CN113139351B - Aggregation simulation method for atomized liquid drops in full well bore - Google Patents
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Abstract
The invention relates to a coalescence simulation method of atomized liquid drops in a full wellbore, belonging to the technical field of wellbore multiphase flow simulation and comprising the following steps: s1: acquiring initial flow parameters of atomized acid in a shaft based on an atomization generator experiment; s2: establishing a flowing coalescence model of the atomized acid in the shaft based on an Euler model and a group balance model; s3: dividing the shaft into n sections, wherein the length of each section is b meters, the width of each section is a meters, establishing a two-dimensional geometric model, and encrypting grids near the well wall. Inputting initial parameters into the front b meters of the shaft for calculation; s4: fitting the front b meters of outlet end parameters by using a user-defined function, compiling and inputting the parameters into a b-2 b well section, and extracting the inlet end parameters after calculation; s5: and repeating the step S4 until the whole shaft is calculated. And (5) completing the simulation of the flow coalescence of the atomized acid in the whole well bore through S1-S5, and performing post-treatment on the result. The method for continuously calculating in sections can simulate the particle size change and the distribution state of liquid drops in a shaft of thousands of meters.
Description
Technical Field
The invention relates to a coalescence simulation method of atomized liquid drops in a whole wellbore, belonging to the technical field of wellbore multiphase flow simulation.
Background
Many karst caves are often developed in fracture-cavity type oil reservoirs, and when conventional acids are used for acidification, a large amount of acid liquor is accumulated, so that the karst caves are expanded, and earthworms Kong Zhongzhi extend, so that the waste of the acid liquor is caused, and the expected transformation target is difficult to achieve. Atomized acid as a novel acidification process penetrates through rocks in a droplet state after being injected into a stratum, can effectively communicate discontinuous fracture-cavity reservoirs, and avoids acid waste. In order to achieve the acidification effect, the atomized acid is required to be in a gas-liquid dispersion state at the bottom of the well. After the acid liquor is atomized at the well head, the acid liquor flows in the shaft for a period of time, during which the liquid drops are coalesced, broken and adhered to the well wall, etc., so that the particle size and the liquid phase volume fraction of the acid liquor are changed when the atomized acid flows to the well bottom. Therefore, the flow process of the atomized acid in the whole wellbore is a main factor influencing the acidizing effect of the fracture-cavity oil reservoir.
Carbonate reservoirs are generally buried deep, and acid solution needs to flow through a shaft of several kilometers to reach the reservoir after being atomized at a well head. The flowing rule of atomized acid in a shaft with the length of thousands of meters cannot be simulated by a physical experiment method, and with the wide application of computer science, a numerical simulation technology is widely applied to the flowing simulation research in the shaft. By utilizing a numerical simulation technology, the flowing, coalescence and crushing rules of the fluid in the well bore can be effectively simulated. The Euler model can simulate the gas-liquid two-phase flow law of the atomized acid as a common model for simulating two-phase flow, but cannot simulate the size and distribution change of a dispersed phase, so that the aggregation and breakage of liquid drops in the flowing process of the atomized acid cannot be explained. A Population Balance Equation (PBE) is a general Equation describing the change of the size and distribution degree of a dispersed phase in a two-phase and multiphase flow system with time and space, can specifically describe the distribution of a discrete phase, and is the most widely applied mathematical model for researching the particle size distribution of droplets at present.
Because the diameter of the shaft is millimeter (68 mm) and the difference is very different from the well depth (4000 m) of several kilometers, the whole shaft is directly modeled, so that huge calculation grids need to be divided, the performance requirement on a computer is high, the divided grids are low in precision, and large errors exist in the calculation process. In order to accurately simulate the state of atomized acid reaching the bottom of a well after flowing through a shaft with the length of thousands of meters, two problems of long distance and simulation precision are solved at the same time. The segmented continuous calculation can be divided into a plurality of segments according to the requirements of simulation precision and time in principle, and a better simulation effect is achieved in the whole shaft simulation.
At present, most researchers mainly focus on an atomization generation stage and a droplet spraying stage, and the flow rule and the coalescence and breakage phenomenon of atomized acid in a long distance in a shaft are rarely reported. Therefore, aiming at the difficult problem of simulation of the long buried depth and the small hole diameter of the well bore, it is necessary to provide a modeling method which can be used for the whole well bore, and a simulation method which is used for the particle size change of atomized acid flowing in the well bore and accompanied with liquid drop coalescence and breakage and the like is constructed by fully utilizing an euler model, a population balance model and a User Defined Function (UDF).
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method which can accurately simulate the flow process of atomized acid in the whole shaft and can reflect the coalescence phenomenon of liquid drops. The simulation of the flow of atomized acid from a well head to a well bottom and the coalescence process of liquid drops is realized by utilizing a population balance model and an Euler-Euler multiphase flow model.
The technical scheme of the invention is as follows:
a simulation method for coalescence of atomized liquid drops in a full well bore comprises the following steps:
s1: through an atomization generator experiment, gas-liquid parameters corresponding to the optimal atomization rate under experimental conditions are obtained, wherein the gas-liquid parameters comprise gas inlet flow velocity v g Liquid inlet flow velocity v l Gas density ρ g Acid liquid density ρ l Volume ratio of gas to liquid V, injection speed V, viscosity of acid solution mu l Gas viscosity [ mu ] g Inlet temperature T, droplet diameter D, surface tension sigma, and injection pressure P 0 . Since the experiment of the atomization generator is a mature technology at the present stage, and the required parameters are only required to be obtained through the experiment, which is not the core content of the invention, the experiment of the atomization generator is not described again.
S2: based on the gas-liquid parameters in the S1, a flow model and a droplet size change model of the atomized acid in the shaft are given; after the acid liquid and the gas are atomized at the wellhead, the atomized acid is injected into a shaft, the atomized acid flows downwards in the shaft, the particle size of liquid drops is changed along with the phenomena of coalescence and crushing, and the phenomenon of adhesion to the wall of the shaft occurs; preferably, the model of the atomized acid in the wellbore consists essentially of the following governing equation:
(a) The euler model for the flow of atomized acid in the wellbore is:
in the formulae (1) and (2), subscript i is a gas phase or a liquid phase, t is time, α is a volume fraction, ρ is a density, v is a velocity, P is a partial pressure, F is a partial pressure g,l Is the alternate acting force between gas and liquid, g is the acceleration of gravity, mu g And mu l The viscosity of the gas phase and the liquid phase respectively is the parameter acid liquid viscosity mu obtained in the step S1 l Gas viscosity [ mu ] g ；
(b) The population balance equation used to describe droplet size distribution and variation is as follows:
in the formula (3), V is the volume of the droplet, V' is the volume before the size of the droplet is changed, n (V) is a function of the density of the droplet,
in terms of the rate of change of the volume of the droplets, a (V, V ') is the coalescence frequency of the droplets with volumes V and V ', δ (V) is the breaking frequency of the droplets, and β (V | V ') is the probability density function of the breaking of the droplets;
the formula (1) and the formula (2) are euler models and are used for describing the flowing of atomized acid in a shaft, and the formula (3) is a size change model of atomized acid liquid drops;
s3: dividing the actual shaft into a plurality of solution domains according to the size of the actual shaft, and solving in a segmented manner, wherein the diameter of the actual shaft is a meters, and the length of the actual shaft is B meters; dividing the length of a shaft into n sections, wherein each section is B meters long, B multiplied by n = B, establishing a two-dimensional geometric model with the width of a meter and the length of B meters, recording the first section as i =1, respectively setting parameters measured in the step S1 as inlet boundary conditions, namely setting gas inlet flow velocity, liquid inlet flow velocity, injection pressure, inlet temperature, liquid volume fraction and liquid droplet particle size during initial injection at an inlet end, setting gravity acceleration, gas-liquid interface surface tension, gas density, acid liquid density, gas viscosity and acid liquid viscosity in an integral simulation area, applying an Euler model and a liquid droplet size change model to the simulation area of the section i =1, solving the flow model and the liquid droplet size change model in the step S2 by using a finite element method, namely formulas (1) (2) (3) in the step S2, and obtaining the section of outlet end parameters, wherein the outlet end parameters comprise gas flow velocity, liquid volume fraction, liquid droplet particle size distribution and outlet pressure, and calculation of the shaft wall is finished because atomized acid has the characteristics of fast central velocity and slow velocity in the flow process of the shaft wall when the flow velocity reaches the outlet end;
s4: writing a code function by using a user-defined function (UDF) to process outlet end parameters obtained by S3, fitting a shaft diameter as an abscissa x and an outlet end parameter value y (such as liquid phase flow rate) as an ordinate into a functional relationship y = f (x) (usually a piecewise function), wherein the functions comprise a gas phase flow rate fitting function, a liquid phase volume fraction fitting function and a liquid droplet particle size distribution fitting function, and the y parameters are parameters to be obtained at an outlet end and comprise a gas-liquid flow rate, a liquid volume fraction and liquid droplet particle size distribution; compiling the fitted function, inputting the compiled function into the (i + 1) th section as an inlet boundary condition, and calculating the flow of the atomized acid in the well section; after the calculation is finished, similar to the step S3, extracting parameters of the outlet end of the well section, namely the gas flow rate, the liquid volume fraction and the liquid drop particle size distribution in the step S3;
s5: repeating the step S4 for iterative calculation, taking the outlet end parameter obtained in the previous section as input data of the next section of calculation domain, and continuing iterative calculation until the total length of the shaft is calculated, wherein i = n; the temperature and pressure in the actual wellbore can change along with the increase of the buried depth, but because the wellbore length in each selected calculation interval is shorter and the variation range of the temperature and the pressure is smaller, the environmental pressure and the environmental temperature are set to be constant in each calculation domain for simplifying the calculation.
The simulation of the flow coalescence of the atomized acid in the whole well bore is completed through S1-S5, an Euler flow model is combined with a liquid drop size change model, and the phenomena of flow, collision, coalescence crushing and the like of the atomized acid in the well bore are simulated; by adopting a segmented continuous calculation mode, the complete simulation of the whole shaft can be realized, the grid quality can be ensured, and the accuracy of a simulation result can be ensured.
Preferably, in step S3, the segmentation range should be determined according to the length of the wellbore, and considering the limitation of the borehole diameter, for the simulation of a deeper wellbore, each segment of the calculation domain should not exceed 500 meters, and the finer the segmentation is, the higher the accuracy of the simulation result is.
The invention has the beneficial effects that:
1. the traditional multiphase flow research focuses on dividing the flow pattern and the flow state of gas-liquid two-phase flow in a shaft, and the particle size distribution of liquid drops is an important factor for determining whether atomized acid can achieve the expected acidification effect. The invention combines the Euler model and the population balance model to simulate the atomized acid flow and the liquid drop coalescence process in the shaft, realizes the simulation of the gas-liquid two-phase flow process and the liquid drop size change, and can obtain the change of macroscopic parameters (gas-liquid flow rate) and the microscopic phenomenon (liquid drop particle size).
2. The flow coalescence simulation method for the atomized liquid drops in the long shaft, which is provided by the invention, can simulate parameters such as a flow state and liquid drop particle size distribution when atomized acid flows to the bottom of the shaft, and can obtain a simulation result of each section of calculation domain, so that the continuity of the calculation result can be conveniently verified; the calculation domains are divided as required, so that the calculation precision can be greatly improved, the accuracy of a simulation result is ensured, and the simulation device is flexible and is convenient to adjust the simulation range in time.
Drawings
FIG. 1 is a technical flow chart of the present invention.
FIG. 2 is a cloud plot of the particle size distribution at the exit end of a 500m well bore in example 1.
Fig. 3 a-3 c are the parameter distributions at the outlet end of a 500m well bore in example 1, fig. 3a is the gas-liquid flow velocity distribution, fig. 3b is the liquid phase volume fraction distribution, and fig. 3c is the droplet size distribution.
Fig. 4 a-4 b are sectional continuously calculated wellbore droplet size distributions in example 1, 500 meters is taken as one section, and gas and liquid flow velocity change curves in a wellbore with the total length of 4000 meters are calculated, wherein fig. 4a is a gas and liquid flow velocity change curve, and fig. 4b is a liquid and liquid flow velocity change curve.
Fig. 5 is a graph of the variation of the distribution of the particle sizes of wellbore droplets calculated in a stepwise continuous manner in example 1.
Detailed Description
The present invention will be further described by way of examples, but not limited thereto, with reference to the accompanying drawings.
Example 1:
a simulation method for coalescence of atomized liquid drops in a full well bore comprises the following steps:
s1: obtaining gas-liquid parameters corresponding to the optimal atomization rate under experimental conditions through an atomization generator experiment, wherein the gas-liquid parameters comprise gas inlet flow velocity v g Liquid inlet flow velocity v l Gas-liquid volume ratio V, gas density ρ g Acid liquid density ρ l Gas viscosity [ mu ] g Viscosity of acid solution mu l Injection pressure P 0 Inlet temperature T, droplet size D, surface tension σ. Parameters optimized by experiments are used as initial conditions of numerical simulation, and specific parameters are shown in table 1.
Table 1 parameter setting table
S2: based on the gas-liquid parameters in the S1, a flow model and a droplet size change model of the atomized acid in the shaft are given; after the acid liquid and the gas are atomized at the well head, the atomized acid liquid is injected into the shaft, and the atomized acid flows downwards in the shaft, and the particle size of the liquid drops is changed or the liquid drops are attached to the wall of the well along with the phenomena of coalescence, crushing and the like. The flow model of the atomized acid in the wellbore essentially comprises the following governing equation:
(a) The euler model of the flow of atomized acid in the wellbore is:
in the formulae (1) and (2), the subscript i is a gas phase or a liquid phase, t is time, α is a volume fraction, ρ is a density, v is a velocity, P is a partial pressure, F is a partial pressure g,l Is the alternate acting force between gas and liquid, g is the acceleration of gravity, mu g And mu l The viscosity of the gas phase and the liquid phase respectively;
(b) The population balance equation used to describe droplet size distribution and variation is:
in the formula (3), V is the volume of the droplet, V' is the volume before the size of the droplet is changed, n (V) is a function of the density of the droplet,
in terms of the rate of change of the volume of the droplets, a (V, V ') is the coalescence frequency of the droplets with volumes V and V ', δ (V) is the breakage frequency of the droplets, and β (V | V ') is a probability density function of breakage of the droplets; the contents of the functions are well known in the art.
The Euler model is given in the formula (1) and (2) for describing the flow of the atomized acid in the shaft, and the atomized acid drop size change model is given in the formula (3).
Initial conditions are shown in table 1, as the atomized acid has turbulence in the shaft, a widely-applied readable k-epsilon turbulence model is adopted for solving, the step S2 is a model for simulating the flow of the atomized acid in the shaft and the particle size distribution state of droplets, namely an Euler model and a group balance model, namely a mathematical model used in the subsequent step S3, and the solved result is that the simulation of the flow of the atomized acid in the shaft and the particle size distribution state of the droplets in a simulation area in the following description is completed, so that outlet end parameters are obtained. The Realizable k-epsilon turbulence model is a method for solving a flow model, namely an Euler model, and is a mature method.
S3: and (3) dividing the solution into a plurality of solution domains according to the actual wellbore size (assuming that the diameter is 0.068 m and the well depth is 4000 m) and carrying out sectional solution. The length of a shaft is divided into 8 sections, each section is 500 meters long, a two-dimensional geometric model with the width of 0.068 meter and the length of 500 meters is established, liquid drops are easy to adhere to the shaft wall and stop flowing, therefore, the encryption processing is carried out near the shaft wall when the meshes are divided, the encryption degree of the meshes is different according to the difference of computer performance, and the encryption means that the meshes near the shaft wall are denser compared with uniform meshes. Here, the calculation procedure will be described by taking a calculation domain with a length of 500 meters as an example, and the calculation domain should be reduced as much as possible in the actual simulation. Setting inlet boundary conditions according to the parameters measured in S1, setting gas inlet flow rate, liquid inlet flow rate, injection pressure, inlet temperature, liquid volume fraction and liquid droplet particle size at initial injection at the inlet end, and assuming that the gas volume is V g Volume of liquid is V l When the gas-liquid volume ratio V is V g /V l Volume fraction of liquid is V l /(V l +V g ) And setting gravity acceleration, gas-liquid interface surface tension, gas density, acid liquid density, gas viscosity and acid liquid viscosity on the whole simulation area, and applying an Euler model and a droplet size change model to the simulation area. And (3) obtaining the section of outlet end parameters by using the mathematical model in the step (S2), wherein the outlet end parameters comprise gas flow rate, liquid volume fraction, droplet particle size distribution and outlet pressure, and the outlet pressure is in an obtained range, but the flowing state of the atomized acid in the shaft is mainly analyzed by the gas-liquid flow rate, the liquid volume fraction and the droplet particle size, and the relation with the pressure is not large, so that the pressure is not analyzed. Because the atomized acid has the characteristics of high central speed of a shaft and low speed of a shaft wall in the flowing process, the atomized acid can flow along the shaft wall when the shaft wall is in a smooth stateThis period is considered complete when the nearby atomized acid flows to the outlet end. Because the aspect ratio of the calculation domain is too large, the overall presentation effect is not good, and here, only the particle size distribution cloud chart (fig. 2) at the outlet end is intercepted as a display, and the main parameters at the outlet end are obtained: the gas-liquid flow rate, the liquid phase volume fraction, and the droplet diameter are shown in fig. 3a, 3b, and 3 c.
S4: and constructing a User Defined Function (UDF) by using the exit end parameters obtained in the S3, wherein the function comprises the following steps:
gas phase flow rate fitting function:
liquid phase flow rate fitting function:
liquid phase volume fraction fitting function:
droplet size distribution fitting function:
where x is the wellbore diameter location coordinate. Compiling a user-defined function, inputting the compiled function into a 500-1000 m well section as an entrance boundary condition, and simulating the flow of atomized acid in the 500-1000 m well section. After the calculation is finished, similar to the step S3, the outlet end data of the 500-100 meter well section is extracted.
S5: and repeating the step S4 to continue iterative computation, compiling the outlet end data obtained from the previous section as input data of the next section of computation domain, and continuing iterative computation until the total computation length reaches 4000 meters. Because the influence of the heat transfer process is not considered in the simulation, the set environment temperature is unchanged in the calculation process, but the pressure change can influence parameters such as flow rate, gas compressibility and the like, and the pressure setting of the shaft is consistent with the pressure when the calculation of the previous section of shaft is completed.
The simulation of the flowing process of the atomized acid in the whole shaft is completed through S1-S5, and the Euler flowing model is combined with the liquid drop size change model, so that the simulation of phenomena of flowing, collision, coalescence, crushing and the like of the atomized acid in the shaft is realized. The flow rate gradually decreases due to friction or other resistance of the atomized acid in the wellbore, as shown in fig. 4a and 4 b. Because the particle size of the droplets is an important index for considering whether the acidification effect can be realized when the atomized acid reaches the bottom of the well, the change of the particle size of the droplets is of great concern. The variation and distribution of droplet size throughout the wellbore is shown in figure 5.
The atomized acid is influenced by the factors of drop gravity, gas-liquid surface tension, resistance and the like in the flowing process, and the speed is attenuated. And the difference of gas-liquid properties causes the flow velocity decay rate of the two to be different. The liquid drops are easy to coalesce in the flowing process, the liquid drops near the well wall are easy to adhere to the well wall, and the speed of the liquid drops is quickly reduced. The atomized acid continuously collides with liquid drops in the flowing process to generate coalescence, wherein the flow velocity of the liquid drops in the center of a shaft is the highest, the collision probability is the highest, and the particle size of the liquid drops is the largest; and after the liquid drops are attached to the well wall, the flow velocity is slow and even reduced to zero, so that the particle size coalescence degree of the liquid drops near the well wall is lower. From the gas-liquid flow rate and the droplet size in fig. 4a, 4b and 5, the atomized acid still maintains a high flow rate when flowing to the bottom of the well, and the particle size distribution is between 0.5 and 3mm, which shows that the droplet coalescence degree is not high at the bottom of the well, and the atomized acid can continuously enter the reservoir in a gas-liquid entrained state to be acidified.
The technical feasibility of the atomized acid acidification scheme is further verified through the implementation case. The method is suitable for flow simulation with large calculation domain length-width ratio under large scale, can not only realize the simulation with the same size and truly restore the flow process in the shaft, but also can compare with the previous section result and find errors in time, thereby avoiding the waste of overlong operation time due to parameter setting errors.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.
Claims (2)
1. A coalescence simulation method for atomized liquid drops in a full well bore is characterized by comprising the following steps:
s1: obtaining gas-liquid parameters corresponding to the optimal atomization rate under experimental conditions through an atomization generator experiment, wherein the gas-liquid parameters comprise gas inlet flow velocity v g Liquid inlet flow velocity v l Gas density ρ g Acid liquid density ρ l Volume ratio of gas to liquid V, injection speed V, viscosity of acid solution mu l Gas viscosity [ mu ] g Inlet temperature T, droplet diameter D, surface tension sigma, and injection pressure P 0 ；
S2: based on the gas-liquid parameters in the S1, giving a flow model and a droplet size change model of the atomized acid in the shaft; after the acid liquid and the gas are atomized at the wellhead, the atomized acid is injected into a shaft, the atomized acid flows downwards in the shaft, the particle size of liquid drops is changed along with the phenomena of coalescence and crushing, and the phenomenon of adhesion to the wall of the shaft occurs;
the model of atomized acid in the wellbore includes the following governing equation:
(a) The euler model for the flow of atomized acid in the wellbore is:
in the formulae (1) and (2), the subscript i is a gas phase or a liquid phase, t is time, α is a volume fraction, ρ is a density, v is a velocity, and P is a local regionPressure, F g,l Is the alternate acting force between gas and liquid, g is the acceleration of gravity, mu g And mu l The viscosity of the gas phase and the liquid phase respectively;
(b) The population balance equation used to describe droplet size distribution and variation is as follows:
in the formula (3), V is the volume of the droplet, V' is the volume before the size of the droplet is changed, n (V) is a function of the density of the droplet,
in terms of the rate of change of the volume of the droplets, a (V, V ') is the coalescence frequency of the droplets with volumes V and V ', δ (V) is the breaking frequency of the droplets, and β (V | V ') is the probability density function of the breaking of the droplets;
the formula (1) and the formula (2) are euler models and are used for describing the flowing of atomized acid in a shaft, and the formula (3) is a size change model of atomized acid liquid drops;
s3: dividing the actual shaft into a plurality of solution domains according to the size of the actual shaft, and solving in a segmented manner, wherein the diameter of the actual shaft is a meters, and the length of the actual shaft is B meters; dividing the length of a shaft into n sections, wherein each section is B meters long, B × n = B, establishing a two-dimensional geometric model with the width of a meter and the length of B meters, recording the first section as i =1, setting parameters measured in the step S1 as inlet boundary conditions respectively, namely setting gas inlet flow velocity, liquid inlet flow velocity, injection pressure, inlet temperature, liquid volume fraction and liquid drop particle size during initial injection at an inlet end, setting gravity acceleration, gas-liquid interface surface tension, gas density, acid liquid density, gas viscosity and acid liquid viscosity on a simulation area, applying an Euler model and a liquid drop size change model on the i =1 section of the simulation area, and obtaining outlet end parameters of the section by utilizing the flow model and the liquid drop size change model in the step S2, wherein the outlet end parameters comprise gas flow velocity, liquid volume fraction, liquid drop particle size distribution and outlet pressure, and determining that the calculation is completed when the flow velocity at the shaft wall reaches the outlet end;
s4: writing a code function by using a user-defined function to process the outlet end parameters obtained in the S3, fitting the diameter of the shaft as an abscissa x and the outlet end parameter value y as an ordinate to obtain a functional relation y = f (x), wherein the functions comprise a gas phase flow rate fitting function, a liquid phase volume fraction fitting function and a liquid droplet particle size distribution fitting function, and the y parameters are parameters to be obtained at the outlet end and comprise a gas-liquid flow rate, a liquid volume fraction and liquid droplet particle size distribution; compiling the fitted function, inputting the compiled function into the (i + 1) th section as an inlet boundary condition, and calculating the flow of the atomized acid in the well section; after the calculation is finished, extracting the outlet end parameter of the well section;
the user-defined functions include:
gas phase flow rate fitting function:
liquid phase flow rate fitting function:
liquid phase volume fraction fitting function:
droplet size distribution fitting function:
s5: repeating the step S4 for iterative calculation, taking the outlet end parameter obtained in the previous section as input data of the next section of calculation domain, and continuing iterative calculation until the total length of the shaft is calculated, wherein i = n; the ambient pressure and ambient temperature are set constant within each calculation domain.
2. The method of simulating coalescence of atomized droplets within a full wellbore of claim 1, wherein in step S3, each segment of the computational domain does not exceed 500 meters.
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| CN104847314A (en) * | 2015-06-08 | 2015-08-19 | 四川大学 | High-temperature high-pressure oil and gas vertical-well single-phase flow perforation well completion parameter optimization method |
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| CN113139351A (en) | 2021-07-20 |
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