CN-116335640-B - Wellhead back pressure wave and wave speed prediction model, method and equipment thereof

CN116335640BCN 116335640 BCN116335640 BCN 116335640BCN-116335640-B

Abstract

The invention provides a wellhead back pressure wave and a prediction model, a method and equipment of the pressure wave, wherein the prediction method of the pressure wave comprises the steps of S1, determining the liquid type and the flow state of single-phase fluid in an annulus, S2, determining the start time T a , the end time T b , the start depth h k,a , the end depth h k,b , the initial flow Q k and the initial back pressure P k0 of a medium k liquid section to be calculated, S3, performing time and space discretization on a calculation area to form X multiplied by Y grid nodes, wherein X= ((T b -T a )/Δt)+1,Y＝((h k,b -h k,a )/deltaz) +1, the space coordinate of a certain position point in the calculation area at the moment T j is (T j ,z i ), and S4, according to the prediction model of the annulus pressure field, obtaining the pressure value of all the position points in the annulus liquid section in the T a ～T b period through iterative calculation. According to the method, the pressure values of all discrete points of the single-phase liquid in the annulus are calculated in an iterative mode through the discretization method, and the prediction accuracy of the annular pressure wave can be ensured.

Inventors

WU LANG
ZHAO CHANGQING
FENG YUQI
YANG XIANGYU
ZENG FANKUN
LIU SHIBIN
HUANG WEI
FENG BIN
YANG CHUAN
WANG CHUNQUAN
XIAN MING
LIU YANG
NIE SHIJUN

Assignees

中国石油天然气集团有限公司
中国石油集团川庆钻探工程有限公司

Dates

Publication Date: 20260508
Application Date: 20211215

Claims (10)

1. The prediction model of the single-phase wellhead back pressure annular pressure wave is characterized in that the prediction model of the annular pressure wave is shown in formulas (1) - (4): In the formulas (1) to (4), i-1, i+1 represents any three position nodes spaced by Δz from each other in the annular liquid phase section, k represents liquid medium in the annular liquid phase section, k represents drilling fluid when k is 1, k represents head fluid when k is 2, k represents cement slurry when k is 3, t represents the current time, t+Δt represents the next time, Δt is time step, Δz is space step, v k (z i , t+Δt) represents the velocity of any point i of the annular medium k liquid section at t+Δt time, m/s, v k (z i , t) represents the velocity of any point i of the annular medium k liquid section at t time, m/s, ρ k (z i , t) represents the density of any point i of the annular medium k liquid section at t time, kg/m 3 ;v k (z i-1 , t) represents the velocity of any point i-1 of the annular medium k liquid section at t time, m/s, ρ k (z i-1 , t) represents the velocity of any point i-1 of the annular medium k liquid section at t time, kg/m 3 ;P k (z i-1 , t) represents the velocity of any point i-1 of the annular medium k liquid section at t time, m+35, ρ+1, t) represents the velocity of any point i of the annular medium k liquid section at t time, ρ+35, and ρ+1, p+1, t) represents the velocity of any point i of the annular medium k liquid in the annular medium k liquid section at t time, and ρ+1 at any point of any point at t time, ρ+35, p+1, kg/m 3 ;v k (z i-1 , t+Δt) denotes the velocity of any point i-1 of the K-liquid section of the medium in the annulus at the moment of t+Δt, m/s, v k (z i+1 , t+Δt) denotes the velocity of any point i+1 of the K-liquid section of the medium in the annulus at the moment of t+Δt, m/s, P k (z i , t+Δt) denotes the pressure of any point i of the K-liquid section of the medium in the annulus at the moment of t+Δt, pa, K k denotes the consistency coefficient of the medium K, pa.s n ;P k0 denotes the initial back pressure value of the K-liquid section of the medium, pa, ρ k0 denotes the density of the medium K when the wellhead back pressure is P k0 , kg/m 3 , d is the diameter of the annulus, m, b k is the velocity coefficient of the simplified momentum equation of the K-liquid section of the medium, m -1 .Pa.S n ;n k is the rheological parameter of the K-liquid section of the medium, Z i-1 、z i and z i+1 are the i-1 th, respectively, on the space coordinates, the i-th and i+1th nodes.
2. The prediction method of the single-phase wellhead back pressure annular pressure wave is characterized by comprising the following steps of: s1, determining the liquid type and the flow state of single-phase fluid in an annulus according to the current well cementation process; S2, determining the start time T a , the end time T b , the start depth h k,a of the medium k liquid segment, the end depth h k,b of the medium k liquid segment, the initial flow Q k and the initial back pressure P k0 corresponding to the medium k liquid segment to be calculated; S3, performing time and space discretization on a calculation region of a k liquid section of the medium to form X multiplied by Y grid nodes, wherein X= ((T b -T a )/Δt)+1,Y＝((h k,b -h k,a )/deltaz) +1, the space coordinate of a certain position point in the calculation region at the time T j is (T j ,z i ), and z i is the displacement corresponding to the ith node on the space coordinate; S4, obtaining pressure values of all position points in the annular liquid phase section in the period T a ～T b through iterative calculation according to the predictive model of the annular pressure field as claimed in claim 1.
3. The method for predicting single-phase wellhead back pressure annular pressure waves of claim 2, wherein the iterative calculation comprises: S41, inputting initial values of iteration parameters, initial conditions and boundary conditions, wherein the initial values are j=2, t 1 ＝T a ,i＝3,z 1 ＝0,z 2 =Δz, the initial conditions are v k (z,T a )＝Q k /A k ,P k (h k,a ,t)＝P 0 , and the boundary conditions are P k (h k,b ,t＝P Back pressure ; S42, calculating a moment t j corresponding to the j-th node on the displacement coordinate, wherein t j ＝t j-1 +deltat; S43, calculating displacements z i and z i+1 corresponding to the ith and (i+1st) nodes on the space coordinates, wherein z i ＝z i-1 +Δz,z i+1 ＝z i +Δz; S44, calculating at least one of the speed v k (z i ,t j of the ith node at the time t j , the speed v k (z i-1 ,t j at the (i-1) th node and the speed v k (z i+1 ,t j ) at the (i+1) th node according to the formula (1) and the formula (2); S45, calculating at least one of the density rho k (z i ,t j of the ith node at the time t j , the density rho k (z i-1 ,t j of the ith-1 node and the density rho k (z i+1 ,t j of the (i+1) th node according to the formula (3); S46, calculating at least one of the pressure P k (z k,i ,t j of the ith node at the time t j , the pressure P k (z k,i-1 ,t j at the (i-1) th node and the pressure P k (z k,i+1 ,t j ) at the (i+1) th node according to the formula (4); S47, comparing i with Y-1, if 2< i < Y-1, letting i=i+1, returning the updated i value to the step S43, and calculating the speed, density and pressure of the next node at the time t j again until i=Y-1, and outputting the pressure value of each node at the time t j ; S48, comparing j with X, if 1<j is less than or equal to X, enabling j=j+1, returning the updated j value to the step S42, and calculating the speed, the density and the pressure of each node i at the next moment again until j is more than X, and outputting the pressure value of each node in the liquid section k in the period T a ～T b ; And S49, if the liquid type of the single-phase fluid is 1, finishing calculation, and if the liquid type of the single-phase fluid is greater than 1, repeating the steps S41 to S48, and calculating the pressure value of each node in other liquid segments in the period T a ～T b .
4. The method for predicting a single-phase wellhead back pressure annular pressure wave according to claim 2, wherein Δt is in a value range of 0.001s to 0.01s, and Δz is in a value range of 10m to 20m.
5. The method for predicting single-phase wellhead back pressure annular pressure waves according to claim 2, further comprising the step of drawing a pressure wave surface graph according to the iterative calculation result, wherein the ordinate of the pressure wave surface graph is pressure, and the abscissa is time and position depth.
6. The method for predicting single-phase wellhead back pressure annular pressure waves according to claim 2, wherein different types of liquid phase media are in constant cross-section contact and the fluid flow state is laminar.
7. The prediction model of the single-phase wellhead back pressure annular pressure wave velocity is characterized in that the prediction model of the annular pressure wave velocity is shown as formulas (1) - (5): in the formulas (1) to (5), i-1, i+1 represents any three position nodes spaced by Δz from each other in the annular liquid phase section, k represents liquid medium in the annular liquid phase section, k represents drilling fluid when k is 1, k represents head fluid when k is 2, k represents cement slurry when k is 3, t represents the current time, t+Δt represents the next time, Δt is time step, Δz is space step, v k (z i , t+Δt) represents the velocity of any point i of the annular medium k liquid section at t+Δt time, m/s, v k (z i , t) represents the velocity of any point i of the annular medium k liquid section at t time, m/s, ρ k (z i , t) represents the density of any point i of the annular medium k liquid section at t time, kg/m 3 ;v k (z i-1 , t) represents the velocity of any point i-1 of the annular medium k liquid section at t time, m/s, ρ k (z i-1 , t) represents the velocity of any point i-1 of the annular medium k liquid section at t time, kg/m 3 ;P k (z i-1 , t) represents the velocity of any point i-1 of the annular medium k liquid section at t time, m+35, ρ+1, t) represents the velocity of any point i of the annular medium k liquid section at t time, ρ+35, and ρ+1, p+1, t) represents the velocity of any point i of the annular medium k liquid in the annular medium k liquid section at t time, and ρ+1 at any point of any point at t time, ρ+35, p+1, kg/m 3 ;v k (z i-1 , t+Δt) represents the velocity of any point i-1 of the K-liquid segment of the medium in the annulus at time t+Δt, m/s, v k (z i+1 , t+Δt) represents the velocity of any point i+1 of the K-liquid segment of the medium in the annulus at time t+Δt, m/s, P k (z i , t+Δt) represents the pressure of any point i of the K-liquid segment of the medium in the annulus at time t+Δt, pa, K k represents the consistency coefficient of the medium K, pa.s n ;P k0 represents the initial back pressure value of the K-liquid segment of the medium, pa, ρ k0 represents the density of the medium K when the wellhead back pressure is P k0 , kg/m 3 , d is the annulus diameter, m, b k is the velocity coefficient of the simplified momentum equation of the K-liquid segment of the medium, m -1 .Pa.S n ;n k is the rheological parameter of the K-liquid segment of the medium, the dimensionless, v Wave-guide is the velocity of the pressure wave, m/s, s is the displacement difference between two adjacent pressure peaks, m, t is the time difference between two adjacent pressure peaks, m, z is the time difference between the two pressure peaks, and z i+1 is the coordinate of the space i-1, respectively the i-th and i+1th nodes.
8. The method for predicting the pressure wave velocity of the single-phase wellhead back pressure annulus is characterized by comprising the following steps of: According to the prediction model of the annular pressure wave velocity of claim 7, obtaining pressure values of all position points in the annular liquid phase section in the period T a ～T b through iterative calculation; drawing a pressure wave surface diagram according to an iterative calculation result, wherein the ordinate of the pressure wave surface diagram is pressure, and the abscissa is time and position depth; The pressure wave surface is tracked and the annulus pressure wave velocity v Wave-guide is calculated by equation (5).
9. An apparatus for predicting monophasic wellhead back pressure annulus pressure waves, the apparatus comprising: A processor; The memory stores a computer program, when the computer program is executed by the processor, the method for predicting the single-phase wellhead back pressure annular pressure wave is implemented according to any one of claims 2-6, so as to obtain a prediction result of the annular pressure wave.
10. A computer readable storage medium storing a computer program, wherein the computer program when executed by a processor implements the method of predicting single-phase wellhead back pressure annular pressure waves of any one of claims 2-6 to obtain a prediction of annular pressure waves.

Description

Wellhead back pressure wave and wave speed prediction model, method and equipment thereof Technical Field The invention relates to the technical field of well cementation of oil and gas well engineering, in particular to a prediction model of single-phase wellhead back pressure annular pressure wave, a prediction method of single-phase wellhead back pressure annular pressure wave, a prediction model of single-phase wellhead back pressure annular pressure wave transmission speed, a prediction method of single-phase wellhead back pressure annular pressure wave transmission speed, equipment and a computer readable storage medium storing a computer program. Background For the problem of transient pressure fluctuation of a well shaft flow field of deep well pressure control well cementation, main concerns relate to the following points of a propagation mode of pressure waves in the well shaft, time spent for transmitting to the bottom of the well, a pressure fluctuation range when the bottom of the well is reached, and the like, wherein the pressure waves are generated by changing flow or adjusting opening of a throttle valve when back pressure is applied. The time for transmitting the pressure wave to the bottom of the well has important significance for the design of the pressure control well cementation construction parameters. When the formation fluid is monitored to invade the annular space during pressure control well cementation, back pressure is generated at the wellhead by adjusting the throttle valve to act on the whole shaft, so that the bottom hole pressure and the formation pressure gradually tend to be balanced. The back pressure generated by wellhead valving propagates from the wellhead to the bottom of the well in the form of pressure waves, which requires some time, i.e., the propagation time of the pressure wave in the wellbore. When gas invasion occurs, the flow in the annulus is gas-liquid two-phase flow, the pressure wave speed is rapidly reduced due to the compressibility of the gas and the momentum exchange of the interface between the gas and the liquid phase, and when gas invasion does not occur, the flow in the annulus is pure liquid phase single-phase flow. The transmission process of the back pressure wave of the pressure control well cementation well head is mainly characterized in that on one hand, the types of fluid are different, for well drilling, the types of fluid are single fluid, multiphase flow can possibly occur, the types of well cementation fluid are various, the well cementation fluid belongs to single phase flow under the condition of no gas invasion, and on the other hand, the sizes of the pipe columns are different, in well drilling, the sizes of the pipe columns are the sizes of drill pipes, and in well cementation, the sizes of the pipe columns are the sizes of the sleeves. Most of the documents are researching a method and a means for predicting wellhead back pressure during well drilling, but the method for predicting wellhead back pressure during well drilling is not suitable for calculating wellhead back pressure value during well cementation. Many students study a method for predicting the wellhead back pressure value during pressure control well cementation, but most of the methods are used for researching wellhead back pressure generated under the condition of gas-liquid two-phase flow caused by gas invasion, and relatively few wellhead back pressure transmission researches are carried out when gas invasion does not occur. For example, a pressure control drilling method based on multiphase flow calculation of a drilling annulus shaft is disclosed in the patent document with publication number CN 102943620A, and the method comprises the specific steps of obtaining basic parameters of multiphase flow calculation of the drilling annulus shaft, determining types of fluid in the well shaft annulus, considering multiphase multicomponent complex flow factors, establishing a multiphase flow control equation set in the well shaft annulus, combining technological processes under different working conditions of pressure control drilling, establishing a solution condition of the multiphase flow control equation set, dividing time and space domains of the multiphase flow calculation into grids, performing numerical discrete on the multiphase flow control equation, solving wellhead back pressure required by pressure control drilling, and adjusting wellhead throttle valve based on calculated wellhead back pressure value to realize pressure control drilling. The method can obtain the wellhead back pressure value required by controlling pressure drilling under the condition that the drilling fluid contains gas, but is not suitable for calculating or analyzing the wellhead back pressure condition in the well cementation state. The patent document with the name of CN 105178943A discloses a method for correcting wellbore pressure in real time, which comprises the steps of calcul