CN112651098A - Hooke law-based formation pressure calculation method and system - Google Patents
Hooke law-based formation pressure calculation method and system Download PDFInfo
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Abstract
A method and system for calculating the stratum pressure based on Hooke's law are disclosed. The method can comprise the following steps: calculating the bulk modulus of the fluid according to a longitudinal wave equation; calculating the dry bulk modulus according to the bulk modulus of the fluid; calculating effective stress according to the dry bulk modulus and through Hooke's law; and calculating the formation pressure according to the effective stress and the overburden pressure. The invention deduces the theoretical relationship between the effective stress and the rock speed based on the wave equation and the elementary elastic theory, and predicts the formation pressure by combining the effective stress principle, without constructing a normal compaction trend line, thereby being better suitable for predicting the carbonate formation pressure.
Description
Technical Field
The invention relates to the field of oil and gas geophysical exploration, in particular to a stratum pressure calculation method and a stratum pressure calculation system based on Hooke's law.
Background
The abnormal formation pressure is a phenomenon commonly existing in a hydrocarbon-containing basin and has close relation with the generation, migration and accumulation of oil and gas. The change of the formation pressure can be researched to find out the basic rules of the oil-gas migration direction, the enrichment characteristics, the oil-gas pressure and the lithology change characteristics and the like. Abnormal formation pressure, especially abnormal high pressure, is directly related to drilling and fracturing safety, thereby being related to personal and property safety and being related to the exploration process of oil and gas. The abnormal pressure prediction is made before drilling, and the method has very important significance for finding oil and gas reservoirs, designing reasonable drilling fluid density and well body structure, guaranteeing drilling safety, improving the drilling success rate, reducing the drilling cost and protecting oil and gas reservoirs.
Because the logging data is less influenced by human factors and can continuously change along with the well depth, the data continuity is good, the longitudinal resolution and the reliability are high, and parameters such as the sound wave speed, the density, the resistivity and the like of the stratum have a certain relation with the pore pressure of the stratum and show a certain regularity. Are recognized as more desirable methods for determining the pore pressure of the formation. In the logging information, various logging methods (such as acoustic time difference logging, compensated density logging, resistivity logging, neutron logging, etc.) capable of detecting the change of the formation rock porosity can be used for detecting the formation pore pressure. Deep lateral resistivity and sonic moveout are two methods commonly used to predict formation pore pressure. The basic principle is based on the under-compaction theory, and in the normal compaction of the stratum, along with the increase of the buried depth, the porosity of the shale is reduced, so that the water content of the stratum is reduced, and the wave velocity and the resistivity are increased. In an abnormally high pressure stratum, the porosity of the stratum is increased, so that the water content of the stratum is increased, and the wave velocity and the resistivity are reduced. The formation pore pressure is predicted from this inverse relationship. Because the acoustic logging is more compact, the resistivity logging is less influenced by the environment such as well bore and stratum conditions, and the acoustic logging data are complete and easy to collect. The acoustic wave time difference data are selected to calculate the formation pore pressure, and the method is representative, universal and comparable. The method for predicting the formation pore pressure of a single well or a single region of a drilled region by using acoustic logging information is a common and effective method for establishing a formation pore pressure profile of the single well or the single region.
However, some conventional methods or models based on the under-compaction theory, such as the equivalent depth method, the Eaton method, the Bowers method and the like, cannot adapt to the carbonate formation well in theory. The carbonate rock abnormal formation pressure cause is different from the under-compaction mechanism of the clastic sedimentary rock, the longitudinal wave velocity-porosity relation is dispersed, and the carbonate rock formation pressure prediction by adopting a conventional method has great uncertainty. Therefore, there is a need to develop a method and system for calculating formation pressure based on hooke's law.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention provides a stratum pressure calculation method and a stratum pressure calculation system based on Hooke's law, which can deduce the theoretical relationship between effective stress and rock speed based on a wave equation and an elementary elastic theory, predict the stratum pressure by combining the effective stress principle, do not need to construct a normal compaction trend line, and better adapt to the carbonate stratum pressure prediction.
According to one aspect of the invention, a method of formation pressure calculation based on hooke's law is presented. The method may include: calculating the bulk modulus of the fluid according to a longitudinal wave equation; calculating a dry bulk modulus from the fluid bulk modulus; calculating effective stress according to the dry bulk modulus through Hooke's law; and calculating the formation pressure according to the effective stress and the overburden pressure.
Preferably, the longitudinal wave equation is:
wherein, VpsatIs the velocity of longitudinal wave of fluid, musatIs the fluid shear modulus, ρsatIs the density of the fluid, KsatIs the bulk modulus of the fluid.
Preferably, the fluid bulk modulus is calculated by equation (2):
preferably, the dry bulk modulus is calculated by equation (3):
wherein, KdryTo dry bulk modulus, K0Is the rock matrix equivalent modulus, KfPhi is the bulk modulus of the mixed fluid and phi is the porosity.
Preferably, the effective stress is calculated by equation (4):
σ＝(ΔV/V)·Kdry (4)
wherein σ is the effective stress and Δ V/V is the volume strain.
Preferably, the formation stress is calculated by equation (5):
Pf＝POV-σ (5)
wherein, PfIs formation stress, POVIs overburden pressure.
According to another aspect of the invention, a formation pressure calculation system based on hooke's law is proposed, characterized in that it comprises: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: calculating the bulk modulus of the fluid according to a longitudinal wave equation; calculating a dry bulk modulus from the fluid bulk modulus; calculating effective stress according to the dry bulk modulus through Hooke's law; and calculating the formation pressure according to the effective stress and the overburden pressure.
Preferably, the longitudinal wave equation is:
wherein, VpsatIs the velocity of longitudinal wave of fluid, musatIs the fluid shear modulus, ρsatIs the density of the fluid, KsatIs the bulk modulus of the fluid.
Preferably, the fluid bulk modulus is calculated by equation (2):
preferably, the dry bulk modulus is calculated by equation (3):
wherein, KdryTo dry bulk modulus, K0Is the rock matrix equivalent modulus, KfPhi is the bulk modulus of the mixed fluid and phi is the porosity.
Preferably, the effective stress is calculated by equation (4):
σ＝(ΔV/V)·Kdry (4)
wherein σ is the effective stress and Δ V/V is the volume strain.
Preferably, the formation stress is calculated by equation (5):
Pf＝POV-σ (5)
wherein, PfIs formation stress, POVIs overburden pressure.
The method and apparatus of the present invention have other features and advantages which will be apparent from or are set forth in detail in the accompanying drawings and the following detailed description, which are incorporated herein, and which together serve to explain certain principles of the invention.
Drawings
The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts.
Fig. 1 shows a flow chart of the steps of a method for formation pressure calculation based on hooke's law according to the present invention.
Fig. 2a, 2b, 2c, 2d, 2e, 2f show schematic diagrams of predicted formation pressure, formation pressure coefficient, compressional velocity, shear velocity, density and poisson's ratio, respectively, according to an embodiment of the invention.
Detailed Description
The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
Fig. 1 shows a flow chart of the steps of a method for formation pressure calculation based on hooke's law according to the present invention.
In this embodiment, the formation pressure calculation method based on hooke's law according to the present invention may include: step 101, calculating the volume modulus of the fluid according to a longitudinal wave equation; 102, calculating a dry bulk modulus according to the bulk modulus of the fluid; 103, calculating effective stress according to the dry bulk modulus and a hooke's law; and 104, calculating the formation pressure according to the effective stress and the overburden pressure.
In one example, the compressional wave equation is:
wherein, VpsatIs the velocity of longitudinal wave of fluid, musatIs the fluid shear modulus, ρsatIs the density of the fluid, KsatIs the bulk modulus of the fluid.
In one example, the fluid bulk modulus is calculated by equation (2):
in one example, the dry bulk modulus is calculated by equation (3):
wherein, KdryTo dry bulk modulus, K0Is the rock matrix equivalent modulus, KfPhi is the bulk modulus of the mixed fluid and phi is the porosity.
In one example, the effective stress is calculated by equation (4):
σ＝(ΔV/V)·Kdry (4)
wherein σ is the effective stress and Δ V/V is the volume strain.
In one example, the formation stress is calculated by equation (5):
Pf＝POV-σ (5)
wherein, PfIs formation stress, POVIs overburden pressure.
Specifically, according to the effective stress principle:
Pov＝σ+Pf (6)
overburden pressure POVIs the effective stress sigma and porosity caused by the mutual contact between rock particlesSupporting effect of medium fluid, i.e. formation pressure PfTo be commonly supported. Thus, if overburden pressure P is calculatedOVAnd effective stress σ, the formation pressure P can be calculatedf. Overburden pressure POVRefers to the pressure caused by the combined weight of the fluid in the formation matrix and rock pores covering a certain depth or more, and the effective stress sigma refers to the stress acting on the formation rock framework particles.
The formation pressure calculation method based on hooke's law according to the present invention may include:
according to the longitudinal wave equation (1), the following factors are also included:
μsat＝ρsatVssat 2 (7)
wherein, VssatSubstituting the formula (7) into the formula (1) to obtain the formula (2) to calculate the bulk modulus of the fluid for the transverse wave velocity of the rock containing the saturated fluid, and further calculating the dry bulk modulus through the formula (3) according to the gassmann equation.
According to elementary elastic theory, the following results are obtained:
in the formula, σsatFor the effective stress of the rock containing saturated fluid, the delta V/V is the volume strain calculated by Hooke's law and has a certain relation with the burial depth, so that the delta V/V can be expressed as a function of the burial depth, can be a simple linear function, can also be a relatively complex logarithmic function and the like, and is tested and determined according to the result data of actual work area lithology test, well logging interpretation and the like.
As previously mentioned, in the principle equation of effective stress for calculating formation pressure, the effective stress σ refers to the stress acting on the formation rock skeleton particles, so σ ═ σdry. Similarly, the effective stress is calculated by the formula (4) by applying the elementary elasticity theory.
Based on the equation of wood, the bulk modulus of the mixed fluid can be found:
assuming that the rock matrix is composed of n minerals, the bulk modulus of each mineral is Ki(i-1 … n) and the volume fraction of each mineral is fi(i ═ 1 … n). According to the upper limit theory of Voigt there is
According to reus offline theory:
based on a VRH average model, the equivalent modulus K of the rock matrix can be obtained0Comprises the following steps:
K0＝(KV+KR)/2 (12)。
and calculating the formation pressure according to the effective stress and the overburden pressure by a formula (5).
Hydrostatic pressure refers to the pressure of the water column under the open system communicating with the rock surface and the earth's surface, corresponding to the vertical height from the target layer to the water column of the water source. The calculation formula of the hydrostatic pressure is as follows:
PHY＝0.098ρw·depth (13)
in the above formula PHYIs hydrostatic pressure in kg/cm2；ρwIs the relative density of formation water in kg/cm3(ii) a Will the formation pressure PfWith hydrostatic pressure PHYIn addition, a pressure coefficient can be obtained, namely:
Pcoef＝Pf/PHY (14)。
the method deduces the theoretical relationship between the effective stress and the rock speed based on the wave equation and the elementary elastic theory, predicts the formation pressure by combining the effective stress principle, does not need to construct a normal compaction trend line, and is better suitable for predicting the formation pressure of the carbonate rock.
Application example
To facilitate understanding of the solution of the embodiments of the present invention and the effects thereof, a specific application example is given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention and that any specific details thereof are not intended to limit the invention in any way.
Taking a certain block of the Tarim basin as an example, the formation pressure is predicted. The logging curves which are necessary when the pressure prediction model is collected to carry out single-well formation pressure prediction specifically comprise a longitudinal wave velocity curve, a transverse wave velocity curve, a density curve and a porosity curve.
Fig. 2a, 2b, 2c, 2d, 2e, 2f show schematic diagrams of predicted formation pressure, formation pressure coefficient, compressional velocity, shear velocity, density and poisson's ratio, respectively, according to an embodiment of the invention.
The measured curve is substituted into a model to calculate the well formation pressure as shown in fig. 2a, and the formation pressure coefficient is calculated based on equation (14), the result is shown in fig. 2 b. In the figure, the leftmost solid line of the first column is hydrostatic pressure, the rightmost solid line is overburden formation pressure, and the middle solid line is formation pressure; the second solid line is the formation pressure coefficient. Fig. 2c, 2d, 2e, and 2f show longitudinal wave velocity, transverse wave velocity, density, and poisson's ratio in this order. 6634 and 6680m are reservoir development segments, pressure coefficient has ascending trend, and is consistent with actual drilling condition
In conclusion, the invention deduces the theoretical relationship between the effective stress and the rock speed based on the wave equation and the elementary elastic theory, and predicts the formation pressure by combining the effective stress principle, does not need to construct a normal compaction trend line, and is better suitable for predicting the carbonate formation pressure.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
According to an embodiment of the present invention, there is provided a formation pressure calculation system based on hooke's law, characterized by comprising: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: calculating the bulk modulus of the fluid according to a longitudinal wave equation; calculating the dry bulk modulus according to the bulk modulus of the fluid; calculating effective stress according to the dry bulk modulus and through Hooke's law; and calculating the formation pressure according to the effective stress and the overburden pressure.
In one example, the compressional wave equation is:
wherein, VpsatIs the velocity of longitudinal wave of fluid, musatIs the fluid shear modulus, ρsatIs the density of the fluid, KsatIs the bulk modulus of the fluid.
In one example, the fluid bulk modulus is calculated by equation (2):
in one example, the dry bulk modulus is calculated by equation (3):
wherein, KdryTo dry bulk modulus, K0Is the rock matrix equivalent modulus, KfPhi is the bulk modulus of the mixed fluid and phi is the porosity.
In one example, the effective stress is calculated by equation (4):
σ＝(ΔV/V)·Kdry (4)
wherein σ is the effective stress and Δ V/V is the volume strain.
In one example, the formation stress is calculated by equation (5):
Pf＝POV-σ (5)
wherein, PfIs formation stress, POVIs overburden pressure.
The system deduces the theoretical relationship between the effective stress and the rock speed based on the wave equation and the elementary elastic theory, predicts the formation pressure by combining the effective stress principle, does not need to construct a normal compaction trend line, and is better suitable for predicting the formation pressure of the carbonate rock.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.
Claims (10)
1. A method for calculating formation pressure based on hooke's law, comprising:
calculating the bulk modulus of the fluid according to a longitudinal wave equation;
calculating a dry bulk modulus from the fluid bulk modulus;
calculating effective stress according to the dry bulk modulus through Hooke's law;
and calculating the formation pressure according to the effective stress and the overburden pressure.
2. The hooke's law based formation pressure calculation method as claimed in claim 1, wherein the compressional wave equation is:
wherein, VpsatIs the velocity of longitudinal wave of fluid, musatIs the fluid shear modulus, ρsatIs the density of the fluid, KsatIs the bulk modulus of the fluid.
3. The hooke's law based formation pressure calculation method as claimed in claim 1, wherein the fluid bulk modulus is calculated by equation (2):
4. the hooke's law based formation pressure calculation method as claimed in claim 1, wherein the dry bulk modulus is calculated by equation (3):
wherein, KdryTo dry bulk modulus, K0Is the rock matrix equivalent modulus, KfPhi is the bulk modulus of the mixed fluid and phi is the porosity.
5. The hooke's law based formation pressure calculation method as claimed in claim 1, wherein the effective stress is calculated by equation (4):
σ＝(ΔV/V)·Kdry (4)
wherein σ is the effective stress and Δ V/V is the volume strain.
6. The hooke's law based formation pressure calculation method as claimed in claim 1, wherein the formation stress is calculated by equation (5):
Pf＝POV-σ (5)
wherein, PfIs formation stress, POVIs overburden pressure.
7. A formation pressure calculation system based on hooke's law, the system comprising:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
calculating the bulk modulus of the fluid according to a longitudinal wave equation;
calculating a dry bulk modulus from the fluid bulk modulus;
calculating effective stress according to the dry bulk modulus through Hooke's law;
and calculating the formation pressure according to the effective stress and the overburden pressure.
8. The hooke's law based formation pressure calculation system of claim 7, wherein the fluid bulk modulus is calculated by equation (2):
9. the hooke's law based formation pressure calculation system of claim 7, wherein the dry bulk modulus is calculated by equation (3):
wherein, KdryTo dry bulk modulus, K0Is the rock matrix equivalent modulus, KfPhi is the bulk modulus of the mixed fluid and phi is the porosity.
10. The hooke's law based formation pressure calculation system of claim 7, wherein the formation stress is calculated by equation (5):
Pf＝POV-σ (5)
wherein, PfIs formation stress, POVIs overburden pressure.
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