Wellbore fluid rheological property prediction method based on high-temperature high-pressure viscometer readingTechnical Field
The invention belongs to the field of petroleum drilling, and particularly relates to a method for predicting and analyzing rheological characteristics of wellbore fluid along with well depth change in a high-temperature high-pressure drilling process.
Background
In the drilling process, for drilling in a shallow stratum, the influence of temperature and pressure on the rheological property of the drilling fluid is small, and for drilling in a deep stratum, the influence of high temperature and high pressure on the rheological property of the drilling fluid is large, so that the influence of the high temperature and high pressure condition on the rheological property of the drilling fluid is required to be evaluated and analyzed, and further, theoretical basis is provided for improving the calculation precision of the bottom pressure of the high temperature and high pressure well, adjusting the rheological property of the drilling fluid and the like.
Particularly, as petroleum exploration and development gradually develop to a deep layer, the number of high-temperature and high-pressure (the pressure is more than 70MPa and the temperature is more than 150 ℃) deep wells and ultra-deep wells continuously increases, meanwhile, the problem of narrow density window is caused by abnormal complexity of geological conditions, the drilling fluid system is more complex, and the rheological property of the drilling fluid cannot be well described by the existing model, so that a method capable of predicting the rheological property of the fluid in the well bore of the high-temperature and high-pressure deep well and the ultra-deep well is urgently needed in order to accurately describe the rheological property of the drilling fluid in the well bore of the high-temperature and high-pressure deep well and the ultra-deep.
Disclosure of Invention
One of the technical problems to be solved by the present invention is to provide a method for predicting rheological properties of wellbore fluid, which can accurately describe rheological properties of drilling fluid in wellbores of high-temperature and high-pressure deep wells and ultra-deep wells, improve wellbore pressure calculation accuracy, and accurately adjust drilling fluid performance.
To address the above technical problems, embodiments of the present application first provide a method for predicting rheological properties of a wellbore fluid based on high temperature and high pressure viscometer readings. The method comprises the following steps: acquiring high-temperature and high-pressure rheological test data of the drilling fluid to be predicted, and establishing a reading matrix under different temperature and pressure at each rotating speed of the viscometer and a temperature change matrix and a pressure change matrix corresponding to the reading matrix by using the data; performing normalization pretreatment on each reading in the reading matrix to obtain a reading proportion matrix; determining a relation of the reading proportion along with the change of the temperature/pressure at each rotating speed by using the reading proportion matrix, the temperature change matrix and the pressure change matrix; constructing a viscometer reading prediction model according to the reading proportion-temperature/pressure change relational expression and each matrix at each rotating speed; and acquiring the pressure and temperature distribution condition of the shaft, predicting the distribution rule of the readings corresponding to the rotating speeds in the shaft according to the viscometer reading prediction model, and selecting a rheological model to calculate the rheological parameter distribution rule in the whole shaft according to the distribution rule.
Preferably, the viscometer reading prediction model is represented by the following expression:
wherein,indicating rotational speed RPMiLower temperature T0+ΔTi,kPressure P0+ΔPi,jCorresponding reading, ζi,j,kRepresenting a reading scale factor, theta, in a reading scale matrixi,0,0Indicating rotational speed RPMiLower initial temperature T0Initial pressure P0Corresponding reading, Δ Ti,kRepresents the amount of change in temperature, Δ Pi,jIndicating the amount of pressure change.
Preferably, the reading scale matrix is represented as follows:
the temperature change matrix is represented as follows:
the pressure change matrix is represented as follows:
in the formula, ζi,j,kIndicating RPM in the reading matrixi(i-0, 1, …, i), temperature TkAnd pressure PjReading under the conditionsPerforming normalization pretreatment to obtain a reading scale factor; delta Ti,kIndicating rotational speed RPMiLower temperature TkRelative to the initial temperature T0Amount of change, Δ Pi,jIndicating rotational speed RPMiDown force PjRelative to the initial pressure P0The variation of (b), j and k represent natural numbers.
Preferably, each reading in the reading matrix is subjected to a normalization pre-processing at a rotation speed RPMiLower temperature TkPressure PjCorresponding readingCalculating the reading for the moleculeDuty revolution RPMiLower initial temperature T0Initial pressure P0Corresponding reading thetai,0,0To obtain a reading scale factor ζi,j,k。
Preferably, the relationship of the reading proportion to the temperature change at each rotating speed is determined by the following steps:
extracting rotating speed RPM from reading proportion matrixiLower initial pressure P0The reading scale factor zeta corresponding to each temperaturei,0,k；
According to the extracted reading scale factor zetai,0,kPerforming regression analysis according to a first preset relation model to obtain a regression coefficient in the first preset relation model, thereby determining the reading at the rotating speedThe relation of the proportion changing with the temperature is used as a first relation.
Preferably, the first relation is:
therein, ζi,0,kIndicating rotational speed RPMiLower initial pressure P0Temperature TkThe corresponding reading scale factors, a, b and c, all represent regression coefficients of the first relation, Δ Ti,kRepresents the temperature TkRelative to the initial temperature T0The amount of change in (c).
Preferably, the relationship of the reading proportion to the pressure change at each rotating speed is determined by the following steps:
extracting rotating speed RPM from reading proportion matrixiLower temperature TkThe reading scale factor zeta corresponding to each pressurei,j,k；
According to the extracted reading scale factor zetai,j,kPerforming regression analysis according to the second preset relation model to obtain the temperature TkThe regression coefficient d in the corresponding second preset relation modelkAnd determining a relation of the reading proportion at the rotating speed to the temperature change as a second relation.
Preferably, the second relation is:
ζi,j,k＝ζi,0,k+dk×ΔPi,j j＝0,1,...,j k＝0,1,...,k
therein, ζi,j,kIndicating rotational speed RPMiLower temperature TkPressure PjCorresponding reading scale factor, ζi,0,kIndicating rotational speed RPMiLower initial pressure P0Temperature TkCorresponding reading scale factor, Δ Pi,jRepresents a pressure PjRelative to the initial pressure P0Amount of change of dkRepresents the temperature TkThe corresponding regression coefficients.
Preferably, the viscometer reading prediction model is constructed by: obtaining a regression coefficient vector according to the second preset relation model, and determining a relation between a regression coefficient in the regression coefficient vector and the temperature variation quantity according to the regression coefficient vector and the temperature variation matrix to be used as a third relation; and determining the relationship between the reading scale factors corresponding to different temperatures and different pressures at different rotating speeds and the temperature variation and the pressure variation according to the first relational expression, the second relational expression and the third relational expression, and taking the relationship as a fourth relational expression to further obtain a reading prediction model of the viscometer.
Preferably, the regression coefficient vector is:
D＝[d1,d2,...,dk]
wherein D represents a regression coefficient vector;
the third relation is as follows:
wherein f, g and h all represent regression coefficients of the third relation, Δ Ti,kRepresents the temperature TkRelative to the initial temperature T0The amount of change in (c).
Preferably, the fourth relation is:
therein, ζi,j,kIndicating rotational speed RPMiLower temperature TkPressure PjCorresponding reading scale factor, Δ Pi,jRepresents a pressure PjRelative to the initial pressure P0A, b and c each represent a regression coefficient of the first relation, Δ Ti,kRepresents the temperature TkRelative to the initial temperature T0The amount of change in (c).
Compared with the prior art, one or more embodiments in the above scheme can have the following advantages or beneficial effects:
the invention provides a method for predicting rheological characteristics of drilling fluid in a high-temperature and high-pressure well shaft based on readings of a high-temperature and high-pressure viscometer, which can meet the requirements of accurate acquisition of rheological parameters of the drilling fluid, drilling hydraulic parameters and drilling fluid performance adjustment of the drilling fluid in the drilling process of a high-temperature and high-pressure well.
The high-temperature high-pressure shaft drilling fluid rheological property prediction model (which can be called as a viscometer reading prediction model) can meet the prediction of the high-temperature high-pressure deep well and ultra-deep well shaft drilling fluid rheological property, and provides basic parameters for the shaft pressure calculation and the drilling fluid rheological property adjustment of the high-temperature high-pressure oil and gas well. The method is easy to realize, is not limited by rheological model selection, is suitable for all common rheological models, can quickly obtain rheological parameter distribution rules in a drilling fluid shaft, and can meet the requirements of rheological parameter calculation and analysis of high-temperature and high-oil gas wells.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure and/or process particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
The accompanying drawings are included to provide a further understanding of the technology or prior art of the present application and are incorporated in and constitute a part of this specification. The drawings expressing the embodiments of the present application are used for explaining the technical solutions of the present application, and should not be construed as limiting the technical solutions of the present application.
FIG. 1 is a schematic flow chart of a method of predicting rheological properties of a wellbore fluid based on high temperature and high pressure viscometer readings according to an embodiment of the application.
FIG. 2 is a schematic flow chart illustrating a method for predicting rheological properties of a wellbore fluid based on high temperature and high pressure viscometer readings, in accordance with an embodiment of the present disclosure.
FIG. 3 is a schematic representation of the rheological parameters of the Carson rheological model as a function of wellbore predicted based on viscometer readings according to an embodiment of the present application.
Detailed Description
The following detailed description of the embodiments of the present invention will be provided with reference to the accompanying drawings and examples, so that how to apply the technical means to solve the technical problems and achieve the corresponding technical effects can be fully understood and implemented. The embodiments and the features of the embodiments can be combined without conflict, and the technical solutions formed are all within the scope of the present invention.
Additionally, the steps illustrated in the flow charts of the figures may be performed in a computer system such as a set of computer-executable instructions. Also, while a logical order is shown in the flow diagrams, in some cases, the steps shown or described may be performed in an order different than here.
According to the embodiment of the invention, based on high-temperature and high-pressure rheological experimental data, viscometer reading prediction models under different temperature and pressure conditions at different rotating speeds of a viscometer are obtained, and then rheological model selection and rheological parameter calculation analysis are carried out, so that rheological characteristics of drilling working fluid in the whole shaft are obtained, and basic parameters are provided for high-temperature and high-pressure drilling shaft pressure calculation and drilling fluid performance regulation.
FIG. 1 is a schematic flow chart of a method of predicting rheological properties of a wellbore fluid based on high temperature and high pressure viscometer readings according to an embodiment of the application. The implementation steps of the method are briefly described below with reference to fig. 1.
In step S110, high-temperature and high-pressure rheological test data of the drilling fluid to be predicted are obtained, and a reading matrix at different temperature and pressure at each rotation speed of the viscometer, and a temperature change matrix and a pressure change matrix corresponding to the reading matrix are established using the data.
At a certain rotational speed RPMi(i-0, 1, … i) as an example, the high temperature and high pressure rheology test data includes the temperature T of the testk(k 0,1, … k), test pressure Pj(j＝0,1,…j) And RPM for rotational speediDifferent temperatures TkPressure PjReading of lower thetai,j,kAnd i, j, and k represent natural numbers. Establishing the rotational speed RPM based on the test dataiDifferent temperatures T ofkPressure PjReading matrix [ theta ] ofi,j,k]It can be expressed as:
then, with T0For the initial temperature, a temperature change matrix Δ T corresponding to the reading of each measurement point in the matrix (1) is calculated, and can be represented by the following matrix:
in the formula,. DELTA.Ti,kIndicating rotational speed RPMiLower temperature TkRelative to the initial temperature T0The amount of change in (c).
Then, with P0And (3) calculating a pressure change matrix corresponding to the reading of each measuring point in the matrix (1) for the initial pressure, wherein the pressure change matrix can be represented by the following matrix:
in the formula,. DELTA.Pi,jIndicating rotational speed RPMiDown force PjRelative to the initial pressure P0The amount of change in (c).
In step S120, each reading in the reading matrix is subjected to normalization preprocessing to obtain a reading ratio matrix.
Specifically, in normalizing the pre-processing of each reading in the reading matrix, at the RPM of the rotation speediLower temperature TkPressure PjCorresponding reading thetai,j,kCalculate the reading θ for the moleculei,j,kDuty revolution RPMiLower initial temperature T0Initial pressure P0Corresponding reading thetai,0,0To obtain a reading scale factorζi,j,k。
The resulting read scale matrix ζ is represented as follows:
in the formula, ζi,j,kIndicating RPM in the reading matrixi(i-0, 1, …, i), temperature TkAnd pressure PjReading under conditions thetai,j,kAnd (4) performing normalization pretreatment to obtain a reading scale factor.
In step S130, a temperature/pressure variation relation is determined for each rotation speed using the reading ratio matrix, the temperature variation matrix, and the pressure variation matrix.
Specifically, a relationship (first relationship) of the reading ratio with respect to the temperature change at each rotation speed is determined by the following steps.
Firstly, extracting the RPM from the reading proportion matrixiLower initial pressure P0At each temperature TkCorresponding reading scale factor zetai,0,k. Then, according to the extracted reading scale factor zetai,0,kAnd carrying out regression analysis according to the first preset relation model to obtain a regression coefficient in the first preset relation model, and determining a relation of the reading proportion at the rotating speed changing along with the temperature to serve as a first relation.
Wherein the first relational expression (which is also the first preset relational model before the non-regression analysis) is shown as the following expression:
wherein a, b and c each represent a regression coefficient of the first relation, Δ Ti,kRepresents the temperature TkRelative to the initial temperature T0The corresponding value can be obtained by the first row vector of the matrix (2).
That is, first, the vector ζ in the matrix ζ is decimatedj＝[ζi,0,0 ζi,0,1 … ζi,0,k]To obtainAfter the group of vectors is reached, regression analysis is carried out on the expression (5) to obtain the regression coefficients a, b and c.
Next, a relationship (second relationship) of the reading ratio with respect to the pressure change at each rotation speed is determined by the following steps.
Firstly, extracting the RPM from the reading proportion matrixiLower temperature TkThe reading scale factor zeta corresponding to each pressurei,j,k。
Specifically, each column vector of the formula (4) is extracted, that is, ζ ═ ζ1 ζ2 … ζk]Therein ζ ofk＝[ζi,0,k ζi,1,k… ζi,j,k]T。
Then, according to the extracted reading scale factor zetai,j,kPerforming regression analysis according to the second preset relation model to obtain the temperature TkThe regression coefficient d in the corresponding second preset relation modelkAnd determining a relation of the reading proportion at the rotating speed to the temperature change as a second relation.
When the temperature is constant, the reading is compared with the pressure difference delta Pi,jHas a linear relation, so that the data zeta in each column vector of the proportionality coefficient matrix zetai,j,kAnd Δ Pi,jAlso linearly varying. At this time, the measured value is measured by Δ Pi,jAs an independent variable,. DELTA.Pi,jWhen equal to 0, ζi,0,kKnown, can bekExpressed as the following equation, the second relation (also the second predetermined relational model before non-regression analysis):
ζi,j,k＝ζi,0,k+dk×ΔPi,j j＝0,1,...,j k＝0,1,...,k (6)
therein, ζi,0,kIndicating rotational speed RPMiLower initial pressure P0Temperature TkCorresponding reading scale factor, Δ Pi,jRepresents a pressure PjRelative to the initial pressure P0The variation of (2) which can be derived from the column vectors of the matrix (3) to give the corresponding value, dkRepresents the temperature TkThe corresponding regression coefficient is calculated by column vector ζkRegression analysis is carried out on the data to obtain the regression coefficient dk。
Carrying out regression analysis on each column vector of the matrix zeta according to equation (6) to obtain d corresponding to each column vectorkD is obtainedkThe regression coefficient vector is composed as follows:
D＝[d1 d2 … dk] (7)
in step S140, a viscometer reading prediction model is constructed from the temperature/pressure variation relationship for the reading ratios at each rotation speed and each matrix.
Specifically, the viscometer reading prediction model is constructed by the following steps.
Firstly, obtaining a regression coefficient vector according to a second preset relation model, and determining a relation between a regression coefficient in the regression coefficient vector and a temperature variation quantity according to the regression coefficient vector and a temperature variation matrix to be used as a third relation;
specifically, a row vector Δ T of an arbitrary row in the region is selected according to equation (2)j，ΔTj＝[0 ΔTi,1 … ΔTi,k]Then by Δ TjIs an independent variable and D is a dependent variable, and the following equation (a third relation equation) is applied:
wherein f, g and h all represent regression coefficients of the third relation, Δ Ti,kRepresents the temperature TkRelative to the initial temperature T0The amount of change in (c).
And then, determining the relationship between the reading scale factors corresponding to different temperatures and different pressures at different rotating speeds and the temperature variation and the pressure variation according to the first relational expression, the second relational expression and the third relational expression, and taking the relationship as a fourth relational expression to further obtain a reading prediction model of the viscometer.
I.e., joint equations (5), (6) and (8), a fourth relationship is established as:
wherein,ζi,j,kindicating rotational speed RPMiLower temperature TkPressure PjThe corresponding reading scale factor.
Since the fourth relation is characterized by the RPMiLower different temperature TkPressure PjCorresponding reading scale factor ζi,j,kAnd temperature variation amount delta Ti,kAnd the pressure change amount Δ Pi,jThe simplified viscometer reading prediction model can be obtained according to a fourth relation:
wherein,indicating rotational speed RPMiLower temperature T0+ΔTi,kPressure P0+ΔPi,jCorresponding reading, ζi,j,kRepresenting a reading scale factor, theta, in a reading scale matrixi,0,0Indicating rotational speed RPMiLower initial temperature T0Initial pressure P0Corresponding reading, Δ Ti,kRepresents the amount of change in temperature, Δ Pi,jIndicating the amount of pressure change.
The above is to construct the rotational speed RPMiBased on the same principle, the method can also construct a viscometer reading prediction model for obtaining other rotation speeds.
After a viscometer reading prediction model is constructed for each rotational speed, the fluid rheology is analyzed at each location in the wellbore by using the reading prediction model.
In step S150, wellbore pressure and temperature distribution conditions are obtained, and a distribution rule of readings corresponding to each rotation speed in the wellbore is obtained according to the viscometer reading prediction model, and accordingly, a rheological model is selected to calculate a rheological parameter distribution rule in the entire wellbore.
For example, the depth H of the boreholexHas a temperature data of TxPressure data ofPxAnd the well depth H in the shaft can be respectively calculatedxRelative to temperature T0And an initial pressure P0Temperature change amount Δ T ofxAnd the pressure change amount Δ Px. Namely, the existence of:
ΔTx＝Tx-T0
ΔPx＝Px-P0 (11)
obtaining depth array (H) by the above equationx，ΔTx，ΔPx) Where X is 1,2, …, X. Subsequently, a preset reading prediction model is utilized to determine viscometer readings at various locations within the wellbore based on the temperature and pressure variations described above. Wherein, the reading prediction model is constructed by using the steps S110 to S140. Specifically, setting X to 1, starting the cycle from 1 to ending X, and substituting the corresponding temperature difference and pressure difference into the corresponding equation (10) to calculate the rotating speed to be RPMiAnd (4) the distribution of the readings in the shaft, if all the rotating speed cycles are finished, jumping to the next step (selecting a rheological model), if the micro-cycle is finished, i is i +1, and continuously calculating and analyzing the rotating speed to be RPMi+1The distribution of readings in the wellbore.
The viscometer reading prediction model represents the functional relationship between the readings corresponding to different temperatures and different pressures at the rotational speed of the viscometer and the readings corresponding to the initial temperature and the initial pressure at the rotational speed, and also represents the functional relationship between the readings corresponding to different temperatures and different pressures at the rotational speed and the temperature variation and the pressure variation, so that the method can obtain the temperature variation delta T according to the obtained temperature variation delta TxAnd the pressure change amount Δ PxAnd calculating to obtain readings corresponding to different temperatures and different pressures at the rotating speed, thereby obtaining the readings at each depth of the shaft.
After determining the rheological model of the drilling fluid system and the readings at each location in the wellbore, determining rheological parameters at each location in the wellbore from the readings at each location in the wellbore based on the rheological model.
The high-temperature high-pressure shaft drilling fluid rheological property prediction model can meet the prediction of the high-temperature high-pressure deep well and ultra-deep well shaft drilling fluid rheological properties, and provides basic parameters for shaft pressure calculation and drilling fluid rheological property regulation of high-temperature high-pressure oil and gas wells. The method is easy to realize, is not limited by the selection of the rheological model, is suitable for all common rheological models, can quickly obtain the rheological parameter distribution rule in the shaft, and can meet the requirements of rheological parameter calculation and analysis of the high-temperature high-oil and gas wells.
To demonstrate the availability and advantages of the method of rheological analysis of wellbore fluids provided by the present invention, a well is exemplified and further described with reference to fig. 2 and 3.
A certain well is drilled by using the oil-based drilling fluid, a high-temperature high-pressure rheological experiment is carried out on the drilling fluid, and high-temperature high-pressure test data are obtained, wherein the specific experimental data are shown in the following table.
The experimental data were analyzed according to the calculation procedure given in the invention.
As shown in FIG. 2, first, i is set, and RPM is calculated according to equation (1)iDetermining a temperature change matrix and a pressure change matrix according to the formula (2) and the formula (3), then calculating a zeta matrix according to the formula (4), and extracting a first row vector zeta of the zeta matrixjFor the coefficient d of formula (6)kRegression analysis is performed to obtain the formula (7), and then the data of the formula (7) is extracted to obtain the regression coefficient of the formula (8), and further obtain the formula (9), and finally obtain the formula (10). Judging whether all the prediction models under all the rotating speeds are obtained, if not, making i equal to i +1, resetting i, and calculating rotating speed RPMi+1The final regression coefficients of each rotation speed formula (9) obtained by the prediction model are shown in the following tableThe following steps:
wellbore temperature, pressure, and temperature pressure data are then obtained as shown in table 3.
According to the table (2), calculating the predicted value of the corresponding reading of each rotating speed along with the depth according to T0，P0And performing rheological model optimization on the measured rheological data, and determining that the Carson rheological model can well describe the rheological characteristics of the Carson rheological model through the rheological model optimization, so that the well needs to predict the distribution condition of the Carson viscosity and the Carson yield value in the whole well bore. After the rheological model is determined, the rheological parameter calculation analysis is carried out on the whole shaft by using the reading data obtained by prediction, the shaft rheological parameter section is drawn, and finally the change conditions of the calculated Carson viscosity and the Carson yield value along with the shaft are shown in figure 3.
Although the embodiments of the present invention have been described above, the above descriptions are only for the convenience of understanding the present invention, and are not intended to limit the present invention. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.