CN110965996A - Method for detecting dynamic communication strength between wells - Google Patents
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Abstract
The invention provides a method for detecting the dynamic communication strength between wells. The detection method comprises the following steps: step 10: establishing a characterization model of the effect of the bound water and the stagnant pore, a characterization model of the effect of the residual oil and a microscopic seepage characterization model of the double medium effect; step 20: establishing a macroscopic seepage model of movable water; step 30: establishing a tracer recovery rate model, determining a water circulation ratio parameter according to a macroscopic seepage model of movable water, a characterization model of the effect of bound water and non-flowing pores, a characterization model of the effect of residual oil and a microscopic seepage characterization model of double medium effect, and determining the communication strength between at least one pair of injection and production wells in the oil reservoir according to the water circulation ratio parameter. The communication strength between at least one pair of injection and production wells in the oil reservoir is determined according to the water circulation ratio parameters, and the communication strength between adjacent wells can be well determined. By adopting the method, the reliability and the accuracy of the result of the communication strength between the detection wells can be improved.
Description
Technical Field
The invention relates to oil exploitation, in particular to a method for detecting the dynamic communication strength between wells.
Background
The well tracing test technology is one of the few technologies capable of carrying out the distribution research of the characteristic parameters between wells in a semi-quantitative manner. It adds substance (including special tracer or other distinguishable displacement fluid) with same or similar property state to the traced fluid into the oil deposit through the shaft, monitors the seepage condition and oil layer physical characteristic between the corresponding wells in the plane, longitudinal direction and layer, and completes the parameter analysis and explanation between wells from the perspective of interwell monitoring and oil deposit and geology.
With the definition of test purpose and the development of tracing among wells, the tracing test interpretation method is also continuously perfected and developed. There are three main methods currently being explained: analytical method, numerical simulation method, and semi-analytical method.
(1) Analysis method
However, when a well pattern is slightly complex, an analytical expression cannot be obtained, so that theoretical interpretation errors are increased.
(2) Numerical method
The basic principle of the numerical method is to utilize a multi-phase multi-component model, take a tracer as a component and process the injection, migration and production processes of the tracer, and according to practical application experience and theoretical analysis, the method has the defects that the ① migration mechanism is difficult to accurately describe, ② has large workload and high requirement on operators, the ③ solution has poor stability, non-physical phenomena are easy to occur in the calculation process, and the ④ is difficult to fit the multi-peak problem and the multi-well multi-tracer problem.
(3) Semi-analytic method
The semi-analytic method comprises a method for calculating bottom hole concentration by simply utilizing a streamline and a method for calculating by means of the streamline method, wherein the latter method is characterized in that ① solves pressure trend distribution of each layer of an oil reservoir by utilizing a numerical method, ② solves output concentration by utilizing an analytic method, ③ connects the numerical method with the analytic method by utilizing the streamline method.
However, the current test interpretation technology is still based on the principle and theory proposed in the 60-80 s of the 20 th century, and the problems found on site are not further developed and perfected. The practice and theoretical comparison of several domestic mine sites prove that the basic theoretical research at present has at least the following two limitations, which are specifically shown as follows:
(1) although there have been many studies on mass transfer diffusion of porous media, no application of the results to a targeted description of the effects of reservoir porous media and heterogeneous heterogeneities on tracer micro-percolation has been made. The current application theory is established based on pipe flow and lacks pertinence, so that how to quantitatively characterize the porous medium better is reflected in a model explained by an interwell tracing test is one of the research targets.
(2) Existing interpretation methods do not take into account the effect of lateral diffusion on the produced tracer, but field practice has shown that in most cases, quantitative interpretation must take into account multi-directional diffusion, including lateral diffusion. On one hand, the field test interpretation work finds that the interpretation result obviously deviates from the reasonable parameter range and is inconsistent with the actual dynamic state; on the other hand, the results are found to be extremely different by comparison with numerical simulations.
The problems show that the basic theories and the explanation model established on the basis obviously deviate from the reasonable scope, the problems of single consideration factor and one side exist, and the quantitative description of the complex seepage of the porous medium cannot be well adapted.
Disclosure of Invention
The invention mainly aims to provide a method for detecting the strength of inter-well dynamic communication, which aims to solve the problem of large deviation of detection results of the strength of inter-oil-well communication in the prior art.
In order to achieve the above object, according to an aspect of the present invention, there is provided a method for detecting the strength of dynamic communication between wells, the method comprising the steps of: step 10: establishing a characterization model of the effect of the bound water and the stagnant pore, a characterization model of the effect of the residual oil and a microscopic seepage characterization model of the double medium effect; step 20: establishing a macroscopic seepage model of movable water; step 30: establishing a tracer recovery rate model, determining a water circulation ratio parameter according to a macroscopic seepage model of movable water, a characterization model of the effect of bound water and non-flowing pores, a characterization model of the effect of residual oil and a microscopic seepage characterization model of double medium effect, and determining the communication strength between at least one pair of injection and production wells in the oil reservoir according to the water circulation ratio parameter.
Further, the water circulation ratio parameter can be obtained by the following formula:
wherein gamma is the water circulation proportion parameter of the tracer, η is the recovery rate of the tracer, C0The initial injection concentration of the tracer is in mg/L; chThe theoretical concentration of the tracer at the output end is in mg/L.
Further, the ratio of the theoretical concentration of the tracer production end to the initial concentration of the tracer injected can be obtained by the following formula:
wherein the content of the first and second substances,
delta t is the time from the beginning of the injection timing, the slug injection time; x is the distance in the direction of the X axis in the hypertonic channel; u. ofxThe real flow speed of the fluid in the X direction in the pores is expressed in cm/s; a ishThe side length of a hypertonic channel of the matrix agglomerate is cm; dxIs the mass transfer diffusion coefficient in the X direction and has the unit of cm2S; d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2/s；alThe side length of a hypotonic channel of the matrix agglomerate is in cm; dzIs the mass transfer diffusion coefficient in the Z direction and has the unit of cm2S, ξ is an integral variable phifIs flow porosity; soResidual oil saturation; swcIrreducible water saturation; b is the width of half of the hypertonic channel in cm; t is the time taken for the tracer to undergo mass transfer diffusion in the hyperosmotic channel, and is given in units of s.
And further, when the gamma is less than or equal to 10 percent, determining that the communication strength between the oil wells in the oil reservoir is low.
Further, in the process of establishing a characterization model for the effects of bound water and stagnant porosity, in the pore throats through which the tracer flows, there is Cswc＝C，CnonpIs ═ C, where CswcThe concentration of tracer in the bound water is mg/L; c is the concentration of the tracer, and the unit is mg/L; cnonpThe tracer concentration in the non-flowing pores, mg/L.
Further, the diffusion rate of the permeation pathway into the interior of the hypotonic pellet is obtained by the following formula:
wherein J is the diffusion speed of the hypertonic channel into the hypotonic mass in mg3/L.s；amThe side length of the hypotonic agglomerate is cm; phi is porosity; swThe water saturation of the hypotonic clump; d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2S; c is the concentration in the crack or the hypertonic channel, and the unit is mg/L; c is the concentration in mg/L inside the matrix or hypotonic bolus surrounded by hypertonic channels.
Further, in step 30, the amount of change in the concentration of the hypotonic bolus tracer per unit time is obtained by the following equation:
wherein q is the concentration change of the tracer agent in mg/L.s caused by diffusion from the hypertonic channel into the hypotonic bolus in unit volume in unit time.
Further, the following steps, step 21, are included in step 20: establishing a geological model of one-dimensional flow and two-dimensional mass transfer diffusion; step 22: establishing a one-dimensional flowing two-dimensional mass transfer diffusion mathematical model; step 23: and solving a one-dimensional flowing two-dimensional mass transfer diffusion mathematical model.
Further, in step 22, establishing a one-dimensional flowing two-dimensional mass transfer diffusion mathematical model includes establishing a hypertonic channel mass transfer diffusion model and a hypotonic zone mass transfer diffusion model, wherein the hypertonic channel mass transfer diffusion model can be obtained by the following formula:
wherein the content of the first and second substances,
x is the distance in the direction of the X axis in the hypertonic channel; dxIs the mass transfer diffusion coefficient in the X direction and has the unit of cm2/s；uxThe real flow speed of the fluid in the X direction in the pores is expressed in cm/s; chThe concentration of the tracer in the hypertonic channel is mg/L; clIs a hypotonic groupThe concentration of the tracer in the block is mg/L; d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2S; t is the time for the tracer to generate mass transfer diffusion in the hypertonic channel, and the unit is s; b is the width of half of the hypertonic channel in cm; a is the side length of the matrix block mass, and the unit is cm; phi is porosity; phi is afIs flow porosity; soResidual oil saturation; swcIrreducible water saturation; rhorIs the specific gravity of the rock particles, ξ is the integral variable and l is the parameter representing the zone of hypotonicity.
Further, in the hyperosmotic channel mass transfer diffusion model, the boundary and initial conditions of the hyperosmotic channel can be obtained by the following formula:
wherein, C0The initial injection concentration of tracer, mg/L.
The mass transfer diffusion model of the hypotonic region can be obtained by the following formula:
wherein the content of the first and second substances,
althe side length of the hypotonic channel, in cm, is the matrix mass.
In the mass transfer diffusion model of the hypotonic region, the boundaries and initial conditions of the hypotonic region can be obtained by the following equations:
by applying the technical scheme of the invention, the communication strength between at least one pair of injection and production wells in the oil reservoir is determined according to the water circulation ratio parameter by adopting the method for detecting the dynamic communication strength between the wells, so that the problem of the communication strength between adjacent wells can be well determined. By adopting the method, the reliability and the accuracy of the result of the communication strength between the detection wells can be improved.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 shows a one-dimensional flow two-dimensional mass transfer diffusion geological model schematic;
FIG. 2 shows the tracer test and fitting results for well B.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
It should be noted that the terms "first," "second," and the like in the description and claims of this application and in the drawings are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments of the application described herein are, for example, capable of operation in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Spatially relative terms, such as "above … …," "above … …," "above … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial relationship to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is turned over, devices described as "above" or "on" other devices or configurations would then be oriented "below" or "under" the other devices or configurations. Thus, the exemplary term "above … …" can include both an orientation of "above … …" and "below … …". The device may be otherwise variously oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
Exemplary embodiments according to the present application will now be described in more detail with reference to the accompanying drawings. These exemplary embodiments may, however, be embodied in many different forms and should not be construed as limited to only the embodiments set forth herein. It is to be understood that these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art, in the drawings, it is possible to enlarge the thicknesses of layers and regions for clarity, and the same devices are denoted by the same reference numerals, and thus the description thereof will be omitted.
According to the characteristic that tracer seepage has pseudo-oil reservoir characteristic chromatographic effect, and in consideration of micro mechanism and macro phenomenon, a micro seepage characterization model about bound water and no-flow pore effect, residual oil effect and pseudo-dual medium effect is established. A physical model of porous medium mass transfer diffusion is provided, a mathematical model of two-dimensional mass transfer diffusion seepage under (pseudo) dual medium one-dimensional flow considering axial and transverse mass transfer diffusion simultaneously is established, a more perfect half-analytic method for calculating and solving the output concentration of the tracer between wells is established, and automatic fitting of an output concentration curve is realized. On the basis of the model, a calculation method for calculating the invalid-inefficient water circulation ratio of the tracer recovery rate is established. Research results show that the established inter-well tracer test interpretation technology can better describe the inter-well tracer mass transfer diffusion rule under complex conditions, realizes quantitative inversion of tracer tests to a certain extent, and provides theoretical basis and technical support for developing inter-well tracer test design and interpretation. Among them, a medium having both pores and cracks in rock is called "dual medium", a medium having rock characteristics of pores and cracks but having seepage characteristics of "dual medium" is called "pseudo-dual medium".
Referring to fig. 1 to 2, according to an embodiment of the present invention, a method for detecting the strength of dynamic communication between wells is provided.
Specifically, the detection method comprises the following steps: step 10: establishing a characterization model of the effect of the bound water and the stagnant pore, a characterization model of the effect of the residual oil and a microscopic seepage characterization model of the double medium effect; step 20: establishing a macroscopic seepage model of movable water; step 30: establishing a tracer recovery rate model, determining a water circulation ratio parameter according to a macroscopic seepage model of movable water, a characterization model of the effect of bound water and non-flowing pores, a characterization model of the effect of residual oil and a microscopic seepage characterization model of double medium effect, and determining the communication strength between at least one pair of injection and production wells in the oil reservoir according to the water circulation ratio parameter.
In the implementation, the communication strength between at least two oil wells in the oil reservoir is determined according to the water circulation ratio parameter by adopting the detection method for the dynamic communication strength between the wells, so that the problem of the communication strength between adjacent wells can be well determined. By adopting the method, the reliability and the accuracy of the result of the communication strength between the detection wells can be improved.
Wherein, the water circulation proportion parameter can be obtained by the following formula:
wherein gamma is the water circulation proportion parameter of the tracer, η is the recovery rate of the tracer, C0The initial injection concentration of the tracer is in mg/L; chThe theoretical concentration of the tracer at the output end is in mg/L.
The ratio of the theoretical concentration of the tracer production end to the initial tracer injection concentration can be obtained by the following formula:
wherein the content of the first and second substances,
delta t is the time from the beginning of the injection timing, the slug injection time; x is the distance in the direction of the X axis in the hypertonic channel; u. ofxThe real flow speed of the fluid in the X direction in the pores is expressed in cm/s; a ishThe side length of a hypertonic channel of the matrix agglomerate is cm; dxIs the mass transfer diffusion coefficient in the X direction and has the unit of cm2S; d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2/s；alThe side length of a hypotonic channel of the matrix agglomerate is in cm; dzIs the mass transfer diffusion coefficient in the Z direction and has the unit of cm2S, ξ is an integral variable phifIs flow porosity; soResidual oil saturation; swcIrreducible water saturation; b is the width of half of the hyperosmotic channel in cm. And when the gamma is less than or equal to 10 percent, determining that the communication strength between a pair of injection and production wells in the oil reservoir is low.
Further, in the process of establishing a characterization model for the effects of bound water and stagnant porosity, in the pore throats through which the tracer flows, there is Cswc＝C，CnonpIs ═ C, where CswcThe concentration of tracer in the bound water is mg/L; c is the concentration of the tracer, and the unit is mg/L; cnonpThe tracer concentration in the non-flowing pores, mg/L.
The diffusion rate of the permeation pathway into the interior of the hypotonic mass is obtained by the following equation:
wherein J is the diffusion speed of the hypertonic channel into the hypotonic mass in mg3/L.s；amThe side length of the hypotonic agglomerate is cm; phi is porosity; swThe water saturation of the hypotonic clump; d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2S; c is the concentration in the crack or the hypertonic channel, and the unit is mg/L; c is the concentration in mg/L inside the matrix or hypotonic bolus surrounded by hypertonic channels.
In step 30, the amount of change in the concentration of the hypotonic bolus tracer per unit time is obtained by the following equation:
wherein q is the concentration change of the tracer agent in mg/L.s caused by diffusion from the hypertonic channel into the hypotonic bolus in unit volume in unit time.
In step 22, establishing a one-dimensional flowing two-dimensional mass transfer diffusion mathematical model comprises establishing a high-permeability channel mass transfer diffusion model and a low-permeability zone mass transfer diffusion model, wherein the high-permeability channel mass transfer diffusion model can be obtained by the following formula:
wherein the content of the first and second substances,
x is the distance in the direction of the X axis in the hypertonic channelSeparating; dxIs the mass transfer diffusion coefficient in the X direction and has the unit of cm2/s；uxThe real flow speed of the fluid in the X direction in the pores is expressed in cm/s; chThe concentration of the tracer in the hypertonic channel is mg/L; clThe concentration of the tracer in the hypotonic pellet is mg/L; d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2S; t is the time for the tracer to generate mass transfer diffusion in the hypertonic channel, and the unit is s; b is the width of half of the hypertonic channel in cm; a is the side length of the matrix block mass, and the unit is cm; phi is porosity; phi is afIs flow porosity; soResidual oil saturation; swcIrreducible water saturation; rhorIs the specific gravity of the rock particles, ξ is the integral variable and l is the parameter representing the zone of hypotonicity.
In the hyperosmotic channel mass transfer diffusion model, the boundary and initial conditions of the hyperosmotic channel can be obtained by the following formula:
wherein, C0The initial injection concentration of tracer, mg/L.
Further, the mass transfer diffusion model of the hypotonic region can be obtained by the following formula:
wherein the content of the first and second substances,
althe side length of the hypotonic channel, in cm, is the matrix mass.
In the mass transfer diffusion model of the hypotonic region, the boundaries and initial conditions of the hypotonic region can be obtained by the following equations:
Cl(b,x,t)＝Ch(x,t)
Cl(∞,x,t)＝0 (t＞0)
Cl(z,x,0)＝0 (z≥b)
wherein, the characterization model of the effect of the bound water and the stagnant pore is specifically as follows: in the pore throats through which the tracer flows, there is a significant amount of irreducible water saturation, and since the irreducible water is in sufficient contact with the tracer solution, it is believed that the mass transfer diffusion between the two is instantaneously in equilibrium. The concentration of tracer in the bound water was: cswcIs ═ C, where CswcTo bind the tracer concentration in water, the unit is mg/L, and C is the tracer concentration, the unit is mg/L.
Again, the tracer concentration in the pores that are connected but unable to flow is: cnonpIs ═ C, where CnonpThe tracer concentration in the stagnant pores is given in mg/L.
The establishment of the residual oil effect characterization model specifically comprises the following steps: due to residual oil saturation SoThe presence of (a) results in a reduction in the pore volume occupied by the tracer, which in most cases can be equated with a reduction in porosity. And the migration velocity of the tracer in the pore space is influenced, and needs to be considered in the process of establishing the mathematical model.
The microscopic seepage characterization model of the dual medium effect is characterized in that ① low-permeability lumps are discontinuous, homogeneous, isotropic and close in shape and are arranged according to a certain rule, ② high-permeability channels are continuous, nearly uniform, isotropic and wrap around the low-permeability lumps, ③ has no cross flow between the high-permeability channels and the low-permeability lumps, only mass transfer diffusion is generated due to different concentrations of tracers, the influence of the size is small and accords with Fick diffusion law, ④ seepage fields are steady, the high-permeability channels are tracer seepage dominant channels, and the seepage effect of the low-permeability lumps can be ignored.
For (pseudo) dual media, there are two concentration fields, one is the concentration C inside the fracture or hypertonic channel (hereafter collectively referred to as hypertonic channel) and one is the concentration C inside the matrix or hypotonic rock mass surrounded by hypertonic channels (hereafter collectively referred to as hypotonic mass).
Water saturation equal to S in hypotonic agglomerateswIn the case of (1), the irrespective of irreducible water saturation and non-flowing porosity, according to Fick's law, is composed of highThe diffusion rate of the permeation channel into the interior of the hypotonic pellet is:
wherein J is the diffusion rate of the hypertonic channels into the hypotonic bolus in mg3L.s; am is the side length of the hypotonic bolus (assuming the hypotonic bolus is cubic) in cm; phi is porosity; swThe water saturation of the hypotonic clump; d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate, cm 2/s; c is the concentration in the crack or the hypertonic channel (hereinafter collectively referred to as the hypertonic channel), and the unit is mg/L; c is the concentration in mg/L inside the matrix or hypotonic rock mass surrounded by hypertonic channels (hereinafter collectively referred to as hypotonic mass).
Diffusing from the high-permeability channel to the interior of the low-permeability block in unit volume in unit time to cause the concentration variation of the tracer of the low-permeability block to be:
wherein q is the amount of change in tracer concentration in mg/L.s in the hypotonic bolus resulting from diffusion from the hypertonic pathway into the hypotonic bolus per unit volume per unit time.
Order to
Characteristic parameters of mass transfer and diffusion speeds of the high-permeability channel and the low-permeability block are shown as follows:
q＝λ(C-C*)
in the formula, lambda is a characteristic parameter of mass transfer diffusion speed of the high-permeability channel and the low-permeability block mass.
The macroscopic seepage model specifically comprises the following steps:
and in the process 1, a geological model of one-dimensional flow and two-dimensional mass transfer diffusion is established, and basic condition setting of the model is given.
And 2, establishing a mathematical model of one-dimensional flowing two-dimensional mass transfer diffusion.
And 3, solving a one-dimensional flowing two-dimensional mass transfer diffusion mathematical model.
A geological model of one-dimensional flow two-dimensional mass transfer diffusion is established, basic condition setting of the model is given, and the geological model of one-dimensional flow two-dimensional mass transfer diffusion is specifically characterized in that the concentration of a tracer in a Z-axis direction in a ① hypertonic channel is the same, the thickness of a ② hypertonic channel is far smaller than the length of the channel, the flow velocity of a ③ hypotonic zone is 0, the mechanical mixing effect is weak, only mass transfer diffusion in the direction perpendicular to the hypertonic channel is considered, the influence of the upper boundary and the lower boundary of a ④ hypotonic zone is not considered temporarily, and the tracer performance is ⑤ stable.
Establishing a mathematical model of one-dimensional flowing two-dimensional mass transfer diffusion, which specifically comprises the following steps:
the equation of mass transfer diffusion of the high-permeability channel is as follows:
wherein the content of the first and second substances,
wherein Dx is mass transfer diffusion coefficient in X direction and unit is cm2/s；uxThe real flow speed of the fluid in the X direction in the pores is expressed in cm/s; chThe concentration of the tracer in the hypertonic channel is mg/L; clThe concentration of the tracer in the hypotonic pellet is mg/L; d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2S; t is time in units of s; b is half of the width of the hypertonic channel and the unit is cm; a is the side length of the matrix mass (assumed to be cubic) in cm; phi is the total porosity; phi is afIs flow porosity; soResidual oil saturation; swcIrreducible water saturation; rhorIs the specific gravity of rock particles; the subscripts h and l indicate the hypertonic channel and hypotonic zone parameters, respectively.
The mass transfer diffusion equation of the hypotonic region is as follows:
wherein the content of the first and second substances,
in the formula, DzIs the mass transfer diffusion coefficient in the Z direction and has the unit of cm2S; the subscript l indicates the hypotonic region parameters.
The hypertonic channel boundary conditions and initial conditions are:
in the formula, C0The concentration of the tracer in mg/L is the initial injection concentration.
The boundary conditions and initial conditions of the hypotonic region are:
the solving of the one-dimensional flow two-dimensional mass transfer diffusion mathematical model comprises the following steps:
taking Laplace transformation of time t for the mass transfer diffusion equation of the hypotonic region and the boundary condition thereof, and obtaining the general solution as follows:
in the formula, S is a Laplace operator.
Substituting the formula into the boundary condition of the hypotonic region to obtain:
the solution for the hypotonic region can be expressed as:
taking Laplace transformation of time t for a high-permeability channel mass transfer diffusion equation and boundary conditions thereof, and then substituting the Laplace transformation with a low-permeability area mass transfer diffusion speed to obtain:
order:
the equation of mass transfer diffusion of the high-permeability channel is simplified as follows:
the above equation is a second order ordinary differential equation, the general solution of which is:
wherein the content of the first and second substances,
substituting the formula into the boundary condition of the hypertonic channel to obtain:
the Laplace spatial solution of the hyperosmotic channel is thus obtained as:
order:
the formula is simplified as follows:
because there is a relation:
wherein ξ is integralA variable; y is a constant.
Order:
the simplification is as follows:
according to Laplace transformation:
L-1[e-asF(s)]and f (t-a), inverting the formula to obtain a concentration distribution expression on the hypertonic channel:
in the hypotonic region, let
Then there are:
the expression of the tracer concentration in the hypotonic region is obtained by inversion:
For tracer slug monitoring, from the beginning of injection timing, the slug injection time is Δ t, and the theoretical expression of the concentration change of the produced tracer is as follows:
according to the characteristics of the error residual function, the method is further simplified to obtain:
specifically, a microscopic seepage characterization model about the effect of bound water and no-flow pores, the effect of residual oil and the effect of (pseudo) double media is established based on the chromatographic effect of oil reservoir characteristics. A two-dimensional mass transfer diffusion mathematical model of dual medium one-dimensional flow is established, which simultaneously considers axial and transverse mass transfer diffusion. Based on a streamline method and an unstable seepage field, a more complete half-analytic method for calculating and solving the output concentration of the interwell tracer is constructed. And a calculation formula for calculating the invalid-inefficient water circulation ratio of the tracer recovery rate is established.
Firstly, establishing a microscopic seepage characterization model about a bound water and no-flow pore effect, a residual oil effect and a (simulated) double medium effect based on an oil reservoir characteristic chromatographic effect, wherein the specific process comprises the following steps:
establishing a micro seepage characterization model related to the effect of bound water and no-flow pores, establishing a micro seepage characterization model related to the effect of residual oil, and establishing a micro seepage characterization model related to (pseudo) dual medium effect. Secondly, considering axial and transverse mass transfer diffusion simultaneously, establishing a dual medium one-dimensional flow two-dimensional mass transfer diffusion mathematical model, and the specific process is as follows: establishing a geological model of one-dimensional flowing two-dimensional mass transfer diffusion, giving basic condition setting of the model, establishing a mathematical model of one-dimensional flowing two-dimensional mass transfer diffusion, and solving the mathematical model of one-dimensional flowing two-dimensional mass transfer diffusion.
And finally, establishing a calculation method for calculating the ineffective-inefficient water circulation ratio of the tracer recovery rate, and combining the solution of the mass transfer diffusion mathematical model to provide a calculation formula for the ineffective-inefficient water circulation ratio.
The method mainly aims to improve a porous medium mass transfer diffusion mathematical model by combining with the latest theoretical research progress of porous medium mass transfer diffusion, construct an interwell tracer output concentration calculation and solution semi-analytic method and provide a method for quantifying the interwell low-efficiency water circulation proportion by using tracer tests.
From the research angles of oil layer physics, seepage mechanics and oil reservoir engineering, the mass transfer diffusion mechanism, the mathematical model and the solving method of migration of the tracer in the porous medium reservoir stratum are researched in a targeted manner. The method solves the problems that the existing method and technology do not accord with the geological characteristics of the oil reservoir and the fluid seepage characteristics, do not consider the mass transfer diffusion rule of the tracer between wells under complex conditions, and can not realize quantitative interpretation of partial parameters. The inter-well tracing test effect can be scientifically and quantitatively explained by using the tracing test.
The method comprises the following steps: based on the oil reservoir characteristic chromatographic effect, a microscopic seepage characterization method related to the bound water and no-flow pore effect, the residual oil effect and the (pseudo) dual medium effect is established.
The method can be divided into 3 processes: establishing a microscopic seepage characterization method for the effects of bound water and no-flow pores; establishing a microscopic seepage characterization method about the residual oil effect; and 3, establishing a microscopic seepage characterization method for the (pseudo) dual medium effect.
(1) Process 1
In the pore throats through which the tracer flows, there is a large amount of irreducible water saturation, and since the irreducible water is in sufficient contact with the tracer solution, it is believed that the mass transfer diffusion between the two is instantaneously in equilibrium, and the concentration of the tracer in the irreducible water is:
Cswcis ═ C, where CswcThe concentration of tracer in the bound water is mg/L; c is the concentration of the tracer and is expressed in mg/L.
Again, the tracer concentration in the pores that are connected but unable to flow is:
Cnonpis ═ C, where CnonpThe tracer concentration in the stagnant pores is given in mg/L.
(2) Process 2
Due to residual oil saturation SoThe existence of (2) leads to the reduction of the pore volume occupied by the tracer, which can be equivalent to the reduction of the porosity in most cases, and has influence on the calculation of the migration speed of the tracer in the pore space, and the calculation needs to be considered in the process of establishing a mathematical model.
(3) Process 3
For (pseudo) dual media, there are two concentration fields, one is the concentration C inside the fracture or hypertonic channel (hereafter collectively referred to as hypertonic channel) and one is the concentration C inside the matrix or hypotonic rock mass surrounded by hypertonic channels (hereafter collectively referred to as hypotonic mass).
Water saturation equal to S in hypotonic agglomerateswIn the case of (2), irrespective of irreducible water saturation and non-flowing porosity, according to Fick's law, the diffusion rate from the hypertonic channels into the interior of the hypotonic mass is:
Diffusing from the high-permeability channel to the interior of the low-permeability block in unit volume in unit time to cause the concentration variation of the tracer of the low-permeability block to be:
Order to
Characteristic parameters of mass transfer and diffusion speeds of the high-permeability channel and the low-permeability block are shown as follows:
q＝λ(C-C*) In the formula, lambda is a characteristic parameter of mass transfer diffusion speed of the high-permeability channel and the low-permeability block mass.
Step two: establishing a macroscopic seepage mathematical model of movable water
The method can be divided into 3 processes: the method comprises the following steps of 1, establishing a one-dimensional flowing two-dimensional mass transfer diffusion geological model, and giving basic condition setting of the model; establishing a mathematical model of one-dimensional flowing two-dimensional mass transfer diffusion; and 3, solving a one-dimensional flowing two-dimensional mass transfer diffusion mathematical model.
(1) Process 1
A geological model of one-dimensional flow and two-dimensional mass transfer diffusion has the basic conditions that the concentration of tracers in a Z-axis direction in an ① hypertonic channel is the same, the thickness of a ② hypertonic channel is far smaller than the length of the hypertonic channel, the flow speed of a ③ hypotonic zone is 0, the mechanical mixing effect is weak, only mass transfer diffusion in the direction perpendicular to the hypertonic channel is considered, the influence of the upper boundary and the lower boundary of a ④ hypotonic zone is not considered temporarily, and the performance of the tracers is ⑤ stable.
(2) Process 2
The equation of mass transfer diffusion of the high-permeability channel is as follows:
wherein the content of the first and second substances,
in the formula, DxIs the mass transfer diffusion coefficient in the Xx direction and has the unit of cm2/s；uxThe real flow speed of the fluid in the X direction in the pores is expressed in cm/s; chThe concentration of the tracer in the hypertonic channel is mg/L; clThe concentration of the tracer in the hypotonic pellet is mg/L; d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2S; t is time in units of s; b is half of the width of the hypertonic channel and the unit is cm; a is the side length of the matrix mass (assumed to be cubic) in cm; phi is the total porosity; phi is afIs flow porosity; soResidual oil saturation; swcIrreducible water saturation; rhorIs the specific gravity of rock particles; the subscripts h and l indicate the hypertonic channel and hypotonic zone parameters, respectively.
The mass transfer diffusion equation of the hypotonic region is as follows:
The hypertonic channel boundary conditions and initial conditions are:
The boundary conditions and initial conditions of the hypotonic region are:
(3) process 3
Taking Laplace transformation of time t for the mass transfer diffusion equation of the hypotonic region and the boundary condition thereof, and obtaining the general solution as follows:
Substituting the formula into the boundary condition of the hypotonic region to obtain:
the solution for the hypotonic region can be expressed as:
taking Laplace transformation of time t for a high-permeability channel mass transfer diffusion equation and boundary conditions thereof, and then substituting the Laplace transformation with a low-permeability area mass transfer diffusion speed to obtain:
order:
the equation of mass transfer diffusion of the high-permeability channel is simplified as follows:
wherein the content of the first and second substances,
substituting the obtained product into the boundary condition of the hypertonic channel to obtain:
the Laplace spatial solution of the hyperosmotic channel is thus obtained as:
order:
the simplification is as follows:
because there is a relation:
wherein ξ is an integral variable and y isA constant.
Order:
the simplification is as follows:
according to Laplace transformation:
L-1[e-asF(s)]and f (t-a), inverting the formula to obtain a concentration distribution expression on the hypertonic channel:
in the hypotonic region, let
Then there are:
For tracer slug monitoring, from the beginning of injection timing, the slug injection time is Δ t, and the theoretical expression of the concentration change of the produced tracer is as follows:
according to the characteristics of the error residual function, the method is further simplified to obtain:
step three: and establishing a calculation method for calculating the invalid-inefficient water circulation ratio of the tracer recovery rate.
The calculation formula of the ineffective-ineffective water circulation ratio is as follows:
The detection method is adopted to carry out tracing test on the well group M, and in the test process, 4 wells are opened in the interpretation range, wherein 1 well (well name A) of an injection well and 3 wells (well names are B, C, D respectively). During sampling and monitoring for more than 5 months, the oil well B has tracer production, water channeling possibly exists between the oil well B and a water injection well, other wells have no tracer production, and obvious difference exists between the wells. The tracer test data and the fitting of the well B are shown in fig. 2.
The recovery rate is the ratio of the amount of the tracer produced by each well to the amount of the tracer injected, and the recovery rate can qualitatively explain the condition of the dynamic communication between the wells to a certain extent. The recovery rate of the tracer for the well group is 7%.
The results of the tracer tests and fitting according to fig. 2 show that when the test is over, the invalid-inefficient water circulation ratio is calculated using the method, with the results: 35 percent.
According to the calculation result of the invalid-inefficient water circulation ratio, the relatively serious water injection inrush exists between corresponding wells.
In addition to the foregoing, it should be noted that reference throughout this specification to "one embodiment," "another embodiment," "an embodiment," or the like, means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment described generally throughout this application. The appearances of the same phrase in various places in the specification are not necessarily all referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with any embodiment, it is submitted that it is within the scope of the invention to effect such feature, structure, or characteristic in connection with other embodiments.
In the foregoing embodiments, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A method for detecting the dynamic communication strength between wells is characterized by comprising the following steps:
step 10: establishing a characterization model of the effect of the bound water and the stagnant pore, a characterization model of the effect of the residual oil and a microscopic seepage characterization model of the double medium effect;
step 20: establishing a macroscopic seepage model of movable water;
step 30: establishing a tracer recovery rate model, determining a water circulation ratio parameter according to the macroscopic seepage model of the movable water, the characterization model of the effect of the bound water and the stagnant pore, the characterization model of the effect of the residual oil and the characterization model of the microscopic seepage of the dual medium effect, and determining the communication strength between at least one pair of injection and production wells in the oil reservoir according to the water circulation ratio parameter.
2. The detection method according to claim 1, wherein the water circulation ratio parameter is obtained by the following formula:
wherein γ is the water circulation ratio parameter of the tracer;
η is the recovery rate of tracer;
C0the initial injection concentration of the tracer is in mg/L;
Chthe theoretical concentration of the tracer at the output end is in mg/L.
3. The detection method according to claim 2, wherein the ratio of the theoretical concentration of the tracer production end to the initial concentration of the tracer injected is obtained by the following formula:
wherein the content of the first and second substances,
delta t is the time from the beginning of the injection timing, the slug injection time;
x is the distance in the direction of the X axis in the hypertonic channel;
uxthe real flow speed of the fluid in the X direction in the pores is expressed in cm/s;
ahthe side length of a hypertonic channel of the matrix agglomerate is cm;
Dxis the mass transfer diffusion coefficient in the X direction and has the unit of cm2/s；
D is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2/s；
alThe side length of a hypotonic channel of the matrix agglomerate is in cm;
Dzis the mass transfer diffusion coefficient in the Z direction and has the unit of cm2/s；
ξ is an integral variable;
φfis flow porosity;
Sois residual oil saturation；
SwcIrreducible water saturation;
b is the width of half of the hypertonic channel in cm;
t is the time taken for the tracer to undergo mass transfer diffusion in the hyperosmotic channel, and is given in units of s.
4. The method of claim 2, wherein the communication strength between production wells in the reservoir is determined to be low when γ is less than or equal to 10%.
5. The detection method according to claim 1, wherein in the process of establishing the characterization model for the bound water and stagnant porosity effect, the tracer flows through the pore throat with Cswc＝C，CnonpWherein the amount of the compound represented by formula (I),
Cswcthe concentration of tracer in the bound water is mg/L;
c is the concentration of the tracer, and the unit is mg/L;
Cnonpthe tracer concentration in the non-flowing pores, mg/L.
6. The method of detection according to claim 1, wherein in said step 30, the diffusion rate of the permeation pathway into the interior of the hypotonic pellet is obtained by the following formula:
wherein J is the diffusion speed of the hypertonic channel into the hypotonic mass in mg3/L.s；
amThe side length of the hypotonic agglomerate is cm;
phi is porosity;
Swthe water saturation of the hypotonic clump;
d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2/s；
C is the concentration in the crack or the hypertonic channel, and the unit is mg/L;
c is the concentration in mg/L inside the matrix or hypotonic bolus surrounded by hypertonic channels.
7. The detection method according to claim 2, wherein in the step 30, the amount of change in the concentration of the hypotonic bolus tracer per unit time is obtained by the following formula:
wherein q is the concentration change of the tracer agent in mg/L.s caused by diffusion from the hypertonic channel into the hypotonic bolus in unit volume in unit time.
8. The detection method according to claim 1, wherein the step 20 comprises the steps of,
step 21: establishing a geological model of one-dimensional flow and two-dimensional mass transfer diffusion;
step 22: establishing a one-dimensional flowing two-dimensional mass transfer diffusion mathematical model;
step 23: and solving a one-dimensional flowing two-dimensional mass transfer diffusion mathematical model.
9. The detection method according to claim 8,
in step 22, establishing a one-dimensional flowing two-dimensional mass transfer diffusion mathematical model includes establishing a high-permeability channel mass transfer diffusion model and a low-permeability zone mass transfer diffusion model, wherein the high-permeability channel mass transfer diffusion model can be obtained by the following formula:
wherein the content of the first and second substances,
x is the distance in the direction of the X axis in the hypertonic channel;
Dxis the mass transfer diffusion coefficient in the X direction and has the unit of cm2/s；
uxThe real flow speed of the fluid in the X direction in the pores is expressed in cm/s;
Chthe concentration of the tracer in the hypertonic channel is mg/L;
Clthe concentration of the tracer in the hypotonic pellet is mg/L;
d is the effective mass transfer diffusion coefficient between the high-permeability channel and the low-permeability agglomerate and the unit is cm2/s；
t is the time for the tracer to generate mass transfer diffusion in the hypertonic channel, and the unit is s;
b is the width of half of the hypertonic channel in cm;
a is the side length of the matrix block mass, and the unit is cm;
phi is porosity;
φfis flow porosity;
Soresidual oil saturation;
Swcirreducible water saturation;
ρris the specific gravity of rock particles;
ξ is an integral variable;
l is a parameter representing a hypotonic region.
10. The detection method according to claim 9, wherein in the hyperosmotic channel mass transfer diffusion model, the boundary and initial conditions of the hyperosmotic channel are obtained by the following formula:
wherein, C0The initial injection concentration of the tracer agent is mg/L;
the mass transfer diffusion model of the hypotonic region can be obtained by the following formula:
althe side length of a hypotonic channel of the matrix agglomerate is in cm;
in the low-permeability zone mass transfer diffusion model, the boundary and initial conditions of the low-permeability zone can be obtained by the following formula:
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