CN113898331A - Well spacing optimization method for oil reservoir balanced displacement differentiation in high water cut period - Google Patents
Well spacing optimization method for oil reservoir balanced displacement differentiation in high water cut period Download PDFInfo
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Abstract
The invention provides a high water cut oil reservoir balanced displacement differential well spacing optimization method, which comprises the following steps: step 1, determining the total flow of oil and water at a seepage interface; step 2, determining the relationship between the seepage resistance per unit length and the saturation of the movable oil; step 3, determining the relation between the movable oil saturation and the injection-production well spacing; step 4, determining seepage resistance and liquid production amount between injection wells and production wells; and 5, optimizing and determining the balanced displacement reasonable injection-production well spacing. The differential well spacing optimization method for the balanced displacement of the oil reservoir in the high water cut period is based on the established standard of the planar balanced displacement, and comprehensively considers the differences of the physical properties and the utilization degree of the reservoir on the basis of the oil-water two-phase flow seepage theory.
Description
Technical Field
The invention relates to the technical field of oilfield development, in particular to a method for optimizing a differential well spacing for balanced displacement of an oil reservoir in a high water-cut period.
Background
As the development of an oil field gradually enters a high-water-content stage, due to the fact that reservoirs are heterogeneous and injection-production well distances are different, the difference of well water content of a well region is large, so that the anisotropic seepage resistance between injection-production wells is not matched with the injection-production well distances, balanced displacement is difficult to form, and the residual oil potential in an old region is a main measure for stable production and gradual control reduction, so that a method for calculating the well distance of the oil reservoir balanced displacement in the high-water-content stage is urgently needed, the final balanced displacement of the well region is taken as a target, and reference is provided for well position screening of a new well in the old region.
As the development of the oil field gradually enters the stage of medium and high water content, the difference of water content of a well region is large due to the heterogeneous reservoir and the difference of injection and production well distances, so that the anisotropic seepage resistance between injection and production wells is not matched with the injection and production well distances, and balanced displacement is difficult to form. At present, a calculation method aiming at a reasonable well spacing is relatively general, and is mainly calculated based on parameters such as average permeability, average formation pressure and the like, and the difference such as the exploitation condition difference and the development condition is not considered.
In the application No.: 201611268862.8, relates to a method for determining the reasonable well spacing of a low permeability reservoir, which comprises the following steps: 1) carrying out an indoor seepage experiment, and acquiring corresponding relation data of indoor seepage velocity experiment data and time and corresponding relation data of pressure gradient and time; 2) a three-parameter mathematical model of the pressure gradient and the seepage velocity is established according to the data: 3) fitting the model parameters by adopting indoor seepage experimental data to determine undetermined parameters; 4) deriving an equal-yield one-source one-sink plane radial stable flow pressure P distribution formula according to the three-parameter model; 5) calculating the relation between the productivity and the reasonable well spacing under different core permeability, and obtaining a chart of the relation between the oil well production allocation and the reasonable well spacing under the condition of different permeability; 6) and determining the reasonable well spacing according to the pressure distribution and the relationship chart between the oil well production allocation and the reasonable well spacing. This patent requires complex laboratory experiments to determine the fitting parameters and does not take into account the effect of water content on the injection-production well spacing.
Therefore, a novel high-water-cut-period oil reservoir balanced displacement differential well spacing optimization method is invented, and the technical problems are solved.
Disclosure of Invention
The invention aims to provide a differential well spacing optimization method for the balanced displacement of the oil reservoir in the high water cut stage, which comprehensively considers the differences of the physical properties and the utilization degree of the reservoir based on the established standard of the planar balanced displacement and based on the oil-water two-phase flow seepage theory.
The object of the invention can be achieved by the following technical measures: the high water cut oil reservoir balanced displacement differential well spacing optimization method comprises the following steps: step 1, determining the total flow of oil and water at a seepage interface; step 2, determining the relationship between the seepage resistance per unit length and the saturation of the movable oil; step 3, determining the relation between the movable oil saturation and the injection-production well spacing; step 4, determining seepage resistance and liquid production amount between injection wells and production wells; and 5, optimizing and determining the balanced displacement reasonable injection-production well spacing.
The object of the invention can also be achieved by the following technical measures:
in the step 1, the total flow of oil and water at the seepage interface is determined by considering the starting pressure and combining a Darcy law formula.
In step 1, the total flow of oil and water passing through the seepage section is:
wherein:
in the formula, QwWater flow rate, m3/d；KwWater phase permeability, 10-3μm2(ii) a A-cross sectional area of seepage, m2；μw-formation water viscosity, mPa · s; p is the pressure of any point in the oil reservoir, MPa; x is the distance between any point in the oil deposit and an injection well, m and G are starting pressure gradients, MPa/m;
oil flow through the percolation cross section:
in the formula, QoOil flow, m3/d；KoOil phase Permeability, 10-3μm2；μo-underground crude oil viscosity, mPa · s;
total flow of oil and water through the cross section:
wherein:
in the formula, mur-oil-water viscosity ratio, dimensionless quantity; K-Absolute Permeability, 10-3μm2(ii) a B, volume coefficient of crude oil, dimensionless quantity; h-effective thickness of oil layer, m; k is a radical ofrwRelative permeability of water, 10-3μm2；kroRelative permeability of oil, 10-3μm2(ii) a L is the distance between injection wells and production wells, m.
In step 2, determining the relationship between the seepage resistance per unit length and the saturation of the movable oil according to the linear theory of the oil content and the saturation of the movable oil in a log-log coordinate system.
In step 2, obtaining the seepage resistance on the dx length in the two-phase seepage area according to an oil-water total flow formula of the seepage section:
the total seepage resistance of the two-phase seepage zone is as follows:
wherein:
in the formula: omegao-specific length seepage resistance, N, muo-underground crude oil viscosity, mPa · s; mu.sr-oil-water viscosity ratio, dimensionless quantity; K-Absolute Permeability, 10-3μm2(ii) a B, volume coefficient of crude oil, dimensionless quantity; h-effective thickness of oil layer, m; k is a radical ofrwRelative permeability of water, 10-3μm2；kroRelative permeability of oil, 10-3μm2(ii) a L is the injection-production well spacing, m;
the oil content f is plotted in a log-log coordinate system by taking the oil content as the ordinate and the flowable oil saturation as the abscissaoAnd the movable oil saturation z in a linear relation, and the slope of the straight line is 1<μr<10, the straight line intercept is kept unchanged, and the straight line intercept becomes smaller along with the increase of the oil-water viscosity ratio, and the intercept is in inverse proportion to the oil-water viscosity ratio;
Wherein: z is 1-Sw-Sor
In the formula: f. ofo-oil content, decimal fraction; sw-water saturation, decimal; z-mobile oil saturation, decimal; a, b-lgfo-lgz curve of relationship parameter, decimal; sor-residual oil saturation, fractional;
the oil content is as follows:
in the formula, QoOil flow, m3/d；QwWater flow rate, m3/d；
Obtaining a relation between the seepage resistance per unit length and the movable oil saturation:
in step 3, according to μrωoAnd z, wherein μrIs the oil-water viscosity ratio, omegaoAnd determining the relation between the saturation of the movable oil and the distance between the injection well and the production well as the unit length seepage resistance and the unit length seepage resistance z.
In the step 3, the process is carried out,
μrωothe relationship with z can be expressed as:
μrωo＝A+Bz+Cz2
in the formula: a, B, C-murωoAnd z, a curve fitting coefficient;
according to the equation of motion of the isosaturation surface, namely the Bekery equation:
in the formula: x-water saturation of SwM, the position of the plane of (d) reached at time t; x is the number of0-original oil-water interface position, m; f. ofw-water cut, decimal; phi is rock porosity, decimal; q-total flow of oil and Water, m3D; t-time at a certain moment; sw-water saturation at x, decimal;
due to fw(Sw)＝1-fo(Sw) So fw'(Sw)＝-fo'(Sw) Thus, the above formula is rewritten as:
the position at which a certain water saturation plane arrives at time t is:
in the formula: x is the number of2Water saturation of
M, the position of the plane of (d) reached at time t; x is the number of0-original oil-water interface position, m; f. ofw-water cut, decimal; phi is rock porosity, decimal;
at x2Water saturation, decimal fraction;
the two formulas are divided to obtain:
the oil content derivative is:
then the following equation can be derived:
wherein the L-new well has a water saturation of SwThe distance of the plane (a) in the time t, namely the reasonable injection-production well distance (m); l is2Old well water saturation of
The distance, m, of the plane of (a) moving at time t; l is0-distance, m, of the original oil-water interface from the water injection well; z is a radical of2-mobile oil saturation, decimal, of old wells; b-lgfo-lgz curve regression coefficients;
so the relationship of z to L:
in step 4, the total resistance of the two-phase seepage zone is:
wherein the content of the first and second substances,
the liquid production amounts at this time were:
wherein, Δ P-production pressure difference, MPa; g-starting pressure gradient, MPa/m.
In step 5, optimizing and determining a balanced displacement reasonable injection-production well spacing according to the relation between the average stratum water saturation and the outlet end water saturation, and dividing the time into a plurality of small sections, wherein the initial water content, the average stratum water saturation and the outlet end water saturation are known; and (3) solving seepage resistance, average water saturation, outlet end water saturation and water content in the t +1 time period according to the data of the t time period, wherein the well spacing is the solved reasonable injection-production well spacing when the final water content reaches a given target value.
In step 5, the relationship between the average water saturation of the formation for two adjacent time steps:
and the average stratum water saturation and the outlet end water saturation meet the following conditions:
in the formula (I), the compound is shown in the specification,
-formation average water saturation, decimal, at the ith time step;
-formation average water saturation, decimal, at time step i + 1; q-fluid production from the ith time step to the (i + 1) th time step, m3/d；fw-water cut, decimal fraction at ith time step; b, volume coefficient of crude oil, dimensionless quantity; h-effective thickness of oil layer, m; l is the injection-production well spacing, m; phi is rock porosity, decimal;
-the average water saturation, decimal, of the formation at a certain time;
-water saturation, decimal fraction of the outlet section;
-water cut, decimal fraction of the outlet section;
-the derivative of the moisture content of the outlet section with time, i.e. the moisture content change speed, decimal;
solving by an iterative method to obtain the water saturation of the outlet end at the time t, further obtaining the water content at the time t, and obtaining the final water content; setting the variation range of the reasonable injection-production well distance and the time point when the water content reaches the given target value, wherein if the water content reaches the given target value at the time point, the well distance is the calculated reasonable injection-production well distance, otherwise, the injection-production well distance is changed, and the calculation is carried out again until the final water content at the given time point is calculated to reach the target value.
The method for optimizing the well spacing for the balanced displacement of the oil reservoir in the high water cut stage is based on the oil-water two-phase flow seepage theory, comprehensively considers the heterogeneity, the utilization degree difference and the water cut difference of the reservoir, and utilizes the oil-water two-phase seepage theory and the oil reservoir engineering method to obtain the method for optimizing the well spacing for the balanced displacement of the oil reservoir in the high water cut stage.
Drawings
FIG. 1 illustrates lgf of the present inventionw-lgz schematic diagram of theoretical curve law;
FIG. 2 shows a graph of μ according to the present inventionrωo-a schematic diagram of the theoretical curve z;
FIG. 3 shows lgf in an example embodiment of the present inventionw-lgz graph of relationship;
FIG. 4 shows μ in an example embodiment of the present inventionrωo-a plot of the z-relationship;
fig. 5 is a flowchart of an embodiment of the high water cut reservoir equilibrium displacement differential well spacing optimization method of the present invention.
Detailed Description
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
As shown in fig. 5, fig. 5 is a flowchart of the high water cut reservoir equilibrium displacement differential well spacing optimization method of the present invention.
And (4) considering the starting pressure and combining a Darcy law formula to determine the total flow of oil and water at the seepage interface.
The total flow of oil and water through the seepage section is:
wherein:
in the formula, QwWater flow rate, m3/d；KwWater phase permeability, 10-3μm2(ii) a A-cross sectional area of seepage, m2；μw-formation water viscosity, mPa · s; p is the pressure of any point in the oil reservoir, MPa; x is the distance between any point in the oil deposit and an injection well, m and G are starting pressure gradients, MPa/m;
oil flow through the percolation cross section:
in the formula, QoOil flow, m3/d；KoOil phase Permeability, 10-3μm2；μo-underground crude oil viscosity, mPa · s;
total flow of oil and water through the cross section:
wherein:
in the formula, mur-oil-water viscosity ratio, dimensionless quantity; K-Absolute Permeability, 10-3μm2(ii) a B, volume coefficient of crude oil, dimensionless quantity; h-effective thickness of oil layer, m; k is a radical ofrwRelative permeability of water, 10-3μm2；kroRelative permeability of oil, 10-3μm2(ii) a L is the distance between injection wells and production wells, m.
And 102, determining the relationship between the seepage resistance per unit length and the saturation of the movable oil. According to the linear theory of the oil content and the mobile oil saturation in a log-log coordinate system (figure 1), the relationship between the seepage resistance per unit length and the mobile oil saturation is determined.
And (3) obtaining the seepage resistance on the dx length in the two-phase seepage zone according to an oil-water total flow formula of the seepage section:
the total seepage resistance of the two-phase seepage zone is as follows:
wherein:
in the formula: omegao-resistance to seepage per unit length, N.
Drawing f in a log-log coordinate system with the oil content as ordinate and the flowable oil saturation as abscissaoThe oil content and z (movable oil saturation) are in a linear relation, and the slope of the straight line is 1<μr<Is retained in 10And as the oil-water viscosity ratio increases, the straight line intercept becomes smaller, and the intercept is inversely proportional to the oil-water viscosity ratio.
Wherein: z is 1-Sw-Sor
In the formula: f. ofo-oil content, decimal fraction; sw-water saturation, decimal; z-mobile oil saturation, decimal. a, b-lgfoLgz curve of relationship parameter, decimal.
The oil content is as follows:
obtaining a relation between the seepage resistance per unit length and the movable oil saturation:
and 103, determining the relation between the movable oil saturation and the injection-production well spacing. According to μrωo(μrIs the oil-water viscosity ratio, omegaoSeepage resistance per unit length) and z (seepage resistance per unit length), and determining the relation between movable oil saturation and injection-production well spacing (figure 2).
μrωoThe relationship with z can be expressed as:
μrωo＝A+Bz+Cz2
in the formula: a, B, C-murωoAnd z, and a curve fitting coefficient.
According to the equation of motion of the isosaturation surface, namely the Bekery equation:
in the formula: x-water saturation of SwM, the position of the plane of (d) reached at time t; x is the number of0-original oil-water interface position, m; f. ofw-water cut, decimal; phi is rock porosity, decimal; q-total flow of oil and Water, m3D; t-the time of a certain moment.
Due to fw(Sw)＝1-fo(Sw) So fw'(Sw)＝-fo'(Sw) Thus, the above formula is rewritten as:
the position at which a certain water saturation plane arrives at time t is:
in the formula: x is the number of2Water saturation of
M, the position of the plane of (d) reached at time t; x is the number of0-original oil-water interface position, m; f. ofw-water cut, decimal; phi-rock porosity, decimal.
The two formulas are divided to obtain:
the oil content derivative is:
then the following equation can be derived:
wherein the L-new well has a water saturation of SwThe distance of the plane (a) in the time t, namely the reasonable injection-production well distance (m); l is2Old well water saturation of
The distance, m, of the plane of (a) moving at time t; l is0-distance, m, of the original oil-water interface from the water injection well; z is a radical of2-mobile oil saturation, decimal, of old wells.
So the relationship of z to L:
and step 104, determining the total resistance and the liquid production amount of the two-phase seepage area.
And determining the total resistance and the liquid production rate of the two-phase seepage area.
The total resistance of the two-phase seepage zone is as follows:
wherein the content of the first and second substances,
the liquid production amounts at this time were:
and 105, optimizing and determining the balanced displacement reasonable injection-production well spacing. And optimizing and determining the balanced displacement reasonable injection-production well spacing according to the relation between the average stratum water saturation and the outlet end water saturation.
The time is divided into a number of small segments, known as initial water cut, average formation water saturation, and outlet end water saturation. And (3) calculating seepage resistance, average water saturation, outlet end water saturation and water content in the t +1 time period according to the data of the t time period, wherein the well spacing is the calculated reasonable injection-production well spacing when the final water content reaches a given target value.
Relationship between stratigraphic average water saturation for two adjacent time steps:
and the average stratum water saturation and the outlet end water saturation meet the following conditions:
and solving to obtain the water saturation of the outlet end at the time t by an iterative method, further obtaining the water content at the time t, and obtaining the final water content. Setting the variation range of the reasonable injection-production well distance and the time point when the water content reaches the given target value, wherein if the water content reaches the given target value at the time point, the well distance is the calculated reasonable injection-production well distance, otherwise, the injection-production well distance is changed, and the calculation is carried out again until the final water content at the given time point is calculated to reach the target value.
In one embodiment of the present invention, the method comprises the following steps:
step 1, determining the total flow of oil and water at a seepage interface.
And (4) considering the starting pressure and combining a Darcy law formula to determine the total flow of oil and water at the seepage interface.
Total flow of oil and water through the cross section:
wherein:
in the formula, muw-formation water viscosity ratio, 0.454mPa · s; mu.soViscosity of underground crude oil, 1.08 mPas; mu.sr-oil-water viscosity ratio, 2.38; K-Absolute Permeability, 10-3μm2(ii) a B-crude oil volume coefficient, 1.2; h-effective thickness of oil layer, m; k is a radical ofrwRelative permeability of water, 10-3μm2；kroRelative permeability of oil, 10-3μm2(ii) a L is the injection-production well spacing, m; g-start pressure gradient, 0.02 MPa/m.
TABLE 1 parameter table for each oil production well
And 2, determining the relationship between the seepage resistance per unit length and the saturation of the movable oil. And determining the relationship between the seepage resistance per unit length and the mobile oil saturation according to the linear theory of the oil content and the mobile oil saturation in a log-log coordinate system.
The flow curve is scored from the phase permeation curve of the target area, and lgf is obtainedo-lgz (fig. 3), yielding a-0.036 and b-3.
The seepage resistance per unit length and the mobile oil saturation are expressed by the following relation:
and 3, determining the relation between the movable oil saturation and the injection-production well spacing. According to μrωo(μrIs the oil-water viscosity ratio, omegaoSeepage resistance per unit length) and z (seepage resistance per unit length), and determining the relation between movable oil saturation and injection-production well spacing.
Mu can also be plotted by the phase permeation curverωo-z (fig. 4), and regression through a cubic function, to obtain the corresponding parameters a-2.22, B-105.12, and C-208.39.
μrωoThe relationship with z follows the following law:
μrωo＝-2.22+105.12z-208.39z2
relationship of z to L:
wherein the L-new well has a water saturation of SwThe distance of the plane (a) in the time t, namely the reasonable injection-production well distance (m); l is2Old well water saturation of
The distance, m, of the plane of (a) moving at time t; l is0-distance, m, of the original oil-water interface from the water injection well; z is a radical of2-mobile oil saturation, decimal, of old wells.
And 4, determining the total resistance and the liquid production amount of the two-phase seepage area.
The total resistance of the two-phase seepage zone is as follows:
wherein the content of the first and second substances,
the liquid production amounts at this time were:
in the formula, delta P is the production pressure difference of 10 MPa; g-start pressure gradient, 0.02 MPa.
And 5, optimizing and determining the balanced displacement reasonable injection-production well spacing. And optimizing and determining the balanced displacement reasonable injection-production well spacing according to the relation between the average stratum water saturation and the outlet end water saturation.
If the initial water content value is known, then the set target value of the water content is given, and the corresponding water saturation is found according to the water content, and further the average water saturation of the stratum is obtained (table 2).
TABLE 2
Correspondence table
And setting a reasonable injection-production well spacing change range (200- & gt 800m), and solving the injection-production well spacing when the water content reaches a target value by an iteration method, namely the reasonable injection-production well spacing.
TABLE 3 reasonable interval between injection and production wells
Claims (10)
1. The method for optimizing the well spacing difference of the oil reservoir in the high water cut stage in the balanced displacement is characterized by comprising the following steps of:
step 1, determining the total flow of oil and water at a seepage interface;
step 2, determining the relationship between the seepage resistance per unit length and the saturation of the movable oil;
step 3, determining the relation between the movable oil saturation and the injection-production well spacing;
step 4, determining seepage resistance and liquid production amount between injection wells and production wells;
and 5, optimizing and determining the balanced displacement reasonable injection-production well spacing.
2. The method for optimizing the differential well spacing in the balanced displacement of the oil reservoir in the high water cut stage according to claim 1, wherein in step 1, the total oil-water flow of the seepage interface is determined by considering starting pressure and combining Darcy's law formula.
3. The method for optimizing the balanced displacement differential well spacing of the oil reservoir in the high water cut stage according to claim 2, wherein in the step 1, the total flow rate of oil and water passing through a seepage section is as follows:
wherein:
in the formula, QwWater flow rate, m3/d；KwWater phase permeability, 10-3μm2(ii) a A-cross sectional area of seepage, m2；μw-formation water viscosity, mPa · s; p is the pressure of any point in the oil reservoir, MPa; x is the distance between any point in the oil deposit and an injection well, m and G are starting pressure gradients, MPa/m;
oil flow through the percolation cross section:
in the formula, QoOil flow, m3/d；KoOil phase Permeability, 10-3μm2；μo-underground crude oil viscosity, mPa · s;
total flow of oil and water through the cross section:
wherein:
in the formula, mur-oil-water viscosity ratio, dimensionless quantity; K-Absolute Permeability, 10-3μm2(ii) a B, volume coefficient of crude oil, dimensionless quantity; h-effective thickness of oil layer, m; k is a radical ofrwRelative permeability of water, 10-3μm2；kroRelative permeability of oil, 10-3μm2(ii) a L is the distance between injection wells and production wells, m.
4. The method for optimizing the well spacing in the balanced displacement differentiation of the oil reservoir with the high water cut period according to claim 1, wherein in step 2, the relationship between the seepage resistance per unit length and the mobile oil saturation is determined according to the linear theory of the oil content and the mobile oil saturation in a log-log coordinate system.
5. The method for optimizing the well spacing in the oil reservoir with high water cut according to the claim 4, wherein in the step 2, the seepage resistance in the dx length in the two-phase seepage zone is obtained according to the oil-water total flow formula of the seepage section:
the total seepage resistance of the two-phase seepage zone is as follows:
wherein:
in the formula: omegao-specific length seepage resistance, N, muo-underground crude oil viscosity, mPa · s; mu.sr-oil-water viscosity ratio, dimensionless quantity; K-Absolute Permeability, 10-3μm2(ii) a B, volume coefficient of crude oil, dimensionless quantity; h-effective thickness of oil layer, m; k is a radical ofrwRelative permeability of water, 10-3μm2；kroRelative permeability of oil, 10-3μm2(ii) a L is the injection-production well spacing, m;
the oil content f is plotted in a log-log coordinate system by taking the oil content as the ordinate and the flowable oil saturation as the abscissaoAnd the movable oil saturation z in a linear relation, and the slope of the straight line is 1<μr<10, the straight line intercept is kept unchanged, and the straight line intercept becomes smaller along with the increase of the oil-water viscosity ratio, and the intercept is in inverse proportion to the oil-water viscosity ratio;
Wherein: z is 1-Sw-Sor
In the formula: f. ofo-oil content, decimal fraction; sw-water saturation, decimal; z-mobile oil saturation, decimal; a, b-lgfo-lgz curve of relationship parameter, decimal; sor-residual oil saturation, fractional;
the oil content is as follows:
in the formula, QoOil flow, m3/d；QwWater flow rate, m3/d；
Obtaining a relation between the seepage resistance per unit length and the movable oil saturation:
6. the method for optimizing the well spacing difference of the reservoir with high water cut according to the claim 1, wherein in the step 3, the well spacing difference is optimized according to the murωoAnd z, wherein μrIs the oil-water viscosity ratio, omegaoAnd determining the relation between the saturation of the movable oil and the distance between the injection well and the production well as the unit length seepage resistance and the unit length seepage resistance z.
7. The method for optimizing the balanced displacement differential well spacing of the oil reservoir with high water cut as claimed in claim 6, wherein in step 3,
μrωothe relationship with z can be expressed as:
μrωo＝A+Bz+Cz2
in the formula: a, B, C-murωoAnd z, a curve fitting coefficient;
according to the equation of motion of the isosaturation surface, namely the Bekery equation:
in the formula: x-water saturation of SwM, the position of the plane of (d) reached at time t; x is the number of0-original oil-water interface position, m; f. ofw-water cut, decimal; phi is rock porosity, decimal; q-total flow of oil and Water, m3D; t-time at a certain moment; sw-water saturation at x, decimal;
due to fw(Sw)＝1-fo(Sw) So fw'(Sw)＝-fo'(Sw) Thus, the above formula is rewritten as:
the position at which a certain water saturation plane arrives at time t is:
in the formula: x is the number of2Water saturation of
M, the position of the plane of (d) reached at time t; x is the number of0-original oil-water interface position, m; f. ofw-water cut, decimal; phi is rock porosity, decimal;
at x2Water saturation, decimal fraction;
the two formulas are divided to obtain:
the oil content derivative is:
then the following equation can be derived:
wherein the L-new well has a water saturation of SwThe distance of the plane (a) in the time t, namely the reasonable injection-production well distance (m); l is2Old well water saturation of
The distance, m, of the plane of (a) moving at time t; l is0-distance, m, of the original oil-water interface from the water injection well; z is a radical of2-mobile oil saturation, decimal, of old wells; b-lgfo-lgz curve regression coefficients;
so the relationship of z to L:
8. the method for optimizing the well spacing difference of the reservoir in the high water cut stage according to claim 7, wherein in the step 4, the total resistance of the two-phase seepage zone is as follows:
wherein the content of the first and second substances,
the liquid production amounts at this time were:
wherein, Δ P-production pressure difference, MPa; g-starting pressure gradient, MPa/m.
9. The method for optimizing the well spacing difference of the oil reservoir in the high water cut stage according to the claim 1, wherein in the step 5, the reasonable injection and production well spacing of the balanced displacement is determined according to the relation optimization of the average water saturation of the stratum and the water saturation of the outlet end, the time is divided into a plurality of small sections, and the initial water cut, the average water saturation of the stratum and the water saturation of the outlet end are known; and (3) solving seepage resistance, average water saturation, outlet end water saturation and water content in the t +1 time period according to the data of the t time period, wherein the well spacing is the solved reasonable injection-production well spacing when the final water content reaches a given target value.
10. The method for optimizing the balanced displacement differential well spacing of the oil reservoir with high water cut as claimed in claim 9, wherein in step 5, the relation between the average water saturation of the stratum at two adjacent time steps is as follows:
and the average stratum water saturation and the outlet end water saturation meet the following conditions:
in the formula (I), the compound is shown in the specification,
-formation average water saturation, decimal, at the ith time step;
-formation average water saturation, decimal, at time step i + 1; q-fluid production from the ith time step to the (i + 1) th time step, m3/d；fw-water cut, decimal fraction at ith time step; b, volume coefficient of crude oil, dimensionless quantity; h-effective thickness of oil layer, m; l is the injection-production well spacing, m; phi is rock porosity, decimal;
-the average water saturation, decimal, of the formation at a certain time;
-water saturation, decimal fraction of the outlet section;
-water cut, decimal fraction of the outlet section;
-the derivative of the moisture content of the outlet section with time, i.e. the moisture content change speed, decimal;
solving by an iterative method to obtain the water saturation of the outlet end at the time t, further obtaining the water content at the time t, and obtaining the final water content; setting the variation range of the reasonable injection-production well distance and the time point when the water content reaches the given target value, wherein if the water content reaches the given target value at the time point, the well distance is the calculated reasonable injection-production well distance, otherwise, the injection-production well distance is changed, and the calculation is carried out again until the final water content at the given time point is calculated to reach the target value.
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