic parameter and / or the new elastic parameter in a specific water saturation range according to the sensitivity function of the elastic parameter and / or the sensitivity function of the new elastic parameter.

[0076] Further, determining the sensitivity function of the elastic parameter or the new sensitivity function of the elastic parameter comprises: according to y(S w ) and the following formula to determine y(S w )’s sensitivity function A w : Among them, S w represents water saturation, y(S w ) represents the elastic parameters or new elastic parameters at different water saturations.

[0077] Specifically, y(S w ) represents different water saturation S w The elastic parameter or new elastic parameter under y represents any elastic parameter. Determine the sensitivity function, refer to Figure 7a Shown is the sensitivity of conventional elastic parameters to water and gas as fluid types in rock samples. Figure 7bShown is the sensitivity of conventional elastic parameters to the fluid types of water and oil in rock samples. Figure 7a and Figure 7b It can be seen that the conventional elastic parameters (ratio of longitudinal and transverse wave velocity V p / V s , Poisson's ratio P'sratio, bulk modulus K sat , Lamé constant Lamda and shear modulus Mu) are not sensitive to pore fluid saturation, especially when the fluid types are water and oil, the sensitivity to water saturation is very low (sensitivity is less than 5%).

[0078] S1043: Determine the elastic parameter having a sensitivity greater than a sensitivity threshold and / or the new elastic parameter as an elastic parameter sensitive to water saturation.

[0079] Based on the sensitivity function calculation formula of step S1042, refer to Figure 8a The sensitivity of conventional elastic parameters and new elastic parameters at different water saturations when the fluid type is water and gas. It can be seen that the new elastic parameters pore space modulus M and pore fluid bulk modulus K f At a specific water saturation ( Figure 8a When the specific water saturation is 0%-80%, the sensitivity to water saturation is between 17% and 40%, while the sensitivity of conventional elastic parameters to water saturation between 0% and 80% is less than 10% (ref. Figure 8a In addition to K f and the rest of the broken lines other than M, that is Figure 7a ).

[0080] refer to Figure 8b The sensitivity of conventional elastic parameters and new elastic parameters at different water saturations when the fluid type is water and oil. It can be seen that the new elastic parameters pore space modulus M and pore fluid bulk modulus K f At a specific water saturation ( Figure 8b When the specific water saturation is 0%-60%, the sensitivity to water saturation is between 10%-30%, while the sensitivity of conventional elastic parameters to water saturation between 0%-60% is less than 5% (ref. Figure 8b K f and the broken line outside M, that is Figure 7b ).

[0081] It can be seen that no matter the fluid type is water and gas or water and oil, the two new elastic parameters are sensitive to water saturation within a certain range, but this does not affect their sensitive characteristics to water saturation. Therefore, the specific water saturation means the water saturation within a certain range.

[0082] In the case of fluid types of water and gas and water and oil, the new elastic parameters M and K f The sensitivity in a specific water saturation range is significantly higher than the sensitivity of conventional elastic parameters to water. In the embodiment of the present invention, the sensitivity threshold is preferably set to 10%, and the sensitivity threshold may also be set to other values ​​according to the actual needs, and the present invention does not make specific restrictions. The elastic parameter with a sensitivity greater than 10% of the sensitivity threshold and / or the new elastic parameter is determined as an elastic parameter sensitive to water saturation, so the new elastic parameters M and K are determined. f is an elastic parameter sensitive to water saturation. Among them, the bulk modulus of pore fluid K f It is more sensitive to water saturation than the pore space modulus M. In addition, these two elastic parameters have clear physical meanings, and they will inevitably become new important parameters for predicting reservoir rock saturation.

[0083] The method determines a new elastic parameter that is sensitive to water saturation, solves the problem in the prior art that conventional elastic parameters of tight reservoirs are low in sensitivity to water saturation, and thus improves the accuracy of calculating water saturation.

[0084] Through the above technical solution, the rock sample is scanned to obtain a three-dimensional digital core model, wherein the three-dimensional digital core model includes a rock matrix model and a pore model of the three-dimensional digital core; according to the rock matrix model and the pore model of the three-dimensional digital core, an elastic parameter model of the three-dimensional digital core at multiple water saturations is constructed; the elastic parameter model of the three-dimensional digital core at multiple water saturations is simulated to obtain elastic simulation parameters, wherein the elastic model parameters include both conventional elastic parameters and new elastic parameters; and then the elastic parameter having a sensitivity greater than a sensitivity threshold and / or the new elastic parameter is determined as an elastic parameter sensitive to water saturation.

[0085] The embodiment of the present invention determines elastic parameters sensitive to water saturation, which solves the problem that conventional elastic parameters in the prior art are insensitive to water saturation, so that elastic parameters sensitive to water saturation can be further used as predictions of actual well logging or seismic water saturation.

[0086] On the other hand, the present invention also provides a method for predicting water saturation, the method comprising: determining the elastic parameter K sensitive to water saturation according to the method for determining the elastic parameter sensitive to water saturation f ; Based on the elastic parameter K that is sensitive to water saturation f And the following formula, construct the water saturation prediction model: S w =a*K fb , where S w Indicates water saturation, K f represents the bulk modulus of the saturated fluid, and a and b represent the unknown coefficients of the water saturation prediction model.

[0087] Specifically, after determining the elastic parameters sensitive to water saturation, in order to further use the elastic parameters sensitive to water to characterize the prediction of actual well logging or seismic water saturation, the present invention also needs to construct a water saturation prediction model. Figure 8a and Figure 8b It can be seen that the new sensitive elastic parameter K f The sensitivity to water saturation is greater than the new sensitive elastic parameter M. Therefore, the embodiment of the present invention preferably uses the new elastic parameter K f Construct a water saturation prediction model, the formula is as follows: S w =a*K f b Where a and b represent the unknown coefficients of the water saturation prediction model. Figure 9a is the elastic parameter model when the fluid types in the pores of the rock sample are water and gas, Figure 9a The discrete points in are the elastic parameters K at different water saturations determined in step S1042 above. f The value of Figure 8a Middle K f The corresponding point on the polyline. Figure 9b is the elastic parameter model when the fluid types in the pores of the rock sample are water and oil, Figure 9b The discrete points in are the elastic parameters K at different water saturations determined in step S1042 above. f The value of Figure 8b Middle K f The corresponding point on the broken line. As can be seen from the figure, the constructed model can well characterize the bulk modulus K of the pore fluid in dense rock. f According to the existing technical means, the water saturation prediction model S is fitted based on the discrete points. w =a*K f b The unknown coefficients a and b are 59.7 and 0.76, respectively.

[0088] When the rock pore fluid bulk modulus K is determined f When there is a certain deviation from the theoretical value, the present invention adopts the following method to correct the bulk modulus of the fluid, that is, taking the minimum value as a reference, correcting it to the bulk modulus of saturated gas, and correcting all bulk moduli with the corresponding difference of the value. The same correction method is also applied to the case where the fluid type is saturated with water and oil.

[0089] After the elastic parameters sensitive to water saturation are determined, a water saturation prediction model is constructed using the elastic parameters sensitive to water saturation, and the water saturation prediction model is used to predict the water saturation in the target wellbore or predict the water saturation in earthquakes.

[0090] In another aspect, the present invention further provides a method for determining water saturation of a target wellbore, the method comprising: determining a bulk modulus K of a rock matrix in the target wellbore according to a plurality of parameter curves of the target wellbore; s , the bulk modulus K of dry rock dry and the bulk modulus K of the saturated fluid rock sat ; According to the bulk modulus K of the rock matrix in the target wellbore s , the bulk modulus K of dry rock dry , bulk modulus of saturated fluid rock K sat and the method for determining elastic parameters sensitive to water saturation, determining the bulk modulus K of the pore fluid f ; and according to the water saturation prediction model and the pore fluid bulk modulus K f , determine the target wellbore water saturation.

[0091] Furthermore, the plurality of parameter curves include a longitudinal wave velocity curve, a shear wave velocity curve, a density curve and a saturation curve.

[0092] Specifically, after the water saturation prediction model is determined and constructed, the elastic parameter model can be used to predict the actual wellbore water saturation. First, the existing technical means such as logging curves can be used to obtain multiple parameter curves of the target wellbore to be explored, and the multiple parameter curves include a longitudinal wave velocity curve, a shear wave velocity curve, a density curve, and a saturation curve. The bulk modulus K of the rock matrix in the target wellbore can be determined based on the multiple parameter curves. s , the bulk modulus K of dry rock dry and the bulk modulus K of the saturated fluid rock sat , and the elastic parameter K sensitive to water saturation can be determined by using the formula in step S1041 above f After determining the elastic parameter K that is sensitive to water saturation f Finally, the water saturation prediction model S constructed by combining the above steps is w =a*K f b , the water saturation of the target wellbore can be predicted. The prediction method of seismic water saturation is the same as the prediction method of the target wellbore water saturation, which will not be repeated here.

[0093] Through the above technical solution, the method for determining the water saturation of the target wellbore can be applied in the field of well logging water saturation measurement or seismic water saturation measurement, so as to quantitatively evaluate the oil and gas content of tight reservoirs, and quantitatively analyze the water saturation of water and oil, and the water saturation of water and gas in tight reservoirs. It overcomes the shortcomings of conventional methods in the identification of oil and water reservoirs and the low reliability of oil and water saturation prediction, provides a new method for the exploration and development of tight reservoirs, and also has high application value in the fields of three-dimensional digital core and computational rock physics.

[0094] Accordingly, if Fig.10 The present invention also provides a system for determining elastic parameters sensitive to water saturation, the determination system comprising: a scanning device 10, used to scan a rock sample to obtain a three-dimensional digital core model, wherein the three-dimensional digital core model comprises a rock matrix model and a pore model of the three-dimensional digital core; a construction device 11, used to construct an elastic parameter model of the three-dimensional digital core at multiple water saturations according to the rock matrix model and the pore model of the three-dimensional digital core; an acquisition device 12, used to simulate the elastic parameter model of the three-dimensional digital core at multiple water saturations to obtain elastic simulation parameters; and a determination device 13, used to determine the elastic parameters sensitive to water saturation according to the elastic simulation parameters and a sensitivity threshold.

[0095] The details of determining the elastic parameters sensitive to water saturation and the effects thereof can be found in the related description of the method for determining the elastic parameters sensitive to water saturation, which will not be elaborated here.

[0096] Accordingly, the present invention also provides a water saturation prediction model system, the system comprising: a construction device for determining the elastic parameter K sensitive to water saturation determined by the determination method; f ; Based on the elastic parameter K that is sensitive to water saturation f And the following formula, construct the water saturation prediction model: S w =a*K f b Among them, S w Indicates water saturation, K f represents the bulk modulus of the saturated fluid, and a and b represent the unknown coefficients of the water saturation prediction model.

[0097] For details of the above water saturation prediction and its effect, please refer to the relevant instructions for predicting water saturation, which will not be repeated here.

[0098] Accordingly, the present invention also provides a system for determining the water saturation of a target wellbore, the system comprising: a first determining device for determining the bulk modulus K of the rock matrix in the target wellbore according to a plurality of parameter curves of the target wellbore; s , the bulk modulus K of dry rock dry and the bulk modulus K of the saturated fluid rock sat ; A second determining device for determining the bulk modulus K of the rock matrix in the target wellbore s , the bulk modulus K of dry rock dry , bulk modulus of saturated fluid rock K sat and the method for determining elastic parameters sensitive to water saturation, determining the bulk modulus K of the pore fluid f ; and a third determining device for the water saturation prediction model and the pore fluid bulk modulus K f , determine the target wellbore water saturation.

[0099] The first determining device, the second determining device and the third determining device can be the same determining device or different determining devices, and the present invention does not make specific limitations. For details of the above-mentioned determination of the target wellbore water saturation and its effect, please refer to the relevant description of the above-mentioned method for determining the target wellbore water saturation, which will not be repeated here.

[0100] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0101] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0102] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0103] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0104] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0105] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0106] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0107] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0108] The above are only embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A method for determining elastic parameters sensitive to water saturation, characterized in that: The determination method comprises: Scanning the rock sample to obtain a three-dimensional digital core model, wherein the three-dimensional digital core model includes a rock matrix model and a pore model of the three-dimensional digital core; constructing an elastic parameter model of the three-dimensional digital core at multiple water saturations according to the rock matrix model and the pore model of the three-dimensional digital core; Simulating the elastic parameter model of the three-dimensional digital core at multiple water saturations to obtain elastic simulation parameters; and An elastic parameter sensitive to water saturation is determined according to the elastic simulation parameter and the sensitivity threshold.

2. The method for determining elastic parameters sensitive to water saturation according to claim 1, characterized in that: The elastic parameter model of the three-dimensional digital core at multiple water saturations includes an elastic parameter model of the pores of the three-dimensional digital core, The step of constructing the elastic parameter model of the three-dimensional digital core at multiple water saturations includes: Based on the pore model of the three-dimensional digital core, multiple water saturations corresponding to the fluid types in the pores are obtained according to multiple preset water saturations, and According to the fluid type in the pore, elastic parameters of multiple water saturations corresponding to the fluid type in the pore are obtained to construct an elastic parameter model of the pores at multiple water saturations of the three-dimensional digital core.

3. The method for determining elastic parameters sensitive to water saturation according to claim 2, characterized in that: The method of obtaining a plurality of water saturations corresponding to the fluid types in the pores according to a plurality of preset water saturations based on the pore model of the three-dimensional digital core includes: According to the preset water saturation S and the following formula, the minimum value n of the number of water layers k to be filled is determined: in, is the porosity of the i-th layer, N is the number of pore layers, represents the pore ratio of water, and k represents the number of water layers that need to be filled; According to the minimum value n and the pore proportion of water Get multiple water saturations corresponding to the fluid types in the pores.

4. The method for determining elastic parameters sensitive to water saturation according to claim 1, characterized in that: The elastic simulation parameters include longitudinal wave velocity, shear wave velocity and elastic parameters, and the elastic parameters include longitudinal and shear wave velocity ratio, bulk modulus, Poisson's ratio, Lamé constant and shear modulus. Determining the elastic parameters sensitive to water saturation according to the elastic simulation parameters and the sensitivity threshold comprises: Determining a sensitivity function of the elastic parameter and a new sensitivity function of the elastic parameter according to the elastic simulation parameter; Determining the sensitivity of the elastic parameter and / or the new elastic parameter in a specific water saturation range according to the sensitivity function of the elastic parameter and / or the sensitivity function of the new elastic parameter; and The elastic parameter having a sensitivity greater than a sensitivity threshold and / or the new elastic parameter is determined as an elastic parameter sensitive to water saturation.

5. The method for determining elastic parameters sensitive to water saturation according to claim 4, characterized in that: Determining the sensitivity function of the new elastic parameter according to the elastic simulation parameter includes: According to the following formula, the new elastic parameters are determined, wherein the new elastic parameters include the pore space modulus M and the pore fluid bulk modulus K f : M=(K sat -K dry ) / b 2 , as well as According to the new elastic parameter, a sensitivity function of the new elastic parameter is determined, Among them, K s represents the bulk modulus of the rock matrix, K dry represents the bulk modulus of dry rock, K s With K dry Determined according to the longitudinal wave velocity, shear wave velocity and elastic parameters; K sat represents the bulk modulus of fluid-saturated rock, K sat Determined according to the longitudinal wave velocity, the shear wave velocity and the elastic parameters; Represents the porosity of a rock sample.

6. The method for determining elastic parameters sensitive to water saturation according to claim 5, characterized in that: The determining of the sensitivity function of the elastic parameter or the new sensitivity function of the elastic parameter comprises: According to y(S w ) and the following formula to determine y(S w )’s sensitivity function A w : Among them, S w represents water saturation, y(S w ) represents the elastic parameters or new elastic parameters at different water saturations.

7. A method for constructing a water saturation prediction model, characterized in that: The method comprises: The method for determining an elastic parameter sensitive to water saturation according to claim 5 is used to determine the elastic parameter K sensitive to water saturation. f ; According to the elastic parameter K which is sensitive to water saturation f And the following formula to construct the water saturation prediction model: S w =*K f b Among them, S w Indicates water saturation, K f represents the bulk modulus of the saturated fluid, and a and b represent the unknown coefficients of the water saturation prediction model.

8. A method for determining target wellbore water saturation, characterized in that: The method comprises: According to multiple parameter curves of the target wellbore, the bulk modulus K of the rock matrix in the target wellbore is determined. s , the bulk modulus K of dry rock dry and the bulk modulus K of the saturated fluid rock sat ; According to the bulk modulus K of the rock matrix in the target wellbore s , the bulk modulus K of dry rock dry , bulk modulus of saturated fluid rock K sat and the method for determining elastic parameters sensitive to water saturation as claimed in claim 5, for determining the bulk modulus K of the pore fluid d ;as well as The water saturation prediction model and the pore fluid bulk modulus K according to claim 7 f , determine the target wellbore water saturation.

9. The method for determining target wellbore water saturation according to claim 8, characterized in that: The plurality of parameter curves include a longitudinal wave velocity curve, a shear wave velocity curve, a density curve, and a saturation curve.

10. A system for determining elastic parameters sensitive to water saturation, characterized in that: The determination system comprises: A scanning device, used for scanning the rock sample to obtain a three-dimensional digital core model, wherein the three-dimensional digital core model includes a rock matrix model and a pore model of the three-dimensional digital core; A construction device, for constructing an elastic parameter model of the three-dimensional digital core at multiple water saturations according to a rock matrix model and a pore model of the three-dimensional digital core; an acquisition device, used to simulate the elastic parameter model of the three-dimensional digital core at multiple water saturations to obtain elastic simulation parameters; and The determining device is used to determine the elastic parameter sensitive to water saturation according to the elastic simulation parameter and the sensitivity threshold.

11. A system for constructing a water saturation prediction model, characterized in that: The system comprises: Constructing a device for determining the elastic parameter K sensitive to water saturation according to the method for determining the elastic parameter sensitive to water saturation according to claim 5 f ; According to the elastic parameter K which is sensitive to water saturation f And the following formula to construct the water saturation prediction model: S w =*K f b Among them, S w Indicates water saturation, K f represents the bulk modulus of the saturated fluid, and a and b represent the unknown coefficients of the water saturation prediction model.

12. A system for determining a target wellbore water saturation, characterized in that: The system comprises: The first determining device is used to determine the bulk modulus K of the rock matrix in the target wellbore according to a plurality of parameter curves of the target wellbore. s , the bulk modulus K of dry rock dry and the bulk modulus K of the saturated fluid rock sat ; The second determining device is used to determine the bulk modulus K of the rock matrix in the target wellbore according to the bulk modulus K s , the bulk modulus K of dry rock dry , bulk modulus of saturated fluid rock K sat and the method for determining elastic parameters sensitive to water saturation as claimed in claim 5, for determining the bulk modulus K of the pore fluid f ;as well as The third determining device is used for the water saturation prediction model and the pore fluid bulk modulus K according to claim 7. f , determine the target wellbore water saturation.

Images