CN114595963A - Bottom water reservoir horizontal bottom water ridge entering form description method based on production dynamic data - Google Patents

Bottom water reservoir horizontal bottom water ridge entering form description method based on production dynamic data Download PDF

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CN114595963A
CN114595963A CN202210219926.4A CN202210219926A CN114595963A CN 114595963 A CN114595963 A CN 114595963A CN 202210219926 A CN202210219926 A CN 202210219926A CN 114595963 A CN114595963 A CN 114595963A
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张贵才
王翔
胡俊杰
蒋平
马珍福
邵现振
钱军
李月胜
唐林
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China University of Petroleum East China
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Abstract

The invention relates to a bottom water reservoir horizontal bottom water ridge entering form description method based on production dynamic data, which comprises the following steps: (1) acquiring production dynamic data of a target block or an oil reservoir developed horizontal well, and reservoir physical property parameters, fluid physical property parameters and seepage properties of a layer position where the horizontal well is located; (2) judging the developed horizontal well bottom water breakthrough times and corresponding breakthrough times, selecting a single point to breakthrough a horizontal well, calculating bottom water ridge shape parameters of different development times before bottom water breakthrough by combining a substance balance principle, and describing by using a water cone shape description formula; (3) obtaining the change rule of the water cone width index along with development time by utilizing nonlinear fitting and multiple linear regression; (4) and describing the water ridge entering form of the multi-point breakthrough horizontal well bottom, and calculating the water ridge volume under different development time. The technical scheme of the invention can provide guidance for the optimization design of the stable yield increasing measures of the bottom water oil reservoir, is simple and practical, and has important guiding significance for the development of the bottom water oil reservoir.

Description

Bottom water reservoir horizontal bottom water ridge entering form description method based on production dynamic data
Technical Field
The invention relates to a bottom water reservoir horizontal bottom water ridge entering form description method based on production dynamic data, and belongs to the technical field of oil and gas field development.
Background
In the development of the bottom water reservoir, a high-speed water flow channel is formed after bottom water enters suddenly, water content rises rapidly, yield is reduced greatly, yield increasing measures such as water control and the like need to be taken to improve the development effect, and for the optimal design of yield stabilizing and increasing measures of a bottom water reservoir horizontal well, the horizontal bottom water ridge entering form needs to be described so as to better guide production.
Chinese patent document CN109958404B discloses a method for calculating parameters of bottom water coning and water plugging profile control agent for bottom water reservoir, which can accurately perform experimental study on the influence of the vertical well type and the rising rule of the bottom water, the experimental result is real and credible, and the rising dynamics of the bottom water can be observed more intuitively, but the method does not determine the bottom water breakthrough time, and the formula for calculating the volume of the water cone considers that the oil saturation in the water cone is the residual oil saturation under consideration.
The application number CN112664173A patent of the invention discloses a quantitative characterization method for a bottom water reservoir water cone, which is characterized in that a bottom water reservoir water cone height expression is established according to a statics principle and an established oil layer flow velocity expression, and then the water cone height of the bottom water reservoir is characterized, but the method does not provide a bottom water rising form characterization method for a horizontal well.
A great deal of research is carried out on the description method of the horizontal bottom water ridge advance form of the bottom water reservoir at home and abroad, and most of the research is based on an oil-water two-phase seepage equation, takes the coupling of longitudinal flow and horizontal flow into consideration, and does not take the actual production condition of an oil well into consideration. In order to describe the horizontal bottom-hole water ridge shape more conveniently, a bottom-water reservoir horizontal bottom-hole water ridge shape description method based on production dynamic data needs to be established so as to guide production more conveniently.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a bottom water reservoir horizontal bottom water ridge entering form description method based on production dynamic data, which judges the bottom water breakthrough times and the corresponding breakthrough time of developed horizontal wells based on the analysis of the production dynamic data, describes the bottom water ridge entering form, calculates the water ridge volumes at different development times and provides guidance for the optimization design of the bottom water reservoir horizontal well stable yield increasing measures.
The technical scheme of the invention is as follows:
a bottom water reservoir horizontal bottom water ridge entering form description method based on production dynamic data comprises the following steps:
(1) acquiring production dynamic data of a target block or an oil reservoir developed horizontal well, and reservoir physical property parameters, fluid physical property parameters and seepage properties of a layer position where the horizontal well is located;
(2) judging the developed horizontal well bottom water breakthrough times and corresponding breakthrough times, selecting a single point to breakthrough a horizontal well, calculating bottom water ridge shape parameters of different development times before bottom water breakthrough by combining a substance balance principle, and describing by using a water cone shape description formula;
(3) obtaining the change rule of the water cone width index along with development time by utilizing nonlinear fitting and multivariate linear regression;
(4) and describing the water ridge entering form of the multi-point breakthrough horizontal well bottom, and calculating the water ridge volume under different development time.
Preferably, in the step (1), the production dynamic data comprises development date and corresponding daily liquid yield, daily water yield and water content, and is derived by an oil well production dynamic data acquisition system;
the physical parameters of the reservoir comprise oil layer thickness, water-avoiding height (distance between an oil-water interface and a horizontal well), porosity and permeability, and are obtained from development data such as oil well oil reservoir design books and the like;
the fluid physical property parameters comprise oil/water density, oil/water viscosity and crude oil volume coefficient, and are obtained through development data such as fluid physical property analysis reports;
the seepage properties comprise the relative permeability of oil/water under different water saturation degrees, and are obtained from development data such as a reservoir phase seepage report.
Preferably, in the step (2), when the bottom water energy is different, the problem of single-point or multi-point breakthrough of the bottom water exists in the horizontal well, and for the single-point breakthrough of the horizontal well, a bottom water ridge similar to a water cone of a vertical well is provided; for the multi-point breakthrough horizontal well, providing a water cone similar to a straight well at each breakthrough point, wherein the water cones of the plurality of breakthrough points are communicated to form a water ridge, namely the water ridge of the bottom water of the horizontal well is a parallel connection body of the plurality of water cones;
the specific implementation process of the step (2) is as follows:
firstly, determining the breakthrough time of bottom water: firstly, calculating a K value by using production dynamic data and deriving, then drawing a K value derivative-accumulated liquid yield curve and a water content-accumulated liquid yield curve under the same coordinate system, and judging the number of times of water breakthrough at the horizontal well bottom and corresponding time by combining the two curves;
calculating the value K of the accumulated oil and the accumulated liquid of the horizontal well at different time from the start of production according to the following formulatK value at time t:
Figure BDA0003536603430000021
in order to more conveniently judge the bottom water breakthrough point and improve the accuracy of judgment, for KtThe derivative is calculated as follows:
Figure BDA0003536603430000031
in the formula (1) (2):
Figure BDA0003536603430000032
and
Figure BDA0003536603430000039
cumulative fluid production at-t and t +1, m3；
Figure BDA0003536603430000033
And
Figure BDA0003536603430000034
cumulative oil production at times t and t +1, m3。
An accumulated liquid collecting point corresponding to a peak value appearing on an accumulated liquid collecting curve by the K value derivative is the accumulated liquid collecting point when the bottom water breaks through, a time point corresponding to the accumulated liquid collecting amount is the bottom water breakthrough time, the first peak value corresponds to the first bottom water breakthrough time, the second peak value corresponds to the second bottom water breakthrough time, and the rest is done in turn;
the water cone shape description formula is as follows:
Figure BDA0003536603430000035
in the formula (3), H is any height (H is less than or equal to H) in the water cone, and m is; r-radius of water cone at any height in water cone, m; h is the maximum height of the water cone, m; b, water cone width index, representing water cone width, and determined by reservoir physical properties (permeability, porosity, oil-water viscosity ratio, water avoidance height and the like).
Further preferably, the maximum height H of the water cone rise is:
the rising rate of bottom water is constant before the breakthrough of the horizontal well, and the maximum height H of the water cone rising at the moment ttThe calculation formula is:
Figure BDA0003536603430000036
in formula (4): t is tmaxBottom water breakthrough time, d; hmaxWater-clearance height (distance from oil-water interface to horizontal well), m;
water cone width index b:
cumulative oil production t moment before bottom water breaks through from horizontal well
Figure BDA0003536603430000037
The average oil saturation of the bottom water wave reach area in different time before the bottom water breaks through is the same, and according to the material balance principle, the oil quantity produced by the horizontal well under the condition of a single water cone is all from the bottom water wave reach area (namely the water cone area), so that the following formula is established:
Figure BDA0003536603430000038
in the formula: n is a radical ofP-cumulative oil production when bottom water breakthrough occurs, t; bo-crude oil volume factor, decimal; rho-crude oil density, t/m3(ii) a Phi-reservoir porosity, decimal; soi-original oil saturation, decimal;
Figure BDA0003536603430000041
-bottom water swept area average oil saturation, decimal; vwcBottom water and reservoir volume, m3。
Mean oil saturation of bottom water swept zone
Figure BDA0003536603430000042
Figure BDA0003536603430000043
In the formula (6), the reaction mixture is,
Figure BDA0003536603430000044
the average water saturation of the bottom water wave zone when the bottom water breaks through;
calculating water cone shape curves at different moments, and taking a straight line r as a rotating body volume of a rotating shaft of 0, namely the volumes of bottom water waves and oil layers at different moments, namely:
Figure BDA0003536603430000045
the water cone width index at any time t before the bottom water breaks through can be obtained by establishing an equation according to the formula (5) and the formula (7):
Figure BDA0003536603430000046
the maximum height H of the bottom water at different moments before the bottom water breaks throughtAnd water cone width index btThe water cone shape description formula (3) is substituted to carry out single-point breakthrough horizontal well bottom water ridge shape description.
Further preferably, the average water saturation of the bottom water swept area at the time of bottom water breakthrough in the formula (6)
Figure BDA0003536603430000047
The calculation method is as follows:
under the condition of not considering gravity and capillary force, calculating the water content under the corresponding water saturation according to the following formula from the relative permeability of oil/water under different water saturation:
Figure BDA0003536603430000048
in the formula (f)w-water cut, decimal; mu.so-oil phase viscosity, mpa · s; mu.sw-viscosity of the aqueous phase, mpa · s; kro-oil phase relative permeability, decimal; krwWater phase relative permeability, decimal.
Drawing a relation curve of oil-water relative permeability and water content to water saturation in the same coordinate system, reading the irreducible water saturation in the curve, and adding the original oil saturation and the irreducible water saturation to be 1; method for obtaining two-phase permeability before water breakthrough by using graphical methodThe average water saturation of the flow area is as follows: in the fw-Sw relation curve, a tangent is made to the fw-Sw curve through the saturation Swc of the bound water, the tangent is extended to enable the tangent to intersect with a transverse line with fw equal to 1 at one point, and the water saturation corresponding to the intersection point is the average water saturation in the bottom water wave and area when the bottom water breaks through in the two-phase area
Figure BDA0003536603430000051
Preferably, in the step (3), the water cone width index in the step (2) is dimensionless, the change rule of the water cone width index along with the dimensionless development time is obtained through nonlinear fitting, and the average water cone width index prediction formula is obtained by performing multiple linear regression on 4 oil reservoir characterization parameters (permeability, porosity, oil-water viscosity ratio and water-avoiding height);
the specific implementation process of the step (3) is as follows:
i: dimensionless
Water cone width index b calculated by breaking through each single point into horizontal well at different moments before breaking through bottom watertDividing the water cone width index of the horizontal well by the arithmetic mean value of the water cone width index at different moments to perform dimensionless calculation, wherein the calculation formula is as follows:
Figure BDA0003536603430000052
dividing different production time before each single point breaks through the bottom water of the horizontal well by the bottom water break-through time of the horizontal well to perform time dimensionless operation, wherein the dimensionless production time range is between 0 and 1, and the calculation formula is as follows:
Figure BDA0003536603430000053
II: non-linear fit
Drawing the values of all single-point breakthrough horizontal wells in the same coordinate system by taking the dimensionless water cone width index as a vertical coordinate and the dimensionless production time as a horizontal coordinate, and performing nonlinear fitting according to the following formula to obtain the change rule of the water cone width index along with development time;
Figure BDA0003536603430000054
in the formula, m, n and q are fitting coefficients;
III: multiple linear regression
The water cone width index is determined by permeability, porosity, oil-water viscosity ratio and water avoidance height, and the average water cone width index of breaking through a horizontal well at a single point
Figure BDA0003536603430000055
And performing multiple linear regression with the 4 reservoir characterization parameters, wherein the multiple linear regression analysis model is as follows:
Figure BDA0003536603430000061
in the formula, beta0、β1、β2、β3、β4Referred to as regression coefficients; epsilon is a random error term, and epsilon follows a normal distribution with parameters of mu and sigma, i.e. epsilon-N (0, sigma)2) (ii) a k-permeability; phi-porosity;
Figure BDA0003536603430000062
-oil-water viscosity ratio; hmax-height of water avoidance;
and substituting the permeability, the porosity, the oil-water viscosity ratio and the water avoidance height of the block horizontal well into a formula (13) to obtain a predicted value of the average water cone width index, and substituting the value into a formula (12) to obtain the change rule of the water cone width index along with the development time.
Preferably, in the step (4), based on the horizontal well production dynamic data, bottom water ridge entering form description is carried out on the multi-point breakthrough horizontal well, water ridge volumes under different breakthrough times are calculated, for the multi-point breakthrough horizontal well, a water cone similar to a straight well is still arranged at each breakthrough point, and the water cones of the multiple breakthrough points are communicated to form a water ridge, namely the bottom water ridge of the horizontal well is a parallel connection body of the multiple water cones.
The specific implementation process of the step (4) is as follows:
a. the water cones which can be formed by breaking through the horizontal well at multiple points have upper limit (n), after the production for a long time, all the water cones break through in sequence after the oil well enters a high water content stage, and the breakthrough time (t) of the ith water conei) Determining by the step I;
b. calculation of a first water cone form parameter of a plurality of water cones
First water cone breakthrough time (t)1) The other water cones do not break through, and the accumulated oil yield is the sum of the volume of the oil layer affected by the first water cone and the volume of the oil layer affected by the other water cones which do not break through;
c. water cone wave and volume calculation during breakthrough of n water cones
And c, when the second water cone breaks through, subtracting the oil yield of the first water cone from the accumulated oil yield to obtain the sum of the oil yields of the second water cone and the un-broken water cones, considering that the oil is not produced after the first water cone breaks through, and the volume of the water cone swept oil layer is not changed after the water cone breaks through, comparing the second water cone with the first water cone during calculation, calculating the swept volume of the water cone when the second water cone breaks through according to the step b, and calculating the swept volumes of the water cones during the break-through of other water cones in sequence.
d. Calculation of Water Ridge volume
The horizontal well bottom water ridge is a parallel connection body of a plurality of water cones, the total volume of the water ridges can be obtained by adding the volumes of n water cones when the water cones break through, and the calculation formula is as follows:
Figure BDA0003536603430000063
in the formula: vwcIs the total volume of the water ridge.
Further preferably, the calculation process of step b is as follows:
b-1, maximum rising height of ith water cone when the first water cone breaks through
Figure BDA0003536603430000071
The rising rate of the bottom water is constant before the breakthrough of the horizontal well, and the maximum rising height of the water cone which does not break through the water cone when the first water cone breaks through is calculated according to the following formula:
Figure BDA0003536603430000072
b-2, i th water cone width index when the first water cone breaks through
Figure BDA0003536603430000073
Determining the width index of any un-broken water cone when the first water cone breaks through according to the step (3);
b-3, i-th water cone wave and oil layer volume when the first water cone breaks through
Figure BDA0003536603430000074
Will be provided with
Figure BDA0003536603430000075
And
Figure BDA0003536603430000076
the ith water cone and oil layer volume are calculated by substituting the following formula:
Figure BDA0003536603430000077
b-4, the volume of water cone and oil layer (V) of the first breakthrough water cone1)
When the first water cone breaks through, n-1 water cones do not break through, at the moment, the cumulative swept oil layer volume of the bottom water is calculated according to the material balance principle, the swept oil layer volume of the first broken water cone is equal to the cumulative swept oil layer volume of the bottom water minus the cumulative swept oil layer volume of the n-1 unbroken water cones, and the calculation formula is as follows:
Figure BDA0003536603430000078
the invention has the beneficial effects that:
the technical scheme of the invention can judge the number of times of breakthrough of the bottom water of the developed horizontal well and the corresponding breakthrough time, describe the bottom water ridge shape, analyze the parameter change rule of the horizontal bottom water ridge shape of the bottom water reservoir, calculate the volume of the bottom water ridge at different development time, provide guidance for the optimization design of the stable yield increasing measures of the bottom water reservoir, is simple and practical, and has important guiding significance for the development of the bottom water reservoir.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of a water cone shape description formula of the present invention;
FIG. 3 is a schematic diagram illustrating determination of breakthrough time of single-point breakthrough horizontal well bottom water according to the present invention;
FIG. 4 is a schematic diagram illustrating determination of breakthrough time of bottom water of a multi-point breakthrough horizontal well according to the present invention;
FIG. 5 is a schematic diagram of the nonlinear fitting of the water cone width exponent b according to the present invention.
Detailed Description
The present invention will be further described by way of examples, but not limited thereto, with reference to the accompanying drawings.
Example 1:
as shown in fig. 1, the present embodiment provides a method for describing a horizontal bottom-hole water ridge entering shape of a bottom-water reservoir based on production dynamic data, which includes the following steps:
(1) acquiring production dynamic data of a target block or an oil reservoir developed horizontal well, and reservoir physical property parameters, fluid physical property parameters and seepage properties of a layer position where the horizontal well is located;
(2) judging the developed horizontal well bottom water breakthrough times and corresponding breakthrough times, selecting a single point to breakthrough a horizontal well, calculating bottom water ridge shape parameters of different development times before bottom water breakthrough by combining a substance balance principle, and describing by using a water cone shape description formula;
(3) obtaining the change rule of the water cone width index along with development time by utilizing nonlinear fitting and multivariate linear regression;
(4) and describing the water ridge entering form of the multi-point breakthrough horizontal well bottom, and calculating the water ridge volume under different development time.
In the step (1), the production dynamic data comprises development date and corresponding daily liquid yield, daily water yield and water content, and is derived by an oil well production dynamic data acquisition system; the physical parameters of the reservoir comprise oil layer thickness, water-avoiding height (distance between an oil-water interface and a horizontal well), porosity and permeability, and are obtained from development data such as oil well oil reservoir design books and the like; the fluid physical property parameters comprise oil/water density, oil/water viscosity and crude oil volume coefficient, and are obtained through development data such as fluid physical property analysis reports; the seepage properties comprise the relative permeability of oil/water under different water saturation degrees, and are obtained from development data such as a reservoir phase seepage report.
The physical property parameters of the reservoir, the physical property parameters of the fluid and the seepage property of the horizon in which one horizontal well in the target block or the oil reservoir developed horizontal well is located are shown in table 1.
Table 1: data table of reservoir physical property parameter, fluid physical property parameter and seepage property of horizon where horizontal well is located
Figure BDA0003536603430000081
Figure BDA0003536603430000091
In the step (2), for the developed horizontal well selected in the step 1, the production dynamic data of the developed horizontal well is utilized to judge the bottom water breakthrough times and the corresponding breakthrough time, a single-point breakthrough horizontal well is selected, and bottom water ridge (cone) advancing form parameters of different development times before breakthrough of the bottom water are calculated by combining the material balance principle.
The specific implementation process of the step (2) is as follows:
firstly, determining the breakthrough time of bottom water: firstly, calculating a K value by using production dynamic data and deriving, then drawing a K value derivative-accumulated liquid yield curve and a water content-accumulated liquid yield curve under the same coordinate system, and judging the number of times of water breakthrough at the horizontal well bottom and corresponding time by combining the two curves;
calculating the value K of the accumulated oil and the accumulated liquid of the horizontal well at different time from the start of production according to the following formulatK value at time t:
Figure BDA0003536603430000092
in order to judge the bottom water breakthrough point more conveniently and improve the accuracy of the judgment, K is selectedtThe derivative is calculated as follows:
Figure BDA0003536603430000093
in the formulae (1) and (2):
Figure BDA0003536603430000094
and
Figure BDA0003536603430000095
cumulative fluid production at-t and t +1, m3；
Figure BDA0003536603430000096
And
Figure BDA0003536603430000097
cumulative oil production at times t and t +1, m3。
An accumulated liquid collecting point corresponding to a peak value appearing on an accumulated liquid collecting curve by the K value derivative is the accumulated liquid collecting point when the bottom water breaks through, a time point corresponding to the accumulated liquid collecting amount is the bottom water breakthrough time, the first peak value corresponds to the first bottom water breakthrough time, the second peak value corresponds to the second bottom water breakthrough time, and the rest is done in turn; the obtained breakthrough time of a target block or a single point in an oil reservoir developed horizontal well is 88 days after production, and a bottom water breakthrough time judgment schematic diagram is shown in fig. 3.
The water cone shape description formula is as follows:
Figure BDA0003536603430000101
in the formula (3), H is any height (H is less than or equal to H) in the water cone, and m is; r-radius of water cone at any height in water cone, m; h is the maximum height of the water cone, m; b, water cone width index, representing water cone width, and determined by reservoir physical properties (permeability, porosity, oil-water viscosity ratio, water avoidance height and the like).
Maximum height H of water cone rising:
the rising rate of bottom water is constant before the breakthrough of the horizontal well, and the maximum height H of the water cone rising at the moment ttThe calculation formula is as follows:
Figure BDA0003536603430000102
in formula (4): t is tmax-bottom water breakthrough time, d; hmaxWater-clearance height (distance from oil-water interface to horizontal well), m; before the bottom water breaks through, the maximum rising height of the bottom water at different moments is uniformly increased along with the production time, and on the 88 th day after production, the bottom water rises to the water-avoiding height, and the well is 6.5 m. The corresponding maximum bottom water rise heights for different days of production before breakthrough were calculated and listed in column 3 of table 2.
Water cone width index b:
cumulative oil production at t moment before bottom water breaks through from horizontal well
Figure BDA0003536603430000103
The average oil saturation of the bottom water wave reach area in different time before the bottom water breaks through is the same, and according to the material balance principle, the oil quantity produced by the horizontal well under the condition of a single water cone is all from the bottom water wave reach area (namely the water cone area), so that the following formula is established:
Figure BDA0003536603430000104
in the formula: n is a radical ofP-cumulative oil production when bottom water breakthrough occurs, t; b iso-crude oil volume factor, decimal; rho-crude oil density, t/m3(ii) a Phi-reservoir porosity, decimal; soi-original oil saturation, decimal;
Figure BDA0003536603430000105
-bottom water swept area average oil saturation, decimal; vwcBottom water wave and reservoir volume, m3。
Mean oil saturation of bottom water swept zone
Figure BDA0003536603430000111
Figure BDA0003536603430000112
In the formula (6), the reaction mixture is,
Figure BDA0003536603430000113
the average water saturation of the bottom water wave zone when the bottom water breaks through;
calculating the water cone shape curves at different moments, and taking a straight line r as the volume of a rotating body of a rotating shaft of 0, namely the volume of bottom water waves and oil layers at different moments, namely:
Figure BDA0003536603430000114
the water cone width index at any time t before the bottom water breaks through can be obtained by establishing an equation according to the formula (5) and the formula (7):
Figure BDA0003536603430000115
the maximum height H of the bottom water at different moments before the bottom water breaks throughtAnd water cone width index btThe water cone shape description formula (3) is substituted to carry out single-point breakthrough horizontal well bottom water ridge shape description.
Average water saturation of bottom water swept area at bottom water breakthrough in formula (6)
Figure BDA0003536603430000116
The calculation method is as follows:
under the condition of not considering gravity and capillary force, calculating the water content under the corresponding water saturation according to the following formula from the relative permeability of oil/water under different water saturation:
Figure BDA0003536603430000117
in the formula (f)w-water cut, decimal; mu.so-oil phase viscosity, mpa · s; mu.sw-viscosity of the aqueous phase, mpa · s; kro-oil phase relative permeability, decimal; krwWater phase relative permeability, decimal.
Drawing a relation curve of the relative permeability of oil and water, the water content and the water saturation in the same coordinate system, reading the irreducible water saturation in the curve, and adding the original oil saturation and the irreducible water saturation to be 1; the average water saturation of the two-phase seepage zone before the water breakthrough is obtained by a graphical method, which comprises the following steps: in the fw-Sw relation curve, a tangent is made to the fw-Sw curve through the saturation Swc of the bound water, the tangent is extended to enable the tangent to intersect with a transverse line with fw equal to 1 at one point, and the water saturation corresponding to the intersection point is the average water saturation in the bottom water wave and area when the bottom water breaks through in the two-phase area
Figure BDA0003536603430000121
Calculating the corresponding accumulated oil production amount of different production days before the bottom hole water breaks through according to the step II, and listing the accumulated oil production amount in the 2 nd column in the table 2; calculating the corresponding bottom water swept volumes of different days of production before the bottom water breakthrough according to formula (5), listed in column 4 of table 2; the corresponding water cone width indices for different days of production before the bottom hole breakthrough were calculated according to equation (8) and are listed in column 5 of table 2.
Table 2: water cone parameter calculation table at different moments before single-point breakthrough of horizontal well bottom water breakthrough
Figure BDA0003536603430000122
In the step (3), the water cone width index in the step (2) is subjected to dimensionless operation, the change rule of the water cone width index along with the dimensionless development time is obtained through nonlinear fitting, and the average water cone width index prediction formula is obtained by performing multiple linear regression on 4 oil reservoir characterization parameters;
the specific implementation process of the step (3) is as follows:
i: dimensionless
Water cone width index b calculated by breaking through each single point into horizontal well at different moments before breaking through bottom watertDividing the water cone width index by the arithmetic mean value of the water cone width index of the horizontal well at different moments to perform dimensionless calculation, wherein the calculation formula is as follows:
Figure BDA0003536603430000123
dividing different production time before each single point breaks through the bottom water of the horizontal well by the bottom water break-through time of the horizontal well to perform time dimensionless operation, wherein the dimensionless production time range is between 0 and 1, and the calculation formula is as follows:
Figure BDA0003536603430000124
II: non-linear fitting
Drawing the values of all single-point breakthrough horizontal wells in the same coordinate system by taking the dimensionless water cone width index as a vertical coordinate and the dimensionless production time as a horizontal coordinate, and performing nonlinear fitting according to the following formula to obtain the change rule of the water cone width index along with development time;
Figure BDA0003536603430000131
in the formula, m, n and q are fitting coefficients;
III: multiple linear regression
The water cone width index is composed of permeability, porosity and oilThe water viscosity ratio and the water avoidance height are determined, and the average water cone width index of the horizontal well is broken through at a single point
Figure BDA0003536603430000132
And performing multiple linear regression with the 4 reservoir characterization parameters, wherein the multiple linear regression analysis model is as follows:
Figure BDA0003536603430000133
in the formula, beta0、β1、β2、β3、β4Referred to as regression coefficients; epsilon is a random error term, and epsilon follows a normal distribution with parameters of mu and sigma, i.e. epsilon-N (0, sigma)2) (ii) a k-permeability; phi-porosity;
Figure BDA0003536603430000134
-oil-water viscosity ratio; hmax-height to avoid water.
And substituting the permeability, the porosity, the oil-water viscosity ratio and the water avoidance height of the block horizontal well into a formula (13) to obtain a predicted value of the average water cone width index, and substituting the value into a formula (12) to obtain the change rule of the water cone width index along with the development time.
Dimensionless is performed according to the method in step I to
Figure BDA0003536603430000135
As the abscissa, in
Figure BDA0003536603430000136
And (3) drawing a curve for a vertical coordinate, drawing the values of all the single points breaking through the horizontal well in the same coordinate system, and obtaining a change rule of the water cone width index along with development time through nonlinear fitting as shown in fig. 5.
Figure BDA0003536603430000137
Average water cone breaking through single point of horizontal wellWidth index
Figure BDA0003536603430000138
And performing multiple linear regression with the permeability, porosity, oil-water viscosity ratio and water avoidance height to obtain an average water cone width index prediction formula as follows:
Figure BDA0003536603430000139
in the formula, k-permeability, phi-porosity,
Figure BDA00035366034300001310
oil-to-Water viscosity ratio, Hmax-height of water avoidance.
In the step (4), based on the horizontal well production dynamic data, bottom water ridge entering form description is carried out on the multi-point breakthrough horizontal well, the water ridge volumes under different breakthrough times are calculated, for the multi-point breakthrough horizontal well, each breakthrough point is still a water cone similar to a straight well, and the water cones of the multiple breakthrough points are communicated to form a water ridge, namely the bottom water ridge of the horizontal well is a union of the multiple water cones.
The specific implementation process of the step (4) is as follows:
a. the water cones which can be formed by breaking through the horizontal well at multiple points have upper limit (n), after the production for a long time, all the water cones break through in sequence after the oil well enters a high water content stage, and the breakthrough time (t) of the ith water conei) Determining by the step I;
b. calculation of a first water cone form parameter of a plurality of water cones
First water cone breakthrough time (t)1) The other water cones do not break through, and the accumulated oil yield is the sum of the volume of the oil layer affected by the first water cone and the volume of the oil layer affected by the other water cones which do not break through;
c. water cone wave and volume calculation during breakthrough of n water cones
And c, when the second water cone breaks through, subtracting the oil yield of the first water cone from the accumulated oil yield to obtain the sum of the oil yields of the second water cone and the un-broken water cones, considering that the oil is not produced after the first water cone breaks through, and the volume of the water cone swept oil layer is not changed after the water cone breaks through, comparing the second water cone with the first water cone during calculation, calculating the swept volume of the water cone when the second water cone breaks through according to the step b, and calculating the swept volumes of the water cones during the break-through of other water cones in sequence.
d. Calculation of Water Ridge volume
The horizontal well bottom water ridge is a parallel connection body of a plurality of water cones, the total volume of the water ridges can be obtained by adding the volumes of n water cones when the water cones break through, and the calculation formula is as follows:
Figure BDA0003536603430000141
in the formula: vwcIs the total volume of the water ridge.
The calculation process of step b is as follows:
b-1, maximum rising height of ith water cone when the first water cone breaks through
Figure BDA0003536603430000142
The rising rate of the bottom water is constant before the breakthrough of the horizontal well, and the maximum rising height of the water cone which does not break through the water cone when the first water cone breaks through is calculated according to the following formula:
Figure BDA0003536603430000143
b-2, i th water cone width index when the first water cone breaks through
Figure BDA0003536603430000144
Determining the width index of any un-broken water cone when the first water cone breaks through according to the step (3);
b-3, i-th water cone wave and oil layer volume when the first water cone breaks through
Figure BDA0003536603430000151
Will be provided with
Figure BDA0003536603430000152
And
Figure BDA0003536603430000153
substituting the following formula to calculate the ith water cone wave and the oil layer volume:
Figure BDA0003536603430000154
b-4, the volume of water cone and oil layer (V) of the first breakthrough water cone1)
When the first water cone breaks through, n-1 water cones do not break through, at the moment, the cumulative swept oil layer volume of the bottom water is calculated according to the material balance principle, the swept oil layer volume of the first broken water cone is equal to the cumulative swept oil layer volume of the bottom water minus the cumulative swept oil layer volume of the n-1 unbroken water cones, and the calculation formula is as follows:
Figure BDA0003536603430000155
the oil-water viscosity ratio of a target block or a multi-point breakthrough horizontal well in an oil reservoir developed horizontal well is 2018, the permeability is 3616mD, the water-avoiding height is 5m, the porosity is 0.391, and the predicted value of the average water cone width index of the well is 0.0047545176 by taking the property parameters into formula (19). Two points of breakthrough exist in the well, and the judgment schematic diagram of the breakthrough time of bottom water is shown in figure 4. The breakthrough time of the first breakthrough water cone is 31 days after production, the accumulated oil production is calculated to be 183.1t, and the breakthrough time of the second breakthrough water cone is 62 days after production, and the accumulated oil production is calculated to be 257.9 t.
According to the method in the step 4.2, when the water cone of the first breakthrough is broken through, the maximum rising height of the water cone of the second breakthrough is 2.5m, the width index of the water cone is 0.0046992, and the water cone wave and the oil layer volume of the first breakthrough are calculated to be 1287.4m3。
According to the method in the step b, the water cone wave and the oil layer volume of the second breakthrough are calculated to be 3571.4m3The bottom water ridge of the horizontal well isThe volume of the water wave and oil reservoir breaking through the bottom of the horizontal well at multiple points is 4858.8m3。
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (8)

1. A bottom water reservoir horizontal bottom water ridge entering form description method based on production dynamic data is characterized by comprising the following steps:
(1) acquiring production dynamic data of a target block or an oil reservoir developed horizontal well, and reservoir physical property parameters, fluid physical property parameters and seepage properties of a layer position where the horizontal well is located;
(2) judging the developed horizontal well bottom water breakthrough times and corresponding breakthrough times, selecting a single point to breakthrough a horizontal well, calculating bottom water ridge shape parameters of different development times before bottom water breakthrough by combining a substance balance principle, and describing by using a water cone shape description formula;
(3) obtaining the change rule of the water cone width index along with development time by utilizing nonlinear fitting and multivariate linear regression;
(4) and describing the water ridge entering form of the multi-point breakthrough horizontal well bottom, and calculating the water ridge volume under different development time.
2. The bottom water reservoir horizontal bottom water ridge entry morphology description method based on production dynamic data as claimed in claim 1, wherein in step (1), the production dynamic data comprises development date and corresponding daily liquid production, daily water production and water cut;
the physical parameters of the reservoir comprise oil layer thickness, water-avoiding height, porosity and permeability;
the fluid physical property parameters comprise oil/water density, oil/water viscosity and crude oil volume coefficient;
the seepage properties include the magnitude of the oil/water relative permeability at different water saturations.
3. The bottom water reservoir horizontal bottom water ridge shape description method based on production dynamic data as claimed in claim 2, characterized in that the specific implementation process of step (2) is as follows:
firstly, determining the breakthrough time of bottom water: firstly, calculating a K value by using production dynamic data and deriving, then drawing a K value derivative-accumulated liquid yield curve and a water content-accumulated liquid yield curve under the same coordinate system, and judging the number of times of water breakthrough at the horizontal well bottom and corresponding time by combining the two curves;
calculating the value K of the accumulated oil and the accumulated liquid of the horizontal well at different time from the start of production according to the following formulatK value at time t:
Figure FDA0003536603420000011
in order to judge the bottom water breakthrough point more conveniently and improve the accuracy of the judgment, K is selectedtThe derivative is calculated as follows:
Figure FDA0003536603420000021
in the formulae (1) and (2):
Figure FDA0003536603420000022
and
Figure FDA0003536603420000023
cumulative fluid production at-t and t +1, m3；
Figure FDA0003536603420000024
And
Figure FDA0003536603420000025
cumulative oil production at times t and t +1, m3；
An accumulated liquid collecting point corresponding to a peak value appearing on an accumulated liquid collecting curve by the K value derivative is the accumulated liquid collecting amount when the bottom water breaks through, a time point corresponding to the accumulated liquid collecting amount is the bottom water breaking time, a first peak value corresponds to a first bottom water breaking time, a second peak value corresponds to a second bottom water breaking time, and the like;
the water cone shape description formula is as follows:
Figure FDA0003536603420000026
in the formula (3), H is any height (H is less than or equal to H) in the water cone, and m is; r-radius of water cone at any height in water cone, m; h is the maximum height of the water cone, m; b, water cone width index, representing water cone width, and determined by reservoir physical properties (permeability, porosity, oil-water viscosity ratio, water avoidance height and the like).
4. The bottom water reservoir horizontal bottom water ridge profiling method based on production dynamics data as claimed in claim 3, characterized in that the maximum height of water cone rise H:
the rising rate of bottom water is constant before the breakthrough of the horizontal well, and the maximum height H of the water cone rising at the moment ttThe calculation formula is as follows:
Figure FDA0003536603420000027
in formula (4): t is tmaxBottom water breakthrough time, d; hmaxWater-clearance height (distance from oil-water interface to horizontal well), m;
water cone width index b:
cumulative oil production t moment before bottom water breaks through from horizontal well
Figure FDA0003536603420000029
The average oil saturation of the bottom water swept area is the same in different time before the bottom water breaks through, and according to the substance balance principle, the oil quantity produced by the horizontal well under the condition of a single water cone is from the bottom water swept area because of the dynamic production dataThis equation holds true:
Figure FDA0003536603420000028
in the formula: n is a radical ofP-cumulative oil production when bottom water breakthrough occurs, t; b iso-crude oil volume factor, decimal; rho-crude oil density, t/m3(ii) a Phi-reservoir porosity, decimal; soi-original oil saturation, decimal;
Figure FDA0003536603420000031
-bottom water swept area average oil saturation, decimal; vwcBottom water and reservoir volume, m3；
Mean oil saturation of bottom water swept zone
Figure FDA0003536603420000032
Figure FDA0003536603420000033
In the formula (6), the reaction mixture is,
Figure FDA0003536603420000034
the average water saturation of the bottom water wave zone when the bottom water breaks through;
calculating water cone shape curves at different moments, and taking a straight line r as a rotating body volume of a rotating shaft of 0, namely the volumes of bottom water waves and oil layers at different moments, namely:
Figure FDA0003536603420000035
the water cone width index at any time t before the bottom water breaks through can be obtained by establishing an equation according to the formula (5) and the formula (7):
Figure FDA0003536603420000036
the maximum height H of the bottom water at different moments before the bottom water breaks throughtAnd water cone width index btThe water cone shape description formula (3) is substituted to carry out single-point breakthrough horizontal well bottom water ridge shape description.
5. The method for describing the horizontal bottom water ridge entry profile of a bottom water reservoir based on production dynamics data as claimed in claim 4, wherein the average saturation of the bottom water swept area at the time of bottom water breakthrough in equation (6)
Figure FDA0003536603420000037
The calculation method is as follows:
the water content at the corresponding water saturation is calculated from the oil/water relative permeability at different water saturations according to the following formula:
Figure FDA0003536603420000038
in the formula (f)w-water cut, decimal; mu.so-oil phase viscosity, mpa · s; mu.sw-viscosity of the aqueous phase, mpa · s; kro-oil phase relative permeability, decimal; krw-relative permeability of the aqueous phase, decimal;
drawing a relation curve of the relative permeability of oil and water, the water content and the water saturation in the same coordinate system, reading the irreducible water saturation in the curve, and adding the original oil saturation and the irreducible water saturation to be 1; the average water saturation of the two-phase seepage zone before the water breakthrough is obtained by a graphical method, which comprises the following steps: in the fw-Sw relation curve, a tangent is made to the fw-Sw curve through the saturation Swc of the bound water, the tangent is extended to enable the tangent to intersect with a transverse line with fw equal to 1 at one point, and the water saturation corresponding to the intersection point is the average water saturation in the bottom water wave and area when the bottom water breaks through in the two-phase area
Figure FDA0003536603420000041
6. The bottom water reservoir horizontal bottom water ridge shape description method based on production dynamic data as claimed in claim 5, characterized in that the implementation process of step (3) is as follows:
i: dimensionless
Water cone width index b calculated by breaking through each single point into horizontal well at different moments before breaking through bottom watertDividing the water cone width index of the horizontal well by the arithmetic mean value of the water cone width index at different moments to perform dimensionless calculation, wherein the calculation formula is as follows:
Figure FDA0003536603420000042
dividing different production time before each single point breaks through the bottom water of the horizontal well by the bottom water break-through time of the horizontal well to perform time dimensionless operation, wherein the dimensionless production time range is between 0 and 1, and the calculation formula is as follows:
Figure FDA0003536603420000043
II: non-linear fitting
Drawing the values of all single-point breakthrough horizontal wells in the same coordinate system by taking the dimensionless water cone width index as a vertical coordinate and the dimensionless production time as a horizontal coordinate, and performing nonlinear fitting according to the following formula to obtain the change rule of the water cone width index along with development time;
Figure FDA0003536603420000044
in the formula, m, n and q are fitting coefficients;
III: multiple linear regression
The water cone width index is determined by permeability, porosity, oil-water viscosity ratio and water avoidance height, and the average water cone width index of breaking through a horizontal well at a single point
Figure FDA0003536603420000045
And performing multiple linear regression with the 4 reservoir characterization parameters, wherein the multiple linear regression analysis model is as follows:
Figure FDA0003536603420000046
in the formula, beta0、β1、β2、β3、β4Referred to as regression coefficients; epsilon is a random error term, epsilon follows a normal distribution with parameters mu, sigma, i.e. epsilon-N (0, sigma)2) (ii) a k is the permeability; phi-porosity;
Figure FDA0003536603420000051
-oil-water viscosity ratio; hmax-height of water avoidance;
and substituting the permeability, the porosity, the oil-water viscosity ratio and the water avoidance height of the block horizontal well into a formula (13) to obtain a predicted value of the average water cone width index, and substituting the value into a formula (12) to obtain the change rule of the water cone width index along with the development time.
7. The bottom water reservoir horizontal bottom water ridge shape description method based on production dynamic data as claimed in claim 6, characterized in that the step (4) is implemented by the following steps:
a. the water cone which can be formed by breaking through the horizontal well at multiple points has an upper limit, after the oil well enters a high water cut stage after long-time production, all the water cones break through in sequence, and the breakthrough time of the ith water cone is determined by the first step;
b. calculation of a first water cone form parameter of a plurality of water cones
When the first water cone breaks through, other water cones do not break through, and the accumulated oil yield is the sum of the volume of the oil layer affected by the first water cone and the volume of the oil layer affected by the other water cones which do not break through;
c. water cone wave and volume calculation during breakthrough of n water cones
When the second water cone breaks through, the accumulated oil yield minus the oil yield of the first water cone is the sum of the oil yields of the second water cone and the un-broken water cones, the oil is not produced after the first water cone breaks through, the volume of the water cone swept oil layer is not changed after the water cone breaks through, the second water cone is compared with the first water cone during calculation, the swept volume of the water cone during the break through of the second water cone is calculated according to the step b, and the water cone swept volume calculation during the break through of other water cones is analogized in turn;
d. calculation of Water Ridge volume
The horizontal well bottom water ridge is a parallel connection body of a plurality of water cones, the total volume of the water ridge can be obtained by adding the volume when n water cones break through, and the calculation formula is as follows:
Figure FDA0003536603420000052
in the formula: vwcIs the total volume of the water ridge.
8. The bottom water reservoir horizontal bottom water ridge profiling method based on production dynamics data of claim 7, wherein the calculation process of step b is as follows:
b-1, maximum rise height of ith water cone during breakthrough of first water cone
Figure FDA0003536603420000053
The rising rate of the bottom water is constant before the breakthrough of the horizontal well, and the maximum rising height of the water cone which does not break through the water cone when the first water cone breaks through is calculated according to the following formula:
Figure FDA0003536603420000061
b-2, i water cone width index when the first water cone breaks through
Figure FDA0003536603420000062
Determining the width index of any un-broken water cone when the first water cone breaks through according to the step (3);
b-3, i-th water cone wave and oil layer volume when the first water cone breaks through
Figure FDA0003536603420000063
Will be provided with
Figure FDA0003536603420000064
And
Figure FDA0003536603420000065
the ith water cone and oil layer volume are calculated by substituting the following formula:
Figure FDA0003536603420000066
b-4, the volume of water cone and oil layer (V) of the first breakthrough water cone1)
When the first water cone breaks through, n-1 water cones do not break through, at the moment, the cumulative swept oil layer volume of the bottom water is calculated according to the material balance principle, the swept oil layer volume of the first broken water cone is equal to the cumulative swept oil layer volume of the bottom water minus the cumulative swept oil layer volume of the n-1 unbroken water cones, and the calculation formula is as follows:
Figure FDA0003536603420000067
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