CN113466105B - Method for determining starting pressure gradient of compact gas reservoir - Google Patents

Method for determining starting pressure gradient of compact gas reservoir Download PDF

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CN113466105B
CN113466105B CN202110743392.0A CN202110743392A CN113466105B CN 113466105 B CN113466105 B CN 113466105B CN 202110743392 A CN202110743392 A CN 202110743392A CN 113466105 B CN113466105 B CN 113466105B
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pressure gradient
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曾凡辉
张涛
郭建春
王永红
王道成
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Southwest Petroleum University
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Abstract

The invention provides a method for determining a starting pressure gradient of a compact gas reservoir, which comprises the following steps: taking a single capillary in a compact gas reservoir matrix as a research object, and establishing a motion equation of gas-liquid two-phase flow of the single capillary by considering the influence of interface capillary force and effective slip factors; based on the established motion equation, acquiring a water phase flow velocity equation and a water phase flow equation of a single capillary, and performing scale upgrading through a fractal theory to obtain a water phase flow equation of a core scale; and (4) according to the water phase flow equation of the core scale, making the water phase flow be 0, and calculating to obtain a corresponding starting pressure gradient. The method overcomes the difficulty that the starting pressure gradient of the dense gas reservoir cannot be represented by a theoretical model in the prior art, and enables the calculation of the starting pressure gradient to be faster and more accurate.

Description

Method for determining starting pressure gradient of compact gas reservoir
The technical field is as follows:
the invention relates to the field of petroleum and natural gas development, in particular to a method for determining a compact gas reservoir starting pressure gradient.
Background
Dense gas resources in China are rich, the development potential is large, and the dense gas resource becomes one of the most important fields for increasing, storing and increasing the yield of natural gas in China. Compared with the conventional oil and gas reservoir, the permeability of the reservoir matrix of the compact gas reservoir is low, and the industrial productivity can be obtained only by adopting a hydraulic fracturing development mode.
The low-permeability compact gas reservoir has fine pore throat, poor pore connectivity, larger capillary resistance and generally higher water saturation, and the gas seepage easily generates unique seepage characteristics different from medium-high permeability gas reservoirs. Experiments show that when the water saturation of the rock core is greater than a certain threshold value, the gas seepage shows the low-speed non-Darcy seepage characteristic, namely, a starting pressure gradient exists. Dense gas reservoir initiation pressure gradients are prevalent during matrix infiltration. The previous research is mainly based on experimental determination, but the experimental method has no universality and can not accurately reveal the mechanism of the influence of water saturation on the starting pressure gradient; at present, the factor of starting pressure gradient of the dense gas reservoir is not fully known, and only macroscopic phenomena are obtained through experimental phenomena, so that the seepage characteristics of gas in the matrix cannot be accurately reflected.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a method for determining the starting pressure gradient of a dense gas reservoir, and overcomes the difficulty that the starting pressure gradient of the dense gas reservoir cannot be represented by a theoretical model in the prior art.
The purpose of the invention is realized by the following technical scheme.
The application provides a method for determining a gradient indicating curve of starting pressure of a compact gas reservoir, which comprises the following steps:
(1) taking a single capillary in a compact gas reservoir matrix as a research object, and establishing a motion equation of gas-liquid two-phase flow of the single capillary by considering the influence of interface capillary force and effective slip factors;
(2) acquiring a water phase flow rate equation and a water phase flow equation of a single capillary based on the motion equation established in the step (1), and performing scale upgrading through a fractal theory to acquire a water phase flow equation of a core scale;
(3) and (4) according to the water phase flow equation of the core scale, making the water phase flow be 0, and calculating to obtain a corresponding starting pressure gradient.
Further, the expression of the interfacial capillary force in the step (1) is as follows:
Figure BDA0003143501970000011
in the formula, pcIs the capillary force, gamma is the interfacial tension, r is the capillary radius, and theta is the contact angle.
Further, the effective slip expression in step (1) is:
Figure BDA0003143501970000012
in the formula IseFor effective slip length, /)saIs the apparent slip length; lstFor true slip length, μbIs the bulk fluid viscosity, μdFor effective viscosity, λ is the pore diameter, C-liquid constant.
Further, the equation of motion of the gas-liquid two-phase flow of the single capillary in the step (1):
Figure BDA0003143501970000021
in the formula: Δ p is the driving pressure difference, MPa; p is a radical ofcCapillary force, MPa; lseEffective slip length, nm; r is the capillary radius, nm; tau iswUltimate shear stress, MPa; μ is the fluid effective viscosity, mPa · s; v. ofwFluid flow velocity, nm/s; l is the actual distance of the capillary, nm; swIs% water saturation.
Further, the equation of the flow rate of the water phase of the single capillary in the step (2) is as follows:
Figure BDA0003143501970000022
in the formula, vw-sThe flow rate of the aqueous phase.
Further, the water phase flow equation of the single capillary in the step (2) is as follows:
Figure BDA0003143501970000023
in the formula, qw-sThe flow rate of the aqueous phase is single capillary.
The water phase flow process of the core scale in the step (2) is as follows:
Figure BDA0003143501970000024
in the formula, Qw-sThe flow rate of the aqueous phase at core size, rbmaxIs the maximum diameter of the capillary, rbminThe number of the capillary tubes is the minimum diameter of the capillary tube, and N is the total number of the capillary tubes on the cross section of the unit body; dfIs the pore fractal dimension.
The expression of the starting pressure gradient in the step (3) is as follows: 100
Figure BDA0003143501970000031
In the formula, Gt-sTo initiate the pressure gradient.
Compared with the prior art, the invention has the beneficial technical effects that:
(1) the method solves the problem that the starting pressure gradient of the compact gas reservoir cannot be theoretically represented in the conventional method, and can quantitatively represent the starting pressure gradient of the compact gas reservoir.
(2) The method is based on a gas-liquid two-phase motion equation, and can calculate the starting pressure gradient of the compact gas reservoir under different capillary parameter combinations.
Drawings
FIG. 1 is a graph of single capillary start pressure gradient versus slip length.
FIG. 2 is a graph of single capillary startup pressure gradient versus water saturation change.
FIG. 3 is a graph of single capillary start-up pressure gradient versus wetting angle.
FIG. 4 is a graph of the variation of the single capillary startup pressure gradient versus the ultimate shear stress.
FIG. 5 is a graph of core scale induced pressure gradient versus change in water saturation.
FIG. 6 is a graph of the variation of the core dimension initiation pressure gradient versus the ultimate shear stress.
FIG. 7 is a graph of core dimension initiation pressure gradient versus wetting angle.
FIG. 8 is a graph of core dimension initiation pressure gradient versus slip length.
FIG. 9 is a graph of a core scale initiated pressure gradient chart and an indication of fit.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Step 1, taking a single capillary in a compact gas reservoir matrix as a research object, considering the influence of interface capillary force and effective slippage factors, and establishing a motion equation of gas-liquid two-phase flow of the single capillary.
The capillary force expression of the two-phase interface is as follows:
Figure BDA0003143501970000032
in order to characterize the effective slip of the fluid flow in the capillary, the real slip length and the effective slip length are introduced.
Figure BDA0003143501970000041
Establishing a gas-liquid two-phase motion equation according to the combination of the flow stress balance of the gas drive water and the Newton's internal friction law:
Figure BDA0003143501970000042
in the formula: p is a radical ofcCapillary force, MPa; lseEffective slip length, nm; lsaIs the apparent slip length, nm; lstIs the true slip length, nm; Δ p is the driving pressure difference, MPa; r is the capillary radius, nm; tau iswUltimate shear stress, MPa; μ is the fluid effective viscosity, mPa · s; v. ofwFluid flow velocity, nm/s; l is the actual distance of the capillary, nm; swIs% water saturation.
And 2, acquiring a water phase flow rate equation and a water phase flow equation of a single capillary based on the motion equation established in the step 1, and performing scale upgrading through a fractal theory to acquire a core scale water phase flow equation.
The flow rate of the aqueous phase integrated for equation (3) is:
Figure BDA0003143501970000043
the single capillary water phase flow equation obtained by integrating the water phase flow rate is as follows:
Figure BDA0003143501970000044
according to the fractal theory, the total number N of capillary tubes on the cross section of the unit body with the reservoir pore diameter being more than or equal to lambda is as follows:
Figure BDA0003143501970000045
the derivation of λ in equation (6) can be found:
Figure BDA0003143501970000046
let λmin/λmaxBeta, then DfCan be expressed as:
Df＝d-lnφ/ln β (8)
in the formula: n is the total number of the capillary tubes on the cross section of the unit body; lambda [ alpha ]maxMaximum reservoir pore diameter, nm; lambda [ alpha ]minIs the minimum reservoir pore diameter, nm; dfIs a pore fractal dimension without dimension; d is the Euclidean dimension, d is 2; phi is porosity,%.
The cross section of the unit body can be regarded as the composition of capillary pipes with different diameters, and then the cross section area of the unit body can be calculated as follows:
Figure BDA0003143501970000051
in the formula: a is the cross section of the unit body, nm2；
The total flow equation of the capillary is obtained by integrating the flow equation of the single capillary through a fractal theory:
Figure BDA0003143501970000052
wherein q isw-sIs the water flow of a single capillary, m3/s；Qw-sIs the total flow rate, m3/s；rbmaxIs the maximum diameter of the capillary，nm；rbminIs the minimum diameter of the capillary tube, nm.
When the corresponding pressure gradient is the starting pressure gradient when the fluid just flows, namely when the water phase flow is 0, a single-capillary starting pressure gradient expression (11) and a total starting pressure gradient expression (12) can be respectively obtained:
Figure BDA0003143501970000053
Figure BDA0003143501970000061
wherein G isc-sStarting a pressure gradient for a single capillary, wherein the pressure gradient is MPa/m; gt-sThe total starting pressure gradient is MPa/m.
In order to facilitate the understanding and application of the technical scheme by the technical personnel in the field, calculation analysis is carried out by adopting actual calculation examples. The basic parameters used in the practical example are shown in table 1:
table 1 basic parameters
Figure BDA0003143501970000062
(2) Calculation results
As can be seen from fig. 1: the smaller the pore size, the greater the effect on the startup pressure gradient. Taking the pore diameters of the single capillary as 50nm and 800nm as examples, under the condition of different sliding lengths, the starting pressure gradient is reduced along with the increase of the sliding length, because the effective pore diameter considering effective sliding is generally larger than the effective sliding not considered, in contrast, the larger the sliding length is, the larger the flow space is, and the larger the sliding length is, in combination with the inverse relation between the pore diameter and the starting pressure gradient, the larger the sliding length is, so that the starting pressure gradient is smaller. It can also be seen from fig. 1 that the effect of the slip length on the start-up pressure gradient is more significant at small pipe diameters (50nm) and hardly changes at large pipe diameters (800nm), which indicates that the effect of the effective slip length on the start-up fracture gradient is negligible with increasing pipe diameter.
As can be seen from fig. 2: under the conditions of different water saturation, the starting pressure gradient and the pipe diameter of the capillary are in a negative correlation relationship. Under the condition of large pipe diameter, the water saturation has little influence on the starting pressure gradient; as the tube diameter decreases, the water saturation increases and the start-up pressure gradient increases.
As can be seen from fig. 3 and 4: the influence of wetting angle and ultimate shear stress on the starting pressure gradient shows a large difference; the whole wetting angle has little influence on the starting pressure gradient, and the starting pressure gradient can be obviously increased only when the wetting angle is 90 degrees; the influence of the ultimate shear stress on the starting pressure gradient is very obvious, and the starting pressure gradient is increased along with the increase of the ultimate shear stress, because the larger the ultimate shear stress is, the more difficult the fluid is to generate shear deformation, and the flow resistance is increased; at a pipe diameter of 200nm, the ultimate shear stress is increased by 1Pa, the starting pressure gradient is increased by 12.4 percent, the larger the ultimate shear stress is, the larger the difference of the starting pressure gradient is, and the difference is reduced along with the increase of the pipe diameter.
As can be seen from fig. 5 and 6: compared with the single capillary starting pressure gradient, under the condition of given fractal parameters, the total starting pressure gradient is increased along with the increase of water saturation and ultimate shear stress; the ultimate shear stress has the most remarkable influence on the starting pressure gradient, and at high water content (100%), the starting pressure gradient is increased by 20MPa/m every time the ultimate shear stress is increased by 20Pa, but the amplification is gradually reduced along with the reduction of the water saturation.
As can be seen from fig. 7 and 8: in contrast to water saturation and ultimate shear stress, wetting angle and slip length are not the main factors affecting the magnitude of the startup pressure gradient, but are also not negligible.
As can be seen from fig. 9: at the same water saturation and the same maximum and minimum capillary diameter ratio (r)max/rmin100), the starting pressure gradient is reduced along with the increase of the maximum pipe diameter, because the larger the maximum pipe diameter is, the more effective pipe diameters are contained integrally, and the smaller the capillary force is; if the ratio of the maximum to the minimum capillary diameter (r)max/rmin100), the start-up pressure gradient increases with increasing water saturationLarge; by the aid of the starting pressure gradient calculation model, starting pressure gradient change curves corresponding to different maximum minimum pipe diameter ratios along with water saturation are calculated. Because different cores have different water saturation and pore distribution, namely different maximum tubular diameter ratios, the change curve can be used for fitting a relation between water saturation and starting pressure gradient of different cores in the same block, can be quickly fitted and calculated to obtain a starting pressure gradient indicating curve of the block, and can also be used for correcting errors of conventional experiments and further improving timeliness.
In practical application, corresponding relation formulas can be obtained through fitting by calculating the starting pressure gradients corresponding to different maximum minimum pipe diameter ratios and different water saturation degrees. Fitting the data in the practical calculation example to obtain an empirical relation of water saturation and starting pressure gradient as
Figure BDA0003143501970000071
TABLE 2 fitting calculation results
Water saturation/% 1 20 40 60 80
rmax/r min 200/2 300/3 500/5 600/6 1000/10
TPG/MPa/m 0.17 0.855 1.76 4.08 7.79
While the present invention has been described in detail by way of the embodiments, it should be understood that the present invention is not limited to the embodiments disclosed herein, but is intended to cover other embodiments as well. But all the modifications and simple changes made by those skilled in the art without departing from the technical idea and scope of the present invention belong to the protection scope of the technical solution of the present invention.

Claims (2)

1. A method for determining a compact gas reservoir initiation pressure gradient, comprising the steps of:
(1) taking a single capillary in a compact gas reservoir matrix as a research object, and establishing a motion equation of gas-liquid two-phase flow of the single capillary by considering the influence of interface capillary force and effective slip factors;
the effective slip expression in the step (1) is as follows:
Figure FDA0003524773700000011
in the formula IseFor effective slip length, /)saIs the apparent slip length; lstFor true slip length, μbIs the bulk fluid viscosity, μdFor effective viscosity, μ is the effective viscosity of the fluid and λ is the poreDiameter, C is the liquid constant; theta is a contact angle;
the equation of motion of the gas-liquid two-phase flow of the single capillary in the step (1):
Figure FDA0003524773700000012
wherein Δ p is a driving pressure difference, pcIs the capillary force, r is the capillary radius, lseFor effective slip length, τwFor ultimate shear stress, μ is the effective viscosity of the fluid, vwFor fluid flow rate, L is the actual distance of the capillary, swThe water saturation;
(2) acquiring a water phase flow rate equation and a water phase flow equation of a single capillary based on the motion equation established in the step (1), and performing scale upgrading through a fractal theory to acquire a water phase flow equation of a core scale;
the water phase flow rate equation of the single capillary in the step (2) is as follows:
Figure FDA0003524773700000013
in the formula, vw-sThe flow rate of the water phase;
the water phase flow equation of the single capillary in the step (2) is as follows:
Figure FDA0003524773700000014
in the formula, qw-sThe flow rate of the water phase is single capillary;
the water phase flow process of the core scale in the step (2) is as follows:
Figure FDA0003524773700000021
in the formula, Qw-sFlow rate of water phase at core scale，rbmaxIs the maximum diameter of the capillary tube, rbminIs the minimum diameter of capillary, N is the total number of capillary on the cross section of unit body, DfA fractal dimension for the pore;
(3) according to the water phase flow equation of the core scale, making the water phase flow be 0, and calculating to obtain a corresponding starting pressure gradient;
the expression of the starting pressure gradient in the step (3) is as follows:
Figure FDA0003524773700000022
in the formula, Gt-sTo initiate the pressure gradient.
2. A method of determining a dense gas reservoir initiation pressure gradient as claimed in claim 1, wherein the interfacial capillary force in step (1) is expressed by:
Figure FDA0003524773700000023
in the formula, pcIs the capillary force, gamma is the interfacial tension, r is the capillary radius, and theta is the contact angle.
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CN112883657A (en) * 2021-01-13 2021-06-01 中国长江三峡集团有限公司 Single-pile vertical bearing time-varying effect calculation method considering soil body non-Darcy consolidation

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH0875512A (en) * 1994-09-08 1996-03-22 Tokyo Gas Co Ltd Fluidic flowmeter
WO2001086283A2 (en) * 2000-05-11 2001-11-15 Ontogen Corporation Apparatus and method for multiple channel high throughput purification
DE102008061456B3 (en) * 2008-12-10 2010-05-12 Siemens Aktiengesellschaft Method for determining the speed of a vehicle during a braking operation
CN103776748A (en) * 2014-02-14 2014-05-07 武汉科技大学 Predication method for effective permeability of Bingham fluid in porous medium
CN106545336A (en) * 2015-09-16 2017-03-29 中国石油化工股份有限公司 Consider the Productivity of tight gas reservoir seepage flow mechanism
CN111929219A (en) * 2020-08-12 2020-11-13 西南石油大学 Shale oil reservoir oil-water two-phase relative permeability calculation method
CN112883657A (en) * 2021-01-13 2021-06-01 中国长江三峡集团有限公司 Single-pile vertical bearing time-varying effect calculation method considering soil body non-Darcy consolidation

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