CN111400978A - Critical liquid carrying flow calculation method considering liquid drop deformation and multi-parameter influence - Google Patents
Critical liquid carrying flow calculation method considering liquid drop deformation and multi-parameter influence Download PDFInfo
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Abstract
The invention relates to a critical liquid carrying flow calculation method considering liquid drop deformation and multi-parameter influence in the field of reasonable gas reservoir production allocation. The method solves the problem that the judgment of the accumulated liquid of the gas well has deviation at present, and mainly comprises the following steps: firstly, solving a maximum size parameter of an ellipsoidal liquid drop based on a liquid drop crushing principle; then, based on the balance of the gravity, the drag force and the buoyancy force borne by the liquid drop, obtaining a critical liquid carrying flow velocity expression; then, considering the influence of the change of the incident flow area of the liquid drops on the drag coefficient due to deformation and the influence of parameters such as friction resistance of different pressures, temperatures and pipe diameters on gas-liquid phases, gas-liquid surface tension and the like, establishing a critical liquid carrying flow calculation model considering multiple parameters; and finally, solving the model in a multi-parameter iteration mode to obtain the gas well critical liquid carrying flow. The invention has the following beneficial effects: the gas well accumulated liquid can be accurately predicted, the influence of a plurality of parameters on the critical liquid carrying flow is considered, the calculation is accurate, and the use is convenient.
Description
Technical Field
The invention relates to a critical liquid carrying flow calculation method considering liquid drop deformation and multi-parameter influence, and belongs to the field of reasonable production allocation of gas reservoirs.
Background
As most gas fields adopt depletion type exploitation, the stratum energy is reduced along with production, all liquid generated in a shaft is not enough to be brought out, the liquid is accumulated at the bottom of the shaft, back pressure is generated on the stratum, and the effective liquid carrying energy is further reduced. In severe cases, the well killing or gas well production stopping can be caused, and the phenomenon of gas well liquid accumulation is caused. Therefore, according to the gas well liquid carrying principle, the calculation of the critical liquid carrying flow is researched, reference is provided for reasonable production allocation of the gas well, the gas well can be continuously produced in a liquid carrying mode, the generation of gas well accumulated liquid is reduced, and the method has important significance for efficient production of the gas well.
In the calculation of the flow, the drag coefficient, the friction coefficient and the surface tension of the key parameters are all fixed values, but in practical application, the well condition is complex, and when the temperature, the pressure and the well diameter of a well head change, the key parameters for calculating the critical liquid carrying flow all change and are no longer fixed values. The critical liquid carrying flow calculated by using the fixed value cannot accurately reflect the capability of the gas well capable of carrying liquid for production, and the judgment of the accumulated liquid of the gas well has deviation. The method aims to solve the problem that the calculation of the critical flow rate in the current critical liquid carrying flow rate calculation has deviation and the liquid accumulation condition of the gas well cannot be accurately judged so as to adapt to the gas wells with different production conditions, and the liquid drop deformation, the drag coefficient, the friction coefficient and the surface tension can be changed along with the changes of temperature, pressure and the diameter of an oil pipe, so that the critical liquid carrying flow rate of the gas well is more accurately calculated, and the reasonable production allocation of the gas well is guided.
Disclosure of Invention
The purpose of the calculation method is: the critical liquid carrying flow calculation method considering the liquid drop deformation and the multi-parameter influence is provided for accurately predicting the liquid loading of the gas well in the water-gas reservoir development process, and a basis is provided for the water-gas reservoir production scheme.
In order to achieve the above purpose, the invention adopts the following steps:
firstly, solving a maximum size parameter of an ellipsoidal liquid drop based on a liquid drop crushing principle; then, based on the balance of the gravity, the drag force and the buoyancy force borne by the liquid drop, obtaining a critical liquid carrying flow velocity expression; then, considering the influence of the change of the incident flow area of the liquid drops on the drag coefficient due to deformation, and the influence of different pressures, temperatures and pipe diameters on the friction resistance of gas-liquid phases and the surface tension of the gas-liquid phases, establishing a critical liquid carrying flow velocity calculation model considering multiple parameters; and finally, solving the model in a multi-parameter iteration mode to obtain the gas well critical liquid carrying flow rate, and further obtaining the critical liquid carrying flow rate through the conversion relation between the gas well flow rate and the flow rate.
In the above method for calculating the critical liquid carrying flow rate considering the deformation of the droplet and the influence of multiple parameters, the calculating the critical liquid carrying flow rate includes the following steps: firstly, calculating gas density, gas viscosity and liquid density in a shaft according to the temperature and pressure of a gas well and the inner diameter of the shaft; then according to the density difference of the gas phase and the liquid phase, calculating the surface tension of the gas phase and the liquid phase by adopting a Liyuan equation; and finally setting an initial value of the critical liquid-carrying flow rate, and calculating the Reynolds number by combining the gas density and the gas viscosity.
In the critical liquid carrying flow calculation method considering the deformation of the liquid drop and the influence of multiple parameters, the critical liquid carrying flow of the multiple parameters is considered through iterative calculation, the drag coefficient and the friction coefficient of the influence of temperature, pressure, the inner diameter of a shaft and the Reynolds number are calculated according to a Shore expectation formula, the gas-liquid two-phase drag coefficient is calculated based on an L ee formula, the critical liquid carrying flow rate is calculated by combining the Reynolds number and the gas-liquid surface tension calculated by the previous calculation, the difference value between the critical liquid carrying flow rate and the initial critical liquid carrying flow rate is smaller than 0.0001m/s, if the difference value is not smaller than 0.0001m/s, the critical liquid carrying flow rate calculated at this time is used as a new initial critical liquid carrying flow rate, iterative operation is repeated, if the difference value is larger than the previous value, the critical liquid carrying flow rate calculated at this time is the minimum liquid carrying flow rate of the continuous liquid carrying of the gas well, and the corresponding critical liquid carrying flow is further calculated through the conversion relation between the gas.
In the method for calculating the critical liquid carrying flow considering the deformation of the liquid drop and the influence of multiple parameters, after the critical liquid carrying flow is calculated, the critical liquid carrying flow charts of the gas wells under different pressures and pipe diameters are established.
The invention has the following beneficial effects: (1) the deformation of the liquid drop in the high-speed air flow is considered; (2) the change of drag coefficient, friction coefficient and surface tension with temperature, pressure and oil pipe diameter is considered; (3) the calculation is accurate and the lookup is convenient.
Drawings
Fig. 1 is a flow chart of calculating the critical liquid carrying flow rate according to the present invention.
Fig. 2 is a force analysis and deformation diagram of the liquid drop in the well bore.
FIG. 3 is a chart of critical liquid carrying flow according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
As shown in fig. 1, it is a flow chart for calculating the critical liquid carrying flow rate of the present invention, and the present invention adopts the following steps:
firstly, establishing a physical model of liquid drops in a shaft, and microscopically based on a liquid drop crushing principle, namely, the liquid drops are maintained to be not crushed in an ellipsoidal shape under the action of surface tension and gas phase turbulence force, and solving the maximum size parameter of the ellipsoidal liquid drops; then, macroscopically, based on the balance of three forces of gravity, drag force and buoyancy borne by the liquid drop, obtaining a critical liquid carrying flow velocity expression; then, considering the influence of the change of the incident flow area of the liquid drops on the drag coefficient due to deformation, and the influence of different pressures, temperatures and pipe diameters on the friction resistance of gas-liquid phases and the surface tension of the gas-liquid phases, establishing a critical liquid-carrying flow velocity mathematical model considering multiple parameters; and finally, solving the model in a multi-parameter iteration mode to obtain the gas well critical liquid carrying flow rate, and further obtaining the gas well critical liquid carrying flow rate through the conversion relation between the gas well flow rate and the flow rate.
In the above method for calculating the critical liquid carrying flow rate considering the deformation of the droplet and the influence of multiple parameters, the calculating the critical liquid carrying flow rate includes the following steps:
the method for calculating the critical liquid carrying flow considering the deformation of the liquid drop and the influence of multiple parameters is characterized in that a physical model of the liquid drop flowing in a shaft is established:
(1) microscopically, a droplet in a high velocity gas stream is maintained unbroken by the turbulent forces that attempt to break it up and the surface tension that tries to hold it intact on its own.
(2) As shown in b) and c) of figure 2, the turbulent force of the gas phase causes a pressure difference to exist between the front and the back of the liquid drop along the moving direction, and under the action, the liquid drop is changed from a spherical shape to an ellipsoidal shape, so that the incident flow area of the liquid drop isSThe diameter in the Z-axis direction ish.
(3) As shown in a) of fig. 2, on a macroscopic scale, the liquid droplets are balanced in the gas flow by three forces of self-gravity, buoyancy and drag, when the liquid droplets are free to settle to a maximum velocity. The minimum velocity of the air stream to cause the droplets to be carried out of the ground by the air streamv gSlightly greater than the settling velocity of the dropletsv l. Thenv=v lIs the minimum critical speed sought.
And secondly, the method for calculating the critical liquid carrying flow considering the deformation of the liquid drop and the influence of multiple parameters is characterized in that the maximum size parameter of the ellipsoidal liquid drop is obtained according to the fact that the liquid drop on the microcosmic scale is maintained not to be broken by the surface tension and the gas phase turbulent flow force.
(1) According to the surface free energy formula of Adamson, the surface area infinitesimal of the ellipsoidal liquid drop is obtainedSThe corresponding surface free energy of the liquid dropletE S。
The surface free energy formula of Adamson is as follows:
in the formula (I), the compound is shown in the specification,e ssurface free energy per unit area, W/m2；σSurface tension, N/m.
When the surface area of the ellipsoidal liquid drop is infinitesimalSThe corresponding surface free energies of the droplets are:
in the formula (I), the compound is shown in the specification,E Sis the surface free energy, W/m.
(2) According to the turbulent kinetic energy formula of White unit volume, solving the volume infinitesimal of the liquid drop of the ellipsoidShWhen it is subjected to the turbulent kinetic energy of the gasE T。
Wherein the turbulent kinetic energy per unit volume of White is as follows:
in the formula (I), the compound is shown in the specification,e Tsurface free energy per unit volume of fluid, W/m3；ρ gIs gas density, Kg/m3；
Is the radial velocity, m/s.
When the volume infinitesimal of the ellipsoid liquid drop isShWhen in use, the turbulent kinetic energy of the gas is as follows:
in the formula (I), the compound is shown in the specification,E Tis the turbulent kinetic energy, W/m.
Wherein the method is known from Taitel
Namely:
in the formula (I), the compound is shown in the specification,v gis the critical liquid carrying flow velocity, m/s;f sgthe coefficient of friction resistance of gas-liquid two phases.
(3) And obtaining a liquid drop balance relational expression based on the liquid drop balance condition. That is, microscopically, according to the fact that the liquid drop maintains the ellipsoidal shape without being broken under the action of surface tension and gas phase turbulent force, the sum of the surface free energy and the turbulent kinetic energy of the liquid drop is zero, and then the liquid drop balance relational expression is as follows:
(4) by changing the volume relation of the dropletsV=S·h，And carrying the liquid drop balance relational expression obtained in the step (3) to obtain the ellipsoidal liquid drop size parameter.
Considering that the drop is spherical to ellipsoidal and its volume remains the same, the drop is made of a material with a high thermal conductivityS=V / hIn pairs of two sideshAfter the micro-separation is carried out, the reaction solution is obtained,S / h = -V / h 2 and the diameter of the ellipsoidal liquid drop in the Z-axis direction, which can be obtained under the condition of bringing the liquid drop into the balance, is as follows:
the area of the incident flow is:
and thirdly, the method for calculating the critical liquid carrying flow considering the deformation of the liquid drop and the influence of multiple parameters is characterized in that macroscopically, based on the balance of three forces of gravity, drag force and buoyancy on the liquid drop, the expression of the critical liquid carrying flow rate is further obtained according to the size parameters of the liquid drop obtained in the last step.
Wherein, the liquid drop can be obtained by the balance of gravity, drag force and buoyancy force:
in the formula (I), the compound is shown in the specification,ρ lis liquid density, Kg/m3；CDIs the drag coefficient of gas phase and liquid phase.
And the size parameter of the ellipsoidal liquid drop obtained in the previous stepS、h、V=S∙hBy substituting into this relation, the critical liquid-carrying flow rate is obtainedv gExpression:
fourthly, calculating the surface tension of the critical liquid-carrying flow velocity parameterσAnd a Reynolds number Re, comprising the steps of:
(1) according to gas well temperatureTPressure, pressurepAnd wellbore inner diameterDCalculating gas density in the wellboreρ gViscosity of gasμAnd density of liquidρ l(ii) a Then according to the gas-liquid two-phase density difference, adopting Liyuan's formula to calculate gas-liquid surface tensionσ：
In the formula (I), the compound is shown in the specification,T rto compare the temperatures.
(2) Setting the initial value of critical liquid-carrying flow ratev g0Calculating Reynolds number Re by combining gas density and gas viscosity:
fifthly, the drag coefficient required by iterative calculation of critical liquid carrying flow velocity is obtainedC DCoefficient of friction resistancef sgIn combination with the fourth stepReynolds number Re obtained by calculation and gas-liquid surface tensionσAnd (4) iteratively calculating the critical liquid carrying flow rate. The method comprises the following steps:
(1) first, the temperature of the gas well is calculated and consideredTPressure, pressurepAnd wellbore inner diameterDDrag coefficient influenced by Reynolds number ReC DCoefficient of frictionf sgCalculating drag coefficient of spherical liquid drop by using Shao Ming Wang formulaC DS：
For the ellipsoidal droplets of the present invention, the drag coefficient thereofC DThe shape correction was taken to be 4.97 times the spherical drop drag coefficient calculated with the shore formula:
C D=4.97C DS
the gas-liquid two-phase friction coefficient is calculated by adopting the L ee formulaf sg：
And calculating the critical liquid carrying flow rate by combining the Reynolds number obtained by the calculation and the gas-liquid surface tension:
(2) then calculate the critical liquid-carrying flowv gInitial value of critical liquid-carrying flow velocityv g0If the difference value is less than 0.0001m/s, taking the calculated critical liquid carrying flow rate as a new initial critical liquid carrying flow rate value, and repeating the fifth step of iterative operation;
(3) if so, the critical liquid carrying flow rate obtained by the calculation is the minimum liquid carrying flow rate of the gas well for carrying liquid continuously, and the corresponding critical liquid carrying flow rate is calculated through the conversion relation between the flow rate and the flow rate:
in the formula:q cis the critical liquid carrying flow of gas, m3/d；AIs the cross-sectional area of the pipe, m2；pIs pressure, MPa;Zis the gas deviation coefficient;Tis the temperature, K.
And sixthly, the method for calculating the critical liquid carrying flow considering the liquid drop deformation and the multi-parameter influence is characterized in that after the critical liquid carrying flow is calculated, sensitivity analysis is carried out on the influence of the drag coefficient, the surface tension and the friction coefficient on the critical liquid carrying flow of the gas well, and a critical liquid carrying flow chart of the gas well under different pressures and pipe diameters is established.
As shown in fig. 3, for gas wells at different pressures and pipe diameters, the corresponding critical liquid carrying flow values can be looked up from the chart. When the reasonable production allocation design of the gas well is carried out, the gas well can be continuously produced with liquid taking by considering that the yield of the gas well is larger than the searched critical liquid carrying flow.
Compared with the prior art, the invention has the following beneficial effects: (1) the deformation of the liquid drop in the high-speed air flow is considered; (2) the change of drag coefficient, friction coefficient and surface tension with temperature, pressure and oil pipe diameter is considered; (3) the calculation is accurate and the lookup is convenient.
The above description is only an exemplary embodiment of the present invention, and is not intended to limit the scope of the present invention. Any equivalent changes and modifications that can be made by one skilled in the art without departing from the spirit and principles of the invention should fall within the protection scope of the invention.
Claims (6)
1. A critical liquid carrying flow calculation method considering liquid drop deformation and multi-parameter influence is characterized by comprising the following steps: firstly, solving a maximum size parameter of an ellipsoidal liquid drop based on a liquid drop crushing principle; then, based on the balance of the gravity, the drag force and the buoyancy force borne by the liquid drop, obtaining a critical liquid carrying flow velocity expression; then, considering the influence of the change of the incident flow area of the liquid drops on the drag coefficient due to deformation, and the influence of different pressures, temperatures and pipe diameters on the friction resistance of gas-liquid phases and the surface tension of the gas-liquid phases, establishing a critical liquid carrying flow velocity calculation model considering multiple parameters; and finally, solving the model in a multi-parameter iteration mode to obtain the gas well critical liquid carrying flow rate, and further calculating the critical liquid carrying flow rate through the conversion relation between the gas well flow rate and the flow rate.
2. The method for calculating the critical liquid carrying flow considering the deformation of the liquid drop and the influence of multiple parameters according to claim 1, wherein the calculating the critical liquid carrying flow velocity expression comprises the following steps: firstly, according to the surface tension and gas phase turbulent flow force of micro-upper liquid drop the ellipsoid is maintained and is not broken, and the maximum size parameter of the ellipsoid-shaped liquid drop is obtained, including incident flow areaSAndZdiameter of shafth(ii) a Wherein ellipsoidal droplets are determinedZDiameter of shafthComprises the following steps:
in the formula (I), the compound is shown in the specification,σsurface tension, N/m;ρ gis gas density, Kg/m3；v gIs the critical liquid carrying flow velocity, m/s;f sgthe coefficient of friction resistance of gas-liquid two phases;
the incident flow area of the ellipsoidal liquid drop is obtained as follows:
wherein V is the volume of the ellipsoidal droplet, m3。
3. The method for calculating the critical liquid carrying flow considering the deformation of the liquid drop and the influence of multiple parameters according to claim 1, wherein the calculating the critical liquid carrying flow velocity expression comprises the following steps: secondly, according to the macroscopically, three-force equilibrium based on the gravity, drag and buoyancy forces to which the liquid drops are subjected, and according to the claims2, obtaining the critical liquid carrying flow rate according to the obtained droplet size parametersv gThe expression of (1);
wherein:
in the formula (I), the compound is shown in the specification,gtaking 9.8 m/s as gravity acceleration2；ρ lIs liquid density, Kg/m3；CDIs the drag coefficient of gas phase and liquid phase.
4. The method for calculating the critical liquid carrying flow considering the deformation of the liquid drop and the influence of multiple parameters according to claim 1, wherein the step of calculating the critical liquid carrying flow rate comprises the following steps: further, calculating gas density, gas viscosity and liquid density in the shaft according to the temperature and pressure of the gas well and the inner diameter of the shaft; then according to the density difference of the gas phase and the liquid phase, calculating the surface tension of the gas phase and the liquid phase by adopting a Liyuan equation; and finally setting an initial value of the critical liquid-carrying flow rate, and calculating the Reynolds number by combining the gas density and the gas viscosity.
5. The method for calculating the critical liquid carrying flow considering the deformation of liquid drops and the influence of multiple parameters is characterized in that the method for calculating the critical liquid carrying flow considering the influence of multiple parameters mainly comprises the following steps of calculating a drag coefficient and a friction coefficient considering the influence of temperature, pressure, the inner diameter of a shaft and a Reynolds number, calculating a gas-liquid two-phase drag coefficient according to a Shore expectation formula, calculating a gas-liquid two-phase friction coefficient based on an L ee formula, substituting the Reynolds number and the gas-liquid surface tension calculated in the method in claim 4 into a critical liquid carrying flow velocity expression obtained in the method in claim 3, establishing a critical liquid carrying flow calculation model considering multiple parameters through the conversion relation of the flow velocity and the flow of a gas well, calculating the critical liquid carrying flow velocity, taking the difference between the calculated critical liquid carrying flow velocity and the initial value of the critical liquid carrying flow velocity as a judgment condition of less than 0.0001m/s, if the difference is not, taking the calculated critical liquid carrying flow velocity as a new critical liquid carrying initial value, repeating iteration operation, and if the difference is yes, taking the calculated critical liquid carrying flow velocity as a continuous critical liquid carrying velocity as a minimum flow velocity of the gas well, and calculating the minimum carrying flow velocity through the corresponding gas;
the critical liquid carrying flow calculation model considering the deformation of the liquid drops and the influence of multiple parameters comprises the following steps:
in the formula (I), the compound is shown in the specification,v gis the critical liquid carrying flow velocity, m/s;σsurface tension, N/m;gtaking 9.8 m/s as gravity acceleration2；ρ lIs liquid density, Kg/m3；ρ gIs gas density, Kg/m3；f sgThe coefficient of friction resistance of gas-liquid two phases; cDThe drag coefficient of gas-liquid two phases;q ccritical liquid carrying flow rate of gas well, m3/d；AIs the cross-sectional area of the pipe, m2；pIs pressure, MPa;Zis the gas deviation coefficient;Tis the temperature, K.
6. The method for calculating the critical liquid carrying flow considering the liquid drop deformation and the multi-parameter influence according to claim 1, wherein after the critical liquid carrying flow is obtained by adopting the method for calculating the critical liquid carrying flow considering the liquid drop deformation and the multi-parameter influence according to claim 1, a critical liquid carrying flow chart of the gas well under different pressures and pipe diameters is established.
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