Formation karst cave volume inversion system and method in drilling gas cut process

Abstract

The invention relates to a stratum karst cave volume inversion system and method in a drilling gas cut process, and belongs to the technical field of petroleum drilling engineering, and the system comprises a shaft throttling circulation pressure control part, a throttling response parameter acquisition part and a multiphase flow simulation software part. By means of the system, three wellhead throttling response parameters including wellhead back pressure, inlet flow and outlet flow can be obtained, then bottom hole pressure, gas dissolution amount and gas cut flow are predicted based on a multiphase flow model, and stratum karst cave volume inversion is conducted through an oil reservoir model and a gas state equation. According to the method, on-site available parameters are fully utilized, a large amount of data training is not needed, and the method has the advantages of being simple, efficient and high in real-time performance; in addition, related parameters are obtained in the process of taking pressure control measures, and the method has a restraining effect on gas cut development. By means of the method, the volume of the stratum karst cave can be calculated after gas cut occurs in the shaft, and theoretical support is provided for stratum pressure control well drilling and well control measure decision making.

Description

Technical Field

[0001] The invention relates to a system and method for inverting the volume of stratum caves during gas invasion during drilling, and belongs to the technical field of petroleum drilling engineering. Background Art

[0002] With the sustained and rapid development of my country's economy, total energy demand has been rising year by year, and the development of oil and natural gas resources has gradually advanced into deep formations. Carbonate reservoirs in areas such as the Tarim Basin and the Sichuan Basin in my country have developed typical cave-type reservoirs, which are characterized by large storage space and high permeability, and have important oil and gas development value. However, the distribution of caves in the formation is extremely uneven, with strong heterogeneity, and such formations are usually structurally complex, placing higher demands on drilling operations. When drilling into closed caves, complex downhole accidents such as gas invasion and well kicks are very likely to occur, posing a great challenge to drilling well control safety. Accurately determining the size of caves can reasonably formulate drilling fluid density and optimize well control measures and plans, which is extremely important for guiding safe drilling in cave-type formations.

[0003] Currently, the main methods for assessing cave volume in the industry include pre-drilling seismic data interpretation, well logging data analysis, and empirical models of drilling time and torque parameters. Seismic data interpretation roughly estimates cave volume from seismic exploration images, but the seismic identification accuracy is around 15 meters. This technology cannot be used to calculate the volume of caves with diameters less than 15 meters, and the volume calculated by seismic data interpretation has large errors. Conventional well logging data can only reflect the distribution of caves within a limited range around the wellbore, resulting in large errors in predicting the spatial distribution of large cave systems. Empirical models based on parameters such as drilling time and torque are susceptible to fluctuations in formation pressure and vibration of drill tools, resulting in large deviations in cave volume estimates. Therefore, there is an urgent need to develop an efficient dynamic calculation method for cave volume to address the challenge of well control safety during drilling in cave-type formations.

[0004] This paper proposes a system and method for inverting formation cave volume during gas invasion drilling by acquiring wellbore throttling response parameters after gas invasion and combining them with multiphase flow models and gas state equations. This method effectively utilizes wellbore response parameters to rapidly invert formation cave volume, providing theoretical and technical support for safe drilling in cave-like formations. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the purpose of the present invention is to provide a system and method for inverting the volume of formation caves during drilling gas invasion. This system and method does not require shutting down the well. It only needs to take throttling measures and record the wellbore response parameters. The cave volume can be inverted by combining multiphase flow models, reservoir models and gas state equations. It is not only simple to operate, but also has a certain inhibitory effect on on-site gas invasion.

[0006] The technical solutions of the present invention are as follows: The present invention provides a system for inverting the volume of karst caves in the process of gas invasion during drilling. The system comprises a throttling response parameter acquisition part, a wellbore throttling circulation pressure control part and a multiphase flow simulation software part. The throttling response parameter acquisition part includes an inlet flowmeter, an outlet flowmeter, and a pressure sensor for measuring wellhead back pressure. The inlet and outlet flowmeters measure the real-time flow at the drill string inlet and annulus outlet, respectively, and the pressure sensor measures the wellhead back pressure. When gas intrusion occurs at the bottom of the well or the wellhead throttle valve is adjusted, the above equipment collects response parameters in real time. The wellbore throttling circulation pressure control section includes a gas intrusion monitoring device at the wellhead, a throttling pipeline, and a throttle valve. The gas intrusion monitoring device relies on data from the outlet and inlet flowmeters. When the outlet flow rate exceeds the inlet flow rate, the gas intrusion monitoring device will detect gas intrusion and issue a warning. The throttle valve is then adjusted to change the wellhead back pressure, thereby reducing the outlet flow rate and suppressing the development of gas intrusion. In addition to the aforementioned hardware, the system also includes multiphase flow simulation software, which primarily performs information input, model calculations, and outputs calculation results. The throttling response parameters collected by the outlet flow meter, inlet flow meter, and pressure sensor, as well as model calculation-related parameters, are input into the software as information. The built-in multiphase flow model in the software can calculate the cave volume and output the results for display.

[0007] The present invention also provides a method for inverting the volume of formation caves during drilling gas invasion, comprising the following steps: Step 1: After detecting gas intrusion, take throttling circulation measures, and at every Δt time, t 1. t 2. t 3. Record the wellhead back pressure, inlet flow rate, and outlet flow rate at all times; calculate the mud pool increment based on the inlet flow rate and outlet flow rate. Based on the mathematical relationship between the mud pool increment, gas dissolved volume, and gas invasion volume, and in combination with the gas state equation, calculate the hypothetical gas invasion mass flow rate; Step 2: Obtain the basic parameters for wellbore multiphase flow calculation, establish a transient multiphase flow model and solution method for the wellbore after gas invasion, and determine the model solution conditions.

[0008] Step 3: Substitute the wellhead back pressure and the assumed gas intrusion mass flow rate as boundary conditions into the multiphase flow model and iteratively solve the 0~ t 1. t 1~ t 2. t 2~ t 3. The actual gas intrusion mass flow rate within time and inversion t 1. t 2. t 3. Bottom hole pressure at time 3;t 1. t 2. t The gas state equation in the cave at time 3 and the reservoir model are used to solve the cave volume in the formation.

[0009] According to the present invention, preferably, in step 1, assuming that when gas invasion is detected, the gas just enters the wellbore, then t =0 time, wellhead back pressure P c is atmospheric pressure; when gas invasion is detected at the bottom of the well, t 1. t 2, adjust the throttle valve opening and t 1. t 2. t Record wellhead back pressure and inlet flow at 3 o'clock Q in and export traffic Q out The time interval for collecting throttling response parameters is Δt. A smaller Δt can avoid the rapid expansion of gas in the wellbore. t 1. t 1~ t 2. t 2~ t The increase in the mud pool during 3 hours can be achieved by t 1. t 2. t The difference between the outlet flow and the inlet flow at time 3 is multiplied by the time interval for calculation;

[0010] Gas in the formation's karst caverns enters the wellbore annulus through fractures, causing the annular fluid volume to change, leading to an increase in the mud pool volume. Gas dissolves and expands, but in the early stages of gas invasion, the gas expansion rate is extremely small, and the expansion volume is negligible. Based on the principle of constant wellbore volume, a mathematical relationship can be derived between the bottomhole gas invasion volume and the wellhead mud pool increment:

[0011] V G = V L + V dis (1) Where, V G is the gas invasion volume, m 3 ; V dis is the amount of dissolved gas, m 3 ; V L is the volume added to the mud pool, m 3 ; Based on the gas state equation, we can get Δt The gas intrusion mass flow rate during the time is: (2) Among them, M g is the molar mass of the gas, kg / mol; P wf is the bottom hole pressure, Pa; Z g is the gas compressibility factor, dimensionless; R is the gas constant (8.314), J / (mol·K); T is the gas temperature, K; Before performing multiphase flow model calculations, Δ t The volume of gas dissolved in time is unknown, so we can assume that the volume of gas dissolved is ; At the same time, Δ t The average bottom hole pressure during the time is also unknown, so we can assume it to be the initial bottom hole pressure; thus we can get 0~ t 1. t 1~ t 2. t 2~ t The assumed gas intrusion mass flow rate during the 3-hour period is: (3) Where, is the assumed gas intrusion mass flow rate, kg / s; is the assumed dissolved gas volume, m 3 .

[0012] According to the present invention, preferably, in step 2, basic parameters for wellbore multiphase flow calculation are obtained, including wellbore trajectory, wellbore structure, drill bit assembly, fluid physical properties, initial temperature distribution, and drilling pump parameters, a transient multiphase flow model for the wellbore after gas invasion is established, and the wellbore pressure field, gas-liquid distribution, and solubility distribution are calculated; the model includes a gas phase mass conservation equation, a liquid phase mass conservation equation, a gas-liquid two-phase momentum conservation equation, and corresponding auxiliary equations; the auxiliary equations include a gas compressibility factor calculation model, a gas viscosity calculation model, a gas density calculation model, a gas solubility calculation model, and a friction pressure drop calculation model.

[0013] The gas phase mass conservation equation in the gas invasion section is: (4) The gas phase mass conservation equation in the non-gas invasion section is: (5) The liquid phase mass conservation equation is: (6) The gas-liquid two-phase momentum conservation equation is: (7) Where,R s , solubility of gas in drilling fluid, m 3 / m 3 ; A , annulus cross-sectional area, m 2 ; q = q gas / Δ H q , gas intrusion mass flow rate per unit length, kg / (s·m); Δ H q , depth of gas production section, m; g, acceleration of gravity, m / s 2 ; r gsc , gas density under standard conditions, kg / m 3 ; r g , gas density, kg / m 3 ; r l , drilling fluid density, kg / m 3 ; u g , gas flow rate, m / s; u l , drilling fluid velocity, m / s; E g , gas volume fraction, dimensionless; E l , drilling fluid volume fraction, dimensionless; , friction pressure drop, Pa / m; B l is the drilling fluid volume coefficient, %; P is the pressure, Pa; z is the vertical length, m; The finite difference method is used to discretize and solve the above multiphase flow model. The difference format is as follows: The difference format of the gas phase continuity equation in the gas invasion section is:

[0014] (40) The difference format of the gas phase continuity equation in the non-gas invasion section is: (41) The difference format of the liquid phase continuity equation is (42) The difference format of the momentum equation is: (43) (44) (45) (46) j is a spatial node, dimensionless; n is a time node, dimensionless; Determine the model based on the actual project t =0, t 1. t 2. Initial and boundary conditions at time t.

[0015] According to the present invention, preferably, in step 3, 0~ t Taking the calculation process of the actual gas invasion mass flow rate in step 1 as an example, the wellhead back pressure and the assumed gas invasion mass flow rate in step 1 are used as boundary conditions and the multiphase flow model is used to calculate the 0~ t Bottom hole pressure at each time step within 1 time , calculate 0~ according to the trapezoidal formula t Average bottom hole pressure within 1 hour ; (52) Where, i is the number of time nodes; is the bottom hole pressure at the starting time node 0, Pa; for i Bottom hole pressure at the time node, Pa; dt is the time step, s; N 1 for t The number of time nodes in 1 time, N 1= t 1 / dt; Solubility calculated from the multiphase flow model R s The distribution of t The height of drilling fluid entering the annulus within 1 hour, that is, the length of the liquid column where gas dissolves H R1 , the dissolved gas content is obtained according to the following formula V dis,1 ; (53) Where, j is the number of spatial nodes; V dis,1 0~ t Amount of dissolved gas in 1 hour, m 3 ; H R1 0~ t Height of drilling fluid entering the annulus within 1 second, m; R s,j for j Solubility at spatial nodes; A a is the cross-sectional area of ​​the annulus, m2 ; dz is the spatial step length, m; Calculated by the following formula: (54) V L,1 0~ t The volume of the mud pool increased in 1 time, m 3 ; Compare the calculated gas intrusion mass flow rate q gas,1 and the assumed gas intrusion mass flow rate The error between them, if the error satisfies: (55) The calculation ends and the output is 0~ t The actual gas intrusion mass flow rate within 1 time q gas,1 and t Bottom hole pressure at moment 1 P wf,1 Otherwise, q gas,1 Assign the value of , recalculate the multiphase flow model; t 1~ t 2. t 2~ t The actual gas intrusion mass flow rate within 3 hours q gas,2 、 q gas,3 ,and t 2. t Bottom hole pressure at time 3 P wf,2 、 P wf,3 , the calculation is the same as above steps; When there is no gas invasion, the initial gas mass in the cave is m , 0~ t 1. t 1~ t 2. t 2~ t The outflowing gas masses are q gas,1 Δ t 、 q gas,2 Δ t 、 q gas,3 Δ t ; From this we can calculate t 1. t 2.t Residual mass of gas in the cave at time 3 m 1. m 2. m 3. Set t 1. t 2. t The cave pressure at 3 moments is P v1 、 P v2 、 P v3 ; The reservoir model adopts the linear gas production model: q gas = J ( P v - P wf )(56) J is the reservoir model productivity index, kg / (Pa·s); P v is the cave pressure, Pa; According to the gas state equation and reservoir model, the following equations are obtained: (61) In the equation, R, T, Mg, Δ t is a constant; q gas,1 、q gas,2 、 q gas,3 、 Z g,1 、 Z g,2 、 Z g,3 、 P wf,1 、 P wf,2 、 P wf,3 All can be solved by multiphase flow model; the above 6 equations can be solved by combining P v1 、 P v2 、 P v3 、 J 、 V 、 m , and thus the cave pressure P v , reservoir model productivity index J and the volume of stratum caves V .

[0016] This system and method can be used to obtain three wellhead throttling response parameters: wellhead back pressure, inlet flow rate, and outlet flow rate. Bottomhole pressure, dissolved gas content, and gas invasion flow rate are then predicted based on a multiphase flow model. The reservoir model and gas equation of state are then used to invert the formation cave volume. This method fully utilizes parameters available in the field, eliminating the need for extensive data training and boasts simplicity, efficiency, and real-time performance. Furthermore, the method captures relevant parameters during the implementation of pressure control measures, effectively curbing the development of gas invasion.

[0017] The beneficial effects of the present invention are: By using the system and method for calculating the volume of formation caverns during gas invasion during drilling provided by the present invention, it is possible to simply obtain the wellhead throttling response parameters, invert the bottomhole parameters that are difficult to obtain using the multiphase flow model, and calculate the cavern volume using the reservoir model and the gas state equation. This method has the following main advantages: (1) By adjusting the throttling valve at the wellhead, the wellbore response parameters can be obtained, which is simple to operate and has a certain inhibitory effect on gas invasion and overflow on site; (2) The multiphase flow model takes into account the dissolved volume of the gas invading gas in the drilling fluid, which can more accurately determine the gas invasion volume, thereby reducing the calculation error of the cavern volume; (3) The non-ideal gas state equation that takes into account the influence of the gas compressibility factor is adopted, which is more consistent with the real gas properties and improves the calculation accuracy. Other features and advantages of the present invention will be described in detail in the subsequent specific implementation method section. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the specific embodiments of the present invention, the following briefly introduces the drawings required for the description of the specific embodiments, so as to be used together with the following specific embodiments to explain the embodiments of the present invention, but does not constitute a limitation of the embodiments of the present invention. In the drawings:

[0019] Figure 1 This is a schematic diagram of the inversion system for formation cave volume during drilling gas invasion; Figure 2 This is a flowchart of the method for inverting the volume of formation caves during drilling gas invasion; Figure 3 This is a schematic diagram of the mathematical relationship between the gas invasion volume at the bottom of the well and the increment of the mud pool at the wellhead; Figure 4 This is a flow chart of a method for solving a transient multiphase flow model in a wellbore after gas invasion; Figure 5 It is a principle diagram for solving cave volume based on gas state equation; Among them, 1-inlet flowmeter; 2-outlet flowmeter; 3-gas intrusion monitoring device; 4-pressure sensor; 5-mud pump; 6-throttle valve; 7-throttle pipeline; 8-mud pool; 9-information input and storage device; 10-model calculation software; 11-result output interface; 12-annulus; 13-drill pipe; 14-formation; 15-formation invading gas; 16-drill bit; 17-caves; 18-fractures; 19-gas in caves; 20-invading annulus gas; 21-gas dissolved in drilling fluid; 22-mud pool increment; 23-initial mud pool volume; 24-annulus channel; 25-drill pipe channel. DETAILED DESCRIPTION

[0020] The present invention will be further described below with reference to embodiments and accompanying drawings, but is not limited thereto.

[0021] Example 1 A system for inverting the volume of karst caves during drilling gas invasion, such as Figure 1 As shown, the system includes a wellbore throttling circulation pressure control part ( Figure 1 3, 6, 7), throttling response parameter collection part ( Figure 1 1, 2, 4) and multiphase flow simulation software ( Figure 1 9, 10, and 11). The wellbore throttling circulation pressure control section includes a gas intrusion monitoring device at the wellhead, a throttle valve, and a throttle pipeline. The gas intrusion monitoring device relies on data from the inlet and outlet flowmeters. When the outlet flow rate exceeds the inlet flow rate, the gas intrusion monitoring device detects the occurrence of gas intrusion and issues a warning. The throttle valve is then adjusted to change the wellhead back pressure, thereby reducing the outlet flow rate and suppressing the development of gas intrusion. The throttling response parameter collection section includes an inlet flowmeter, an outlet flowmeter, and a pressure sensor that measures wellhead back pressure. The inlet and outlet flowmeters measure the real-time flow rate at the drill string inlet and annulus outlet, respectively, and the pressure sensor measures the wellhead back pressure. When gas intrusion occurs at the bottom of the well or the wellhead throttle valve is adjusted, the above equipment collects response parameters in real time. The multiphase flow simulation software includes information input and storage devices, model calculation software and result output interface, which mainly performs information input, model calculation and calculation result output; the throttling response parameters collected by the outlet flow meter, inlet flow meter and pressure sensor, as well as the model calculation related parameters are input into the software as information. The built-in multiphase flow model in the software can calculate the cave volume and output the results for display.

[0022] The specific working process of the gas invasion process and system is as follows: During normal drilling, the drilling fluid in the mud pool (8) is pumped into the drill pipe (13) through the mud pump (5). The inlet flow meter (1) can measure and record the inlet flow rate of the drilling fluid. The drilling fluid flows through the drill pipe and drill bit (16), and flows out of the wellbore through the annulus (12), and returns to the mud pool through the throttle pipeline (7). The outlet flow meter (2) on the pipeline can measure and record the outlet flow rate of the drilling fluid, and the pressure sensor (4) can measure and record the wellhead back pressure. If a cave (17) is encountered during drilling, the gas in the cave invades the wellbore annulus through the crack (18), thereby affecting the bottom hole pressure and the annulus liquid phase volume, and further affecting the drilling fluid outlet flow rate. The gas invasion monitoring device (3) at the wellhead determines the occurrence of gas invasion by analyzing the difference between the inlet flow meter and the outlet flow meter. At this time, the opening of the throttle valve (6) is adjusted to control the outlet flow rate, and the gas invasion is handled by the throttle cycle. From the moment gas intrusion is detected, the throttle valve opening is adjusted every Δt, and the inlet flow rate, outlet flow rate, and wellhead back pressure are recorded once using the inlet flow meter, outlet flow meter, and pressure sensor, for a total of three times. The recorded data is transmitted to the information input and storage device (9), and the formation cave volume is calculated using the model calculation software (10) and displayed in real time through the result output interface (11).

[0023] Example 2 A method for inverting the volume of formation caves during drilling gas invasion is based on the system and workflow described in Example 1. The system can intermittently collect throttling response parameters such as drilling fluid outlet flow rate, inlet flow rate, and wellhead back pressure, and calculate the volume of formation caves using model software. The specific flow of the method for calculating the volume of formation caves is as follows:

[0024] Figure 2 This is a flowchart of the method for inverting the volume of formation caves during drilling gas invasion, which includes the following steps: Step 1: After detecting gas intrusion, take throttling circulation measures, and at every Δt time, t 1. t 2. t Record the wellhead back pressure, inlet flow rate, and outlet flow rate at time 3. Calculate the mud pool increment using the inlet and outlet flow rates. Based on the mathematical relationship between the mud pool increment, dissolved gas volume, and gas intrusion volume, and in conjunction with the gas state equation, calculate the hypothetical gas intrusion mass flow rate.

[0025] Step 2: Obtain the basic parameters for wellbore multiphase flow calculation, establish a transient multiphase flow model and solution method for the wellbore after gas invasion, and determine the model solution conditions.

[0026] Step 3: Substitute the wellhead back pressure and the assumed gas intrusion mass flow rate as boundary conditions into the multiphase flow model and iteratively solve the 0~ t 1.t 1~ t 2. t 2~ t 3. The actual gas intrusion mass flow rate within time and inversion t 1. t 2. t The bottom hole pressure at time 3. t 1. t 2. t The gas state equation in the cave at time 3 and the reservoir model are used to solve the cave volume in the formation.

[0027] In step 1, assuming that when gas invasion is detected, the gas just enters the wellbore. t = 0, wellhead back pressure ( P c ) is atmospheric pressure. When gas invasion is detected at the bottom of the well, the drilling fluid inlet flow rate is not changed, and no shut-in measures are taken. The throttle valve opening is adjusted to implement throttling circulation. Within a period of time after the gas invasion is detected (0~ t 3) Adjust the throttle valve opening every certain time (Δt) and collect the wellbore gas invasion response parameters during this period, mainly including wellhead back pressure, drilling fluid inlet flow rate ( Q in ) and drilling fluid outlet flow rate ( Q out ). The above parameters can be respectively Figure 1 The pressure sensor (4), inlet flow meter (1) and outlet flow meter (2) in the wellbore are used to collect the data. To avoid the gas from expanding violently in the wellbore, the time interval for collecting the throttling response parameters is recommended to be 5 minutes. The time of each recording is t 1=5min, t 2=10min, t 3=15min.

[0028] pass t 1. t 2. t The drilling fluid inlet flow rate and drilling fluid outlet flow rate collected at time 3 can be obtained from 0~ t 1. t 1~ t 2. t 2~ t 3. Mud pool increment within 3 hours ( V L ): V L =( Q out - Q in )Δt, where V L, mud pool increment, m 3 ; Q out , drilling fluid outlet flow, m 3 / s; Q in , drilling fluid inlet flow rate, m 3 / s; Δt, sampling time interval, s.

[0029] Figure 3 The mathematical relationship between the gas invasion volume at the bottom of the well and the increment of the mud pool at the wellhead is shown in Fig. 1. In the initial state, the cave contains a portion of gas that has not invaded the wellbore (19), and its volume is V G After gas invasion occurs, the gas in the formation cave will quickly enter the wellbore annulus (24) through the cracks, causing the annular fluid volume to change and reflected in the change of wellhead parameters, such as the mud pool increment (22). The increased volume in the mud pool is V L However, part of the gas (21) will dissolve into the drilling fluid, and the volume of this part is V dis , the only thing that actually occupies the annular fluid volume is the remaining invading gas (20). At the same time, after the gas enters the wellbore, it will expand, and the volume of expansion is V exp According to the law of constant wellbore volume, the mathematical relationship between the bottom hole gas invasion volume and the wellhead mud pool increment can be obtained: V L = V G + V exp - V dis , where V G , gas invasion volume, m 3 ; V exp , gas expansion, m 3 ; V dis , dissolved gas, m 3 .

[0030] Considering that the gas expansion rate in the early stage of gas invasion is extremely small and can be ignored, only the dissolved volume of gas in the drilling fluid is considered. The mathematical relationship between the bottom hole gas invasion volume and the wellhead mud pool increment is: V G = V L + V dis (1) The relationship between the intrusion gas mass and the intrusion gas mass flow rate is: m g = q gas ·Δt; Based on the gas state equation, the following equation can be obtained: , where P wf , bottom hole pressure, Pa; Z g , gas compressibility factor, dimensionless; m g , mass of intruding gas, kg; M g , gas molar mass, kg / mol; R, gas constant (8.314), J / (mol·K); T , gas temperature, K; q gas , gas intrusion mass flow rate, kg / s.

[0031] Combining the above formulas, we can get: (2) Assuming the gas temperature is the formation temperature, it can be calculated using the ground temperature, local geothermal gradient, and current well depth: T = T sur +Δ T · H , where T sur , ground temperature, K; Δ T , geothermal gradient, K / m; H , well depth, m.

[0032] Since the multiphase flow model calculation has not been performed at this time, Δ t The dissolved gas volume and average bottom hole pressure during the time are unknown. Reasonable assumptions can be made on them as the assumptions of the multiphase flow model, and through iterative calculations of the model, the actual dissolved gas volume can be obtained, and then the gas invasion mass flow rate can be calculated. Assuming that the dissolved gas volume is , the average bottom hole pressure is the initial bottom hole pressure. The assumed gas invasion mass flow rate calculated in this step is:

[0033] (3) Where, , assumed gas intrusion mass flow rate, kg / s; , assumed dissolved gas volume, m 3 .

[0034] In step 2, basic parameters for wellbore multiphase flow calculation, such as wellbore trajectory, wellbore structure, drill bit assembly, and fluid properties, are obtained. The basic parameters specifically include: depth measurement, well inclination, casing sizes of different openings, casing running depth, open hole depth, drill bit size, drill bit diameter, drilling fluid density, drilling fluid rheological parameters, current well depth, temperature distribution data, etc.

[0035] A transient multiphase flow model for the wellbore after gas invasion was established. This model can calculate the wellbore pressure field and gas-liquid distribution at different times. The model includes the gas phase mass conservation equation, the liquid phase mass conservation equation, the gas-liquid two-phase momentum conservation equation, and corresponding auxiliary equations.

[0036] In the gas invasion section, the gas phase mass conservation equation is: (4) Similarly, the gas phase mass conservation equation in the non-gas invasion section is: (5) The liquid phase mass conservation equation is: (6) The gas-liquid two-phase momentum conservation equation is: (7) Where, R s , solubility of gas in drilling fluid, m 3 / m 3 ; A , annulus cross-sectional area, m 2 ; q , gas intrusion mass flow rate per unit length, kg / (s·m), q = q gas / Δ H q , Δ H q , depth of gas producing section, m; r gsc , gas density under standard conditions, kg / m 3 ; r g , gas density, kg / m 3 ; r l , drilling fluid density, Kg / m 3 ; u g , gas flow rate, m / s; u l , drilling fluid velocity, m / s; E g, gas volume fraction, dimensionless; E l , drilling fluid volume fraction, dimensionless; g, gravitational acceleration, m / s 2 ; , friction pressure drop, Pa / m; B l is the drilling fluid volume coefficient, %; P is the pressure, Pa; z is the vertical length, m.

[0037] In addition to the multiphase flow control equations described above, the model also includes a variety of auxiliary equations: (1) Gas compressibility factor calculation model The gas compressibility factor is calculated using the PR state equation: (8) (9) (10) (11) (12) (13) (14) Where, , deviation factor, dimensionless; P c , critical pressure, Pa; T c , critical temperature, K.

[0038] (2) Gas viscosity calculation model The viscosity of the gas is calculated using the Lee model: (15) (16) Where, m g , gas viscosity, Pa·s.

[0039] (3) Gas density calculation model The gas density is derived from the equation of state: (17) Where, P sc , pressure under standard conditions, Pa; Z sc , compression factor under standard conditions, dimensionless; T sc , temperature under standard conditions, K; rgsc , gas density under standard conditions, kg / m 3 ; Z g , gas compressibility factor, dimensionless.

[0040] (4) Gas solubility calculation model The solubility of formation invading gas in drilling fluid can be calculated by the following formula: (18) SG g = r g / r air (19) APIs =141.5 / SG l -131.5 (20) SG l = r l / r w (twenty one) The solubility can be used to calculate the amount of dissolved gas in the annulus: (twenty two) Where, R s , gas solubility, m 3 / m 3 ; SG g , relative density of gas, dimensionless; SG l , drilling fluid relative density, dimensionless; APIs , drilling fluid APIs specific gravity, dimensionless; P , gas pressure, Pa; T , gas temperature, K; r w , water density (1000), kg / m 3 ; r l , drilling fluid density, kg / m 3 ; r g , gas density, kg / m 3 ; r air , air density under standard conditions (1.293), kg / m 3 ; V s , drilling fluid volume, m 3 .

[0041] (5) Frictional pressure drop calculation model The single-phase flow friction pressure drop is calculated by the following formula: (twenty three) (twenty four) (25) Where Re is the Reynolds number, dimensionless; D a , annulus diameter, m; D pout , outer diameter of drill pipe, m; u l , drilling fluid velocity, m / s; r l , drilling fluid density, kg / m 3 ; or p , plastic viscosity, Pa·s; t 0, yield value, Pa; f r , friction coefficient, dimensionless.

[0042] The calculation of multiphase flow friction pressure drop requires distinguishing different flow types, which are mainly divided into bubbly flow, slug flow and annular flow.

[0043] The bubbly flow friction pressure drop is calculated by the following formula: (26) (27) (28) (29) Where, Re m , Reynolds number of the mixed fluid, dimensionless; u m , mixed phase superficial velocity, m / s; r m , mixed density, kg / m 3 ; m m is the mixed viscosity, Pa·s; Δ is the effective roughness of the annulus, m.

[0044] The mixed phase apparent velocity, mixed density and mixed viscosity can be calculated by the following formula: u m = u g E g + ul E l (30) r m = r g E g + r l E l (31) m m = m g E g + m l E l (32) Where, m l , drilling fluid viscosity, Pa·s.

[0045] The friction pressure drop of slug flow and bubbly flow is calculated by the following formula: (33) (34) (35) (36) The friction pressure drop of annular bubbly flow is calculated by the following formula: (37) (38) (39) A solution method for the transient multiphase flow model in a wellbore after gas invasion was established, and the solution conditions were determined. The finite difference method was used to numerically discretize and iteratively solve the transient multiphase flow model in a wellbore after gas invasion, using a four-point difference scheme. The difference schemes for the gas and liquid phase continuity equations and the gas-liquid two-phase momentum equation are as follows:

[0046] (1) Gas phase continuity equation The difference format of the gas phase continuity equation in the gas invasion section is:

[0047] (40) The difference format of the gas phase continuity equation in the non-gas invasion section is: (41) (2) Liquid phase continuity equation The difference format of the liquid phase continuity equation is (42) (3) Momentum equation The difference format of the momentum equation is: (43) (44) (45) (46) j is a spatial node and is dimensionless; n is a time node and is dimensionless.

[0048] Determine the initial conditions and boundary conditions of the equation based on engineering practice.

[0049] t =0, t 1. t The initial conditions at the 2 moments are different. t = 0, the formation gas has not yet invaded the wellbore, and the wellbore annulus is a single-phase flow. The initial condition is set as:

[0050] (47) t = t 1. t 2, the model calculation results can be used as the initial conditions. In the calculation of bottom hole pressure, the change of wellhead back pressure should be considered. The initial conditions are set as: (48) Where, P f , friction loss, Pa; u sl , drilling fluid superficial velocity, m / s; u sg , gas superficial velocity, m / s.

[0051] The outlet boundary condition of the wellbore pressure is the wellhead back pressure: P (0, t )= P c (49) The fluid velocity boundary condition is: (50) Figure 4 This is a flow chart of the solution method for the transient multiphase flow model in a wellbore after gas invasion. The specific solution steps are as follows: (1) Assumption t The bottom hole pressure at time +1 is , determine the physical properties of each phase (density, viscosity, compressibility factor, etc.) of gas and liquid according to the auxiliary equation.

[0052] (2) Assumptions t +1 moment annulus position node j The wellbore pressure at , the assumed value is usually referenced t Time annulus position node j Wellbore pressure at Then determine the physical property parameter values ​​of the gas phase and liquid phase at the annular position node.

[0053] (3) Assumptions t +1 moment annulus position node j The gas content is , the assumed value is usually referenced t Time annulus position node j Gas fraction at . Calculate the superficial velocity of the gas and liquid phases and the solubility of the gas phase.

[0054] (4) Using the drift flow model and mass conservation equation, calculate the new gas content , and check whether the new gas content meets If not, return to step (3) and recalibrate until Established.

[0055] (5) Using the hybrid momentum conservation equation, calculate the annular position node j New wellbore pressure , and check whether the new wellbore pressure meets If not, return to step (2) and recalibrate until Established.

[0056] (6) In t At time +1, the wellbore pressure is calculated cyclically until the wellhead is reached and the calculated value of the wellhead pressure is obtained. If the calculated value of the wellhead pressure satisfies , indicating that t The calculated value of the entire wellbore pressure at time +1 is predicted accurately. Otherwise, it is necessary to return to step (1) and recalibrate until Established.

[0057] In step three, step one P c As the wellhead pressure boundary condition, Assuming the gas intrusion mass flow rate, substitute it into the model and iterate to solve 0~ t 1. t 1~ t 2.t 2~ t The actual gas intrusion mass flow rate within 3 hours ( q gas,1 、q gas,2 、 q gas,3 ), and inverse t 1. t 2. t Bottom hole pressure at time 3 ( P wf,1 、 P wf,2 、 P wf,3 ).

[0058] 0~ t 1 as an example of the calculation process of the actual gas invasion mass flow rate, the wellhead back pressure is P c,1 ( t =0), the mud pool increment is V L,1 ( t = t 1), assuming that the amount of dissolved gas is =0, the initial bottom hole pressure is P wf ( t =0). According to formula (3), the assumed gas intrusion mass flow rate can be calculated:

[0059] (51) Through the multiphase flow model calculation, we can get 0~ t The bottom hole pressure of each time step in 1 time is calculated according to the trapezoidal formula from 0 to t Average bottom hole pressure within 1 hour At the same time, the amount of dissolved gas is obtained V dis,1 , we can calculate:

[0060] (52) Where, i is the number of time nodes; is the bottom hole pressure at the starting time node 0, Pa; for i Bottom hole pressure at the time node, Pa; dt is the time step, s; N 1 for t The number of time nodes in 1 time, N 1= t 1 / dt.

[0061] (53) Where, j is the number of spatial nodes; V dis,1 0~ t Amount of dissolved gas in 1 hour, m 3 ; H R1 0~ t Height of drilling fluid entering the annulus within 1 second, m; R s,j for j Solubility at spatial nodes; A a is the cross-sectional area of ​​the annulus, m 2 ; dz is the spatial step size, m.

[0062] (54) V L,1 0~ t The volume of the mud pool increased in 1 time, m 3 .

[0063] Compare the newly calculated gas intrusion mass flow rate q gas,1 and the assumed gas intrusion mass flow rate The error between them, if the error satisfies: (55) The iterative calculation ends and the output is t Actual gas intrusion mass flow rate at time 1 q gas,1 and bottomhole pressure P wf,1 Otherwise, q gas,1 Assign the value of , recalculate the multiphase flow model until it complies with formula (55).

[0064] Similarly, t The wellhead back pressure at time 2 is P c,2 ( t = t 1), the mud pool increment is V L,2 ( t = t 2), assuming that the amount of dissolved gas is = V dis ( t = t 1), the initial bottom hole pressure is Pwf ( t = t 1). t The wellhead back pressure at time 3 is P c,3 ( t = t 2), the mud pool increment is V L,3 ( t = t 3), assuming that the amount of dissolved gas is = V dis ( t = t 2), the initial bottom hole pressure is P wf ( t = t 2). t 1~ t 2. t 2~ t The actual gas intrusion mass flow rate within 3 hours ( q gas,2 、 q gas,3 )and t 2. t Bottom hole pressure at time 3 ( P wf,2 、 P wf,3 ) The calculation is the same as above.

[0065] according to t 1. t 2. t The gas state equation in the cave at time 3 and the reservoir model are used to solve parameters such as the productivity index and cave pressure, and then the cave volume of the formation is calculated.

[0066] To facilitate calculation, the following assumptions are made in the solution process: (1) When the gas in the cave invades the wellbore, it conforms to the linear flow equation of the reservoir: q gas = J ( P v - P wf )(56) Where, J , reservoir model productivity index, kg / (Pa·s); P v , cave pressure, Pa.

[0067] (2) 0~ tDuring the 3rd time, the gas temperature remains unchanged and is the temperature T at the depth of the formation where the cave is located; (3) The cave is connected to the wellbore only through cracks, and formation fluid will not enter the cave.

[0068] Figure 5 The diagram below shows the principle of solving the cave volume based on the gas state equation. When there is no gas invasion, the initial gas mass in the cave is m , 0~ t 1. t 1~ t 2. t 2~ t The outflowing gas masses are q gas,1 Δ t 、 q gas,2 Δ t 、 q gas,3 Δ t .so t 1. t 2. t The remaining mass of gas in the cave pressure at time 3 is:

[0069] (57) correspond t 1. t 2. t The cave pressure at 3 moments is P v1 、 P v2 、 P v3 .

[0070] by t Take the gas state equation in the cave at time 1 as an example: (58) Rearranging the equation yields: (59) At the same time, we can get from formula (56): (60) Will t 2. t The equations at time 3 are written out to obtain the following system of equations: (61) In the equation, R, T, Mg, Δ t is a constant and does not need to be solved. q gas,1 、q gas,2、 q gas,3 0~ t 1. t 1~ t 2. t 2~ t 3. Gas intrusion mass flow rate within time, Z g,1 、 Z g,2 、 Z g,3 、 P wf,1 、 P wf,2 、 P wf,3 for t 1. t 2. t The gas compressibility factor and bottom hole pressure at time 3. The above 9 parameters can be solved by the multiphase flow model.

[0071] P v1 、 P v2 、 P v3 、 J 、 V 、 m The above six equations can be solved to obtain the parameters to be solved. P v and reservoir model productivity index J , and the volume of stratum caves V .

Claims

1. A system for inverting the volume of karst caves in formations during gas invasion during drilling, characterized in that: The system includes a throttling response parameter acquisition part, a wellbore throttling circulation pressure control part and a multiphase flow simulation software part; The throttling response parameter acquisition part includes an inlet flowmeter, an outlet flowmeter, and a pressure sensor for measuring wellhead back pressure. The inlet and outlet flowmeters measure the real-time flow at the drill string inlet and annulus outlet, respectively, and the pressure sensor measures the wellhead back pressure. When gas intrusion occurs at the bottom of the well or the wellhead throttle valve is adjusted, the above equipment collects response parameters in real time. The wellbore throttling circulation pressure control section includes a gas intrusion monitoring device at the wellhead, a throttling pipeline, and a throttle valve. The gas intrusion monitoring device relies on data from the outlet and inlet flowmeters. When the outlet flow exceeds the inlet flow, the gas intrusion monitoring device detects gas intrusion and issues a warning. The wellhead back pressure is then changed by adjusting the throttle valve. The system also includes a multiphase flow simulation software part, which performs information input, model calculation and calculation result output; the throttling response parameters collected by the outlet flow meter, inlet flow meter and pressure sensor, as well as the model calculation related parameters are input into the software as information, and the software calculates the cave volume and outputs the results for display.

2. A method for inverting the volume of karst caves in formations during gas invasion during drilling, characterized in that: The following steps are involved: Step 1: After detecting gas intrusion, take throttling circulation measures, and at every Δt time, t 1. t 2. t 3. Record the wellhead back pressure, inlet flow rate, and outlet flow rate at all times; calculate the mud pool increment based on the inlet flow rate and outlet flow rate. Based on the mathematical relationship between the mud pool increment, gas dissolved volume, and gas invasion volume, and in combination with the gas state equation, calculate the hypothetical gas invasion mass flow rate; Step 2: Obtain basic parameters for wellbore multiphase flow calculation, establish a transient multiphase flow model and solution method for the wellbore after gas invasion, and determine the model solution conditions; Step 3: Substitute the wellhead back pressure and the assumed gas intrusion mass flow rate as boundary conditions into the multiphase flow model and iteratively solve the 0~ t 1. t 1~ t 2. t 2~ t 3. The actual gas intrusion mass flow rate within time and inversion t 1. t 2. t 3. Bottom hole pressure at time 3; t 1. t 2. t The gas state equation in the cave at time 3 and the reservoir model are used to solve the cave volume in the formation.

3. The method for inverting the volume of karst caves in the process of drilling gas invasion according to claim 2, characterized in that: In step 1, assuming that when gas invasion is detected, the gas just enters the wellbore. t =0 time, wellhead back pressure P c is atmospheric pressure; when gas invasion is detected at the bottom of the well, t 1. t 2, adjust the throttle valve opening and t 1. t 2. t Record wellhead back pressure and inlet flow at 3 o'clock Q in and export traffic Q out ; The time interval for collecting throttling response parameters is Δt, 0~ t 1. t 1~ t 2. t 2~ t 3. The increase in the mud pool during the time period, through t 1. t 2. t The difference between the outlet flow and the inlet flow at time 3 is multiplied by the time interval for calculation; According to the law of constant wellbore volume, the mathematical relationship between the bottom hole gas invasion volume and the wellhead mud pool increment is obtained: V G = V L + V dis （1） Where, V G is the gas invasion volume, m 3 ; V dis is the amount of dissolved gas, m 3 ; V L is the volume added to the mud pool, m 3 ; Based on the gas state equation, we get Δ t The gas intrusion mass flow rate during the time is: （2） Among them, M g is the molar mass of the gas, kg / mol; P wf is the bottom hole pressure, Pa; Z g is the gas compressibility factor, dimensionless; R is the gas constant (8.314), J / (mol·K); T is the gas temperature, K; Before performing multiphase flow model calculations, it is assumed that the gas dissolved volume is ; At the same time, Δ t The average bottom hole pressure during the time is assumed to be the initial bottom hole pressure; thus, 0~ t 1. t 1~ t 2. t 2~ t The assumed gas intrusion mass flow rate during the 3-hour period is: （3） Where, is the assumed gas intrusion mass flow rate, kg / s; is the assumed dissolved gas volume, m 3 .

4. The method for inverting the volume of karst caves in the process of gas invasion during drilling according to claim 2, characterized in that: In step 2, basic parameters for wellbore multiphase flow calculations are obtained, including wellbore trajectory, wellbore structure, drill bit assembly, fluid physical properties, initial temperature distribution, and drilling pump parameters. A transient multiphase flow model after gas invasion in the wellbore is established to calculate the wellbore pressure field, gas-liquid distribution, and solubility distribution. The model includes the gas phase mass conservation equation, the liquid phase mass conservation equation, and the gas-liquid two-phase momentum conservation equation.

5. The method for inverting the volume of karst caves in the process of drilling gas invasion according to claim 4, characterized in that: The gas phase mass conservation equation in the gas invasion section is: （4） The gas phase mass conservation equation in the non-gas invasion section is: （5） The liquid phase mass conservation equation is: （6） The gas-liquid two-phase momentum conservation equation is: （7） Where, R s , solubility of gas in drilling fluid, m 3 / m 3 ; A , annulus cross-sectional area, m 2 ; q = q gas / Δ H q , gas intrusion mass flow rate per unit length, kg / (s·m); Δ H q , depth of gas producing section, m; g, acceleration due to gravity, m / s 2 ; ρ gsc , gas density under standard conditions, kg / m 3 ; ρ g , gas density, kg / m 3 ; ρ l , drilling fluid density, kg / m 3 ; u g , gas flow rate, m / s; u l , drilling fluid velocity, m / s; E g , gas volume fraction, dimensionless; E l , drilling fluid volume fraction, dimensionless; , friction pressure drop, Pa / m; B l is the drilling fluid volume coefficient, %; P is the pressure, Pa; z is the vertical length, m; The finite difference method is used to discretize and solve the above multiphase flow model. The difference format is as follows: The difference format of the gas phase continuity equation in the gas invasion section is: （40） The difference format of the gas phase continuity equation in the non-gas invasion section is: （41） The difference format of the liquid phase continuity equation is （42） The difference format of the momentum equation is: （43） （44） （45） （46） j is a spatial node, dimensionless; n is the time node, dimensionless; Determine the model based on the actual project t =0, t 1. t 2. Initial and boundary conditions at time t.

6. The method for inverting the volume of karst caves in the process of drilling gas invasion according to claim 2, characterized in that: In step 3, 0~ t Taking the calculation process of the actual gas invasion mass flow rate in step 1 as an example, the wellhead back pressure and the assumed gas invasion mass flow rate in step 1 are used as boundary conditions and the multiphase flow model is used to calculate the 0~ t Bottom hole pressure at each time step within 1 time , calculate 0~ according to the trapezoidal formula t Average bottom hole pressure within 1 hour ; （52） Where, i is the number of time nodes; is the bottom hole pressure at the starting time node 0, Pa; for i Bottom hole pressure at the time node, Pa; dt is the time step, s; N 1 for t The number of time nodes in 1 time, N 1= t 1 / dt; Solubility calculated from the multiphase flow model R s The distribution of t The height of drilling fluid entering the annulus within 1 hour, that is, the length of the liquid column where gas dissolves H R1 , the dissolved gas content is obtained according to the following formula V dis,1 ; （53） Where, j is the number of spatial nodes; V dis,1 0~ t Amount of dissolved gas in 1 hour, m 3 ; H R1 0~ t Height of drilling fluid entering the annulus within 1 second, m; R s,j for j Solubility at spatial nodes; A a is the cross-sectional area of ​​the annulus, m 2 ; dz is the spatial step length, m; Calculated by the following formula: （54） V L,1 0~ t The volume of the mud pool increased in 1 time, m 3 ; Compare the calculated gas intrusion mass flow rate q gas,1 and the assumed gas intrusion mass flow rate The error between them, if the error satisfies: （55） The calculation ends and the output is 0~ t The actual gas intrusion mass flow rate within 1 time q gas,1 and t Bottom hole pressure at moment 1 P wf,1 Otherwise, q gas,1 Assign the value of , recalculate the multiphase flow model; t 1~ t 2. t 2~ t The actual gas intrusion mass flow rate within 3 hours q gas,2 、 q gas,3 ,and t 2. t Bottom hole pressure at time 3 P wf,2 、 P wf,3 , the calculation is the same as above steps; When there is no gas invasion, the initial gas mass in the cave is m , 0~ t 1. t 1~ t 2. t 2~ t The outflowing gas masses are q gas,1 Δ t 、 q gas,2 Δ t 、 q gas,3 Δ t ; From this we can calculate t 1. t 2. t Residual mass of gas in the cave at time 3 m 1. m 2. m 3. Set t 1. t 2. t The cave pressure at 3 moments is P v1 、 P v2 、 P v3 ; The reservoir model adopts the linear gas production model: q gas = J ( P v - P wf )（56） J is the reservoir model productivity index, kg / (Pa·s); P v is the cave pressure, Pa; According to the gas state equation and reservoir model, the following equations are obtained: （61） In the equation, R, T, Mg, Δ t is a constant; q gas,1 、q gas,2 、 q gas,3 、 Z g,1 、 Z g,2 、 Z g,3 、 P wf,1 、 P wf,2 、 P wf,3 All are solved by multiphase flow model; solve the above 6 equations together P v1 、 P v2 、 P v3 、 J 、 V 、 m , and thus the cave pressure P v , reservoir model productivity index J and the volume of stratum caves V .

Images