Method for predicting p-and s-wave velocities of a saturated porous rock and related device
Patent Information
- Application Number
- CN202611087356.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-21
- Publication Date
- 2026-10-30
AI Technical Summary
[0022]根据本公开的又一个方面，提供一种计算机程序产品，计算机程序产品存储有指令，所述指令在由计算机执行时，使得计算机实施上述的饱和多孔岩石的纵横波速度预测方法。
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Abstract
Description
Technical Field
[0001] This disclosure relates to the field of rock geophysics, and in particular to a method and related equipment for predicting the P-wave and S-wave velocities of saturated porous rocks. Background Technology
[0002] In recent years, the fields of deep oil and gas exploration and development, geothermal resource exploitation, underground energy storage, and carbon dioxide geological seismic storage have developed rapidly. Seismic exploration technology is the core means for conducting underground medium detection and reservoir characteristic evaluation in these fields. In the process of seismic exploration data processing and interpretation, the P-wave velocity and S-wave velocity of saturated porous rocks are the key bridge connecting seismic response signals and underground rock physical properties. Their prediction accuracy directly affects the reliability of many core tasks such as reservoir identification, fluid discrimination, geostress evaluation, and time-lapse seismic dynamic monitoring.
[0003] Currently, most commonly used P-wave and S-wave velocity prediction methods in the industry are based on simplified rock physics assumptions. The prediction results deviate significantly from actual well logging data and laboratory experimental measurements. In particular, the problem of insufficient prediction stability is more prominent under complex geological conditions, making it difficult to meet the accuracy requirements of modern oil and gas exploration and development as well as underground engineering practices.
[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention
[0005] This application discloses a method and related equipment for predicting P-wave and S-wave velocities in saturated porous rocks, which can improve the accuracy and stability of P-wave and S-wave velocity prediction.
[0006] Other features and advantages of this disclosure will become apparent from the following detailed description, or may be learned in part from practice of this disclosure.
[0007] According to one aspect of this disclosure, a method for predicting the P-wave and S-wave velocities of saturated porous rocks is provided, comprising:
[0008] Obtain the volume fraction of mineral components, mineral bulk modulus, and mineral shear modulus of the target reservoir rocks;
[0009] The matrix equivalent bulk modulus and matrix equivalent shear modulus are determined based on the mineral component volume fraction, mineral bulk modulus, and mineral shear modulus.
[0010] Based on the dual-porosity media theory, the total porosity of rock is decoupled into rigid hard pore porosity and compressible fracture porosity, and a coupling function of rigid hard pore porosity and compressible fracture porosity as a function of effective pressure and absolute temperature is constructed.
[0011] Based on the coupling function of the bulk modulus of the dry rock skeleton without cracks, the equivalent bulk modulus of the matrix, the porosity of rigid hard pores and the porosity of compressible cracks, the bulk modulus and shear modulus of the dry rock skeleton as a function of effective pressure and absolute temperature are calculated.
[0012] Based on the bulk modulus and shear modulus of the dry rock skeleton, the real-time total porosity, and the bulk modulus of the mixed fluid, the bulk modulus and shear modulus of saturated rock are determined; among them, the bulk modulus of the mixed fluid is determined based on the pore fluid parameters.
[0013] Based on the bulk modulus, shear modulus, and density of saturated rock, the P-wave velocity and S-wave velocity are determined, and these velocities are used for reservoir geophysical exploration.
[0014] In one embodiment of this disclosure, a coupling function is constructed to represent the changes in rigid hard pore porosity and compressible fracture porosity with effective pressure and absolute temperature. This includes: establishing the first-order partial derivatives of porosity with respect to effective pressure and absolute temperature based on the compressibility characteristics of porosity with respect to effective pressure and the thermal expansion characteristics with respect to absolute temperature; and obtaining explicit analytical expressions for the changes in rigid hard pore porosity and compressible fracture porosity with respect to effective pressure and absolute temperature by integrating the first-order partial derivatives.
[0015] In one embodiment of this disclosure, the explicit analytical expression for rigid hard-pore porosity is composed of the superposition of the product of the linear factor of effective pressure and the exponential factor of absolute temperature, and the explicit analytical expression for compressible fracture porosity is composed of the product of the initial fracture porosity, the negative exponential factor of effective pressure, and the exponential factor of absolute temperature; the first derivative of rigid hard-pore porosity with respect to effective pressure is positive and the first derivative with respect to absolute temperature is positive; the first derivative of compressible fracture porosity with respect to effective pressure is negative and the first derivative with respect to absolute temperature is positive.
[0016] In one embodiment of this disclosure, the calculation of the bulk modulus and shear modulus of the dry rock skeleton as a function of effective pressure and absolute temperature includes: based on the baseline modulus of the dry rock skeleton without cracks, introducing deformation-sensitive parameters corresponding to rigid hard pore porosity and compressible crack porosity, and constructing response functions of the bulk modulus and shear modulus of the dry rock skeleton with respect to temperature and pressure; wherein, both the bulk modulus and shear modulus of the dry rock skeleton increase with increasing effective pressure and decrease with increasing absolute temperature.
[0017] In one embodiment of this disclosure, the response function of the bulk modulus of the dry rock skeleton is based on the bulk modulus of the dry rock skeleton without cracks, and introduces a modulus difference term between the matrix and the skeleton, a rigid hard pore temperature-pressure coupling correction term, and a compressible crack temperature-pressure coupling correction term. The stiffness of the skeleton is reduced by linearly superimposing the correction terms. The response function of the shear modulus of the dry rock skeleton is based on the shear modulus of the dry rock skeleton without cracks, and adopts the same dual pore reduction architecture as the bulk modulus. A pore deformation sensitive parameter is introduced specifically for the calculation of the shear modulus. The sensitive parameter is independent of the sensitive parameter corresponding to the bulk modulus.
[0018] In one embodiment of this disclosure, determining the bulk modulus of a mixed fluid includes: obtaining the liquid phase saturation, gas phase saturation, liquid phase bulk modulus, and gas phase bulk modulus within the pores; and calculating the equivalent bulk modulus of the mixed fluid based on the volume fraction of each phase fluid and the reciprocal relationship of their compressibility coefficients.
[0019] In one embodiment of this disclosure, determining the bulk modulus and shear modulus of saturated rock includes: establishing a constraint relationship between the dry rock skeleton modulus, matrix modulus, total porosity, and fluid modulus based on the Gassmann fluid substitution model; obtaining the bulk modulus of saturated rock by solving the constraint relationship, while keeping the shear modulus of saturated rock constant at the same level as the dry rock skeleton shear modulus.
[0020] In one embodiment of this disclosure, determining the longitudinal wave velocity and the transverse wave velocity includes: based on the linear elastic wave theory, using the bulk modulus, shear modulus, and density of the saturated rock, calculating the longitudinal wave velocity and the transverse wave velocity using the elastic wave velocity analytical formula; wherein, the longitudinal wave velocity is determined by the combination of the bulk modulus and shear modulus of the saturated rock, and the transverse wave velocity is determined by the shear modulus of the saturated rock.
[0021] According to another aspect of this disclosure, an electronic device is provided, comprising: a memory for storing instructions; and a processor for calling the instructions stored in the memory to implement the above-described method for predicting the P-wave and S-wave velocities of saturated porous rocks.
[0022] According to another aspect of this disclosure, a computer program product is provided, which stores instructions that, when executed by a computer, cause the computer to implement the above-described method for predicting the longitudinal and transverse wave velocities of saturated porous rocks.
[0023] The method for predicting the P-wave and S-wave velocities of saturated porous rocks provided in this disclosure accurately obtains the intrinsic bulk modulus and shear modulus of the matrix through equivalent calculations of mineral component volume fractions and corresponding elastic moduli, laying a reliable physical foundation for the entire calculation process. Furthermore, based on the dual-pore medium theory, the total porosity of the rock is decoupled into rigid hard pore porosity and compressible fracture porosity. A coupling function is specifically constructed to describe the dynamic evolution of different pore components under temperature and pressure conditions, solving the problem of inaccurate characterization of time-varying pore structure characteristics in traditional models. This method further incorporates the analysis of dry rock skeletons without fractures. By using the bulk modulus of the framework and the equivalent modulus of the matrix, the elastic modulus of the dry rock framework dynamically changes with effective pressure and absolute temperature, accurately reflecting the coupled influence of temperature and pressure conditions on the framework stiffness. Finally, based on dynamically updated real-time total porosity, the elastic modulus of the dry framework, and pore fluid parameters, the elastic modulus of the saturated rock is calculated, and the P-wave velocity and S-wave velocity are derived. This significantly improves the prediction accuracy and stability of P-wave and S-wave velocities under complex geological conditions, reliably supporting multiple core tasks in reservoir geophysical exploration, such as reservoir identification, fluid discrimination, geostress evaluation, and time-shifting dynamic monitoring. Its applicability and engineering value are significantly superior to traditional prediction methods.
[0024] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description
[0025] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.
[0026] Obviously, the accompanying drawings described below are merely some embodiments of this disclosure. Those skilled in the art can obtain other drawings based on these drawings without any creative effort.
[0027] Figure 1 A flowchart illustrating a method for predicting the P-wave and S-wave velocities of saturated porous rocks according to an embodiment of this disclosure is shown.
[0028] Figure 2 This diagram illustrates the flowchart for constructing the coupling function in an embodiment of this disclosure;
[0029] Figure 3 A flowchart illustrating another method for predicting the P-wave and S-wave velocities of saturated porous rocks in an embodiment of this disclosure is shown.
[0030] Figure 4 The diagram shows a comparison of wave velocities between the traditional DZ model, the model disclosed in this paper, and experimentally measured wave velocities under different effective pressure conditions.
[0031] Figure 5a, Figure 5b , Figure 5c , Figure 5d , Figure 5e and Figure 5f This shows the measured mineral content and physical property parameters curves from well logging.
[0032] Figure 6a A comparison diagram of longitudinal wave velocities is shown;
[0033] Figure 6b A comparison diagram of shear wave velocities is shown;
[0034] Figure 7a This chart shows a comparison of the errors in the prediction of P-wave velocities by rock physics models that take temperature and pressure into account.
[0035] Figure 7b A comparison chart showing the error in predicting shear wave velocities using rock physics models that take temperature and pressure into account;
[0036] Figure 7c A comparison chart showing the error in predicting P-wave velocities using rock physics models that do not consider temperature and pressure is presented.
[0037] Figure 7d A comparison chart showing the error in predicting shear wave velocities using rock physics models that do not consider temperature and pressure is presented.
[0038] Figure 8 A structural block diagram of an electronic device according to an embodiment of the present disclosure is shown. Detailed Implementation
[0039] The exemplary implementation will now be described more fully with reference to the accompanying drawings.
[0040] It should be noted that the example implementation can be implemented in many forms and should not be construed as being limited to the examples set forth herein.
[0041] With the development of deep oil and gas exploration and development, geothermal development, and underground energy storage, the response of rock physical properties and seismic wave propagation characteristics to temperature and pressure conditions has attracted widespread attention. Effective pressure and absolute temperature in formations not only change with burial depth but also fluctuate continuously due to factors such as tectonic movement, fluid migration, and injection-production development. These changes induce alterations in rock pore structure and elastic parameter evolution, which in turn cause changes in seismic wave propagation characteristics, including wave velocity dispersion, attenuation, and variations in reflection response. Therefore, accurately revealing the changing patterns of rock physical properties and wave propagation characteristics under the combined effects of effective pressure and absolute temperature is of great significance for deep oil and gas exploration and development, reservoir dynamic monitoring, geostress assessment, and seismic data interpretation.
[0042] In practical engineering applications, scholars both domestically and internationally have conducted extensive research on the impact of temperature and pressure environments on rock properties. Pore structure models predict rock elastic properties by establishing the relationship between pore parameters such as porosity and fracture aspect ratio and effective pressure. Acoustoelastic models describe the changes in elastic parameters caused by pressure by introducing third-order elastic constants. Empirical models establish empirical relationships between pressure and rock physical parameters through fitting experimental data. Some studies have also established empirical models of pore structure and elastic modulus changes under temperature effects to describe the changes in rock physical properties under thermal influence. However, these existing technologies generally only consider the single effect of effective pressure or absolute temperature on rock properties, lacking a unified description of the coupling mechanism between the two. When rocks are simultaneously affected by pressure and temperature changes, existing models struggle to effectively characterize pore structure, fracture development characteristics, and the changes in elastic parameters, and also fail to reflect the mutual constraints between effective pressure and absolute temperature. This limits their predictive accuracy in applications such as high-temperature, high-pressure oil and gas reservoirs and time-lapse seismic monitoring.
[0043] To address the shortcomings of existing technologies, this implementation scenario, based on the dual-porosity media theory, decouples the total porosity of rock into two categories: rigid hard pore porosity and compressible fracture porosity. Quantitative coupling functions are established for the changes in hard pore porosity, fracture porosity, and the bulk modulus and shear modulus of dry rock as a function of effective pressure and absolute temperature, respectively. This enables dynamic quantitative characterization of rock pore and elastic parameters under temperature and pressure conditions. Furthermore, by incorporating a fluid-saturated rock physics model, the predicted pore parameters and dry rock elastic parameters under temperature and pressure conditions are introduced into the model, allowing for quantitative prediction of the P-wave velocity and S-wave velocity of porous rocks under different effective pressures and absolute temperatures.
[0044] The following detailed description of this exemplary implementation method is provided in conjunction with the accompanying drawings and embodiments.
[0045] Figure 1 This diagram illustrates a flowchart of a method for predicting the P-wave and S-wave velocities of saturated porous rocks according to an embodiment of the present disclosure. Figure 1 As shown, the method for predicting the P-wave and S-wave velocities of saturated porous rocks includes steps S110-S160.
[0046] In S110, the volume fraction of mineral components, mineral bulk modulus, and mineral shear modulus of the target reservoir rock are obtained.
[0047] The obtained mineral composition parameters can be obtained through core X-ray diffraction experiments, well logging curve interpretation, etc. The mineral elastic modulus is the intrinsic physical parameter of the corresponding mineral, which is not affected by temperature and pressure conditions, and is the basic input for the calculation of all subsequent elastic parameters.
[0048] In S120, the matrix equivalent bulk modulus and matrix equivalent shear modulus are determined based on the mineral component volume fraction, mineral bulk modulus, and mineral shear modulus.
[0049] By using the equivalent homogenization method, the non-uniform matrix of multi-mineral mixture is equivalent to a continuous homogeneous medium. The obtained matrix equivalent elastic modulus can accurately characterize the intrinsic contribution of mineral components to the overall elasticity of the rock, and provide a benchmark for the subsequent quantitative calculation of the influence of pore structure.
[0050] In S130, based on the dual-pore medium theory, the total porosity of rock is decoupled into rigid hard pore porosity and compressible fracture porosity, and a coupling function of rigid hard pore porosity and compressible fracture porosity as a function of effective pressure and absolute temperature is constructed.
[0051] Existing models often treat rock pores as a homogeneous whole, failing to distinguish the differences in temperature and pressure responses among different pore components. This step innovatively decouples total porosity into rigid hard pore porosity, which is minimally affected by temperature and pressure, and compressible fracture porosity, which is highly sensitive to temperature and pressure changes. The constructed coupling function simultaneously encompasses the synergistic effect of effective pressure and absolute temperature, enabling precise characterization of the dynamic evolution of pore structure under temperature and pressure conditions.
[0052] In S140, the bulk modulus and shear modulus of the dry rock skeleton as a function of effective pressure and absolute temperature are calculated based on the coupling function of the bulk modulus of the dry rock skeleton without cracks, the equivalent bulk modulus of the matrix, the porosity of rigid hard pores and the porosity of compressible cracks.
[0053] Based on the baseline modulus of a crack-free dry rock skeleton, the elastic modulus of the dry rock skeleton was calculated by coupling the equivalent modulus of the matrix with the thermo-baric coupling function of two types of pores, thus realistically reproducing the synergistic regulatory effect of thermo-baric conditions on the stiffness of the rock skeleton. The pore deformation-sensitive parameters involved can be obtained by fitting and calibrating triaxial thermo-baric experimental data from the core.
[0054] In S150, the bulk modulus and shear modulus of saturated rock are determined based on the bulk modulus of the dry rock skeleton, the shear modulus of the dry rock skeleton, the real-time total porosity, and the bulk modulus of the mixed fluid; wherein, the bulk modulus of the mixed fluid is determined based on the pore fluid parameters.
[0055] The real-time total porosity is the sum of the porosity of rigid hard pores and the porosity of compressible fractures under the current temperature and pressure conditions. The bulk modulus of the mixed fluid is calculated based on the saturation of fluids such as oil, gas, and water within the pores and their respective elastic moduli. The bulk modulus of saturated rock calculated using the fluid-saturated rock physics model can reflect the influence of fluid filling on the overall elasticity of the rock, and the shear modulus of saturated rock is consistent with the shear modulus of the dry rock skeleton, which conforms to the fluid-skeleton interaction law under the low-frequency limit.
[0056] In S160, the P-wave velocity and S-wave velocity are determined based on the bulk modulus, shear modulus, and density of saturated rock. The P-wave velocity and S-wave velocity are used for reservoir geophysical exploration.
[0057] Based on the linear elastic wave theory, the P-wave and S-wave velocities are calculated using the elastic modulus and density of saturated rocks. The obtained P-wave and S-wave velocities can be directly used in geophysical exploration scenarios such as reservoir lithology identification, fluid type determination, geostress assessment, and time-lapse seismic dynamic monitoring, providing reliable data support for engineering applications such as deep oil and gas development, geothermal resource assessment, and underground energy storage monitoring.
[0058] In some embodiments, constructing a coupling function of rigid hard pore porosity and compressible fracture porosity as a function of effective pressure and absolute temperature may include... Figure 2 S201-S202.
[0059] In S201, based on the compressibility characteristics of porosity with effective pressure and the thermal expansion characteristics with absolute temperature, the first-order partial derivatives of porosity with respect to effective pressure and absolute temperature are established.
[0060] Starting from the fundamental thermodynamic mechanisms of rock physics, the complex temperature-pressure coupling problem is decomposed into pressure-induced compression and temperature-induced thermal expansion. By establishing two independent first-order partial derivatives, the rate of porosity reduction under a unit pressure increment and the rate of porosity expansion under a unit temperature increment can be accurately quantified. This differential form of description overcomes the shortcomings of traditional empirical models that simply linearly superimpose temperature and pressure effects, laying the physical foundation for subsequent rigorous analytical solutions and ensuring the applicability of the model across different temperature and pressure ranges.
[0061] In S202, by integrating the first-order partial derivatives, explicit analytical expressions are obtained for the changes in porosity of rigid hard pores and compressible fracture porosity with effective pressure and absolute temperature.
[0062] By analytically integrating the aforementioned system of differential equations, a concise and physically meaningful explicit analytical expression was obtained. Compared to traditional numerical iterative methods, the explicit analytical expression exhibits extremely high computational efficiency, meeting the timeliness requirements of large-scale industrial well logging data processing. More importantly, this expression mathematically guarantees the physical evolution law of porosity exhibiting a nonlinear decrease with increasing pressure (fracture closure) and a monotonically increasing change with increasing temperature, ensuring that the model maintains high numerical stability and reliability when predicting rock physical properties under extreme temperature and pressure conditions.
[0063] In some embodiments, the explicit analytical expression for rigid hard-pore porosity is composed of the superposition of the product of the linear factor of effective pressure and the exponential factor of absolute temperature, and the explicit analytical expression for compressible fracture porosity is composed of the product of the initial fracture porosity, the negative exponential factor of effective pressure, and the exponential factor of absolute temperature; the first derivative of rigid hard-pore porosity with respect to effective pressure is positive and the first derivative with respect to absolute temperature is positive; the first derivative of compressible fracture porosity with respect to effective pressure is negative and the first derivative with respect to absolute temperature is positive.
[0064] For the expression of porosity of rigid hard pores, a structure combining an effective pressure linear factor and an absolute temperature exponential factor is adopted to accurately match the physical characteristics of rigid hard pores: rigid hard pores are mostly intergranular pores formed by primary sedimentation or diagenesis, with strong compressive strength. Constrained by surrounding rigid mineral particles, they only undergo slight expansion due to minute displacement between particles when the effective pressure increases. The linear factor can accurately characterize this weak pressure response characteristic. On the other hand, the thermal expansion of mineral lattice and the thermal relaxation effect of particles caused by temperature increase have a cumulative growth. The exponential factor can accurately match this thermal response law, avoiding the prediction bias caused by the traditional model simplifying hard pores as "completely incompressible" or "linearly compressible". In particular, it improves the porosity prediction accuracy in the low-pressure and low-temperature range.
[0065] For the expression of compressible fracture porosity, a structure is adopted that multiplies the initial fracture porosity by the negative exponential factor of effective pressure and the absolute temperature exponential factor to accurately reproduce the dynamic evolution law of fractures: compressible fractures are mostly secondary pores formed by tectonic movements or later modifications. When the effective pressure increases, the fractures close rapidly and the high-pressure section tends to stabilize. The negative exponential factor can accurately characterize this "pressure-sensitive threshold" characteristic. When the temperature increases, the fracture surface opens due to heat and the effect of mineral thermal expansion driving fracture expansion increases nonlinearly. The exponential factor can accurately match this thermal response characteristic, solving the problem that traditional models cannot describe the nonlinear compaction behavior of fractures, and greatly improving the reliability of fracture porosity prediction under pressure change and high temperature environments.
[0066] The first derivatives of rigid hard-pore porosity with respect to effective pressure and absolute temperature are both positive, consistent with the principle that rigid hard-pores expand slightly with increasing temperature and pressure due to skeletal constraints. Compressible fracture porosity, on the other hand, exhibits negative first derivatives with respect to effective pressure and positive first derivatives with respect to absolute temperature, aligning with the common understanding that fractures close under pressure and open under heat, thus mathematically ensuring the physical reliability of the prediction results. Crucially, the coupling design of temperature and pressure factors in the expression accurately characterizes the mutual constraints between pressure and temperature. For example, high-pressure environments inhibit pore expansion caused by thermal expansion, while high-temperature environments weaken the compressive strength of the rock skeleton and accelerate fracture closure, compensating for the shortcomings of traditional single-factor models that neglect the temperature-pressure coupling effect. Experimental verification shows that the error between the porosity predicted using this analytical expression and the measured values from rock cores can be controlled within 5%, laying a solid foundation for the accurate prediction of the elastic modulus of dry rock skeletons and the P-wave and S-wave velocities of saturated rocks.
[0067] In some embodiments, calculating the bulk modulus and shear modulus of the dry rock skeleton as a function of effective pressure and absolute temperature includes: based on the baseline modulus of the dry rock skeleton without cracks, introducing deformation-sensitive parameters corresponding to rigid hard pore porosity and compressible crack porosity, and constructing response functions of the bulk modulus and shear modulus of the dry rock skeleton with respect to temperature and pressure; wherein, both the bulk modulus and shear modulus of the dry rock skeleton increase with increasing effective pressure and decrease with increasing absolute temperature. This step is a core intermediate link connecting the aforementioned results of the temperature and pressure evolution of the pore structure with the subsequent fluid saturation calculation. It uses the baseline modulus of the dry rock skeleton without cracks as the basis for calculation. This baseline modulus characterizes the intrinsic stiffness of an ideal dry skeleton without cracks and containing only rigid hard pores. Based on this, pore deformation sensitive parameters corresponding to rigid hard pores and compressible cracks are introduced to quantify the differential reduction contribution of the two types of pores to the skeleton stiffness. Finally, an elastic modulus response function of the dry rock skeleton that simultaneously couples the effects of effective pressure and absolute temperature is constructed, and the bulk modulus and shear modulus correspond to independent sensitive parameters, which can match the differential response characteristics of the two types of parameters to the temperature and pressure environment.
[0068] In some embodiments, the response function of the bulk modulus of the dry rock skeleton is based on the bulk modulus of the dry rock skeleton without cracks, and introduces a modulus difference term between the matrix and the skeleton, a rigid hard pore temperature-pressure coupling correction term, and a compressible crack temperature-pressure coupling correction term. The stiffness of the skeleton is reduced by linearly superimposing the correction terms. The response function of the shear modulus of the dry rock skeleton is based on the shear modulus of the dry rock skeleton without cracks, and adopts the same dual pore reduction architecture as the bulk modulus. A pore deformation sensitive parameter is introduced specifically for the calculation of the shear modulus. The sensitive parameter is independent of the sensitive parameter corresponding to the bulk modulus.
[0069] In some embodiments, determining the bulk modulus of the mixed fluid includes: obtaining the liquid phase saturation, gas phase saturation, liquid phase bulk modulus, and gas phase bulk modulus within the pores; and calculating the equivalent bulk modulus of the mixed fluid based on the volume fraction of each fluid phase and the reciprocal relationship of their compressibility coefficients. This step is a crucial link in converting dry rock skeleton parameters to saturated rock parameters. The obtained liquid phase can correspond to common reservoir liquid fluids such as formation water and crude oil, while the gas phase can correspond to gaseous fluids such as natural gas and injected carbon dioxide, fully adapting to actual reservoir conditions where oil, gas, and water coexist. Calculating the equivalent bulk modulus of the mixed fluid based on the volume fraction of each fluid phase and the reciprocal relationship of their compressibility coefficients conforms to the mechanical response law of multiphase fluid mixing systems, eliminating the need for a single simplified assumption about the fluid phases and effectively solving the problem of modulus prediction deviation caused by traditional models that only consider single-phase fluids. The calculation logic is simple and efficient, and it can be adapted to the batch processing needs of large-scale industrial logging data. Moreover, the obtained mixed fluid bulk modulus is linked with the porosity and dry rock skeleton modulus results under the previous temperature and pressure coupling effect, which can accurately characterize the influence of fluid replacement on the elasticity of saturated rock, and provide reliable fluid parameter support for subsequent P-wave and S-wave velocity prediction and time-shift seismic fluid dynamic monitoring.
[0070] In some embodiments, determining the bulk modulus and shear modulus of saturated rock includes: establishing constraint relationships between the dry rock skeleton modulus, matrix modulus, total porosity, and fluid modulus based on the Gassmann fluid substitution model; obtaining the bulk modulus of saturated rock by solving the constraint relationships, while maintaining the shear modulus of saturated rock at the same level as the dry rock skeleton shear modulus. This step is the core link between the dry skeleton and saturated rock parameters, employing the Gassmann fluid substitution model under the low-frequency limit, adapted to the frequency characteristics of seismic exploration. This model conforms to the physical law that fluids are not resistant to shear, clearly demonstrating that the shear modulus after saturation is consistent with the dry skeleton, significantly improving the reliability of fluid substitution calculations and supporting dynamic fluid monitoring in time-lapsed seismic events.
[0071] In some embodiments, determining the P-wave velocity and S-wave velocity includes: based on linear elastic wave theory, using the bulk modulus, shear modulus, and density of saturated rock, calculating the P-wave velocity and S-wave velocity using analytical formulas for elastic wave velocity; wherein the P-wave velocity is determined by the combination of the bulk modulus and shear modulus of the saturated rock, and the S-wave velocity is determined by the shear modulus of the saturated rock. The obtained P-wave and S-wave velocities strictly match the elastic wave propagation law, and their differences can effectively distinguish reservoir lithology and fluid type, directly serving seismic data interpretation and reservoir evaluation.
[0072] This disclosure primarily addresses the problem that existing rock physics models, which typically only consider the single effect of pressure or temperature, struggle to effectively characterize the variations in rock porosity and elastic parameters under the coupled effects of temperature and pressure. It also solves the technical challenge of establishing a quantitative mapping relationship between temperature and pressure conditions and rock porosity, elastic modulus, and seismic wave velocity. By constructing quantitative functional relationships between hard pore porosity, fracture porosity, and the elastic modulus of dry rock as a function of temperature and pressure, and combining this with the theory of fluid-bearing porous media, quantitative prediction of P-wave and S-wave velocities is achieved. This disclosure can quantitatively characterize the changes in rock physical properties under temperature and pressure environments, improving the prediction accuracy of P-wave and S-wave velocities in saturated fluid porous rocks, thereby providing a reliable theoretical basis and technical support for the evaluation of complex oil and gas reservoirs, rock physics analysis, seismic data interpretation, and reservoir dynamic monitoring.
[0073] The following is a reference appendix. Figure 3 A detailed introduction to rock physics modeling and P- and S-wave velocity estimation methods that consider the combined effects of temperature and pressure, such as... Figure 1 As shown, the detailed technical details are as follows:
[0074] First, the mineral composition, such as quartz, clay, and calcite, is determined based on the actual conditions of the study area. These minerals typically exhibit isotropic characteristics due to their random and uniform arrangement. Therefore, the Voigt-Reuss-Hill average can be used to estimate the equivalent elastic modulus of the matrix.
[0075]
[0076]
[0077] in and These represent the bulk modulus and shear modulus of the matrix, respectively. , and They represent the first Volume fraction, bulk modulus, and shear modulus of each mineral. N represents the total number of mineral species.
[0078] Based on the above, the differential equation describing the variation of porosity with effective pressure and temperature can be derived, and its expression is:
[0079]
[0080]
[0081] in, The effective pressure is (i.e., overburden pressure - pore pressure), and T is the absolute temperature (i.e., the increase relative to the initial temperature). Defined as the coefficient of volumetric thermal expansion. This represents the bulk modulus of dry rock.
[0082] Taking into account the differences in compressibility, Shapiro (2003) considered the total porosity Divided into rigid hard holes that are difficult to compress And easily compressible fissures Two parts. Based on its proposed elastic piezoelectric sensitivity model, the volume compressibility of dry rock... It can be represented as:
[0083]
[0084] in, The bulk modulus of a dry rock skeleton without cracks.
[0085] Based on the dual-porosity theory, the porosity of rigid hard pores and fractured pores varying with temperature and pressure can be further expressed as:
[0086]
[0087]
[0088] in, The coefficient of thermal expansion is the coefficient of thermal expansion of a dry rock skeleton without cracks. and These represent the initial hard pore and fracture porosity, respectively, when not subjected to temperature and pressure. , , and It is a sensitive parameter characterizing pore deformation.
[0089] Next, considering the effects of pressure and temperature on the elastic modulus of rock, rigid pores and fractures that vary with temperature and pressure are further added to the matrix, thus transforming the formula... and Substitution In the process, the bulk modulus and shear modulus of the dry rock skeleton are obtained:
[0090]
[0091]
[0092] in, The shear modulus of a dry rock skeleton without cracks.
[0093] Then, based on the Gassmann fluid substitution equation, fluid was added to the dry rock skeleton, and the elastic modulus of the saturated fluid porous rock was calculated:
[0094]
[0095]
[0096] in, The equivalent fluid modulus of a mixed fluid can be calculated as follows:
[0097]
[0098] in, and These represent the bulk modulus of liquids and gases, respectively. Indicates the saturation level of a liquid.
[0099] Finally, the formula and Substituting the obtained saturated fluid porous rock volume and shear modulus, along with the rock density, at the coupled effective pressure and temperature into the following expression, the P-wave and S-wave velocities of the saturated fluid porous rock can be further calculated:
[0100]
[0101] In the above embodiments, firstly, based on the rock mineral composition, the Voigt-Reuss-Hill averaging method is used to calculate the equivalent bulk modulus and shear modulus of the matrix to characterize the equivalent elastic properties of the mixed mineral matrix. Based on this, the concept of a dual-porosity medium is introduced, dividing the rock pore space into two categories: rigid hard pores and easily compressible fractures. A function of porosity as a function of pressure and temperature is established based on the dual-porosity medium theory, obtaining the bulk modulus and shear modulus of the dry rock skeleton under varying temperature and pressure conditions. Finally, the dry rock skeleton modulus obtained under the combined effects of temperature and pressure is introduced into the Gassmann fluid substitution equation, and fluid is added to the dry rock skeleton to obtain saturated rock. Finally, the predicted P-wave velocity and S-wave velocity results coupled with temperature and pressure are obtained. Compared with traditional rock physics models that do not consider the effects of temperature and pressure, the core of this embodiment is to explicitly introduce the coupled influence of effective pressure and temperature on porosity and skeleton elastic parameters into the seismic rock physics modeling process, quantitatively characterizing the variation of rock elastic parameters and wave velocity with temperature and pressure, thereby significantly improving the accuracy and applicability of P-wave and S-wave velocity prediction under complex geological conditions.
[0102] Based on the rock physics modeling method that considers the combined effects of pressure and temperature, and combined with laboratory data and well logging data, a comparative analysis of the model-predicted P-wave and S-wave velocities and the measured P-wave and S-wave velocities was further conducted to verify the rationality and effectiveness of the method proposed in this invention.
[0103] Figure 4 The paper presents a comparison of the P and S wave velocities predicted by the novel model proposed in this disclosure, the conventional David-Zimmerman (DZ) model, and the P and S wave velocities of Vosges sandstone as a function of effective pressure, as measured in a laboratory at room temperature. Figure 4 As can be seen, under low effective pressure conditions, the P-wave and S-wave velocities predicted by the model of this disclosure have a better agreement with the experimental measurements, while the prediction results of the DZ model show some deviation from the experimental values. As the effective pressure increases, the prediction results of the two models gradually converge, and under high pressure conditions, both maintain good consistency with the experimental measurements. This indicates that this disclosure can accurately characterize the influence of effective pressure changes on the elastic properties and wave velocity characteristics of rocks, and has good prediction accuracy and applicability over a wide pressure range.
[0104] Figure 5a , Figure 5b , Figure 5c , Figure 5d , Figure 5e and Figure 5f The diagram displays well-logged measured mineral content, porosity, water saturation, and density values of the seismic rock physics model considering the combined effects of pressure and temperature proposed in this disclosure. These values are then used as input parameters into the seismic rock physics model considering the combined effects of temperature and pressure established in this disclosure. The predicted P-wave and S-wave velocities (red line) are compared with the well-logged measured P-wave and S-wave velocities (blue line) and the prediction results of a traditional rock physics model not considering temperature and pressure (green line). Figure 6a and Figure 6b As shown. From Figure 6a and Figure 6b As can be seen, the prediction results of the rock physics model proposed in this disclosure are in better agreement with the measured P-wave and S-wave velocities, which proves the effectiveness and advantages of the rock physics model that considers the combined effects of temperature and pressure in predicting P-wave and S-wave velocities.
[0105] Figure 7 shows a comparison between the P-wave and S-wave velocity errors predicted by the rock physics model considering the combined effects of temperature and pressure, and the wave velocity error distributions predicted by traditional models. As shown in Figure 7, compared to the traditional rock physics model that does not consider the effects of temperature and pressure, the P-wave and S-wave velocity errors predicted by the rock physics model considering the combined effects of temperature and pressure proposed in this disclosure remain within 10%, and the errors are mainly concentrated near zero, exhibiting an overall approximately normal distribution. This indicates that the model established in this disclosure does not have significant systematic bias and has good stability and predictive reliability.
[0106] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result.
[0107] In some embodiments, certain steps may be omitted, multiple steps may be combined into one step for execution, and / or one step may be broken down into multiple steps for execution.
[0108] Based on the same inventive concept, this disclosure also provides an electronic device. Figure 8 This is a structural block diagram of an electronic device provided in an embodiment of the present invention. Figure 8 As shown, an embodiment of the present invention provides an electronic device including: one or more processors 801, a memory 802, and one or more I / O interfaces 803. The memory 802 stores one or more programs, which, when executed by the one or more processors, enable the one or more processors to implement any of the P-wave and S-wave velocity prediction methods for saturated porous rocks as described in the above embodiments; the one or more I / O interfaces 803 are connected between the processor and the memory, configured to enable information interaction between the processor and the memory.
[0109] Among them, processor 801 is a device with data processing capabilities, including but not limited to central processing unit (CPU); memory 802 is a device with data storage capabilities, including but not limited to random access memory (RAM, more specifically SDRAM, DDR, etc.), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory (FLASH); I / O interface (read-write interface) 803 is connected between processor 801 and memory 802, and can realize information interaction between processor 801 and memory 802, including but not limited to data bus (Bus).
[0110] In some embodiments, the processor 801, memory 802, and I / O interface 803 are interconnected via bus 804, and thus connected to other components of the computing device.
[0111] In some embodiments, the one or more processors 801 include a field-programmable gate array.
[0112] This invention also provides a computer-readable medium. The computer-readable medium stores a computer program, which, when executed by a processor, implements the steps in any of the P-wave and S-wave velocity prediction methods for saturated porous rocks described in the above embodiments. The computer-readable storage medium can be volatile or non-volatile.
[0113] This invention also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code. When the computer-readable code is run in the processor of an electronic device, the processor in the electronic device executes the above-described method for predicting the longitudinal and transverse wave velocities of saturated porous rocks.
[0114] Those skilled in the art will understand that all or part of the steps of the above embodiments can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software implementations, which can be collectively referred to as "circuit", "module" or "system".
[0115] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein.
[0116] This disclosure is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.
Claims
1. A method for predicting the P-wave and S-wave velocities of saturated porous rocks, characterized in that, include: Obtain the volume fraction of mineral components, mineral bulk modulus, and mineral shear modulus of the target reservoir rocks; Based on the volume fraction of the mineral components, the bulk modulus of the minerals, and the shear modulus of the minerals, determine the matrix equivalent bulk modulus and the matrix equivalent shear modulus. Based on the dual-porosity media theory, the total porosity of rock is decoupled into rigid hard pore porosity and compressible fracture porosity, and a coupling function of the rigid hard pore porosity and compressible fracture porosity as a function of effective pressure and absolute temperature is constructed. Based on the coupling function of the bulk modulus of the dry rock skeleton without cracks, the equivalent bulk modulus of the matrix, the porosity of the rigid hard pores, and the porosity of the compressible cracks, the bulk modulus and shear modulus of the dry rock skeleton as a function of effective pressure and absolute temperature are calculated. Based on the bulk modulus of the dry rock skeleton, the shear modulus of the dry rock skeleton, the real-time total porosity, and the bulk modulus of the mixed fluid, the bulk modulus and shear modulus of the saturated rock are determined; wherein, the bulk modulus of the mixed fluid is determined based on pore fluid parameters. Based on the bulk modulus, shear modulus, and density of the saturated rock, the P-wave velocity and S-wave velocity are determined, and these velocities are used for reservoir geophysical exploration.
2. The method as described in claim 1, characterized in that, The coupling function that constructs the rigid hard pore porosity and compressible fracture porosity as a function of effective pressure and absolute temperature includes: Based on the compressibility characteristics of porosity with effective pressure and the thermal expansion characteristics with absolute temperature, the first-order partial derivatives of porosity with respect to effective pressure and absolute temperature are established. By integrating the first-order partial derivatives, explicit analytical expressions are obtained for the changes in rigid hard pore porosity and compressible fracture porosity with effective pressure and absolute temperature.
3. The method as described in claim 2, characterized in that, The explicit analytical expression for rigid hard pore porosity is composed of the superposition of the product of the linear factor of effective pressure and the exponential factor of absolute temperature, and the explicit analytical expression for compressible fracture porosity is composed of the product of the initial fracture porosity, the negative exponential factor of effective pressure, and the exponential factor of absolute temperature. The first derivative of the rigid hard pore porosity with respect to effective pressure is positive, and the first derivative with respect to absolute temperature is positive; the first derivative of the compressible fracture porosity with respect to effective pressure is negative, and the first derivative with respect to absolute temperature is positive.
4. The method as described in claim 1, characterized in that, The calculation of the dry rock skeleton bulk modulus and dry rock skeleton shear modulus as a function of effective pressure and absolute temperature includes: Based on the reference modulus of a dry rock skeleton without cracks, deformation-sensitive parameters corresponding to rigid hard pore porosity and compressible crack porosity are introduced to construct response functions of the bulk modulus and shear modulus of the dry rock skeleton with respect to temperature and pressure. The bulk modulus and shear modulus of the dry rock skeleton both increase with increasing effective pressure and decrease with increasing absolute temperature.
5. The method as described in claim 4, characterized in that, The response function of the bulk modulus of the dry rock skeleton is based on the bulk modulus of the dry rock skeleton without cracks. It introduces the modulus difference term between the matrix and the skeleton, the rigid hard pore temperature-pressure coupling correction term, and the compressible crack temperature-pressure coupling correction term. The stiffness of the skeleton is reduced by linearly superimposing the correction terms. The response function of the dry rock skeleton shear modulus is based on the dry rock skeleton shear modulus without cracks, adopts the same dual pore reduction architecture as the bulk modulus, and introduces a pore deformation sensitive parameter specifically for shear modulus calculation. The sensitive parameter is independent of the sensitive parameter corresponding to the bulk modulus.
6. The method as described in claim 1, characterized in that, Determining the bulk modulus of the mixed fluid includes: Obtain the liquid phase saturation, gas phase saturation, liquid phase bulk modulus, and gas phase bulk modulus within the pores; The equivalent bulk modulus of the mixed fluid is calculated based on the volume fraction of each phase fluid and the reciprocal of its compressibility coefficient.
7. The method as described in claim 1, characterized in that, Determining the bulk modulus and shear modulus of saturated rock includes: Based on the Gassmann fluid substitution model, the constraint relationship between dry rock skeleton modulus, matrix modulus, total porosity and fluid modulus is established; By solving the constraint relationship, the bulk modulus of the saturated rock is obtained, and the shear modulus of the saturated rock remains unchanged as the shear modulus of the dry rock skeleton.
8. The method as described in claim 1, characterized in that, The determination of the P-wave velocity and S-wave velocity includes: Based on the linear elastic wave theory, the longitudinal wave velocity and transverse wave velocity are calculated by using the bulk modulus, shear modulus and density of saturated rock through the analytical formula of elastic wave velocity. The longitudinal wave velocity is determined by the combination of the bulk modulus and shear modulus of the saturated rock, and the transverse wave velocity is determined by the shear modulus of the saturated rock.
9. An electronic device, characterized in that, include: Memory, used to store instructions; A processor is configured to invoke instructions stored in the memory to implement the method for predicting the P-wave and S-wave velocities of saturated porous rocks as described in any one of claims 1-8.
10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the computer instructions are executed by the processor, they implement the method for predicting the longitudinal and transverse wave velocities of saturated porous rocks according to any one of claims 1-8.