A method for predicting the cessation of flow in a self-flowing oil well with depletion production

Abstract

The present invention provides a method for predicting the cessation of flow in a depletion-type self-flowing oil well, which is characterized by comprising the following contents: (1) collecting high-pressure PVT data of the depletion-type self-flowing oil well, and calculating the crude oil volume correction coefficient and the dissolved gas-oil ratio correction coefficient; (2) collecting a formation pressure greater than the bubble point pressure and the corresponding single-phase seepage liquid production index, calculating the liquid production corresponding to different pressures and drawing the inflow dynamic curve; (3) combining the calculated data in (1), calculating the wellbore pressure drop by an iterative method; (4) determining the corresponding relationship between the future liquid production index and the liquid production index of the benchmark inflow dynamic curve, and predicting the inflow dynamic curve under the future formation pressure; (5) drawing a stop-flow prediction curve, reading the liquid production and bottom hole flow pressure at the intersection of the inflow and outflow dynamics under different formation pressures, if there is no intersection, it indicates that the liquid production is 0, and the formation pressure, bottom hole flow pressure and liquid production data corresponding to the intersection point are the stop-flow corresponding parameters, thereby achieving the purpose of stop-flow prediction.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas field development, and in particular relates to a method for predicting the cessation of flow of a depletion-type self-flowing oil well. Technical Background

[0002] During oil and gas field development and production, formation pressure gradually decreases, and as production continues, more and more oil wells are facing the prospect of shutting down. Accurately predicting the timing of oil well shut-down and clarifying flow parameters such as bottomhole pressure, formation pressure, and production at the time of shut-down are crucial for the selection and design of artificial lift processes. Predicting the timing of oil well shut-down is a comprehensive flow problem involving formation seepage and multiphase flow in the wellbore. The physical processes are complex, making accurate prediction difficult. Typically, oil well shut-down prediction only predicts the duration of shut-down. The time required to reach the critical shut-down condition can be predicted based on the calculated flow pressure or the measured formation static pressure change trend. Alternatively, the time required for the oil pressure to drop to the minimum external output pressure can be predicted based on the oil pressure drop trend. However, these methods are empirical, lack theoretical support, and suffer from large prediction errors.

[0003] To this end, this paper proposes a method for predicting the cessation of flow in depletion-type flowing wells. This method utilizes a node system analysis method to plot the formation inflow performance curve (IPR) and the wellbore tubing performance curve (TPC) based on the current formation pressure and wellhead back pressure. This method predicts and analyzes the inflow performance under different formation pressures, thereby accurately predicting the timing of flow cessation. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem of accurately judging the stop-flow prediction of a depletion-type exploitation self-flowing oil well, and provide a method for judging the stop-flow prediction of a depletion-type exploitation self-flowing oil well.

[0005] A method for predicting the cessation of flow in a depletion-type flowing oil well, comprising the following specific steps:

[0006] Step 1: Calculate the crude oil volume coefficient correction factor and the dissolved gas-oil ratio correction factor;

[0007] High-pressure PVT data from depletion-type self-flowing wells were collected, including temperature, bubble point pressure, solution gas-oil ratio, and crude oil volume coefficient under original formation conditions. The high-pressure physical properties of crude oil under original formation conditions were calculated using the Vasquez-Beggs model and the measured values ​​were used to correct the coefficients. The crude oil volume coefficient was calculated using Formula 1.

[0008] The formula 1 is:

[0009] In this formula, R S is the dissolved gas-oil ratio of natural gas under original formation conditions, m 3 / m 3 ;T fis the temperature under original formation conditions, °C; γ API is the relative density of crude oil; γ gc is the relative density of natural gas.

[0010] Among them, when the relative density of crude oil γ API When >0.8762, the constants a1, a2, and a3 are 4.677×10 -4 ,1.751×10 -5 , -1.811×10 -8 ; When the relative density of crude oil γ API When ≤0.8762, the constants a1, a2, and a3 are 4.670×10 -4 ,1.100×10 -5 , 1.377×10 -9 .

[0011] The crude oil volume coefficient correction factor can be obtained by dividing the crude oil volume coefficient under the original formation conditions by the crude oil volume coefficient calculated by the model. This coefficient is calculated by formula 2.

[0012] The second formula is:

[0013] In Formula 2, C Bo B is the correction factor for crude oil volume coefficient; o,m is the crude oil volume coefficient under the measured original formation conditions, m 3 / m 3 .

[0014] The dissolved gas-oil ratio is calculated using Equation 3.

[0015] The formula three is:

[0016] Among them, P b is the bubble point pressure, MPa; when the relative density of crude oil γ API When the relative density of crude oil is γ, the values ​​of constants b1, b2 and b3 are 0.0178, 1.1870 and 23.9310 respectively. API When ≤30, the constants b1, b2, and b3 are 0.0362, 1.0937, and 25.7240 respectively.

[0017] The quotient of the dissolved gas-oil ratio under the original formation conditions and the dissolved gas-oil ratio calculated by the model can be used to obtain the crude oil dissolved gas-oil ratio correction factor, which is calculated using Formula 4.

[0018] The formula 4 is:

[0019] In Formula 4, C Rsis the correction factor of crude oil dissolved gas-oil ratio; R s,m is the gas-oil ratio of crude oil solution under the measured original formation conditions, m 3 / m 3 .

[0020] Step 2: Draw the baseline inflow dynamic curve;

[0021] Collect any formation pressure greater than the bubble point pressure and the corresponding production index during single-phase flow;

[0022] The method for calculating the liquid production corresponding to different bottom hole pressure conditions is as follows:

[0023] When the bottom hole flowing pressure is greater than or equal to the bubble point pressure, the reservoir is a single-phase flow, and the liquid production of the oil well is calculated by formula 5;

[0024] Formula 5: q o =J o (p r -p wf ) (5)

[0025] In Formula 5, q o is the oil well production, m 3 / d;J o is the liquid production index at the bottom hole flowing pressure and high pressure bubble point pressure, m 3 / (d·MPa);p r is the average formation pressure, MPa; p wf is the bottom hole flowing pressure, MPa;

[0026] When the bottom hole flowing pressure is lower than the crude oil bubble point pressure, the vertical well liquid production is calculated by Equation 6;

[0027] The formula six is:

[0028] The horizontal well inflow performance is calculated by Equation 7;

[0029] The formula seven is:

[0030] According to different bottom hole flow pressures and calculated liquid production, an inflow dynamic curve can be drawn on the bottom hole flow pressure-liquid production coordinate axis;

[0031] When the bottom hole pressure is 0, the open flow rate q of the oil well corresponding to the formation pressure of the benchmark inflow dynamic curve can be calculated. omax .

[0032] Step 3: Draw the outflow dynamic curve;

[0033] Collect the oil well pipeline pressure, ground temperature, ground gas-oil ratio, water content, tubing size, well depth and other parameters, combine the crude oil volume coefficient and solution gas-oil ratio prediction model and its correction factor in step 1, and use an iterative method to calculate the wellbore pressure drop. The following steps are included:

[0034] (1) Divide the liquid production into N parts, and set them equal to Divide the wellbore into segments according to the well depth and divide the number of iteration segments N I ;

[0035] (2) assigning a liquid production rate in ascending order according to the liquid production rate in step (1);

[0036] (3) Given boundary conditions: wellhead condition p0 = p t ,

[0037] (4) Calculate p i (j=1):

[0038] (5) Let p = 0.5[p i-1 +p i (j)];

[0039] The bubble point pressure is calculated by formula eight;

[0040] The formula eight is:

[0041] Among them, Rs is the dissolved gas-oil ratio, m 3 / m 3 ; γ gs is the relative density of the gas.

[0042] In this formula eight, the coefficient d is calculated by formula nine.

[0043] The formula nine is:

[0044] Among them, when the relative density of crude oil γ API ≥0.8762, the constants c1, c2, and c3 are 27.62, 0.914328, and 11.172 respectively; when the relative density of crude oil γ API When <0.8762, the constants c1, c2, and c3 are 56.18, 0.84246, and 10.393 respectively.

[0045] In Formula 8, γ gs Calculated by formula 10.

[0046] The formula 10 is:

[0047] If p b>p, then let p b =p;

[0048] Formula 3 calculates the dissolved gas-oil ratio Rs,c when the bubble point pressure is p, and then calculates the actual gas volume in the wellbore, which is calculated by Formula 11;

[0049] The formula 11 is: Q g =Q s -Q o R s，c C Rs (11)

[0050] Where Qs is the total gas production, ×10 4 m 3 / d;Q o is the amount of gas released, ×10 4 m 3 / d.

[0051] The superficial air velocity is calculated by formula 12;

[0052] The formula twelve shown is:

[0053] Among them, B g is the gas volume coefficient, m 3 / m 3 ; A is the area of ​​the oil pipe, m 2 ;

[0054] The p value is used to calculate the true fluid velocity in the wellbore, which is calculated by formula 13;

[0055] The formula 13 shown is:

[0056] Calculate dp / dz(j+1) using the p value, which is calculated using Formula 14;

[0057] The formula 14 is shown as:

[0058] In Formula 14, p is the pressure, Pa; θ is the well inclination (the angle between the well axis and the horizontal direction); v m is the flow rate of the two-phase mixture, m / s; D is the inner diameter of the oil pipe, m; f m is the two-phase friction coefficient; ρ m is the average density of the gas-liquid mixture on any cross section Z.

[0059] Among them, the two-phase friction coefficient f m Calculated by the Mukherjee-Brill model method.

[0060] Average density of gas-liquid mixture ρ m Calculated by formula 15.

[0061] The formula 15 is: m =ρ L H L +ρ G (1-H L ) (15)

[0062] In formula 15, H L is the liquid holdup, calculated using Formula 16 based on experimental data fitting.

[0063] The formula 16 is:

[0064] Among them, c1=-1.089, c2=1.319, c3=-0.961, c4=0.362, c5=0.061; σ is the air-water interfacial tension, N / m;

[0065] (6) Calculate p i (j+1):

[0066] (7) Determine convergence: If |p i (j+1)-p i (j)∣ / p i (j+1)>ε, then let p i (j) = p i (j+1), then repeat steps (5) to (7); otherwise, let p i+1 =p i (j+1), i=i+1, repeat steps (4) to (7) until i=N I , and obtain the bottom hole pressure p at a given liquid production rate wf ;

[0067] (8) Change the liquid production according to the requirements of step (2) and repeat steps (2) to (8).

[0068] Step 4: Predict the formation inflow dynamic curve under different formation pressures in the future;

[0069] (1) Given a series of formation pressures p r1 、p r2 、……p rM When the formation pressure is higher than the bubble point pressure, the corresponding relationship between the future liquid production index and the liquid production index of the benchmark inflow dynamic curve can be determined by formula seventeen.

[0070] The formula 17 is: f =J p (μ o B o ) f / (μ o B o ) p (17)

[0071] Where J represents the liquid extraction index, m 3 / (d·MPa); subscript f indicates a future moment; subscript p indicates current conditions; μ0 is the viscosity of crude oil, mPa·s; B0 is the volume coefficient of crude oil, m 3 / m 3 .

[0072] (2) When the formation pressure is lower than the bubble point pressure, the corresponding relationship between the open-flow rate and the reservoir pressure is at the bubble point pressure is calculated by formula 18;

[0073] The formula 18 is: omaxF =q omaxb (p rF / p rb ) 3 (18)

[0074] Among them, q omaxF The formation pressure is p rF Corresponding open-flow capacity, m 3 / d;q omaxb The formation pressure is p rb Corresponding open-flow capacity, m 3 / d;p rb is the bubble point pressure, MPa; p rF is the future formation pressure, MPa;

[0075] (3) Based on the above results, the inflow dynamic curve under the predicted future formation pressure conditions can be obtained by calculating using formulas 17 to 18;

[0076] Step 5: Draw the spray stop prediction curve;

[0077] The liquid production and bottom hole pressure at the intersection of inflow and outflow dynamics under different formation pressure conditions are read. If there is no intersection, it indicates that the liquid production is 0. The formation pressure, bottom hole pressure and liquid production data corresponding to the final intersection point are the corresponding parameters for stopping flow, achieving the purpose of predicting the stop of flow of flowing wells in the oil field.

[0078] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a schematic diagram of stop-flow prediction based on IPR curve and outflow performance curve which is sensitive to different formation pressures;

[0080] Figure 2 This is a schematic diagram of the measured formation pressure and production after stop-blowing. DETAILED DESCRIPTION

[0081] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0082] like Figure 1 The figure shows a schematic diagram of the IPR curve and outflow performance curve based on different sensitive formation pressures. The stop-flow prediction curve in the figure is drawn by the following method:

[0083] Step 1: Calculate the crude oil volume coefficient correction factor and the dissolved gas-oil ratio correction factor;

[0084] High-pressure PVT data from depletion-type self-flowing wells were collected, including temperature, bubble point pressure, solution gas-oil ratio, and crude oil volume coefficient under original formation conditions. The high-pressure physical properties of crude oil under original formation conditions were calculated using the Vasquez-Beggs model and the measured values ​​were used to correct the coefficients. The crude oil volume coefficient was calculated using Formula 1.

[0085] The formula 1 is:

[0086] In this formula, R S is the dissolved gas-oil ratio of natural gas under original formation conditions, m 3 / m 3 ;T f is the temperature under original formation conditions, °C; γ API is the relative density of crude oil; γ gc is the relative density of natural gas.

[0087] Among them, when the relative density of crude oil γ API When >0.8762, the constants a1, a2, and a3 are 4.677×10 -4 ,1.751×10 -5 , -1.811×10 -8 ; When the relative density of crude oil γ API When ≤0.8762, the constants a1, a2, and a3 are 4.670×10 -4 ,1.100×10 -5 , 1.377×10 -9 .

[0088] The crude oil volume coefficient correction factor can be obtained by dividing the crude oil volume coefficient under the original formation conditions by the crude oil volume coefficient calculated by the model. This coefficient is calculated by formula 2.

[0089] The second formula is:

[0090] In Formula 2, C Bo B is the correction factor for crude oil volume coefficient; o,m is the crude oil volume coefficient under the measured original formation conditions, m 3 / m 3 .

[0091] The dissolved gas-oil ratio is calculated using Equation 3.

[0092] The formula three is:

[0093] Among them, P b is the bubble point pressure, MPa; when the relative density of crude oil γ API When the relative density of crude oil is γ, the values ​​of constants b1, b2 and b3 are 0.0178, 1.1870 and 23.9310 respectively. API When ≤30, the constants b1, b2, and b3 are 0.0362, 1.0937, and 25.7240 respectively.

[0094] The quotient of the dissolved gas-oil ratio under the original formation conditions and the dissolved gas-oil ratio calculated by the model can be used to obtain the crude oil dissolved gas-oil ratio correction factor, which is calculated using Formula 4.

[0095] The formula 4 is:

[0096] In Formula 4, C Rs is the correction factor of crude oil dissolved gas-oil ratio; R s,m is the gas-oil ratio of crude oil solution under the measured original formation conditions, m 3 / m 3 .

[0097] Step 2: Draw the baseline inflow dynamic curve;

[0098] Collect any formation pressure greater than the bubble point pressure and the corresponding production index during single-phase flow;

[0099] The method for calculating the liquid production corresponding to different bottom hole pressure conditions is as follows:

[0100] When the bottom hole flowing pressure is greater than or equal to the bubble point pressure, the reservoir is a single-phase flow, and the liquid production of the oil well is calculated by formula 5;

[0101] Formula 5: q o =J o (p r -p wf ) (5)

[0102] In Formula 5, q o is the oil well production, m 3 / d;J o is the liquid production index at the bottom hole flowing pressure and high pressure bubble point pressure, m 3 / (d·MPa);p r is the average formation pressure, MPa; p wf is the bottom hole flowing pressure, MPa;

[0103] When the bottom hole flowing pressure is lower than the crude oil bubble point pressure, the vertical well liquid production is calculated by Equation 6;

[0104] The formula six is:

[0105] The horizontal well inflow performance is calculated by Equation 7;

[0106] The formula seven is:

[0107] According to different bottom hole flow pressures and calculated liquid production, an inflow dynamic curve can be drawn on the bottom hole flow pressure-liquid production coordinate axis;

[0108] When the bottom hole pressure is 0, the open flow rate q of the oil well corresponding to the formation pressure of the benchmark inflow dynamic curve can be calculated. omax .

[0109] Step 3: Draw the outflow dynamic curve;

[0110] Collect the oil well pipeline pressure, ground temperature, ground gas-oil ratio, water content, tubing size, well depth and other parameters, combine the crude oil volume coefficient and solution gas-oil ratio prediction model and its correction factor in step 1, and use an iterative method to calculate the wellbore pressure drop. The following steps are included:

[0111] (1) Divide the liquid production into N parts, and set them equal to Divide the wellbore into segments according to the well depth and divide the number of iteration segments N I ;

[0112] (2) assigning a liquid production rate in ascending order according to the liquid production rate in step (1);

[0113] (3) Given boundary conditions: wellhead condition p0 = p t ,

[0114] (4) Calculate p i (j=1):

[0115] (5) Let p = 0.5[p i-1 +p i (j)];

[0116] The bubble point pressure is calculated by formula eight;

[0117] The formula eight is:

[0118] Among them, Rs is the dissolved gas-oil ratio, m 3 / m 3 ; γ gs is the relative density of the gas.

[0119] In this formula eight, the coefficient d is calculated by formula nine.

[0120] The formula nine is:

[0121] In Formula 8, γ gs Calculated by formula 10.

[0122] The formula 10 is:

[0123] If p b >p, then let p b =p;

[0124] Formula 3 calculates the dissolved gas-oil ratio Rs,c when the bubble point pressure is p, and then calculates the actual gas volume in the wellbore by formula 11;

[0125] The formula 11 is: Q g =Q s -Q o R s，c C Rs (11)

[0126] Where Qs is the total gas production, ×10 4 m 3 / d;Q o is the amount of gas released, ×10 4 m 3 / d.

[0127] The superficial air velocity is calculated by formula 12;

[0128] The formula twelve shown is:

[0129] Among them, B g is the gas volume coefficient, m 3 / m 3 ; A is the area of ​​the oil pipe, m 2 ;

[0130] The p value is used to calculate the true fluid velocity in the wellbore, which is calculated by formula 13;

[0131] The formula 13 shown is:

[0132] Calculate dp / dz(j+1) using the p value, which is calculated using Formula 14;

[0133] The formula 14 is shown as:

[0134] In Formula 14, p is the pressure, Pa; θ is the well inclination (the angle between the well axis and the horizontal direction); v m is the flow rate of the two-phase mixture, m / s; D is the inner diameter of the oil pipe, m; f m is the two-phase friction coefficient; ρ m is the average density of the gas-liquid mixture on any cross section Z.

[0135] Among them, the two-phase friction coefficient f m Calculated by the Mukherjee-Brill model method.

[0136] Average density of gas-liquid mixture ρ m Calculated by formula 15.

[0137] The formula 15 is: m =ρ L H L +ρ G (1-H L ) (15)

[0138] In formula 15, H L is the liquid holdup, calculated using Formula 16 based on experimental data fitting.

[0139] The formula 16 is:

[0140] Among them, c1=-1.089, c2=1.319, c3=-0.961, c4=0.362, c5=0.061; σ is the air-water interfacial tension, N / m;

[0141] (6) Calculate p i (j+1):

[0142] (7) Determine convergence: If |p i (j+1)-p i (j)∣ / p i (j+1)>ε, then let p i (j) = p i (j+1), then repeat steps (5) to (7); otherwise, let p i+1 =p i (j+1), i=i+1, repeat steps (4) to (7) until i=N I, and obtain the bottom hole pressure p at a given liquid production rate wf ;

[0143] (8) Change the liquid production according to the requirements of step (2) and repeat steps (2) to (8).

[0144] Step 4: Predict the formation inflow dynamic curve under different formation pressures in the future;

[0145] (1) Given a series of formation pressures p r1 、p r2 、……p rM When the formation pressure is higher than the bubble point pressure, the corresponding relationship between the future liquid production index and the liquid production index of the benchmark inflow dynamic curve can be determined by formula seventeen.

[0146] The formula 17 is: f =J p (μ o B o ) f / (μ o B o ) p (17)

[0147] Where J represents the liquid extraction index, m 3 / (d·MPa); subscript f indicates a future moment; subscript p indicates current conditions; μ0 is the viscosity of crude oil, mPa·s; B0 is the volume coefficient of crude oil, m 3 / m 3 .

[0148] (2) When the formation pressure is lower than the bubble point pressure, the corresponding relationship between the open-flow rate and the reservoir pressure is at the bubble point pressure is calculated by formula 18;

[0149] The formula 18 is: omaxF =q omaxb (p rF / p rb ) 3 (18)

[0150] Among them, q omaxF The formation pressure is p rF Corresponding open-flow capacity, m 3 / d;q omaxb The formation pressure is p rb Corresponding open-flow capacity, m 3 / d;p rb is the bubble point pressure, MPa; p rF is the future formation pressure, MPa;

[0151] (3) Based on the above results, the inflow dynamic curve under the predicted future formation pressure conditions can be obtained by calculating using formulas 17 to 18;

[0152] Step 5: Draw the spray stop prediction curve;

[0153] Read the liquid production and bottom hole pressure at the intersection of inflow and outflow dynamics under different formation pressure conditions. If there is no intersection, it means the liquid production is 0. Finally, the formation pressure, bottom hole pressure and liquid production data corresponding to the intersection point are the corresponding parameters for stop flow, achieving the purpose of stop flow prediction of oilfield self-flowing wells. The predicted stop flow parameters can be compared with, for example, Figure 2 The prediction error of this method can be obtained by comparing the measured formation pressure at the time of stop-blowing with the formation static pressure in the production diagram.

Claims

1. A method for predicting the cessation of flow in a depletion-type flowing oil well, characterized in that: The method mainly comprises the following steps: Step (1): Collect high-pressure PVT data from depletion-type self-flowing wells, including temperature, bubble point pressure, solution gas-oil ratio, and crude oil volume coefficient under original formation conditions, and calculate the crude oil volume coefficient correction factor and the solution gas-oil ratio correction factor; Step (2): Collect a formation pressure greater than the bubble point pressure and the corresponding liquid production index during single-phase seepage, calculate the liquid production corresponding to different bottom hole flow pressure conditions, and draw an inflow dynamic curve on the bottom hole flow pressure-liquid production coordinate axis based on the different bottom hole flow pressures and the calculated liquid production; Step (3): combining the crude oil volume coefficient and solution gas-oil ratio prediction model and its correction coefficient in step (1), an iterative method is used to calculate the wellbore pressure drop; Step (4): Determine the corresponding relationship between the future liquid production index and the liquid production index of the benchmark inflow performance curve, and predict the inflow performance curve under future formation pressure conditions. The specific method is as follows: (1) Given a series of formation pressures p r1 、 p r2 、…… p rM When the formation pressure is higher than the bubble point pressure, the corresponding relationship between the future liquid production index and the liquid production index of the benchmark inflow performance curve can be determined by the following calculation method: ； in, J Indicates the liquid production index, m 3 / (d·MPa); subscript f indicates a future moment; subscript p indicates current conditions; μ0 is the viscosity of crude oil, mPa·s; B0 is the volume coefficient of crude oil, m 3 / m 3 ; (2) When the formation pressure is lower than the bubble point pressure, the calculation method for the corresponding relationship between the open-flow rate and the reservoir pressure at the bubble point pressure is: ； in, The formation pressure is Corresponding open-flow capacity, m 3 / d; The formation pressure is Corresponding open-flow capacity, m 3 / d; is the bubble point pressure, MPa; is the future formation pressure, MPa; (3) Based on the above results, the inflow dynamic curve under the predicted future formation pressure conditions can be obtained, which is calculated by the formulas in (1) and (2); Step (5): Draw a stop-flow prediction curve, read the liquid production and bottom hole pressure at the intersection of the inflow dynamics and outflow dynamics under different formation pressure conditions. If they do not intersect, it indicates that the liquid production is 0. Finally, the formation pressure, bottom hole pressure and liquid production data corresponding to the intersection point are the corresponding parameters for stop-flow, achieving the purpose of predicting the stop of flow of oilfield self-flowing wells.

2. A method for predicting the cessation of flow in a depletion-type flowing oil well according to claim 1, characterized in that: The iterative calculation method for wellbore pressure drop in step (3) includes eight steps: Step (S1): Divide the liquid production into N parts, and make them equal to , , …… , ; Divide the wellbore into sections according to the well depth and divide the number of iteration sections N I ; Step (S2): setting a liquid production rate in ascending order according to the liquid production rate in the previous step; Step (S3): Given boundary conditions: wellhead conditions , ( j =1)= ; Step (S4): Calculation p i ( j =1): p i ( j =1)= p i-1 + ( j =1) dH(i≥1); Step (S5): Let p =0.5( p i-1 + p i (j)); The calculation method of bubble point pressure is: Among them, Rs is the dissolved gas-oil ratio, m 3 / m 3 ; γ gs is the relative density of gas; In the calculation formula of the bubble point pressure, the coefficient d is calculated as follows: Among them, when the relative density of crude oil γ API ≥0.8762, the constants c1, c2, and c3 are 27.62, 0.914328, and 11.172 respectively; when the relative density of crude oil is γ API When <0.8762, the constants c1, c2, and c3 are 56.18, 0.84246, and 10.393 respectively; In the calculation of bubble point pressure, γ gs The calculation method is: if p b > p , then let p b = p ; use p The actual gas volume of the wellbore is calculated using the following method: The superficial air velocity is calculated by: Among them, B g is the gas volume coefficient, m 3 / m 3 ; A is the area of ​​the oil pipe, m 2 ; use p The actual fluid velocity of the wellbore is calculated using the following method: use p Calculate the value dp / dz( j +1), which is calculated as: In this formula, p is pressure, Pa; θ is the well inclination angle (the angle between the well axis and the horizontal direction); v m is the flow rate of the two-phase mixture, m / s; D is the inner diameter of the oil pipe, m; f m is the two-phase friction coefficient; ρ m is the average density of the gas-liquid mixture on any cross section Z; Among them, the two-phase friction coefficient f m Calculated by the Mukherjee-Brill model method; Average density of gas-liquid mixture ρ m The calculation method is: In the above formula, H L is the liquid holdup, which is calculated based on the formula established based on experimental data fitting: Among them, c1=-1.089, c2=1.319, c3=-0.961, c4=0.362, c5=0.061; , ; is the air-water interfacial tension, N / m; Step (S6): Calculation p i ( j +1): p i ( j +1)= p t + ( j +1) dH; Step (S7): Determine convergence: If | p i ( j +1)- p i ( j )∣ / p i ( j +1)>ε, then let p i ( j )= p i ( j +1), then repeat steps (S5) to (S7); otherwise, p i+1 = p i ( j +1), i = i +1, repeat steps (S4) to (S7) until i =N I , get the bottom hole pressure at a given liquid production rate p wf ; Step (S8): Change the liquid production rate according to the requirements of step (S2), and repeat steps (S2) to (S8).

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