Method for determining bottom-hole flowing pressure of high-sulfur gas well, storage medium and computer device

Abstract

The present invention discloses a method for determining the bottom-hole flowing pressure of a high-sulfur gas well, a storage medium and a computer device. The method includes: segmenting the high-sulfur gas well borehole according to the sulfur phase state distribution along the high-sulfur gas well borehole; for each section of the well borehole, segmenting the well borehole with a preset length as a unit to obtain a plurality of well borehole units; calculating the physical property parameters of the fluid mixture in each well borehole unit; calculating the actual pressure gradient of each well borehole unit according to the physical property parameters of the fluid mixture in each well borehole unit; adjusting the preset initial value of the pressure gradient based on the difference between the actual pressure gradient and the preset initial value of the pressure gradient; calculating the pressure value at each depth point along the well borehole according to the adjusted pressure gradient. The present invention can consider the influence of the sulfur phase presence and sulfur phase change when calculating the bottom-hole pressure of a high-sulfur gas well, making the calculation result of the high-sulfur gas well more accurate.

Description

Technical Field

[0001] The present invention belongs to the technical field of gas production engineering applications, and particularly relates to a method for determining the bottom-hole flowing pressure of a high-sulfur gas well, a storage medium, and a computer device. Background Art

[0002] At present, there are many pressure drop models considering multiphase flow for calculating the bottom-hole flowing pressure of gas wells, but each method has its own applicability and limitations.

[0003] These models can be classified according to whether the flow pattern is considered. Among them, the typical model that does not consider the flow pattern is the Hagedorn-Brown method. This method is based on the slippage of gas-liquid two-phase flow, and based on the conservation laws of single-phase fluid and mechanical energy, the liquid holdup is calculated by back-calculating a large amount of field test data to form a pressure drop relationship formula for two-phase vertical upward pipe flow applicable to various flow patterns. This method is applicable to vertical and approximately vertical oil wells, gas wells, or condensate oil and gas wells, and is the most accurate when the inclination angle is greater than 70°, and is particularly suitable for the flow calculation of gas wells producing water. The models considering the flow pattern include the Beggs-Brill method, the Duns-Ros method, the Oriszewski method, the Mukherjee-Brill method, etc. Among them, the Beggs-Brill method is based on a large number of experiments with water and air in inclined transparent pipes with diameters of 25.4 mm, 38.1 mm, and a length of 27.4 m, and then the relevant laws of liquid holdup and resistance coefficient of gas-liquid two-phase flow in different inclined pipes are obtained. This method is applicable to vertical wells, deviated wells, and horizontal wells, as well as pipelines with any inclination angle; the Duns-Ros method is based on about 4,000 gas-liquid two-phase pipe flow experiments in a 10-m long vertical pipe in the laboratory, obtaining about 20,000 data points, and summarizing to obtain a flow pattern distribution diagram, and giving the basic equation of the pressure drop model in the form of total pressure drop. This method is applicable to vertical and highly inclined oil wells, vertical gas wells, and condensate oil and gas wells, and is also suitable for oil pipelines, gas pipelines, and condensate oil and gas pipelines. The Oriszewski method is to apply the measured data of 148 oil wells, compare and analyze multiple gas-liquid two-phase flow calculation methods, and then analyze the advantages of different flow patterns, and combine other research results to obtain a pressure drop calculation method for 4 flow patterns. This method is applicable to vertical and approximately vertical oil wells, gas wells, or condensate oil and gas wells; the Mukherjee-Brill method is to determine approximate values of parameters such as liquid holdup and friction coefficient of two-phase flow in inclined (vertical, horizontal) pipes through a large number of experimental studies, using methods such as correlation analysis and dimensional analysis to improve the accuracy of pressure calculation. This method is applicable to directional wells and pressure calculation of two-phase flow in undulating pipes.

[0004] There is little research on the bottom-hole pressure calculation method applicable to high-sulfur gas wells considering the existence of sulfur phases. For example, based on the heat transfer theory and the gas-solid two-phase flow theory, a new model for calculating the temperature and pressure distribution in the wellbore considering the precipitation of sulfur particles in the wellbore is established. This model can be used for the calculation and analysis of the temperature and pressure distribution in the wellbore of high-sulfur gas wells and the volume of precipitated sulfur particles, but it does not consider the influence of water and the phase change of sulfur along the wellbore on the pressure calculation. For example, a mathematical model of gas-liquid-solid multiphase flow and heat transfer in the wellbore of high-sulfur gas wells is established, and a calculation method for sulfur precipitation with multi-field coupling is given. This model considers multi-phase conditions such as sulfur crystal particles, condensate oil, and water existing in the wellbore, and obtains the temperature and pressure field distribution and sulfur precipitation characteristics inside the wellbore by establishing and solving the multi-phase flow and heat transfer model in the wellbore and combining with the sulfur precipitation model. Since the wellbore flow process involves multiple phases, the calculation accuracy of the cross-sectional occupancy rate of each phase in the wellbore seriously affects the calculation accuracy. This model does not clearly describe the calculation process of the cross-sectional liquid holdup. In addition, sulfur can exist in the wellbore in solid and liquid forms, and the treatment measures for sulfur in the wellbore are different under different phase states. This model can judge the sulfur precipitation position, but does not give the distribution of liquid sulfur and solid sulfur in the wellbore.

[0005] To sum up, first, the existing pressure drop calculation methods mainly establish pressure drop calculation models for gas-liquid two-phase flow in conventional gas well production, without considering the existence of liquid sulfur and solid sulfur; second, the existing multi-phase flow calculation methods do not consider the influence of the liquid sulfur phase and oil phase in the phase distribution of sulfur along the wellbore on the wellbore pressure drop and bottom-hole pressure.

[0006] There is an urgent need for a method, storage medium, and computer device for determining the bottom-hole flowing pressure of high-sulfur gas wells. Summary of the Invention

[0007] In view of the above problems, the present invention provides a method, storage medium, and computer device for determining the bottom-hole flowing pressure of high-sulfur gas wells.

[0008] In a first aspect, the present invention provides a method for determining the bottom-hole flowing pressure of a high-sulfur gas well, including the following steps:

[0009] Segment the wellbore of the high-sulfur gas well according to the sulfur phase distribution along the wellbore of the high-sulfur gas well;

[0010] For each section of the wellbore, perform the following steps:

[0011] Further segment the wellbore with a preset length as a unit to obtain a plurality of wellbore units;

[0012] Based on the temperature distribution in the wellbore of the high-sulfur gas well and the initial value of the preset pressure gradient, calculate the physical property parameters of the fluid mixture in each wellbore unit;

[0013] Calculate the actual pressure gradient of each wellbore unit according to the physical property parameters of the fluid mixture in each wellbore unit;

[0014] Adjust the initial value of the preset pressure gradient based on the difference between the actual pressure gradient and the initial value of the preset pressure gradient until the difference between the actual pressure gradient and the initial value of the preset pressure gradient for each wellbore unit is less than the preset threshold;

[0015] Calculate the pressure value at each depth point along the wellbore according to the adjusted pressure gradient.

[0016] According to an embodiment of the present invention, preferably, the sulfur phase state distribution along the wellbore of the high-sulfur gas well is obtained through the following steps:

[0017] Calculate the temperature field distribution along the wellbore of the high-sulfur gas well;

[0018] Based on the temperature field distribution along the wellbore of the high-sulfur gas well and the sulfur phase discrimination model, determine the sulfur phase state distribution along the wellbore.

[0019] According to an embodiment of the present invention, preferably, the temperature field distribution along the wellbore of the high-sulfur gas well is calculated through the following expression:

[0020]

[0021] where, T i is the temperature along the wellbore, K; z is the well depth, m; p i is the pressure along the wellbore, Pa; T e is the outside well environment temperature, K; λ e is the formation thermal conductivity, W / (m·K); f m is the friction factor, dimensionless; C Jm is the constant pressure specific heat capacity of the mixed fluid, J / (kg·K); C pm is the Joule-Thomson coefficient, dimensionless; f(t) is a function reflecting the unsteady characteristics of the formation; r t is the tubing radius, m; U a is the total heat transfer coefficient, W / (m·K); v m is the mixed fluid velocity, m / s; g is the acceleration of gravity, m / s 2 ; α is the well deviation angle, (°).

[0022] According to an embodiment of the present invention, preferably, based on the temperature field distribution along the wellbore of the high-sulfur gas well and the sulfur phase discrimination model, determining the sulfur phase state distribution along the wellbore includes:

[0023] Determine the sulfur precipitation position in the wellbore of the high-sulfur gas well according to the sulfur solubility model;

[0024] Determine the sulfur precipitation well section in the wellbore of the high-sulfur gas well through the sulfur precipitation position in the wellbore of the high-sulfur gas well;

[0025] Determine the sulfur phase distribution in the sulfur precipitation well section according to the melting point temperature curve of elemental sulfur.

[0026] According to an embodiment of the present invention, preferably, the sulfur solubility model is:

[0027]

[0028] where C s is the solubility of sulfur, g / m 3 ; ρ g is the density of natural gas, kg / m 3 ; T is the temperature in the wellbore, K.

[0029] According to an embodiment of the present invention, preferably, based on the wellbore temperature distribution of a high-sulfur gas well and a preset initial pressure gradient, calculate the physical property parameters of the fluid mixture in each wellbore unit, including:

[0030] Calculate the flow velocity of the fluid mixture in each wellbore unit through the following expression:

[0031] v m = v sl + v sg + v ss

[0032] where v m is the flow velocity of the fluid mixture, m / s; v sg , v sl , v ss are the apparent flow velocities of the liquid phase, gas phase, and solid phase respectively, m / s,

[0033] Calculate the density of the fluid mixture in each wellbore unit through the following expression:

[0034] ρ m = ρ l H l + ρ s H s + ρ g (1 - H l - H s )

[0035] where ρ m is the density of the fluid mixture, kg / m 3 ; ρ g , ρ l , ρ s are the densities of the gas phase, liquid phase, and solid phase respectively, kg / m 3 ; H l is the liquid holdup, dimensionless; H s is the cross-sectional occupancy of the solid phase, dimensionless.

[0036] According to an embodiment of the present invention, preferably, the liquid holdup is calculated through the following steps:

[0037] Calculate the liquid-phase velocity number N vl and the gas-phase velocity number N gv under flowing conditions, the liquid viscosity number N l and the pipe diameter number N D ;

[0038] Based on the N l ~CN l relationship curve, determine the value of CN l according to N l ;

[0039] Based on the relationship curve, determine the value of ;

[0040] Based on the relationship curve, determine the value of ;

[0041] According to the value of and the value of , calculate the value of H l .

[0042] According to an embodiment of the present invention, preferably, the actual pressure gradient of each wellbore unit is calculated according to the physical property parameters of the fluid mixture in each wellbore unit through the following expression:

[0043]

[0044] where P i is the pressure along the wellbore, Pa; z is the well depth, m; ρ m is the density of the fluid mixture, kg / m 3 ; v m is the flow velocity of the fluid mixture, m / s; g is the acceleration due to gravity, m / s 2 ; α is the well deviation angle, (°); f m is the friction factor, dimensionless; d is the inner diameter of the tubing, m.

[0045] According to an embodiment of the present invention, preferably, calculating the pressure value at each depth point along the wellbore according to the adjusted pressure gradient includes:

[0046] Draw a relationship curve between the wellbore depth and the pressure according to the preset initial value of the pressure gradient by interpolation.

[0047] In a second aspect, the present invention provides a storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above method for determining the bottom-hole flowing pressure of a high-sulfur gas well are implemented.

[0048] In a third aspect, the present invention provides a controller, which includes a memory and a processor. A computer program is stored on the memory, and when the computer program is executed by the processor, the steps of the above-described method for determining the bottom-hole flowing pressure of a high-sulfur gas well are implemented.

[0049] Compared with the prior art, one or more embodiments of the above solution may have the following advantages or beneficial effects:

[0050] Applying the method for determining the bottom-hole flowing pressure of a high-sulfur gas well of the present invention, the high-sulfur gas wellbore is segmented according to the sulfur phase state distribution along the wellbore of the high-sulfur gas well; for each section of the wellbore, the following steps are executed: taking a preset length as a unit, further segmenting the wellbore to obtain a plurality of wellbore units; based on the wellbore temperature distribution of the high-sulfur gas well and a preset initial value of the pressure gradient, calculating the physical property parameters of the gas-water-sulfur three-phase fluid mixture in each wellbore unit; calculating the actual pressure gradient of each wellbore unit according to the physical property parameters of the fluid mixture in each wellbore unit; based on the difference between the actual pressure gradient and the preset initial value of the pressure gradient, adjusting the preset initial value of the pressure gradient until the difference between the actual pressure gradient and the preset initial value of the pressure gradient in each wellbore unit is less than a preset threshold; calculating the pressure value at each depth point along the wellbore according to the adjusted pressure gradient. The present invention can consider the influence of the simultaneous presence of gas-water-sulfur three phases and sulfur phase change when calculating the bottom-hole pressure of a high-sulfur gas well, making the calculation result of the high-sulfur gas well more accurate.

[0051] Other features and advantages of the present invention will be described in the following specification, and will be partially apparent from the specification, or will be understood by implementing the present invention. The objectives and other advantages of the present invention can be realized and obtained through the structures specifically pointed out in the specification, claims, and drawings. Description of the Drawings

[0052] The drawings are used to provide further understanding of the present invention, and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0053] Figure 1 Shows the flow chart of the method for determining the bottom-hole flowing pressure of a high-sulfur gas well in Embodiment 1 of the present invention;

[0054] Figure 2 Shows the melting point temperature of elemental sulfur in different pressures and gas components in Embodiment 1 of the present invention;

[0055] Figure 3 Shows the sulfur phase state distribution diagram in the wellbore in Embodiment 1 of the present invention;

[0056] Figure 4The flowchart of the bottom-hole flowing pressure determination method for high-sulfur gas wells in the second embodiment of the present invention is shown;

[0057] Figure 5 The Nl-CNl relationship diagram for calculating the liquid holdup in the second embodiment of the present invention is shown;

[0058] Figure 6 The calculation of the liquid holdup in the second embodiment of the present invention is shown Relationship diagram;

[0059] Figure 7 The second embodiment of the present invention is shown Relationship diagram;

[0060] Figure 8 The wellbore temperature distribution diagram calculated by the multiphase flow model in the second embodiment of the present invention is shown;

[0061] Figure 9 The input steps of the gas well pressure calculation parameters in the third embodiment of the present invention are shown;

[0062] Figure 10 The wellbore pressure distribution diagram of the gas well in the third embodiment of the present invention is shown;

[0063] Figure 11 The wellbore temperature distribution diagram of the gas well in the third embodiment of the present invention is shown. Specific implementation manners

[0064] The following will combine the drawings and embodiments to detail the implementation manners of the present invention, so as to fully understand how the present invention uses technical means to solve technical problems and the implementation process of achieving technical effects and implement accordingly. It should be noted that as long as there is no conflict, the various embodiments in the present invention and the various features in each embodiment can be combined with each other, and the formed technical solutions are all within the protection scope of the present invention.

[0065] Since the production output in high-sulfur gas wells is mainly natural gas during the production process, but water, oil, and sulfur are also produced, the wellbore pressure drop calculations under single-phase flow and gas-liquid two-phase flow conditions will not be applicable to the multiphase flow conditions of high-sulfur gas wells. In addition, the phase state of sulfur will change with the wellbore temperature, and the influence degrees of the flow of liquid sulfur and solid sulfur on the wellbore pressure drop calculation are also different. It is necessary to describe the sulfur phase state distribution characteristics along the wellbore under different production conditions. Therefore, the present invention combines the wellbore multiphase flow pressure drop calculation method and the sulfur phase discrimination model to provide a bottom-hole flowing pressure calculation method suitable for high-sulfur gas wells.

[0066] Embodiment 1

[0067] To solve the above technical problems existing in the prior art, the embodiment of the present invention provides a method for determining the bottom-hole flowing pressure of high-sulfur gas wells.

[0068] Reference Figure 1 , the bottom-hole flowing pressure determination method for high-sulfur gas wells in this embodiment includes the following steps:

[0069] S11, segment the high-sulfur gas wellbore according to the sulfur phase distribution along the wellbore of the high-sulfur gas well;

[0070] S12, for each section of the wellbore, further segment the wellbore with a preset length as a unit to obtain a plurality of wellbore units;

[0071] S13, based on the temperature distribution along the high-sulfur gas wellbore and the preset initial pressure gradient, calculate the physical property parameters of the fluid mixture in each wellbore unit;

[0072] S14, calculate the actual pressure gradient of each wellbore unit according to the physical property parameters of the fluid mixture in each wellbore unit;

[0073] S15, calculate the difference between the actual pressure gradient and the preset initial pressure gradient;

[0074] S16, determine whether the difference between the actual pressure gradient of each wellbore unit and the preset initial pressure gradient is less than a preset threshold:

[0075] If so, execute step S17;

[0076] If not, execute step S18;

[0077] S17, calculate the pressure value at each depth point along the wellbore according to the adjusted pressure gradient;

[0078] S18, adjust the preset initial pressure gradient, and return the adjusted pressure gradient as the initial pressure gradient to step S13.

[0079] In step S11, the sulfur phase distribution along the high-sulfur gas wellbore is obtained through the following steps:

[0080] Calculate the temperature field distribution along the high-sulfur gas wellbore;

[0081] Based on the temperature field distribution along the high-sulfur gas wellbore and the sulfur phase discrimination model, determine the sulfur phase distribution along the wellbore.

[0082] In this embodiment, the temperature field distribution along the high-sulfur gas wellbore is calculated through the following expression:

[0083]

[0084] Among them, T i is the temperature along the wellbore, K; z is the well depth, m; p i is the pressure along the wellbore, Pa; Te is the temperature of the external environment of the well, in K; λ e is the formation thermal conductivity, in W / (m·K); f m is the friction factor, dimensionless; C Jm is the constant-pressure specific heat capacity of the mixed fluid, in J / (kg·K); C pm is the Joule-Thomson coefficient, dimensionless; f(t) is a function reflecting the unsteady characteristics of the formation; r t is the tubing radius, in m; U a is the overall heat transfer coefficient, in W / (m·K); v m is the flow velocity of the mixed fluid, in m / s; g is the acceleration due to gravity, in m / s 2 ; α is the well deviation angle, in (°).

[0085] Since elemental sulfur in natural gas from high-sulfur gas reservoirs exists in gaseous form in natural gas, with the decrease of pressure and temperature and the change of other conditions, the gaseous elemental sulfur will undergo a phase change. The decrease of pressure will lead to the decrease of the solubility of natural gas in sulfur, the decrease of the solubility of elemental sulfur, the formation of supersaturation and precipitation, and the gaseous elemental sulfur will turn into liquid or solid. If the temperature is lower than the melting point temperature of sulfur, the supercooled sulfur vapor will directly turn into solid state. Therefore, in this embodiment, based on the temperature field distribution along the wellbore of high-sulfur gas wells and the sulfur phase discrimination model, the sulfur phase distribution along the wellbore is determined, including:

[0086] As Figure 2 shown, the precipitation position of sulfur in the wellbore of high-sulfur gas wells is determined according to the sulfur solubility model;

[0087] The sulfur precipitation section in the wellbore of high-sulfur gas wells is determined through the precipitation position of sulfur in the wellbore of high-sulfur gas wells;

[0088] According to the elemental sulfur melting point temperature curve as Figure 3 shown, the sulfur phase distribution in the sulfur precipitation section is determined.

[0089] In this embodiment, the sulfur solubility model is:

[0090]

[0091] where C s is the solubility of sulfur, in g / m 3 ; ρ g is the density of natural gas, in kg / m 3 ; T is the temperature in the wellbore, in K.

[0092] The method for determining the bottom-hole flowing pressure of high-sulfur gas wells in the embodiments of the present invention comprehensively considers the influence of phase changes and improves the calculation method of the liquid holdup, and can accurately calculate the bottom-hole flowing pressure of high-sulfur gas wells.

[0093] Embodiment 2

[0094] To solve the above technical problems existing in the prior art, an embodiment of the present invention provides a method for determining the bottom-hole flowing pressure of a high-sulfur gas well based on Embodiment 1. In this embodiment, the physical property parameters of the fluid mixture in each wellbore unit include the density and flow rate of the mixture. This embodiment improves step S17 of Embodiment 1.

[0095] Refer to Figure 4 , the method for determining the bottom-hole flowing pressure of a high-sulfur gas well in this embodiment includes the following steps:

[0096] S21, segment the high-sulfur gas wellbore according to the sulfur phase state distribution along the wellbore of the high-sulfur gas well;

[0097] S22, for each segment of the wellbore, further segment the wellbore with a preset length as a unit to obtain a plurality of wellbore units;

[0098] S23, based on the wellbore temperature distribution of the high-sulfur gas well and a preset initial pressure gradient value, calculate the density and flow rate of the fluid mixture in each wellbore unit;

[0099] S24, calculate the actual pressure gradient of each wellbore unit according to the density and flow rate of the fluid mixture in each wellbore unit;

[0100] S25, calculate the difference between the actual pressure gradient and the preset initial pressure gradient value;

[0101] S26, determine whether the difference between the actual pressure gradient and the preset initial pressure gradient value of each wellbore unit is less than a preset threshold:

[0102] If so, execute step S27;

[0103] If not, execute step S28;

[0104] S27, through interpolation, draw a relationship curve between wellbore depth and pressure according to the preset initial pressure gradient value;

[0105] S28, adjust the preset initial pressure gradient value, and use the adjusted pressure gradient as the initial pressure gradient value and return to step S23.

[0106] In this embodiment, the consideration of the sulfur phase is mainly reflected in the calculation of the mixture flow rate and mixture density. The flow rate of the mixture adopts the method of summing the apparent flow rates of gas, liquid, and solid phases. In step S23, based on the wellbore temperature distribution of the high-sulfur gas well and a preset initial pressure gradient value, calculate the flow rate of the fluid mixture in each wellbore unit:

[0107] v m = v sl+v sg +v ss

[0108] wherein, v m is the flow rate of the fluid mixture, m / s; v sg , v sl , v ss are the superficial flow rates of the liquid phase, gas phase and solid phase respectively, m / s,

[0109] The density of the mixture is calculated by the method weighted according to the cross-sectional occupancy of gas, liquid and solid. In step S23, based on the wellbore temperature distribution of the high-sulfur gas well and the preset initial pressure gradient, the density of the fluid mixture in each wellbore unit is calculated:

[0110] ρ m = ρ l H l + ρ s H s + ρ g (1 - H l - H s )

[0111] wherein, ρ m is the density of the fluid mixture, kg / m 3 ; ρ g , ρ l , ρ s are the densities of the gas phase, liquid phase and solid phase respectively, kg / m 3 ; H l is the liquid holdup, dimensionless; H s is the cross-sectional occupancy of the solid phase, dimensionless.

[0112] Furthermore, ρ g , ρ l are calculated through the following expressions:

[0113]

[0114]

[0115] ρ o = (1000γ o + 1.205γ g R s ) / B o

[0116]

[0117]

[0118] where p is the local pressure in the wellbore, in MPa; T is the local temperature in the wellbore, in K; Z is the deviation factor under the conditions of p and T, dimensionless; WOR is the water-oil ratio, in m 3 / m 3 ; SOR is the volume ratio of liquid sulfur to oil, in m 3 / m 3 ; γ o , γ g , γ w , γ sl respectively represent the relative densities of oil, gas, water, and liquid sulfur, dimensionless; B o , B w , B sl are the volume coefficients of oil, water, and liquid sulfur under the conditions of p and T, dimensionless.

[0119] Since multiphase flow is involved in the wellbore, the accuracy of the liquid holdup calculation directly affects the model accuracy. Combining with the Hagedorn-Brown method, the liquid holdup is calculated through the following process:

[0120] ① Calculate 4 dimensionless quantities under flowing conditions;

[0121] ⑤ Liquid-phase velocity number:

[0122] Gas-phase velocity number:

[0123] Liquid viscosity number:

[0124] Pipe diameter number:

[0125] ② From the N Figure 5 shown in l ~CN l relationship curve, determine the value of CN l according to N l ;

[0126] ③ According to the Figure 6 shown in relationship curve, determine the ratio

[0127] ④ According to the Figure 7 shown in relationship curve, determine value;

[0128] ⑤ Calculate

[0129] Since the calculation process of the liquid holdup involves Figures 5 to 7 , for convenient calculation, the Figures 5 to 7 formula can be formulated by means of formula fitting.

[0130] When x represents the liquid viscosity number N l , y represents CN l When Figure 5 the formulation result of is as follows:

[0131]

[0132] When x represents y represents When Figure 6 the formulation result of is as follows:

[0133]

[0134] When x represents y represents When Figure 7 the formulation result of is as follows:

[0135]

[0136] In step S24, according to the following expression, the actual pressure gradient of each wellbore unit is calculated based on the physical property parameters of the fluid mixture in each wellbore unit:

[0137]

[0138] where P i is the pressure along the wellbore, Pa; z is the well depth, m; ρ m is the density of the fluid mixture, kg / m 3 ; v m is the flow velocity of the fluid mixture, m / s; g is the acceleration due to gravity, m / s 2 ; α is the well deviation angle, (°); f m is the friction factor, dimensionless; d is the inner diameter of the tubing, m.

[0139] The method for determining the bottom-hole flowing pressure of a high-sulfur gas well in an embodiment of the present invention, while considering the phase state change in the wellbore of the high-sulfur gas well, considers the influence of the liquid sulfur phase in the liquid-phase mixture density, and gives a detailed calculation method for the cross-sectional liquid holdup, supplements the sulfur phase change discrimination condition, can clearly discriminate the solid-liquid sulfur distribution characteristics in the wellbore, and improves the gas-liquid-solid three-phase wellbore pressure calculation model for high-sulfur gas wells considering phase state changes.

[0140] Embodiment 3

[0141] To solve the above technical problems existing in the prior art, an embodiment of the present invention provides a method for determining the bottom-hole flowing pressure of a high-sulfur gas well based on Embodiment 2, wherein the method of the embodiment of the present invention is applied in the PIPESIM software.

[0142] According to the influence of the sulfur phase distribution along the wellbore on the calculation of the pressure drop in the wellbore, the phase of sulfur will change with the change of the wellbore temperature. The influence degrees of liquid sulfur and solid sulfur on the bottom-hole pressure are different. First, the wellbore needs to be segmented according to the wellbore temperature distribution and the sulfur phase. Then, the pressure drop is calculated. The pressure calculation and the temperature calculation are inseparable because the flow state of the fluid is related to both the temperature and the pressure simultaneously. As Figure 8 shown, it can be found from the comparison of the calculation results of the known multiphase flow calculation methods that the change of the multiphase flow has little difference in the calculation results of the temperature distribution, but has a large difference in the calculation results of the pressure distribution. Therefore, first, use the PIPESIM software to calculate the temperature field distribution along the wellbore. Through the temperature field distribution and combined with the sulfur phase discrimination model, determine the phase distribution law of sulfur along the wellbore, which serves as the basis for the next wellbore pressure calculation ( Figure 2 ).

[0143] The method for determining the bottom-hole flowing pressure of a high-sulfur gas well in this embodiment includes the following steps:

[0144] (1) Starting from the wellhead, the fluid flow rate, physical properties of the fluid, pressure, temperature, etc. at the wellhead are all known;

[0145] (2) Calculate the temperature along the gas well;

[0146] Combined with the wellhead pressure and the reservoir pressure, first, estimate the pressure distribution along the wellbore, and then calculate the temperature along the wellbore according to the following temperature gradient formula:

[0147]

[0148] where, T i is the temperature along the wellbore, K; p i is the pressure along the wellbore, Pa; T e is the ambient temperature outside the well, K; λ e is the formation thermal conductivity, W / (m·K); f m is the friction factor, dimensionless; C Jm is the constant-pressure specific heat capacity of the mixed fluid, J / (kg·K); C pm is the Joule-Thomson coefficient, dimensionless; f(t) is a function reflecting the non-steady state characteristics of the formation.

[0149] (3) Arbitrarily select a pipe section length △h as the unit length for wellbore segmentation;

[0150] (4) For the pipe section △h, assume a pressure drop △p under this pipe section length and calculate the average pressure of this pipe section;

[0151] (5) Calculate the average temperature in the pipe section according to the temperature distribution of the gas well and the pipe section length;

[0152] (6) Determine the physical property parameters at the average pressure and average temperature of this pipe section;

[0153] (7) Calculate the pressure gradient △p / △h of the fluid mixture in this pipe section;

[0154]

[0155] (8) Determine the pressure drop value △p' of the pipe section according to the pressure gradient △p / △h and the length △h of the selected pipe section, and check whether the pressure drop value is close to the previously assumed pressure drop value. If the accuracy requirement is not met, return to step (4) to continue the calculation;

[0156] (9) Iteratively calculate section by section along the wellbore;

[0157] (10) Obtain the pressure value at each depth point along the wellbore through interpolation.

[0158] In practical applications, the temperature in the wellbore gradually decreases from bottom to top due to heat transfer from the external environment of the pipe, and the phase state of sulfur will also change from liquid sulfur to solid sulfur from bottom to top. The well sections with different sulfur phase states should be analyzed separately. Through the above wellbore temperature and pressure calculation method, the temperature and pressure distribution along the wellbore can be obtained. According to the temperature and pressure values at the specified depth of the wellbore, combined with the sulfur solubility model, the sulfur precipitation position can be judged ( Figure 2 ).

[0159] The sulfur solubility model is as follows:

[0160]

[0161] where C s is the solubility of sulfur, g / m 3 ; ρ g is the density of natural gas, kg / m 3 ; T is the temperature in the wellbore, K.

[0162] When the formation temperature of the gas field is very high, the phase state of sulfur in the sulfur precipitation well section needs to be determined. The sulfur phase state can be judged according to the melting point of sulfur, and the melting point of sulfur is related to both pressure and natural gas components. The research results of Woll on the melting point of sulfur are adopted ( Figure 3 ). The above is the solution method of the bottom hole pressure model of the high-sulfur gas well.

[0163] The following takes a production gas well, Well A, as an example to illustrate the method for determining the bottom hole flowing pressure of the high-sulfur gas well in the embodiment of the present invention:

[0164] Step 1: As Figure 9As shown, input the wellhead calculation parameters of the gas well in the PIPESIM software interface: liquid production rate, water-gas ratio, volume water cut, sulfur production rate, wellhead oil pressure, wellhead temperature, etc. Among them, two cases of no sulfur production and sulfur production rate of 0.5 m³ / day are input here for comparison.

[0165] Step 2: Operation result: Display the pressure and temperature distribution diagrams along the wellbore.

[0166] The results show that as Figure 10 shown, the bottom-hole pressure is greater than that without considering sulfur precipitation. As Figure 11 shown, when considering sulfur precipitation, the temperature change in the wellbore is not significant.

[0167] The method for determining the bottom-hole flowing pressure of a high-sulfur gas well in the embodiment of the present invention improves the existing method for calculating the wellbore pressure of a high-sulfur gas well, improves the calculation accuracy of the cross-sectional occupancy rate of each phase in the wellbore, considers the influence of the distribution of liquid sulfur and solid sulfur in different phases of sulfur in the wellbore on the wellbore pressure calculation, and makes the calculation result of the wellbore pressure of a high-sulfur gas well more in line with the actual situation.

[0168] The method for determining the bottom-hole flowing pressure of a high-sulfur gas well in the embodiment of the present invention aims at the problem that after sulfur precipitation occurs in the wellbore of a high-sulfur gas well, gas-liquid-solid three-phase flow will occur, resulting in low accuracy of wellbore pressure calculation. By accurately calculating the wellbore pressure distribution of a high-sulfur gas well and analyzing the variation law of the bottom-hole flowing pressure of the gas well, it can provide a theoretical basis for gas well measure adjustment and improving gas reservoir recovery efficiency.

[0169] The method for determining the bottom-hole flowing pressure of a high-sulfur gas well in the embodiment of the present invention considers the multiphase flow conditions in the wellbore during the production process of a high-sulfur gas well, considers the influence of the presence of gas, water, oil, and sulfur in the wellbore on the bottom-hole pressure calculation during the production process of the gas well, and the influence of the sulfur phase distribution along the wellbore on the pressure drop calculation in the wellbore, and can more accurately calculate the bottom-hole flowing pressure of a high-sulfur gas well.

[0170] Embodiment 4

[0171] To solve the above technical problems existing in the prior art, the embodiment of the present invention also provides a storage medium.

[0172] In one embodiment, the storage medium of this embodiment stores a computer program, and when the program is executed by a processor, it realizes the following method for determining the bottom-hole flowing pressure of a high-sulfur gas well:

[0173] S11, segment the wellbore of the high-sulfur gas well according to the sulfur phase distribution along the wellbore of the high-sulfur gas well;

[0174] S12, for each section of the wellbore, further segment the wellbore with a preset length as a unit to obtain a plurality of wellbore units;

[0175] S13. Calculate the physical property parameters of the fluid mixture in each wellbore unit based on the wellbore temperature distribution of the high-sulfur gas well and the preset initial pressure gradient value.

[0176] S14. Calculate the actual pressure gradient of each wellbore unit according to the physical property parameters of the fluid mixture in each wellbore unit.

[0177] S15. Calculate the difference between the actual pressure gradient and the preset initial pressure gradient value.

[0178] S16. Determine whether the difference between the actual pressure gradient of each wellbore unit and the preset initial pressure gradient value is less than the preset threshold:

[0179] If yes, execute step S17;

[0180] If no, execute step S18;

[0181] S17. Calculate the pressure value at each depth point along the wellbore according to the adjusted pressure gradient.

[0182] S18. Adjust the preset initial pressure gradient value, and return the adjusted pressure gradient as the initial pressure gradient value to step S13.

[0183] In another embodiment, the storage medium of this embodiment stores a computer program, and when the program is executed by a processor, it implements the following method for determining the bottom-hole flowing pressure of a high-sulfur gas well:

[0184] S21. Segment the high-sulfur gas wellbore according to the sulfur phase state distribution along the high-sulfur gas wellbore.

[0185] S22. For each section of the wellbore, further segment the wellbore with a preset length as the unit to obtain multiple wellbore units.

[0186] S23. Calculate the density and flow velocity of the fluid mixture in each wellbore unit based on the wellbore temperature distribution of the high-sulfur gas well and the preset initial pressure gradient value.

[0187] S24. Calculate the actual pressure gradient of each wellbore unit according to the density and flow velocity of the fluid mixture in each wellbore unit.

[0188] S25. Calculate the difference between the actual pressure gradient and the preset initial pressure gradient value.

[0189] S26. Determine whether the difference between the actual pressure gradient of each wellbore unit and the preset initial pressure gradient value is less than the preset threshold:

[0190] If yes, execute step S27;

[0191] If no, execute step S28;

[0192] S27. By interpolation, draw the relationship curve between wellbore depth and pressure according to the preset initial value of the pressure gradient.

[0193] S28. Adjust the preset initial value of the pressure gradient, and use the adjusted pressure gradient as the initial value of the pressure gradient and return to step S23.

[0194] In another embodiment, the storage medium of this embodiment stores a computer program, and when the program is executed by a processor, it implements the following method for determining the bottom-hole flowing pressure of a high-sulfur gas well:

[0195] (1) Starting from the wellhead, the fluid flow rate, physical properties, pressure, temperature, etc. at the wellhead are all known.

[0196] (2) Calculate the temperature along the wellbore.

[0197] Combined with the wellhead pressure and reservoir pressure, first, estimate the pressure distribution along the wellbore, and then calculate the temperature along the wellbore according to the following temperature gradient formula:

[0198]

[0199] where T i is the temperature along the wellbore, K; p i is the pressure along the wellbore, Pa; T e is the outside-wellbore ambient temperature, K; λ e is the formation thermal conductivity, W / (m·K); f m is the friction factor, dimensionless; C Jm is the constant-pressure specific heat capacity of the mixed fluid, J / (kg·K); C pm is the Joule-Thomson coefficient, dimensionless; f(t) is a function reflecting the unsteady characteristics of the formation.

[0200] (3) Arbitrarily select a pipe section length △h as the unit length for wellbore segmentation.

[0201] (4) For the pipe section △h, assume a pressure drop △p under this pipe section length and calculate the average pressure of this pipe section.

[0202] (5) Calculate the average temperature in the pipe section according to the temperature distribution of the gas well and the pipe section length.

[0203] (6) Obtain the physical property parameters at the average pressure and average temperature of this pipe section.

[0204] (7) Calculate the pressure gradient △p / △h of the fluid mixture in this pipe section.

[0205]

[0206] (8) Determine the pressure drop value Δp' of the pipe section according to the pressure gradient Δp / Δh and the length Δh of the selected pipe section, and check whether the pressure drop value is close to the previously assumed pressure drop value. If the accuracy requirement is not met, return to step (4) to continue the calculation;

[0207] (9) Perform iterative calculations section by section along the wellbore;

[0208] (10) Obtain the pressure value at each depth point along the wellbore through interpolation.

[0209] The above-mentioned processor may be a general-purpose processor, including a Central Processing Unit (CPU for short), a Network Processor (NP for short), etc.; it may also be a Digital Signal Processor (DSP for short), an Application Specific Integrated Circuit (ASIC for short), a Field-Programmable Gate Array (FPGA for short), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0210] Optionally, the storage medium may be a non-temporary computer-readable storage medium. For example, the non-temporary computer-readable storage medium may be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, and an optical data storage device, etc.

[0211] The embodiment of the present invention also provides a computer program product, including a computer program, and the steps of the method for determining the bottom-hole flowing pressure of a high-sulfur gas well in any possible implementation manner described above are implemented when the program is executed by a processor.

[0212] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the processes or functions according to the embodiments of the present invention are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that the computer can access or a data storage device such as a server or data center that includes one or more integrated available media. The available medium can be a magnetic medium (for example, a floppy disk, a hard disk, a magnetic tape), an optical medium (for example, a DVD), or a semiconductor medium (for example, a solid state disk (SSD)).

[0213] Embodiment 5

[0214] To solve the above technical problems existing in the prior art, an embodiment of the present invention also provides a computer device.

[0215] In one embodiment, the computer device of this embodiment includes a memory and a processor. A computer program is stored on the memory. When the computer program is executed by the processor, the following method for determining the bottom-hole flowing pressure of a high-sulfur gas well is implemented:

[0216] S11, segment the high-sulfur gas wellbore according to the sulfur phase state distribution along the high-sulfur gas wellbore;

[0217] S12, for each section of the wellbore, further segment the wellbore with a preset length as a unit to obtain a plurality of wellbore units;

[0218] S13, based on the temperature distribution of the high-sulfur gas wellbore and a preset initial value of the pressure gradient, calculate the physical property parameters of the fluid mixture in each wellbore unit;

[0219] S14, calculate the actual pressure gradient of each wellbore unit according to the physical property parameters of the fluid mixture in each wellbore unit;

[0220] S15, calculate the difference between the actual pressure gradient and the preset initial value of the pressure gradient;

[0221] S16. Determine whether the difference between the actual pressure gradient of each wellbore unit and the initial value of the preset pressure gradient is less than a preset threshold:

[0222] If so, execute step S17;

[0223] If not, execute step S18;

[0224] S17. Calculate the pressure value at each depth point along the wellbore according to the adjusted pressure gradient;

[0225] S18. Adjust the initial value of the preset pressure gradient, and return the adjusted pressure gradient as the initial value of the pressure gradient to step S13.

[0226] In another embodiment, the computer device of this embodiment includes a memory and a processor. A computer program is stored on the memory, and when the computer program is executed by the processor, the following method for determining the bottom-hole flowing pressure of a high-sulfur gas well is implemented:

[0227] S21. Segment the high-sulfur gas wellbore according to the sulfur phase distribution along the high-sulfur gas wellbore;

[0228] S22. For each section of the wellbore, further segment the wellbore with a preset length as a unit to obtain multiple wellbore units;

[0229] S23. Based on the wellbore temperature distribution of the high-sulfur gas well and the initial value of the preset pressure gradient, calculate the density and flow velocity of the fluid mixture in each wellbore unit;

[0230] S24. Calculate the actual pressure gradient of each wellbore unit according to the density and flow velocity of the fluid mixture in each wellbore unit;

[0231] S25. Calculate the difference between the actual pressure gradient and the initial value of the preset pressure gradient;

[0232] S26. Determine whether the difference between the actual pressure gradient of each wellbore unit and the initial value of the preset pressure gradient is less than a preset threshold:

[0233] If so, execute step S27;

[0234] If not, execute step S28;

[0235] S27. By interpolation, draw the relationship curve between the wellbore depth and the pressure according to the initial value of the preset pressure gradient;

[0236] S28. Adjust the initial value of the preset pressure gradient, and return the adjusted pressure gradient as the initial value of the pressure gradient to step S23.

[0237] In another embodiment, the computer device of this embodiment includes a memory and a processor. A computer program is stored on the memory. When the computer program is executed by the processor, the following method for determining the bottom-hole flowing pressure of a high-sulfur gas well is implemented:

[0238] (1) Starting from the wellhead, the fluid flow rate, physical properties, pressure, temperature, etc. at the wellhead are all known;

[0239] (2) Calculate the temperature along the wellbore;

[0240] Combining the wellhead pressure and the reservoir pressure, first, estimate the pressure distribution along the wellbore, and then calculate the temperature along the wellbore according to the following temperature gradient formula:

[0241]

[0242] where, T i is the temperature along the wellbore, K; p i is the pressure along the wellbore, Pa; T e is the outside-well environment temperature, K; λ e is the formation thermal conductivity, W / (m·K); f m is the friction factor, dimensionless; C Jm is the constant-pressure specific heat capacity of the mixed fluid, J / (kg·K); C pm is the Joule-Thomson coefficient, dimensionless; f(t) is a function reflecting the unsteady characteristics of the formation.

[0243] (3) Arbitrarily select a pipe section length △h as the unit length for wellbore segmentation;

[0244] (4) For the pipe section △h, assume a pressure drop △p under this pipe section length and calculate the average pressure of this pipe section;

[0245] (5) Calculate the average temperature in the pipe section according to the temperature distribution of the gas well and the pipe section length;

[0246] (6) Obtain the physical property parameters at the average pressure and average temperature of this pipe section;

[0247] (7) Calculate the pressure gradient △p / △h of the fluid mixture in this pipe section;

[0248]

[0249] (8) Determine the pressure drop value △p' of the pipe section according to the pressure gradient △p / △h and the selected pipe section length △h, and check whether the pressure drop value is close to the previously assumed pressure drop value. If the accuracy requirement is not met, return to step (4) to continue the calculation;

[0250] (9) Perform iterative calculations section by section along the wellbore;

[0251] (10) The pressure values at each depth point along the wellbore are obtained by interpolation.

[0252] The above-mentioned memory may include a random access memory (RAM), or may also include a non-volatile memory, such as at least one disk memory. Optionally, the memory may also be at least one storage device located far from the aforementioned processor.

[0253] The above-mentioned processor may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it may also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0254] Although the embodiments disclosed in the present invention are as above, the content described is only an embodiment adopted for the convenience of understanding the present invention, and is not intended to limit the present invention. Any person skilled in the art within the technical field to which the present invention pertains may make any modifications and changes in the form of implementation and details without departing from the spirit and scope disclosed by the present invention. However, the protection scope of the present invention shall still be subject to the scope defined by the appended claims.

Claims

1. A method for determining the bottom-hole flowing pressure of a high-sulfur gas well, characterized in that It includes the following steps: Segment the high-sulfur gas wellbore according to the sulfur phase distribution along the wellbore of the high-sulfur gas well; For each section of the wellbore, perform the following steps: Further segment the wellbore with a preset length as a unit to obtain multiple wellbore units; Based on the temperature distribution of the high-sulfur gas wellbore and the preset initial pressure gradient, calculate the physical property parameters of the fluid mixture in each wellbore unit; Calculate the actual pressure gradient of each wellbore unit according to the physical property parameters of the fluid mixture in each wellbore unit; Based on the difference between the actual pressure gradient and the preset initial pressure gradient, adjust the preset initial pressure gradient until the difference between the actual pressure gradient and the preset initial pressure gradient of each wellbore unit is less than the preset threshold; Calculate the pressure value at each depth point along the wellbore according to the adjusted pressure gradient; Among them, the sulfur phase distribution along the high-sulfur gas wellbore is obtained through the following steps: Calculate the temperature field distribution along the high-sulfur gas wellbore; Based on the temperature field distribution along the high-sulfur gas wellbore and the sulfur phase discrimination model, determine the sulfur phase distribution along the wellbore; Calculate the temperature field distribution along the high-sulfur gas wellbore through the following expression: Among them, T i is the temperature along the wellbore, in K; z is the well depth, in m; p i is the pressure along the wellbore, in Pa; T e is the outside-well environment temperature, in K; λ e is the formation thermal conductivity, in W / (m·K); f m is the friction factor, dimensionless; C Jm is the constant-pressure specific heat capacity of the mixed fluid, in J / (kg·K); C pm is the Joule-Thomson coefficient, dimensionless; f(t) is a function reflecting the unsteady characteristics of the formation; r t is the tubing radius, in m; U a is the total heat transfer coefficient, in W / (m·K); v m is the mixed fluid velocity, in m / s; g is the acceleration due to gravity, in m / s 2 ; α is the well deviation angle; Based on the temperature field distribution along the high-sulfur gas wellbore and the sulfur phase discrimination model, determine the sulfur phase distribution along the wellbore, including: Determine the sulfur precipitation position in the high-sulfur gas wellbore according to the sulfur solubility model; Determine the sulfur precipitation section in the high-sulfur gas wellbore through the sulfur precipitation position in the high-sulfur gas wellbore; Determine the sulfur phase distribution in the sulfur precipitation section according to the elemental sulfur melting point temperature curve; The sulfur solubility model is: Among them, C s is the solubility of sulfur, g / m 3 ; ρ g is the density of natural gas, kg / m 3 ; T is the temperature in the wellbore, K; Calculate the actual pressure gradient of each wellbore unit according to the physical property parameters of the fluid mixture in each wellbore unit through the following expression: Among them, P i is the pressure along the wellbore, Pa; z is the well depth, m; ρ m is the density of the fluid mixture, kg / m 3 ; v m is the flow velocity of the fluid mixture, m / s; g is the acceleration due to gravity, m / s 2 ; α is the well deviation angle; f m is the friction factor, dimensionless; d is the inner diameter of the tubing, m.

2. The method according to claim 1, wherein Based on the temperature distribution of the high-sulfur gas wellbore and the preset initial pressure gradient, calculate the physical property parameters of the fluid mixture in each wellbore unit, including: Calculate the flow velocity of the fluid mixture in each wellbore unit through the following expression: v m = v sl + v sg + v ss wherein, v m is the flow rate of the fluid mixture, m / s; v sg , v sl , v ss are the superficial flow rates of the liquid phase, gas phase and solid phase respectively, m / s Calculate the density of the fluid mixture in each wellbore unit through the following expression: ρ m = ρ l H l + ρ s H s + ρ g (1 - H l - H s ) where ρ m is the density of the fluid mixture, kg / m 3 ; ρ g , ρ l , ρ s are the densities of the gas phase, liquid phase and solid phase respectively, kg / m 3 ; H l is the liquid holdup, dimensionless; H s is the cross-sectional occupancy of the solid phase, dimensionless.

3. The method according to claim 2, characterized in that, The liquid holdup is calculated through the following steps: Calculate the liquid-phase velocity criterion number N under flowing conditions vl , the gas-phase velocity criterion number N gv , the liquid viscosity number N l and the pipe diameter number N D ; Based on N l ~CN l relationship curve, determine CN l according to N l value; Based on the relationship curve, determine the value; Based on the relationship curve, determine the value; Calculate H based on the value of and l .

4. The method according to claim 1, characterized in that, Calculate the pressure value at each depth point along the wellbore according to the adjusted pressure gradient, including: Draw the relationship curve between the wellbore depth and the pressure according to the preset initial pressure gradient by interpolation method.

5. A storage medium, on which a computer program is stored, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1 to 4.

6. A computer device, comprising a memory and a processor, characterized in that, There is a computer program stored on the memory, and when the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1 to 4.

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