A new method for predicting bottom hole flowing pressure of multi-stage fractured horizontal well based on three-phase percolation

Abstract

The present application belongs to the field of gas field development, and particularly relates to a new method for predicting bottom hole flowing pressure of multi-stage fractured horizontal well based on three-phase percolation. In the present application, in order to solve the problem that the traditional flowback model cannot accurately describe the influence of gas release and expansion on flowback dynamic due to the simplification of the multi-phase percolation process, the wellbore choke effect is combined with the three-phase percolation equation of the fracture network, the dynamic iteration algorithm is used to synchronously solve the change of bottom hole flowing pressure and the change of three-phase saturation, the improved trapezoidal integration method is used to ensure the mass conservation, and the whole life cycle dynamic prediction from fracturing fluid flowback to long-term production is realized. The method has theoretical rationality and practical production application value in the actual application of gas reservoir stimulation.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of gas field development, and particularly relates to a new method for predicting bottom hole flowing pressure of multi-stage fractured horizontal well based on three-phase seepage. BACKGROUND

[0002] The traditional flowback model is usually based on the simplified single-phase or two-phase flow assumption, and the complex multi-phase seepage process is oversimplified, and the important role of three phases in the flowback process is ignored. In the actual fracturing flowback process, the fracturing fluid injected into the formation has a complex interaction with the oil, gas and water in the reservoir. With the flowback, the bottom hole pressure gradually decreases, and the gas originally dissolved in the crude oil begins to separate out to form a free gas phase. This process not only increases the complexity of the fluid, but also significantly changes the flow characteristics. The traditional model cannot accurately describe the influence of gas release and expansion on the flowback dynamics, resulting in large deviations in the prediction of flowback rate, productivity and gas breakthrough time. Therefore, we propose a new method for predicting bottom hole flowing pressure of multi-stage fractured horizontal well based on three-phase seepage. SUMMARY

[0003] The purpose of the present application is to solve the technical problem that the flowback process is disconnected from the production seepage in the traditional method by combining the wellbore choke effect with the three-phase seepage equation of the fracture network and using a dynamic iterative algorithm to simultaneously solve the changes of bottom hole flowing pressure and three-phase saturation. The real-time coupling calculation of differential pressure, flow rate and saturation is realized by coupling the choke flow rate term and the fracture seepage term in the coupling formula, and the improved trapezoidal integration method is used to ensure the accurate calculation of the cumulative flowback volume and the mass conservation. The whole life cycle dynamics from fracturing fluid flowback to long-term production can be accurately simulated, which provides reliable technical support for optimizing the flowback system and predicting the productivity. In order to achieve the above purpose, the present application provides a new method for predicting bottom hole flowing pressure of multi-stage fractured horizontal well based on three-phase seepage.

[0004] Firstly, the rock mechanics, reservoir properties, fluid properties and saturation parameters are determined according to the field production data;

[0005] Secondly, a comprehensive coupling mathematical calculation model is built by C#, the flowback volume is calculated according to the derived flowback flow formula, the filtration loss volume is calculated according to the filtration loss flow formula, and the comprehensive coupling mathematical calculation model is brought in;

[0006] Thirdly, the three saturation degrees are updated and iterated based on the material balance principle and the relative permeability model;

[0007] Fourthly, the cumulative flowback volume is calculated by the improved trapezoidal rule to ensure the mass conservation in the simulation process;

[0008] Fifth step, check whether the differential pressure and saturation change meet the convergence accuracy, control the iteration process;

[0009] Sixth step, time is dispersed by using explicit Euler method, and transient change of bottom hole flowing pressure is solved by dynamic iteration;

[0010] Seventh step, real-time drawing of differential pressure, flowback volume and cumulative flowback volume dynamic curve, and output of structured simulation data.

[0011] Compared with the prior art, the method has the following beneficial effects: (1) wide application range, can be applied to gas reservoirs under different conditions; (2) convenient and effective calculation method, high work efficiency; (3) the calculation method is easy to popularize. BRIEF DESCRIPTION OF DRAWINGS

[0012] In the drawings:

[0013] Figure 1 is a technical roadmap of the method;

[0014] Figure 2 is a calculation flowchart;

[0015] Figure 3 is a software calculation result graph. DETAILED DESCRIPTION

[0016] The application will be further described below in combination with embodiments and drawings;

[0017] The application provides a new method for predicting bottom hole flowing pressure of a horizontal well with multi-stage fracturing based on three-phase seepage, and the method comprises the following steps:

[0018] S100: determining Young's modulus of rock, Poisson's ratio, fracture compliance, permeability, formation pressure, matrix seepage characteristic length, fracture height, fracture half-length, first fracture filter area, water phase viscosity, oil phase viscosity, gas phase viscosity, tubing radius, choke radius, choke resistance coefficient, choke pressure, current bottom hole flowing pressure, current water saturation, current oil saturation and the like according to field production data. ​​​​​​​​​​​​​​​​​​​, current gas saturation , residual oil saturation , determine the number of fracture segments , pore volume ;

[0019] S200: build comprehensive coupling mathematical calculation model by C# using Vsual Studio platform:

[0020]

[0021] wherein is the fracture compliance coefficient, with the unit of m 3 / Pa; is the number of fracture segments, dimensionless; is the bottom hole flowing pressure, with the unit of MPa; is the flowback flow, with the unit of m 3 / h; is the filtration flow, with the unit of m 3 / h; is the time, with the unit of h;

[0022] S201: apply Bernoulli equation and introduce continuity equation to consider cross-sectional area change to obtain flowback flow Calculation formula:

[0023]

[0024] wherein is the tubing radius, with the unit of m; is the choke outlet pressure, with the unit of MPa; is the bottom hole flowing pressure, with the unit of MPa; is the mixed liquid density, with the unit of kg / m³; is the choke resistance coefficient, dimensionless; is the choke radius, with the unit of m;

[0025] S202: apply Darcy law to one-way flow and extend to multiple flow summation to obtain filtration flow of all fractures Calculation formula:

[0026]

[0027]

[0028] wherein is the filtration area of the first fracture, with the unit of m 2 ; is the absolute permeability, dimensionless; is the effective viscosity, with the unit of ; is the relative permeability of water phase, dimensionless; is the relative permeability of oil phase, dimensionless; is the relative permeability of gas phase, dimensionless; is the viscosity of water phase, unit is mPa·s; ; is the viscosity of oil phase, unit is mPa·s; ; is the viscosity of gas phase, unit is mPa·s; ; is the characteristic length of matrix seepage, unit is m; is the formation pressure, unit is MPa; wherein

[0029] = + + ;

[0030] is the endpoint relative permeability of water phase, dimensionless, is the endpoint relative permeability of oil phase, dimensionless; is the endpoint relative permeability of oil phase under coexisting water condition, dimensionless; is the current water phase saturation, dimensionless; is the current gas phase saturation, dimensionless; is the current oil phase saturation, dimensionless; is the irreducible water saturation, dimensionless; is the residual oil saturation, dimensionless; is the residual gas saturation, dimensionless; is the Correy index of water phase, dimensionless; is the Correy index of gas phase, dimensionless; is the Correy index of oil phase;

[0031] S300: based on the principle of material balance, iteratively update the three-phase saturations according to the flow calculation results of the current time step:

[0032]

[0033] In the formula, is the water phase production volume in , unit is m 3 ; is the instantaneous filtration volume of water phase in , unit is m 3 ; is the oil phase production volume in , unit is m 3 ; is the produced volume of the oil phase in the time interval, in m 3 ; is the pore volume, in m 3 ;

[0034] S400: cumulative flowback volume is calculated by using improved trapezoidal rule to ensure mass conservation:

[0035]

[0036]

[0037] wherein is the instantaneous flowback volume, in m 3 / h; is the fracture compliance coefficient, in m 3 / Pa; is the pressure of the k-th fracture, in MPa; is the bottom hole flowing pressure, in MPa; is the filtration area of the k-th fracture, in m 2 ; is the absolute permeability, dimensionless; is the total filtration area, in m 2 ; is the effective viscosity, in ; is the matrix seepage characteristic length, in m; is the formation pressure, in MPa; realize the whole life cycle dynamic prediction from fracturing flowback to long-term production;

[0038] S500: time is discretized by using explicit Euler method, flow rate calculation is driven by dynamic pressure change, real-time simulation of physical process is realized, and iteration calculation is performed in each time step :

[0039]

[0040] wherein is the bottom hole flowing pressure, in MPa; is the fracture compliance coefficient, in m 3 / Pa; is the number of fracture segments, dimensionless; is the flowback flow rate, in m 3 / h, is the filtration flow rate, in m 3 / h;

[0041] ​S600: Verify convergence and iteration control, set convergence tolerance = 0.001, verify the change between adjacent iterations:

[0042] and ;

[0043] wherein is the bottom hole flowing pressure, in MPa; is the saturation, dimensionless;

[0044] If not converged, return to step S200 to continue iteration; if converged, output the current time step result and advance to the next time step;

[0045] X gas field rock mechanics parameters Young's modulus = 27500 Mpa, Poisson's ratio = 0.2, fracture compliance = 0.00015 m 3 / Pa, reservoir parameters absolute permeability = 0.0001 mD, formation pressure = 5 MPa, matrix seepage characteristic length = 50 m, water phase viscosity = 0.001 , oil phase viscosity = 0.005 , gas phase viscosity = 0.0001 , relative permeability parameters water phase Correy index = 2.5, gas phase Correy index = 2.2, oil phase Correy index = 2.0, water phase endpoint relative permeability = 0.3, oil phase endpoint relative permeability = 0.8, simulation parameters simulation time 8h, time step = 0.05h, wellbore and operating parameters tubing radius = 0.0315 m, choke radius = 0.008 m, choke resistance coefficient = 0.5, choke outlet pressure = 0.1 MPa, current bottom hole flowing pressure = 15.8 MPa, saturation parameters current water saturation = 0.6, current oil saturation = 0.3, current gas saturation = 0.1, residual oil saturation = 0.15;

[0046] S700: output and visually display the dynamic results of the pressure change, flowback flow, cumulative flowback volume obtained by the iterative calculation, to provide instant reference for field construction decision.

[0047] Compared with the prior art, the present application has the following beneficial effects: (1) wide application range, can be applied to gas wells under different conditions; (2) convenient and effective calculation method, high work efficiency; (3) the calculation method is easy to popularize. Finally, it should be pointed out that: the above examples are only used to illustrate but not to limit the technical solutions of the present application, although the present application has been described in detail with reference to the above examples, those skilled in the art should understand that: the present application can still be modified or equivalently replaced without departing from the spirit and scope of the present application, any modification or partial replacement should be covered in the scope of the claims of the present application.

Claims

1. A new method for predicting the bottom hole flowing pressure of a multi-stage fractured horizontal well based on three-phase seepage, characterized in that, The method comprises the following steps: S100: Young's modulus of rock determined from field production data , Poisson's ratio , fracture compliance ; permeability , formation pressure , matrix permeation characteristic length ; fracture height , fracture half-length , the th fracture's filtration area , water phase viscosity , oil phase viscosity , gas phase viscosity , tubing radius , choke radius , choke resistance coefficient , choke pressure , current bottom hole flowing pressure , current water saturation , current oil saturation , current gas saturation , residual oil saturation , determining the number of fracture segments , pore volume ; S200: build the integrated coupling mathematical calculation model by C# through the Vsual Studio platform: wherein is the fracture compliance, in m3 / Pa; is the number of fracture segments, dimensionless; is the bottom hole flowing pressure, in MPa; is the flowback flow rate, in m3 / h; is the fluid loss flow rate, in m3 / h; is the time, in h; S201: Bernoulli equation is applied and continuity equation is introduced to consider the cross-sectional area change to obtain the flowback flow rate Calculation formula: wherein Rtis the tubing radius in m; Pn is the nozzle outlet pressure in MPa; Pwf is the bottom hole flowing pressure in MPa; ρ is the mixture density in kg / m3; Cn is the nozzle resistance coefficient, dimensionless; Rn is the nozzle radius in m; S202: Apply Darcy's law to the single flow and extend to the multiple flow summation of all fractures to obtain the calculated filtration loss Calculation formula: wherein is the absolute permeability, dimensionless; is the absolute permeability, dimensionless; is the absolute permeability, dimensionless; is the effective viscosity, in mPa-s; ; is the relative permeability of the water phase, dimensionless; is the relative permeability of the oil phase, dimensionless; is the relative permeability of the gas phase, dimensionless; is the viscosity of the water phase, in mPa-s; ; is the viscosity of the oil phase, in mPa-s; ; is the viscosity of the gas phase, in mPa-s; ; is the characteristic length of the matrix, in m; is the formation pressure, in MPa; Wherein = + + ； Krw, end-point relative permeability of the water phase, dimensionless, Kro, end-point relative permeability of the oil phase, dimensionless; Kro, end-point relative permeability of the oil phase in the presence of water, dimensionless; Sw, current water phase saturation, dimensionless; Sg, current gas phase saturation, dimensionless; So, current oil phase saturation, dimensionless; Swc, irreducible water saturation, dimensionless; Sor, residual oil saturation, dimensionless; Sgr, residual gas saturation, dimensionless; Cw, Correy exponent of the water phase, dimensionless; Cg, Correy exponent of the gas phase, dimensionless; Co, Correy exponent of the oil phase; S300: based on the principle of material balance, iteratively update the three-phase saturation according to the flow calculation result of the current time step: wherein is the volume of water phase produced in the time interval, in m3; is the instantaneous filtration loss of water phase in the time interval, in m3; is the volume of oil phase produced in the time interval, in m3; is the instantaneous filtration loss of oil phase in the time interval, in m3; is the volume of oil phase produced in the time interval, in m3; is the instantaneous filtration loss of oil phase in the time interval, in m3; is the volume of oil phase produced in the time interval, in m3; is the instantaneous filtration loss of oil phase in the time interval, in m3; is the pore volume, in m3; S400: calculate the cumulative flowback volume by using the improved trapezoidal rule, and ensure the conservation of mass: wherein is the instantaneous flowback rate, in m3 / h; is the fracture compliance coefficient, in m3 / Pa; is the pressure of the k-th fracture, in MPa; is the bottom hole flowing pressure, in MPa; is the pressure of the k-th fracture, in MPa; is the drainage area of the k-th fracture, in m2; is the absolute permeability, dimensionless; is the total drainage area, in m2; is the effective viscosity, in m2 / s; ; is the matrix seepage characteristic length, in m; is the formation pressure, in MPa; Realize the whole life cycle dynamic prediction from fracturing flowback to long-term production; S500: Time-discretization is performed by using the explicit Euler method, and the flow rate calculation is driven by the dynamic pressure change to realize real-time simulation of the physical process at each time step Inner iteration calculation: wherein Pwf is the bottom hole flowing pressure in MPa; is the fracture compliance coefficient in m3 / Pa; is the number of fracture segments, dimensionless; is the flowback rate in m3 / h, is the fluid loss rate in m3 / h; S600: Verify convergence and iteration control, set convergence tolerance = 0.001, verify change between adjacent iteration steps: and ; wherein Pb is the bottom hole flowing pressure in MPa; S is the saturation, dimensionless; If it does not converge, return to step S200 to continue iteration; if it converges, output the current time step result and advance to the next time step; X gas field rock mechanics parameter Young's modulus = 27500 Mpa, Poisson's ratio = 0.2, fracture compliance = 0.00015 m3 / Pa, reservoir parameter absolute permeability = 0.0001 mD, formation pressure = 5 Mpa, matrix seepage characteristic length = 50 m, water phase viscosity = 0.001 , oil phase viscosity = 0.005 , gas phase viscosity = 0.0001 , relative permeability parameter water phase Correy index = 2.5, gas phase Correy index = 2.2, oil phase Correy index = 2.0, water phase endpoint relative permeability = 0.3, oil phase endpoint relative permeability = 0.8, simulation parameter simulation time 8 h, time step = 0.05 h, wellbore and operating parameter tubing radius = 0.0315 m, choke radius = 0.008 m, choke resistance coefficient = 0.5, choke outlet pressure = 0.1 Mpa, current bottom hole flowing pressure = 15.8 Mpa, saturation parameter current water saturation = 0.6, current oil saturation = 0.3, current gas saturation = 0.1, residual oil saturation = 0.15; S700: output and visually display the dynamic results of pressure change, flowback flow, and cumulative flowback volume obtained by iterative calculation, to provide instant reference for on-site construction decision.

Images