Formation pressure calculation method and system based on Hooke's law

Abstract

Disclosed is a formation pressure calculation method and system based on Hooke's law. The method may include: calculating the bulk modulus of the fluid according to the longitudinal wave equation; calculating the dry bulk modulus according to the fluid bulk modulus; calculating the effective stress according to the dry bulk modulus through Hooke's law; and calculating the formation pressure according to the effective stress and the overlying formation pressure. The present invention derives the theoretical relationship between the effective stress and the rock velocity based on the wave equation and the elementary elastic theory, and predicts the formation pressure in combination with the effective stress principle. It does not need to construct a normal compaction trend line, and is better adapted to the prediction of carbonate formation pressure.

Description

Technical Field

[0001] The present invention relates to the field of oil and gas geophysical exploration, and more specifically, to a formation pressure calculation method and system based on Hooke's law. Background Art

[0002] Abnormal formation pressure is a common phenomenon in oil and gas basins, and is closely related to the generation, migration and accumulation of oil and gas. By studying the changes in formation pressure, we can find out the basic laws of oil and gas migration direction, enrichment characteristics, and oil and gas pressure and lithology change characteristics. Abnormal formation pressure, especially abnormally high pressure, is directly related to drilling and fracturing safety, and thus to personal and property safety, and to the oil and gas exploration process. Predicting abnormal pressure before drilling is of great significance for discovering oil and gas reservoirs, designing reasonable drilling fluid density and wellbore structure, ensuring drilling safety, improving drilling success rate, reducing drilling costs, and protecting oil and gas layers.

[0003] Since logging data is less affected by human factors and can change continuously with the depth of the well, the data has good continuity, high vertical resolution and reliability. The acoustic velocity, density, resistivity and other parameters of the formation have a certain relationship with the formation pore pressure and show a certain regularity. It is recognized as an ideal method to determine the formation pore pressure. In the logging data, a variety of logging methods that can detect the change of formation rock porosity (such as acoustic time difference logging, compensated density logging, resistivity logging and neutron logging, etc.) can be used to detect the formation pore pressure. Deep lateral resistivity and acoustic time difference are two commonly used methods for predicting formation pore pressure. Its basic principle is based on the undercompaction theory. In a normally compacted formation, as the burial depth increases, the porosity of shale decreases, resulting in a decrease in formation water content and an increase in wave velocity and resistivity. In an abnormally high-pressure formation, the formation porosity increases, resulting in an increase in formation water content and a decrease in wave velocity and resistivity. The formation pore pressure is predicted based on this inverse relationship. Compared with density logging and resistivity logging, acoustic logging is less affected by the environment such as borehole and formation conditions, and the acoustic logging data is complete and easy to collect. The use of acoustic time difference data to calculate the formation pore pressure is representative, universal and comparable. Using acoustic logging data to predict the formation pore pressure of a single well or region in a drilled area is a common and effective method to establish a single well or regional formation pore pressure profile.

[0004] However, some conventional methods or models based on undercompaction theory, such as the equivalent depth method, Eaton method, and Bowers method, are not well adapted to carbonate formations in theory. The cause of abnormal formation pressure in carbonate rocks is different from the undercompaction mechanism of clastic sedimentary rocks. The relationship between the longitudinal wave velocity and porosity is dispersed, and the conventional method for predicting formation pressure in carbonate rocks has great uncertainty. Therefore, it is necessary to develop a formation pressure calculation method and system based on Hooke's law.

[0005] The information disclosed in the background technology section of the present invention is only intended to deepen the understanding of the general background technology of the present invention, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art already known to those skilled in the art. Summary of the invention

[0006] The present invention proposes a formation pressure calculation method and system based on Hooke's law, which can derive the theoretical relationship between effective stress and rock velocity based on the wave equation and elementary elasticity theory, and predict formation pressure in combination with the effective stress principle. It does not need to construct a normal compaction trend line, and is better adapted to carbonate rock formation pressure prediction.

[0007] According to one aspect of the present invention, a formation pressure calculation method based on Hooke's law is proposed. The method may include: calculating the fluid bulk modulus according to the longitudinal wave equation; calculating the dry bulk modulus according to the fluid bulk modulus; calculating the effective stress according to the dry bulk modulus by Hooke's law; and calculating the formation pressure according to the effective stress and the overlying formation pressure.

[0008] Preferably, the longitudinal wave equation is:

[0009]

[0010] Among them, Vp sat is the fluid longitudinal wave velocity, μ sat is the fluid shear modulus, ρ sat is the fluid density, K sat is the bulk modulus of the fluid.

[0011] Preferably, the bulk modulus of the fluid is calculated by formula (2):

[0012]

[0013] Preferably, the dry bulk modulus is calculated by formula (3):

[0014]

[0015] Among them, K dry is the dry bulk modulus, K0 is the rock matrix equivalent modulus, K f is the bulk modulus of the mixed fluid, and φ is the porosity.

[0016] Preferably, the effective stress is calculated by formula (4):

[0017] σ=(ΔV / V)·K dry (4)

[0018] Where σ is the effective stress and ΔV / V is the volumetric strain.

[0019] Preferably, the formation stress is calculated by formula (5):

[0020] P f =P OV -σ (5)

[0021] Among them, P f is the formation stress, P OV is the overlying formation pressure.

[0022] According to another aspect of the present invention, a formation pressure calculation system based on Hooke's law is proposed, characterized in that the system comprises: a memory storing computer executable instructions; a processor running the computer executable instructions in the memory to perform the following steps: calculating the fluid bulk modulus according to the longitudinal wave equation; calculating the dry bulk modulus according to the fluid bulk modulus; calculating the effective stress according to the dry bulk modulus through Hooke's law; calculating the formation pressure according to the effective stress and the overlying formation pressure.

[0023] Preferably, the longitudinal wave equation is:

[0024]

[0025] Among them, Vp sat is the fluid longitudinal wave velocity, μ sat is the fluid shear modulus, ρ sat is the fluid density, K sat is the bulk modulus of the fluid.

[0026] Preferably, the bulk modulus of the fluid is calculated by formula (2):

[0027]

[0028] Preferably, the dry bulk modulus is calculated by formula (3):

[0029]

[0030] Among them, K dry is the dry bulk modulus, K0 is the rock matrix equivalent modulus, K f is the bulk modulus of the mixed fluid, and φ is the porosity.

[0031] Preferably, the effective stress is calculated by formula (4):

[0032] σ=(ΔV / V)·K dry (4)

[0033] Where σ is the effective stress and ΔV / V is the volumetric strain.

[0034] Preferably, the formation stress is calculated by formula (5):

[0035] P f =P OV -σ (5)

[0036] Among them, P f is the formation stress, P OV is the overlying formation pressure.

[0037] The methods and apparatus of the present invention have other features and advantages that will be apparent from, or will be described in detail in, the accompanying drawings and subsequent detailed descriptions incorporated herein, which together serve to explain the specific principles of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention in conjunction with the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present invention.

[0039] Figure 1 A flow chart showing the steps of a formation pressure calculation method based on Hooke's law according to the present invention.

[0040] Figure 2a , Figure 2b , Figure 2c , Figure 2d , Figure 2e , Figure 2f Schematic diagrams showing predicted formation pressure, formation pressure coefficient, P-wave velocity, S-wave velocity, density and Poisson's ratio according to an embodiment of the present invention are shown respectively. DETAILED DESCRIPTION

[0041] The present invention will be described in more detail below with reference to the accompanying drawings. Although preferred embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to make the present invention more thorough and complete, and to fully convey the scope of the present invention to those skilled in the art.

[0042] Figure 1 A flow chart showing the steps of a formation pressure calculation method based on Hooke's law according to the present invention.

[0043] In this embodiment, the formation pressure calculation method based on Hooke's law according to the present invention may include: step 101, calculating the fluid bulk modulus according to the longitudinal wave equation; step 102, calculating the dry bulk modulus according to the fluid bulk modulus; step 103, calculating the effective stress according to the dry bulk modulus through Hooke's law; step 104, calculating the formation pressure according to the effective stress and the overlying formation pressure.

[0044] In one example, the longitudinal wave equation is:

[0045]

[0046] Among them, Vp sat is the fluid longitudinal wave velocity, μ sat is the fluid shear modulus, ρ sat is the fluid density, K sat is the bulk modulus of the fluid.

[0047] In one example, the fluid bulk modulus is calculated by equation (2):

[0048]

[0049] In one example, the dry bulk modulus is calculated by equation (3):

[0050]

[0051] Among them, K dry is the dry bulk modulus, K0 is the rock matrix equivalent modulus, K f is the bulk modulus of the mixed fluid, and φ is the porosity.

[0052] In one example, the effective stress is calculated by equation (4):

[0053] σ=(ΔV / V)·K dry (4)

[0054] Where σ is the effective stress and ΔV / V is the volumetric strain.

[0055] In one example, the formation stress is calculated by formula (5):

[0056] P f =P OV -σ (5)

[0057] Among them, P f is the formation stress, P OV is the overlying formation pressure.

[0058] Specifically, according to the effective stress principle:

[0059] Pov =σ+P f (6)

[0060] Overlying formation pressure P OV It is composed of the effective stress σ between the rock particles and the support of the fluid in the pores, that is, the formation pressure P f Therefore, if the overburden pressure P is calculated OV and effective stress σ, the formation pressure P can be calculated f . Overlying formation pressure P OV It refers to the pressure caused by the total weight of the bedrock and the fluid in the rock pores covering a certain depth. The effective stress σ refers to the stress acting on the skeleton particles of the formation rock.

[0061] The formation pressure calculation method based on Hooke's law according to the present invention may include:

[0062] According to the longitudinal wave equation formula (1), because:

[0063] μ sat =ρ sat Vs sat 2 (7)

[0064] Among them, Vs sat is the shear wave velocity of the rock saturated with fluid. Substitute formula (7) into formula (1) to obtain formula (2) to calculate the fluid bulk modulus. Then, according to the Gassmann equation, the dry bulk modulus is calculated by formula (3).

[0065] From the elementary elasticity theory we know that:

[0066]

[0067] In the formula, σ sat is the effective stress of rock saturated with fluid, and ΔV / V is the volume strain calculated by Hooke's law, which has a certain relationship with the burial depth. Therefore, ΔV / V can be expressed as a function of the burial depth, which can be a simple linear function or a more complex logarithmic function. It is tested and determined based on the results of lithology testing, well logging interpretation and other results in the actual work area.

[0068] As mentioned above, in the effective stress principle formula for calculating formation pressure, the effective stress σ refers to the stress acting on the rock skeleton particles of the formation, so σ = σ dry Similarly, by applying elementary elasticity theory, the effective stress can be calculated using formula (4).

[0069] Based on Wood's equation, the bulk modulus of the mixed fluid can be obtained:

[0070]

[0071] Assume that the rock matrix is ​​composed of n minerals, and the bulk modulus of each mineral is K i (i=1…n), the volume fraction of each mineral is f i (i=1…n). According to Voigt upper limit theory, we have

[0072]

[0073] According to Reuss's offline theory:

[0074]

[0075] Based on the VRH average model, the rock matrix equivalent modulus K0 can be obtained as:

[0076] K0=(K V +K R ) / 2 (12).

[0077] Then, the formation pressure is calculated according to the effective stress and the overlying formation pressure using formula (5).

[0078] Hydrostatic pressure refers to the water column pressure in an open system connected to the rock surface and the ground surface, which is equivalent to the vertical height of the water column from the target layer to the water source. The calculation formula for hydrostatic pressure is:

[0079] P HY =0.098ρ w ·depth (13)

[0080] In the above formula, P HY is the hydrostatic pressure, in kg / cm 2 ρ w is the relative density of formation water, in kg / cm 3 ; The formation pressure P f and hydrostatic pressure P HY By dividing, we can also get the pressure coefficient, which is:

[0081] P coef =P f / P HY (14).

[0082] This method derives the theoretical relationship between effective stress and rock velocity based on the wave equation and elementary elasticity theory, and predicts formation pressure in combination with the effective stress principle. It does not need to construct a normal compaction trend line and is better suited to carbonate formation pressure prediction.

[0083] Application Examples

[0084] To facilitate understanding of the solution and effects of the embodiments of the present invention, a specific application example is given below. Those skilled in the art should understand that this example is only for facilitating understanding of the present invention, and any specific details thereof are not intended to limit the present invention in any way.

[0085] Taking a block in the Tarim Basin as an example, the formation pressure is predicted. The necessary logging curves for the pressure prediction model to predict the formation pressure of a single well are collected, including the P-wave velocity curve, S-wave velocity curve, density curve and porosity curve.

[0086] Figure 2a , Figure 2b , Figure 2c , Figure 2d , Figure 2e , Figure 2f Schematic diagrams showing predicted formation pressure, formation pressure coefficient, P-wave velocity, S-wave velocity, density and Poisson's ratio according to an embodiment of the present invention are shown respectively.

[0087] Substitute the measured curve into the model to calculate the formation pressure of the well, as shown in Figure 2a As shown, the formation pressure coefficient is calculated based on formula (14), and the result is as follows Figure 2b As shown in the figure. The leftmost solid line in the first column is the hydrostatic pressure, the rightmost solid line is the overlying formation pressure, the middle solid line is the formation pressure; the second column solid line is the formation pressure coefficient. Figure 2c , Figure 2d , Figure 2e , Figure 2f The order is P-wave velocity, S-wave velocity, density and Poisson's ratio. 6634-6680m is the reservoir development section, and the pressure coefficient has an upward trend, which is consistent with the actual drilling situation.

[0088] In summary, the present invention derives the theoretical relationship between effective stress and rock velocity based on the wave equation and elementary elasticity theory, and predicts formation pressure in combination with the effective stress principle. It does not need to construct a normal compaction trend line, and is better adapted to carbonate formation pressure prediction.

[0089] Those skilled in the art should understand that the purpose of the above description of the embodiments of the present invention is only to exemplarily illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any given examples.

[0090] According to an embodiment of the present invention, a formation pressure calculation system based on Hooke's law is provided, characterized in that the system comprises: a memory storing computer executable instructions; a processor running the computer executable instructions in the memory to perform the following steps: calculating the fluid bulk modulus according to the longitudinal wave equation; calculating the dry bulk modulus according to the fluid bulk modulus; calculating the effective stress according to the dry bulk modulus through Hooke's law; and calculating the formation pressure according to the effective stress and the overlying formation pressure.

[0091] In one example, the longitudinal wave equation is:

[0092]

[0093] Among them, Vp sat is the fluid longitudinal wave velocity, μ sat is the fluid shear modulus, ρ sat is the fluid density, K sat is the bulk modulus of the fluid.

[0094] In one example, the fluid bulk modulus is calculated by equation (2):

[0095]

[0096] In one example, the dry bulk modulus is calculated by equation (3):

[0097]

[0098] Among them, K dry is the dry bulk modulus, K0 is the rock matrix equivalent modulus, K f is the bulk modulus of the mixed fluid, and φ is the porosity.

[0099] In one example, the effective stress is calculated by equation (4):

[0100] σ=(ΔV / V)·K dry (4)

[0101] Where σ is the effective stress and ΔV / V is the volumetric strain.

[0102] In one example, the formation stress is calculated by formula (5):

[0103] P f =P OV -σ (5)

[0104] Among them, P f is the formation stress, P OV is the overlying formation pressure.

[0105] This system derives the theoretical relationship between effective stress and rock velocity based on the wave equation and elementary elasticity theory, and predicts formation pressure in combination with the effective stress principle. It does not need to construct a normal compaction trend line and is better suited to carbonate formation pressure prediction.

[0106] Those skilled in the art should understand that the purpose of the above description of the embodiments of the present invention is only to exemplarily illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any given examples.

[0107] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A formation pressure calculation method based on Hooke's law, characterized in that: include: According to the longitudinal wave equation, the bulk modulus of the fluid is calculated; Calculating a dry bulk modulus based on the fluid bulk modulus; Based on the dry bulk modulus, the effective stress is calculated by Hooke's law; Calculating formation pressure based on the effective stress and overlying formation pressure; Wherein, the longitudinal wave equation is: Among them, Vp sat is the fluid longitudinal wave velocity, μ sat is the fluid shear modulus, ρ sat is the fluid density, K sat is the bulk modulus of the fluid; The bulk modulus of the fluid is calculated by formula (2): Wherein, the dry bulk modulus is calculated by formula (3): Among them, K dry is the dry bulk modulus, K0 is the rock matrix equivalent modulus, K f is the bulk modulus of the mixed fluid, φ is the porosity; The effective stress is calculated by formula (4): σ=(ΔV / V)·K dry (4) Where σ is the effective stress and ΔV / V is the volumetric strain.

2. The formation pressure calculation method based on Hooke's law according to claim 1, wherein: The formation pressure is calculated by formula (5): P f =P OV -σ (5) Among them, P f is the formation pressure, P OV is the overlying formation pressure.

3. A formation pressure calculation system based on Hooke's law, characterized in that: The system includes: a memory storing computer executable instructions; A processor, wherein the processor runs the computer executable instructions in the memory to perform the following steps: According to the longitudinal wave equation, the bulk modulus of the fluid is calculated; Calculating a dry bulk modulus based on the fluid bulk modulus; Based on the dry bulk modulus, the effective stress is calculated by Hooke's law; Calculating formation pressure based on the effective stress and overlying formation pressure; Wherein, the longitudinal wave equation is: Among them, Vp sat is the fluid longitudinal wave velocity, μ sat is the fluid shear modulus, ρ sat is the fluid density, K sat is the bulk modulus of the fluid; The bulk modulus of the fluid is calculated by formula (2): Wherein, the dry bulk modulus is calculated by formula (3): Among them, K dry is the dry bulk modulus, K0 is the rock matrix equivalent modulus, K f is the bulk modulus of the mixed fluid, φ is the porosity; The effective stress is calculated by formula (4): σ=(ΔV / V)·K dry (4) Where σ is the effective stress and ΔV / V is the volumetric strain.

4. The formation pressure calculation system based on Hooke's law according to claim 3, wherein: The formation pressure is calculated by formula (5): P f =P OV -σ (5) Among them, P f is the formation pressure, P OV is the overlying formation pressure.

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