CN113027434A - Method for determining rheological property parameters of polymer-containing liquid in near wellbore zone of perforation completion - Google Patents
Method for determining rheological property parameters of polymer-containing liquid in near wellbore zone of perforation completion Download PDFInfo
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Abstract
A method for determining rheological parameters of polymer-containing liquid in a near wellbore zone of an oil field perforation completion. The method comprises the following steps: dividing the whole control area into 10 control bodies according to a flow dividing surface on the basis of numerically solving the seepage field of the whole perforation control area; developing corresponding 10 groups of variable-diameter cores by using distribution data of flow velocity along the streamline in each control body; simulating a variable-speed seepage field by using a fixed displacement, and measuring rheological parameters and viscosity retention rate before and after polymer-containing liquid flows through each variable-diameter core; calculating the viscosity retention rate of the whole control area by a flow weighting method, determining the position and parameters of the equivalent control body according to the equivalent shearing principle, and manufacturing according to the distribution data of the flow velocity in the equivalent control body along the streamlineThe physical model and the device realize the shear degradation of the polymer-containing liquid by simulating the variable-speed seepage field of the near wellbore zone of the perforated well completion under the condition of constant discharge capacity, inject the polymer solution into the near wellbore zone at the discharge capacity corresponding to the equivalent control volume flow, and measure the shear stress before and after the polymer solution passes through each section of coreτAnd shear rateγAnd then calculating to obtain the rheological parameters of the polymer-containing liquid.
Description
The technical field is as follows:
the invention relates to a method applied to the field of petroleum and natural gas industry, in particular to a method capable of accurately measuring rheological parameters of polymer-containing liquid flowing through a near wellbore zone of perforated completion under the condition that the rheological parameters of the polymer-containing liquid are changed after the polymer-containing liquid is sheared in the near wellbore zone of the perforated completion.
Background art:
in the technology of improving the recovery efficiency of an oil field, polymer aqueous solution or a polymer-containing multi-element system is injected into an oil layer to displace oil, the liquid containing clusters has the shearing degradation characteristic, and the viscosity of the liquid is continuously reduced by shearing of pores of the oil layer after the liquid enters the oil layer. The conventional method for determining the rheological property of the polymer-containing liquid in the stratum comprises an indoor simulation experiment and a field test. The indoor simulation experiment is to pass the polymer-containing liquid through the equal-diameter rock core at a certain seepage velocity and measure the rheological parameters before and after the polymer-containing liquid is sheared by the rock core, although the method can simulate shearing at different seepage velocities, the flow velocity is unchanged in the experiment, which is inconsistent with the situation that the liquid in an actual injection well flows out from the wall of the perforation hole and the velocity is reduced along with the increase of the seepage distance, and a larger error is inevitably caused; in the field test, the polymer-containing liquid injected into the oil layer is reversely discharged from the oil layer, and then the rheological parameters of the polymer-containing liquid are measured, although the polymer-containing liquid really flows through a near wellbore zone, the seepage distance of the polymer-containing liquid collected by the reverse discharge method is 2 times that of the polymer-containing liquid normally injected, and in addition, the polymer-containing liquid has interference of other fluids in the stratum, and the rheological parameters of the polymer-containing liquid also have errors.
The rheological property parameter of the polymer-containing liquid is an important parameter for numerical reservoir simulation and well testing, the liquid seepage velocity in a near-wellbore zone of a perforation completion is higher and is rapidly reduced by dozens of times from high, the rheological property of the polymer-containing liquid is rapidly changed, the viscosity reduction range is far beyond the viscosity reduction range in a well stratum through shear degradation, and the polymer-containing liquid is a main region for shear degradation viscosity reduction of the polymer-containing liquid. If the rapid change of the rheological property of the polymer-containing liquid in the near wellbore zone of the perforated completion is not considered in the numerical reservoir simulation, only the slow change of the rheological property of the traditional polymer-containing liquid in the far wellbore stratum is considered, the precision and the reliability of the numerical reservoir simulation are directly influenced, and even the well testing parameter interpretation method is difficult to apply. Meanwhile, it should be noted that the liquid seepage velocity near the well completion zone, especially near the perforation hole wall, is changed from high speed to low speed by tens of times, which is extremely strong variable speed seepage, if the research is simply carried out according to the constant speed seepage fields with different velocities, and then the seepage results with different velocities are butted, the constant speed seepage distance should be extremely small, otherwise, the method is far away from the reality; and the extremely small constant velocity seepage distance has strong end effect to influence the reliability of the result. Therefore, for the strong variable speed seepage field of the near wellbore zone of the perforation completion, the change of the rheological property of the polymer-containing fluid at different positions of the near wellbore zone is measured according to the change of the seepage speed of the fluid on a flow line along with the seepage distance, and the method is very necessary for determining the change rule of the rheological property parameters of the polymer-containing fluid in the stratum.
The invention content is as follows:
in order to solve the technical problems mentioned in the background technology, the invention provides a method for determining rheological parameters of polymer-containing liquid in a near wellbore zone of a perforated well completion, and the method solves the problem that the seepage velocity of the polymer-containing liquid in the near wellbore zone of the perforated well completion can not be simulated to be accurately changed along with the seepage distance in a prior model experiment.
The technical scheme of the invention is as follows: the method for determining rheological parameters of polymer-containing solution in the near wellbore zone of the perforated completion comprises the following steps:
firstly, establishing a perforation completion near wellbore zone model by using ANSYS software and solving the pressure field and flow rate field data of the polymer-containing solution in the perforation completion near wellbore zone;
and secondly, processing the pressure field and flow velocity field data obtained in the first step by using MATLAB software, wherein the specific path is as follows:
firstly, solving the coordinates of non-equidistant scattered points, seepage velocity at the non-equidistant scattered points, direction vectors and pressure in the directions of the seepage velocity x, y and z obtained by ANSYS software, and calculating the seepage velocity, the seepage velocity direction vectors and the pressure at the equidistant scattered points by an interpolation function ScatteredInterpolant;
secondly, equally dividing the wall of the perforation hole into 10 sections, taking the point at the intersection of each two sections as the starting point of a Streamline, inputting the coordinates of equally spaced scattered points and direction vectors of seepage velocity in x, y and z directions into a Streamline function, calculating to obtain 9 clusters of Streamline tracks, and respectively extracting the coordinates of points on each cluster of Streamline tracks;
generating two-dimensional grid coordinates by using a Meshgrid function again, taking coordinates of points on each cluster of flow lines as interpolation points, and performing interpolation calculation on z values on the generated two-dimensional grid coordinate points by using a Griddata function to obtain curved surfaces passing through each cluster of flow lines, namely shunting surfaces, wherein each shunting surface is a curved surface formed by a plurality of space triangles; the curved surface in the perforation completion near-wellbore area model in ANSYS is treated in the same way, the irregular curved surface is converted into a curved surface consisting of a plurality of space triangles, the whole perforation completion near-wellbore area model is divided into 10 perforation hole control bodies by 9 diversion surfaces, and each section of control body of each perforation hole is surrounded by the model curved surface and the diversion surface;
finally, judging the positions of equidistant space scattered points by using the model curved surface and a plane equation where a space triangle on the shunting surface is located to obtain points in a closed geometric body enclosed by the shunting surface and the model curved surface, namely points in a control body of each section of the perforation hole; calculating the average value of the flow velocity of each section of perforation and the average value of the flow velocity of all points at the same hole depth multiple through the flow velocity data on the perforation, finding the hole depth multiple where the average value of the flow velocity of each section of perforation is located, and finding the hole depth multiple where the midpoint of the flow velocity of each section of the perforation in each section of control body of the perforation is located;
thirdly, according to the result obtained in the second step, the average flow velocity on the isobaric surface and the distance from the isobaric surface along the flow line track to the wall of the perforation hole are obtained, the variation relation of the seepage distance of each control body flow velocity along the flow line track is obtained, and the seepage velocity v in each control body of each section of the perforation hole is drawni(i-1, 2,3, …,10) with percolation distance Li(i ═ 1,2,3, …,10) variation relationship plates; the specific implementation mode is as follows:
firstly, screening out points on each isostatic pressing surface between the wall of the perforation hole and the boundary of the model by utilizing pressure and flow rate data at equidistant three-dimensional space points in each section of control body of the perforation hole and a gradient of 0.1MPa to obtain coordinates of the points on the isostatic pressing surface in each section of control body of the perforation hole, and obtaining the average flow rate on the isostatic pressing surface by applying the flow rate data of the points on each isostatic pressing surface; secondly, taking the point at the hole depth multiple position of the midpoint of the flow velocity of each section of the control body of the perforation hole as the starting point of the streamline, calculating the trajectory of the streamline, carrying out pressure interpolation on the points on the trajectory of the streamline, finding the points on the streamline with the same pressure as each isobaric surface, and calculating the distance from the perforation hole to the points along the trajectory of the streamline, namelyThe distance from the constant pressure surface to the wall of the perforation hole along the flow line track; in each section of control body of the perforation hole, the average flow velocity on each equal pressure surface is substituted into the distance from each equal pressure surface to the perforation hole wall along the flow line track to obtain the variation relation of the seepage distance of each control body flow velocity along the flow line track, and the seepage velocity v in each section of control body of the perforation hole is drawni(i-1, 2,3, …,10) with percolation distance Li(i ═ 1,2,3, …,10) variation relationship plates;
fourthly, analyzing the change relation chart obtained in the third step, when the descending amplitude of the seepage velocity is larger than 0.25/m, the seepage distance is between 0 and 0.1m, in order to realize variable speed seepage under the constant displacement, making a variable diameter core for experiment, and drawing a chart of the change relation of the viscosity retention rate along with the hole depth multiple by combining the hole depth multiple of the flow midpoint of each section of the control body of the perforation hole and the viscosity retention rate of each control body;
the path for manufacturing the variable-diameter core in the step is as follows:
controlling the v in the body according to each section of the perforation hole under the condition of constant displacementiWith LiCalculating the diameter D of the core with variable diameter according to the variation relationiAlong with the length L of the coreiThe relationship of the changes is shown in Table 1:
table 1 variable diameter core data table
Processing an equal-diameter cylindrical core with the length of 10cm and the diameter of 25mm to a variable-diameter core in accordance with the table 1, and casting the variable-diameter core into an equal-diameter cylinder with the external length of 10cm and the diameter of 25mm by using epoxy resin so as to be put into a conventional core holder for use;
after a percolation distance of 0.1m, the percolation speed decreases slowly, so according to viWith LiCalculating the average flow velocity by distance weighting according to the variation relation, and carrying out an experiment by using the equal-diameter rock core;
during the experiment, the polymer solution is sequentially led to pass through a variable-diameter core template and an equal-diameter core, and before the polymer solution passes through each section of core, the measurement is carried outThen the power law index n is calculated according to the shear stress tau and the shear rate gammaiCoefficient of consistency KiApparent viscosity μiAnd the viscosity retention rate of each control body;
fifthly, calculating the viscosity retention rate of the polymer solution in the control area of the whole perforation hole through flow weighting calculation, and obtaining the hole depth multiple h of the equivalent control body of each section of the control body of the perforation hole according to the chart of the relation of the viscosity retention rate obtained in the fourth step along with the change of the hole depth multiplemCalculating the hole depth multiple hmThe initial position of the perforation section of the equivalent control body with the length of 0.1 time of the hole depth is the flow middle point, and v in the equivalent control body is drawneWith LeAnd (5) changing the relation chart. The specific path is as follows:
firstly, the viscosity retention rate e of the body is controlled according to each section of the perforation holeiPerforation depth h corresponding to average flow velocityiFinding out the perforation depth h where the viscosity retention rate e of the whole perforation hole control area ise(ii) a Then passes through each perforation depth hphWith the average flow velocity v thereonphCorresponding to the relationship, calculating the perforation depth heAverage flow velocity v ofe(ii) a Finally applying each perforation depth hphWith the average flow velocity v thereonphThe corresponding relation is calculated by adopting a traversal method, the average flow velocity on a perforation segment with the length of 0.05m and the depth of each perforation as a starting point is calculated, and the sum v is foundeIf the values are equal, the control body corresponding to the perforation hole of the section is the equivalent control body, and v in the equivalent control body is drawneWith LeA variation relation chart;
a sixth step of controlling the internal v of the body according to the equivalent obtained from the fifth stepeWith LeCalculating the sectional area A of the core with variable diameter according to the variation relation charteWith LeChanging the relation, and then manufacturing an equivalent control body physical model according to the relation; the physical model of the equivalent control body is formed by connecting 4 sections of variable-section area rock cores in series, wherein the first section is a cylindrical rock core with the length of 30cm and the variable-section area, the second section and the third section are rectangular rock cores with the length of 50cm and the variable-section area, the fourth section is a rectangular rock core with the length of 20cm and the variable-section area, the 4 sections of variable-section area rock cores are respectively arranged in a holder and a model pipe, and the equivalent control bodyThe effective control body physical model is used for simulating the actual seepage condition of a near wellbore zone of the perforation completion in a set region with the wellbore as the center and the radius of 1.82 m;
seventhly, injecting polymer solution by using the equivalent control body physical model obtained in the sixth step and according to the discharge capacity corresponding to the equivalent control body flow of 1.029ml/min, measuring the shear stress tau and the shear rate gamma of the polymer solution before and after passing through each section of rock core, and calculating to obtain the power law index niCoefficient of consistency KiApparent viscosity μiAnd polymer solution physical model viscosity retention through the entire equivalent control body.
The invention has the following beneficial effects: the core of the method is that a strong variable speed seepage field of a near wellbore zone of a perforation completion is researched by a numerical simulation technology, a whole perforation control area is divided into 10 control bodies according to a streamline surface, the change rule of the seepage speed of fluid in each control body on a streamline track along with the seepage distance is given, corresponding 10 groups of variable diameter cores are researched on the basis of the change rule, the variable speed seepage field is accurately simulated by using a fixed displacement, and rheological parameters and viscosity retention rate before and after polymer-containing fluid flows through the variable diameter cores are measured; the viscosity retention rate of the whole control area is calculated by a flow weighting method, the position and the parameters of an equivalent control body are determined according to the equivalent shearing principle, a physical model and a device with the length of 1.5m are developed according to the distribution data of the flow velocity in the equivalent control body along the streamline, the shearing degradation effect of the variable-speed seepage field of the near-wellbore zone of the perforated well completion on the polymer-containing liquid is accurately simulated under the condition of fixed displacement, and therefore the problem that the seepage velocity of the polymer-containing liquid in the near-wellbore zone of the perforated well completion can not be accurately changed along with the seepage distance in the prior human model experiment is solved.
Description of the drawings:
FIG. 1 is a technical roadmap for the present invention.
Fig. 2 is a single-hole actual control area model of the present invention.
FIG. 3 is a single aperture control region model of the present invention.
FIG. 4 is a single hole control zone stratigraphic grid of the present invention.
Fig. 5 is a cloud view of the control body pressure field of the present invention.
FIG. 6 is a cloud view of the control body velocity field of the present invention.
Figure 7 is a graph of the flow of each section of the perforation of the present invention as a percentage of the total flow.
Figure 8 is a multiple of the hole depth at the midpoint of each control volume flow of the present invention.
Fig. 9 is a 9-cluster flow diagram of the present invention.
Fig. 10 is a shunt surface view of the present invention.
Fig. 11 is an equally spaced three-dimensional space point diagram of the present invention.
Figure 12 is a model of the control bodies for each segment of the perforation of the present invention.
FIG. 13 is a graph of the dimensionless seepage velocity of the present invention as a function of dimensionless seepage distance along the flow line.
FIG. 14 is a graph of the diameter of a variable diameter core of the present invention as a function of length.
Fig. 15 is a photograph of a variable diameter core of the present invention.
FIG. 16 is a graph of the dimensionless consistency factor of the invention as a function of seepage distance.
FIG. 17 is a graph of the dimensionless power-law exponent of the present invention as a function of percolation distance.
FIG. 18 is a graph of the dimensionless viscosity as a function of seepage distance for the present invention
FIG. 19 is a graph of viscosity retention at various control volumes in accordance with the present invention.
Figure 20 is a graph of viscosity retention at different perforation multiples for the present invention.
FIG. 21 is a graph of the diameter of a 30cm long variable diameter cylindrical core of the present invention as a function of core length.
Fig. 22 is a plot of the rectangular core width as a function of core length for the present invention.
FIG. 23 is a photograph of cores from equivalent control volume physical models of the present invention.
FIG. 24 is a graph of dimensionless consistency factor as a function of seepage distance using an equivalent control physical model in accordance with the present invention.
FIG. 25 is a graph showing the relationship between the dimensionless power-law exponent measured by the equivalent control body physical model and the change of the seepage distance
FIG. 26 is a graph of dimensionless apparent viscosity as a function of seepage distance using an equivalent control volume physical model in accordance with the present invention.
The specific implementation mode is as follows:
the invention will be further described with reference to the accompanying drawings in which:
first, from the theoretical point of view, the following technical scheme adopted by the invention to solve the technical problems is as follows:
in the first step, steady state heat transfer modules in ANSYS software are used to simulate steady state seepage.
The seepage field and the heat flow field have a similarity table, the basic differential equations of the seepage field and the heat flow field are Laplace equations, the expression forms of the Fourier law and the Darcy law are similar, and the expression form of the isothermal boundary and the isobaric boundary is similar. Therefore, steady state heat transfer modules in ANSYS software can be used to simulate steady state seepage, where thermal conductivity is equivalent to permeability and temperature is equivalent to pressure, as detailed in table 2. And obtaining seepage field and pressure field data of fluid near the perforation completion hole through modeling, grid division, loading, solving and the like.
Setting the radius of a perforation hole as R (m), the depth of the hole as L (m), the density of the hole as a (hole/m), the phase angle as theta (DEG), the radius of the outer side of a shaft cement sheath as R, establishing a perforation completion near-wellbore zone model by using ANSYS software, solving the data of a polymer solution-containing pressure field and a flow velocity field in the perforation completion near-wellbore zone, and obtaining the number and the coordinate (x) of each grid node in the model, wherein the set formed by all grid nodes in the model is DD，yD，zD) Pressure p at each grid nodeD(xD， yD，zD) Velocity magnitude v at each grid nodeD(x, y, z), x-direction flow velocity direction vector
Direction vector of flow velocity in y direction
And direction of flow velocity in z directionMeasurement of
TABLE 2 comparison of simulated seepage field of temperature field
And secondly, carrying out post-processing on the seepage field and pressure field data through MATLAB software to obtain each section of perforation hole control body.
The perforation holes are equally divided into 10 sections, and Streamline tracks at the joint of any two sections of perforation holes are calculated by using a Streamline function. Since the Streamline function can only process equidistant matrix data, firstly, non-equidistant scattered point data derived from ANSYS is converted into equidistant scattered point data, and the minimum value and the maximum value of x, y and z coordinates of all non-equidistant scattered points, namely x, are respectively found out by using Min and Max functionsmin、xmax、ymin、ymax、zmin、 zmax. Then using Linspace function at xminAnd xmax、yminAnd ymax、zminAnd between zmaxInserting 49 numbers of the matrixes at equal intervals to obtain three one-dimensional matrixes a, b and c, which are detailed in formula (1), formula (2) and formula (3).
And repeatedly increasing the one-dimensional matrix a from one row to 51 rows by using a Meshgrid function, and repeatedly increasing the one-dimensional matrix a to 51 layers, thereby obtaining a 51-row, 51-column and 51-layer three-dimensional matrix A, which is shown in formula (4).
Transpose the one-dimensional matrix B into a column, add it repeatedly to 51 columns, add it repeatedly to 51 layers, get the matrix B, see equation (5).
The vector C is transposed to a vertical, and then repeatedly added to 51 rows and then 51 columns to obtain the matrix C, see equation (6).
A. B, C coordinates (A) formed by elements at the same position in three matricesi,j,k,Bi,j,k,Ci,j,k) The coordinates of the equally spaced scatter points are set, the set of all equally spaced scatter points is set as E, and the value range is the same as the set of the unequally spaced scatter points D. The coordinate of the non-equidistant scattered point set D is the same as the coordinate value range of the equidistant scattered point set E, so that the coverage range of the equidistant scattered points D is larger than that of the non-equidistant scattered points E.
Secondly, using the D coordinate (x) of the scattered points with unequal intervalsD，yD，zD) The seepage velocity v (x) at a non-equidistant scatterD，yD，zD) Direction vector of flow velocity in x direction
Direction vector of flow velocity in y direction
And z-direction flow velocity direction vector
Pressure p (x)D，yD，zD) Calculating to obtain the seepage velocity v (x) at the equidistant scattering point E through an interpolation function ScatteredInterpolantE，yE，zE) Direction vector of flow velocity in x direction
Direction vector of flow velocity in y direction
And z-direction flow velocity direction vector
Pressure p (x)E，yE，zE)。
Dividing the perforation into n sections, classifying 1/4 spherical surfaces at the tail ends of the perforations into the nth section of perforation, and extracting the perforation depth h according to the grid node numberphLocating the point on the perforation hole, calculating the depth h of each perforationphAverage flow velocity v on perforationph. Extracting the flow velocity of each point on the ith section of perforation hole according to the grid node number, and obtaining the average flow velocity v on the ith section of perforation hole by taking the average value of the flow velocities of each pointiThen calculating the area A of the i-th section perforation holei， AiThe mathematical relation expression of the radius of the perforation and the depth of the perforation is r and L is shown in the formula (6), and then the flow rate Q of the perforation in the ith section is calculatediAnd the flow percentage d of the ith section of perforation hole in the whole perforation holei。
Taking the point at the intersection of the two sections as the starting point of the streamline, wherein n groups of points are arranged, and the coordinate of the ith group of points is
Wherein i belongs to { i belongs to Z |1 ≦ i ≦ n }, and α belongs to (0 degrees, 180 degrees). Coordinates of the starting point of the ith group of streamline
Coordinate (x) of equidistant scatter EE，yE，zE) Direction vector of flow velocity in x direction
Direction vector of flow velocity in y direction
And z-direction flow velocity direction vector
Inputting the current into a Streamline function, calculating to obtain the ith group of Streamline tracks, and extracting coordinates (x) corresponding to all points on the tracksLi，yLi，zLi)。
By Min (x)Li)、Max(xLi)、Min(yLi)、Max(yLi) Calculating to obtain the ith group of streamline track coordinates (x)Li，yLi，zLi) Value range x ofLi∈(xLimin，xLimax)，yLi∈(yLimin，yLimax). Using [ F ]]＝Linspace[xLimin，xLimax，n]、[G]＝Linspace[yLimin，yLimax，n]Function at xLiminAnd xLimax、yLiminAnd yLimaxN-1 of the matrixes are inserted at equal intervals to obtain two one-dimensional matrixes F, G shown in formulas (6) and (7).
The one-dimensional matrix F is repeatedly added from one row to n rows using a [ H, J ] ═ mesgrid [ F, G ] function, and the elements in the ith column in the obtained two-dimensional matrix H are all the same and equal to the ith element in the one-dimensional matrix F, and the two-dimensional matrix H is expressed by formula (8).
The one-dimensional matrix L is repeatedly added from one row to n rows using a [ H, J ] ═ mesgrid [ F, G ] function, and the elements in the ith column in the obtained two-dimensional matrix J are all the same and equal to the ith element in the one-dimensional matrix G, and the two-dimensional matrix J is expressed by formula (9).
H. J coordinates (H) formed by elements at the same position in the two matricesi,j,k，Ji,j,k) The coordinates of the intersection points of the two-dimensional grids at equal intervals on the xoy plane are determined, and K is equal to Griddata (x)Li，yLi， zLi，Hi,j,k，Ji,j,k) The function carries out interpolation calculation on the z value of the two-dimensional grid intersection point coordinate to obtain a matrix K, wherein K is Griddata (x)Li，yLi，zLi，Hi,j,k，Ji,j,k) Will fit the shape as zLi＝f(xLi， yLi) The streamline surface of (c) H, J, K is formed by the coordinate point (H) composed of the elements at the same position in the three matrixesi,j,k，Ji,j,k，Ki,j,k) At the dividing plane zLi＝f(xLi，yLi) In this way, the diversion surface that cannot be described analytically can be described by a curved surface consisting of a plurality of triangles, the obtained curved surface, i.e., the diversion surface, can be reconstructed, and the reconstructed diversion surface can be used to divide the whole perforation control area into the control bodies of each section of the perforation, because all pressure and flow rate data are coordinate points (a) consisting of elements at the same position of the matrix A, B, Ci,j,k，Bi,j,k，Ci,j,k) Therefore it is necessary to useSplitter plane and top and bottom surfaces of model facing coordinate point (A)i,j,k，Bi,j,k，Ci,j,k) The reconstructed shunting surfaces are all composed of a plurality of space triangles, the position relation between the space point and the curved surface can be converted into the position relation between the space point and the space triangle on the curved surface, and the point in the closed geometric body enclosed by the top bottom surface of the model and the (i-1) th and i-th shunting surfaces, namely the point in the ith control body, is found out.
Thirdly, calculating the change relation of the seepage velocity in each control body along the seepage distance of the streamline;
using data from the ith control point, the pressure p at the perforation hole wallwfAnd boundary pressure peTake j equal interval pressure values pij(j ═ 1,2,3, …, n), finding a pressure value equal to pijPoint (x) ofij，yij，zij) In order to ensure that enough points on the isobaric surface can be obtained, a section is given to the pressure value of the isobaric surface, if the coordinate of the point on the a MPa isobaric surface is obtained, the coordinate point in the section (a-0.01, a +0.01) is obtained, and then the flow velocity average value v of the points is calculatedpij。
To make the results more general, the average flow velocity v over each isobaric surface is determinedijDivided by the velocity v at the borehole wall at the same injection strength0Obtaining the dimensionless average flow velocity v of each isobaric surfaceDij(ii) a Calculating the pressure difference p between the constant pressure surfaces and the boundary surfacecijDivided by the pressure difference p of the open hole at the same injection strength0Obtaining the dimensionless pressure p of each isobaric surfaceDij。
In order to calculate the distance from each isobaric surface in the ith control body to the perforation hole wall, a point in the middle of the perforation hole wall of the ith section of the perforation hole wall is used
As a starting point, a streamline is drawn using streamline function, and coordinates (x) of a point on the streamline are extractedzLi，yzLij，zzLij) Then finding out the pressure value p of each equal pressure surfaceijConsistent point Mij(xzLi，yzLij，zzLij) Counting the point as the k-th point on the streamline, and calculating MijDistance L to the wall of the perforation holeijI.e. the distance of the isobaric surface from the wall of the perforation hole, LijThe relationship between the coordinates of each point on the streamline is shown in equation 10.
Obtaining the pressure p in the control body of the ith section of perforation holeijSeepage distance L along flow line directionijThe relationship is changed. To make the results more general, L will beijThen remove LijTo obtain LDijThe seepage distance is dimensionless.
The seepage velocity v on the flow line track of the fluid in each section of the hole control body is obtained by integrating the relation between the non-dimensional seepage distance variation of the non-dimensional pressure difference along the flow line direction and the relation between the non-dimensional flow velocity along the non-dimensional pressure variationDijAlong with the seepage distance LDijThe change rule of (2).
Fourthly, developing rheological parameters of each control body, physical models of each control body and analyzing experimental results;
by analysing the seepage velocity v of the fluid in each control body on the trajectory of the flow lineijAlong with the seepage distance LijFinding the seepage velocity vijThe polymer flow condition of the area near the perforation hole wall is simulated by using the variable-diameter core under the condition of constant displacement, and the polymer flow condition of the area far from the perforation hole is simulated by using the equal-diameter core.
Through a variable-diameter and equal-diameter core experiment, polymer-containing liquid passes through the core according to the seepage rule of a near-wellbore zone of the perforated well completion, and through testing the shear stress tau and the shear rate gamma before and after the polymer-containing liquid passes through each section of the core, a power law index n, a consistency coefficient K, an apparent viscosity mu and a viscosity retention rate e of a polymer solution passing through an integer i control body are calculatedi。
Fifthly, determining an equivalent control body;
according to the flow percentage d of the control body according to the ith sectioniAnd viscosity retention rate eiThe viscosity retention e of the entire perforation control zone is calculated by flow weighting according to equation (11). Firstly, the viscosity retention rate e of the body is controlled according to each section of the perforation holeiPerforation depth h corresponding to average flow velocityiFinding out the perforation depth h where the viscosity retention rate e of the whole perforation hole control area iseIf e is exactly equal to eiThen h ise＝hiIf e is at eiAnd ei-1In turn, the perforation depth h is solved by equation set (12)eAnd hiAnd hi-1See formula (13); then passes through each perforation depth hphWith the average flow velocity v thereonphFinding out the perforation depth h according to the corresponding relationeAverage flow velocity v ofe(ii) a Finally applying each perforation depth hphWith the average flow velocity v thereonphThe corresponding relation is calculated by adopting a traversal method, the average flow velocity on the perforation hole segment with the length of L/n and the depth of each perforation as a starting point is found out, and v is obtainedeIf the values are equal, the control body corresponding to the perforation hole section is the equivalent control body.
Sixthly, developing an equivalent control body physical model;
and (3) calculating the change rule of the seepage velocity of the fluid in the equivalent hole control body on the flow line track along with the seepage distance by applying the method in the second step and the method in the third step, calculating the change relation between the core sectional area A and the core length L according to the seepage velocity along with the seepage distance, and manufacturing a corresponding physical model and a matched experimental device. For convenience of manufacture, the model is divided into 4 sections of variable-section-area cores which are connected in series, the first section is a 30 cm-long variable-diameter cylindrical core, the second section and the third section are 50 cm-long variable-section-area rectangular cores, the fourth section is a 20 cm-long variable-section-area rectangular core, the 4 sections of variable-section-area cores are respectively arranged in the holder and the model pipe, and the whole physical model and the device can simulate the actual seepage condition of a near-wellbore zone of a jet-hole well completion by taking a wellbore as a center radius of 1.82 m. The calculation and actual measurement results show that the liquid seepage velocity is extremely low and the velocity change is slow outside the radius, the reduction of the liquid viscosity is mainly influenced by the adsorption and retention of an oil layer, the influence of the reduction of the shear degradation is small, and the method can be used for approximate measurement by using a traditional equal-diameter core simulation method.
Seventhly, applying an equivalent physical model;
the physical model is made by using a rock core with a certain permeability, so that rheological parameters of clustering fluids with different molecular weights and different concentrations in a near-wellbore zone of the perforated well completion can be determined under different injection strengths; and the related research under different permeability conditions can be carried out by changing the permeability of the model.
One specific example is given below, as shown in fig. 1-26, first step, using a steady state heat transfer module in ANSYS software to simulate steady state seepage;
firstly, selecting perforation parameters of perforation depth 0.5m, perforation radius 0.01m, perforation density 16 holes/m and perforation phase 60 degrees, and dividing a single actual control area of perforation, as shown in figure 2, selecting 1/2 as a research object according to the symmetry of the control area.
A single perforation control area model is established in a finite element analysis software ANSYS, the radius of an open hole is 120mm, the perforation depth is 500mm, the perforation aperture is 10mm, and the radius of a model boundary is 3 times of the perforation depth and is 1620 mm. According to the finite element rule, a three-dimensional solid geometric model is built by taking only 360 degrees of theta (if the theta is 60 degrees, the research range is 1/6 cylinders, and if the theta is 90 degrees, the research range is 1/4 cylinders) in one thread pitch. Opening ANSYS software, selecting a hot module in a parameter selection menu, namely selecting Preferences > thermal in a GUI interface,secondly, unit types are selected, namely Preprocesssor > Element type > Add/Edit/Delete > Thermal Mass > Solid > Brick 8node 70 is selected in a GUI interface, and the input Thermal conductivity is 2.108e-6W/(m.K), Preprocessor > Material Model > Thermal > direct, and then corresponding Thermal Conductivity is input. Inputting the model vertex coordinates (0.12, 0, 0), (1.62, 0, 0.375), (0.12, 60, 0.0625), (1.62, 60, 0.0625), forming a face directly with points, and then clicking Volumes > Arbitrary > By Areas > Pick all to fill an adult, as shown in FIG. 3.
In the actual production process, the seepage situation around the well wall surface is concerned, the size of the hole is very small compared with the size of the stratum, in order to research the seepage situation near the perforation wall surface, the area near the perforation hole is divided into 13 layers, in order to ensure the accuracy of the calculation result and the rapidity of the operation, the divided 13 layers are divided into finer layers by adopting a sweeping division method, the stratum far away is divided into more coarse layers by adopting a free division method, and after the model is completed, the solid model has 65 key points, 139 lines, 103 surfaces and 28 individuals. After the grid division is completed, 45256 nodes, 63877 cells are obtained, as shown in fig. 4. And (3) carrying out loading after grid division, wherein the perforation wall surface is a constant-pressure inner boundary of the model, the pressure on the perforation wall surface is 20MPa, the stratum boundary surface is a constant-pressure outer boundary of the model, the pressure on the perforation wall surface is 14.21MPa, the pressure difference between the inner boundary and the outer boundary is 5.79 MPa, the other surfaces of the model are closed boundaries, finally solving is carried out to obtain the distribution of a pressure field and a velocity field as shown in a figure 5 and a figure 6, then extracting the data of the pressure field and the velocity field, wherein the data of the pressure field is the x, y and z coordinates and the pressure of each point in the figure 5, the data of the velocity field is the three-dimensional coordinates, the flow velocity and the direction vectors of the seepage velocity in the x, y and z directions of each point in.
Secondly, post-processing the seepage field and pressure field data through MATLAB software to obtain each section of perforation hole control body;
dividing the perforation into 10 sections equally, and classifying the perforation with the 1/4 spherical surface at the top end into one section, and calculating the percentage of each section of flow in the total flow through the seepage velocity on each section of perforation, as shown in fig. 7; and then, according to the flow velocity at each point on the perforation hole wall, the hole depth multiple at the flow midpoint of each section of perforation hole is obtained, as shown in fig. 8.
MATLAB is used for processing the pressure field data and the flow velocity field data, and Streamline tracks at the intersection of every two sections of perforation holes are calculated by using a Streamline function, and 9 clusters of Streamline are shared among 10 sections of perforation holes, as shown in figure 9. Calculating a Streamline track at the joint of any two sections of perforation holes by applying a Streamline function in MATLAB; using a Meshgrid function, a Min function and a Max function to generate a two-dimensional grid coordinate, taking a point on a streamline track as an interpolation point, taking a point described by the two-dimensional grid coordinate as an interpolated point, and applying a GridData interpolation function to perform interpolation calculation on a z value of the two-dimensional grid coordinate point, so as to obtain a curved surface of the streamline track passing through the joint of any two sections of perforation holes, namely a shunting surface, wherein a streamline between a first section of perforation hole and a second section of perforation hole is taken as an example, and the reconstructed shunting surface is shown in fig. 10. A Linspace function and a mesgrid function are used to generate a matrix of equally spaced three-dimensional spatial points covering the entire perforation control area, as shown in fig. 11, where red dots are derived points in ANSYS software and blue are equally spaced three-dimensional spatial points. And on the basis of the pressure field and the flow velocity field, obtaining the pressure and the flow velocity at the equidistant three-dimensional space point through a GridData interpolation function. The equation of the plane where each triangular patch is located on the shunting plane is used to perform position judgment on equidistant three-dimensional space points to obtain points contained in each section of the hole control body, the outermost layer of points in each section of the hole control body is extracted and is led into GEOMAGIC software to obtain 10 perforation hole control bodies, as shown in FIG. 12.
Thirdly, calculating the change relation of the seepage velocity in each control body along with the seepage distance;
finding an isobaric surface between the wall of the perforation hole and the boundary of the model by utilizing pressure and flow velocity data at equidistant three-dimensional space points in each control body and a gradient of 0.1MPa, solving coordinates of points on the isobaric surface in each control body, and calculating the average flow velocity on each isobaric surface; and then carrying out pressure interpolation on points on the flow lines in each control body, finding points on the flow lines with the same pressure as each isobaric surface, and calculating the distance from the perforation hole wall to the points along the flow line track, namely the distance from the isobaric surface to the perforation hole wall along the flow line track. And combining the average flow velocity on each equal pressure surface and the distance from each equal pressure surface to the wall of the perforation hole along the flow line track to obtain the variation relation of the seepage distance of each control internal flow velocity along the flow line track. Dividing the obtained seepage velocity by the flow velocity on the wall of the open hole completion well under the same pressure difference, dimensionlessly changing the seepage velocity, and dividing the seepage distance from the flow line direction to each equal pressure surface by the maximum seepage distance in the flow line direction, dimensionlessly changing the seepage distance, as shown in fig. 13.
Fourthly, developing physical models of the control bodies and analyzing experimental results;
through analyzing the change rule of the seepage velocity of the fluid in each control body along the seepage distance on the flow line track, the fact that the seepage velocity is reduced fast in the area near the perforation hole is known, so 10 groups of variable-diameter cores are developed to simulate the seepage condition of the area near the perforation hole, the diameter of each variable-diameter core changes along with the length as shown in figure 14, the change trend of the diameter of each control body core along with the length is the same, the maximum diameter of the core at the position of 10cm in length is 2.5cm, the diameter of each control body core gradually increases from the left end to the right end, and the specific size of each control body core is different. The variable diameter core corresponding to the control body No. 1 is shown in figure 15, and the variable diameter cores corresponding to other control bodies are similar to the variable diameter core. And calculating the average flow velocity by adopting a distance weighted calculation mode aiming at the area far away from the perforation hole wall, and enabling the polymer solution to pass through the same group of equal-diameter rock cores at the average flow velocity to simulate the seepage condition of the polymer solution far away from the perforation hole wall. The core used in the experiment is an artificial core, and the water permeability is 800.3 multiplied by 10-3μm2Molecular weight of the dry polymer powder is 1000 × 104The concentration of the polymer solution was 1000mg/L, the experimental water was tap water, and the experimental temperature was 45 ℃. The rheological parameters of the polymer solution at different seepage distances near the wellbore completion zone were experimentally measured and were not quantified as shown in fig. 16, 17 and 18. The viscosity retention rate of the polymerization solution after the polymer solution passes through each control body is calculated through rheological parameters, as shown in figure 19, and the data of figures 8 and 18 are combined to obtainViscosity retention to different perforation depths is shown in fig. 20.
Fifthly, determining an equivalent control body;
based on the viscosity retention rate of each control body, the viscosity retention rate of the whole hole control area is 60.19% through flow weighting; viscosity retention e of control bodies from the perforation segments of FIG. 20iPerforation depth h corresponding to average flow velocityiThe corresponding relationship shows that the viscosity retention rate of 60.19% is located at 0.6575 times of the perforation depth, and the average flow speed at the perforation depth is 2.087 multiplied by 10-4m/s, average flow velocity of 2.087X 10 by the passage method-4The starting positions of the perforation hole sections of m/s are 0.6077 times of hole depths and 0.7077 times of hole depths respectively, and then the control bodies corresponding to the perforation hole sections between the 0.6077 times of hole depths and the 0.7077 times of hole depths are equivalent control bodies.
Sixthly, developing an equivalent control body physical model;
according to the change rule of seepage velocity along with seepage distance on the flow line track of fluid in the equivalent eyelet control body, developing an equivalent control body physical model; the physical model is a variable cross-section rock core with 4 sections connected in series: the first section is a 30cm long variable diameter cylindrical core, and the diameter of the first section is changed along with the length of the core and is shown in figure 21; the second to fourth sections are variable sectional area rectangular cores with the total length of 120cm and the thickness of 5cm, wherein the second and third sections are 50cm long, the fourth section is 20cm long, and the width of the rectangular core is changed along with the length of the core as shown in fig. 22. The picture of each section of the core of the equivalent control body physical model is shown in figure 23, and the whole physical model can accurately simulate the seepage condition of a near wellbore zone within the central radius of 1.82m of a wellbore.
Seventhly, applying an equivalent physical model;
the dimensionless rheological parameters at different seepage distances measured by injecting the polymer solution with a certain discharge capacity by applying the physical model provided by the invention are shown in fig. 24, 25 and 26. In addition, the influence of different factors on the rheological property of the polymer solution can be researched by changing the concentration, molecular weight, speed and the like of the injected polymer-containing liquid, and the influence of the permeability on the rheological property can also be researched by using cores with different permeabilities to make a physical model.
Claims (1)
1. A method for determining rheological parameters of a polymer-containing fluid in a near wellbore zone of a perforated completion, the method comprising the steps of:
firstly, establishing a perforation completion near wellbore zone model by using ANSYS software and solving the pressure field and flow rate field data of the polymer-containing solution in the perforation completion near wellbore zone;
and secondly, processing the pressure field and flow velocity field data obtained in the first step by using MATLAB software, wherein the specific path is as follows:
firstly, solving the coordinates of non-equidistant scattered points, the seepage velocity and the seepage velocity of the non-equidistant scattered points by ANSYS softwarex、y、zThe seepage velocity, the seepage velocity direction vector and the pressure at the scattered points at equal intervals are obtained through calculation of direction vectors and pressures in three directions by an interpolation function ScatteredInterpolant;
secondly, the wall of the perforation hole is equally divided into 10 sections, the point of the intersection of each two sections is used as the starting point of the streamline, and the coordinates and the seepage velocity of the equally spaced scattered pointsx、y、zInputting direction vectors in three directions into a Streamline function, calculating to obtain 9 cluster Streamline tracks and respectively extracting coordinates of points on each cluster Streamline track;
using a Meshgrid function to generate a two-dimensional grid coordinate again, using the coordinate of a point on each cluster of flow lines as an interpolation point, and using a Griddata function to perform interpolation calculation on a z value on the generated two-dimensional grid coordinate point to obtain a curved surface passing through each cluster of flow lines, namely a diversion surface, wherein each diversion surface is a curved surface formed by a plurality of space triangles;
finally, judging the positions of equidistant space scattered points by using the model curved surface and a plane equation where a space triangle on the shunting surface is located to obtain points in a closed geometric body enclosed by the shunting surface and the model curved surface, namely points in a control body of each section of the perforation hole; calculating the average value of the flow velocity of each section of perforation and the average value of the flow velocity of all points at the same hole depth multiple through the flow velocity data on the perforation, finding the hole depth multiple where the average value of the flow velocity of each section of perforation is located, and finding the hole depth multiple where the midpoint of the flow velocity of each section of the perforation in each section of control body of the perforation is located;
thirdly, according to the result obtained in the second step, the average flow velocity on the isobaric surface and the distance from the isobaric surface along the flow line track to the wall of the perforation hole are obtained, the variation relation of the seepage distance of each control body flow velocity along the flow line track is obtained, and the seepage velocity in each control body section of the perforation hole is drawnv i (i=1,2,3, …,10) with percolation distanceL i (i=1,2,3, …,10) change relation plate; the specific path is as follows:
firstly, screening out points on each isostatic pressing surface between the wall of the perforation hole and the boundary of the model by utilizing pressure and flow rate data at equidistant three-dimensional space points in each section of control body of the perforation hole and a gradient of 0.1MPa to obtain coordinates of the points on the isostatic pressing surface in each section of control body of the perforation hole, and obtaining the average flow rate on the isostatic pressing surface by applying the flow rate data of the points on each isostatic pressing surface; secondly, taking points at the hole depth multiple of the midpoint of the flow velocity of each section of the control body of the perforation hole as a streamline starting point, calculating a streamline track, performing pressure interpolation on the points on the streamline track, finding points with the same pressure as each isobaric surface on the streamline, and calculating the distance from the perforation hole to the points along the streamline track, namely the distance from the isobaric surface to the perforation hole wall along the streamline track; in each section of control body of the perforation hole, the average flow velocity on each equal pressure surface is substituted into the distance from each equal pressure surface to the perforation hole wall along the flow line track to obtain the variation relation of the seepage distance of each control body flow velocity along the flow line track, and the seepage velocity in each section of control body of the perforation hole is drawnv i (i=1,2,3, …,10) with percolation distanceL i (i=1,2,3, …,10) change relation plate;
fourthly, analyzing the change relation chart obtained in the third step, when the descending amplitude of the seepage velocity is larger than 0.25/m, the seepage distance is between 0 and 0.1m, in order to realize variable speed seepage under the constant displacement, making a variable diameter core for experiment, and drawing a chart of the change relation of the viscosity retention rate along with the hole depth multiple by combining the hole depth multiple of the flow midpoint of each section of the control body of the perforation hole and the viscosity retention rate of each control body;
fifthly, calculating the viscosity retention rate of the polymer solution in the control area of the whole perforation hole through flow weighting calculation, and obtaining the hole depth multiple of the equivalent control body of each section of the control body of the perforation hole according to the chart of the relation of the viscosity retention rate with the change of the hole depth multiple obtained in the fourth steph mCalculating the hole depth multipleh mThe initial position of the perforation section of the equivalent control body with the length of 0.1 time of the hole depth is the flow middle point, and the inner part of the equivalent control body is drawnv eFollowed byL eA variation relation chart;
a sixth step of controlling the internal body according to the equivalent control body obtained in the fifth stepv eFollowed byL eCalculating the sectional area of the core with variable diameter according to the chart of the variation relationA eFollowed byL eChanging the relation, and then manufacturing an equivalent control body physical model according to the relation; the equivalent control body physical model is formed by connecting 4 sections of variable-section area rock cores in series, the first section is a variable-section area cylindrical rock core, the second section and the third section are variable-section area rectangular rock cores, the fourth section is a variable-section area rectangular rock core with the length different from that of the second section and the third section, the 4 sections of variable-section area rock cores are respectively arranged in the holder and the model pipe, and the equivalent control body physical model is used for simulating the actual seepage condition of a perforation completion near wellbore zone in a set area by taking a wellbore as a central radius;
seventhly, injecting polymer solution by using the physical model of the equivalent control body obtained in the sixth step and according to the discharge capacity corresponding to the flow of the equivalent control body, and measuring the shear stress of the polymer solution before and after passing through each section of the coreτAnd shear rateγThe power law index can be obtained by calculationn i Coefficient of consistencyK i Apparent viscosityμ i And polymer solution physical model viscosity retention through the entire equivalent control body.
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