Numerical simulation method for evaluating critical sand production yield of gas well

Abstract

The invention discloses a numerical simulation method for evaluating gas well sand production critical yield. Mainly solves the problem of sand production of the gas well caused by overhigh production pressure difference and gas production speed in the gas testing and production process after the existing gas well is fractured. The method is characterized by comprising the following steps: establishing a gas well sand production critical mathematical model; according to a gas phase flow equation, the critical bottom hole flowing pressure, the critical production pressure difference and the critical production speed in the critical state are obtained through calculation, the critical flow speed and the critical yield in the production process are obtained according to different wellhead pressure changes, and a reasonable oil and gas well working system is formulated according to the critical flow speed and the critical flow. According to the numerical simulation method for evaluating the gas well sand production critical yield, the critical flow velocity and the critical flow in the production process can be obtained according to different wellhead pressure changes, so that a reasonable oil and gas well working system is formulated, and formation sand production is prevented.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas engineering, in particular to a numerical simulation method for evaluating the critical production of sand production in a gas well. Background Art

[0002] Sand production in gas wells refers to the phenomenon that formation sand flows to the bottom of the well along with the produced gas, which is one of the main contradictions in the oil and gas production process. In recent years, large-scale volume fracturing has been used in deep gas wells. After some wells were put into production, they could not produce due to severe sand production, which posed a safety hazard. At present, sand production and sand control work in oil and gas wells runs through the entire process of oil and gas reservoir exploration and development. Sand prediction, sand control technology, and sand control measures have been studied and reported. Since the causes and rules of sand production in different blocks are inconsistent, the causes of sand production in deep gas wells after fracturing are complex, mainly due to proppant reflux, but some wells also return formation sand at the same time.

[0003] There is no standard for critical determination of deep gas sanding, and there is no method to determine the optimal production conditions to obtain the maximum production capacity, which cannot guide gas well production. It is necessary to establish a new sanding prediction model to form a post-pressure sanding prediction method unique to deep gas wells. At present, there are few critical sanding experiments and no industry standards. In particular, the experimental equipment is expensive, the experimental parameters that can be changed are few, and the experimental repeatability is poor. Therefore, it is not easy to determine the critical sanding production of gas wells. Summary of the invention

[0004] In order to overcome the problem of sand production in gas wells caused by excessive production pressure difference and gas production rate during gas testing and production after existing gas well fracturing, the present invention provides a numerical simulation method for evaluating the critical production of sand production in gas wells. The numerical simulation method for evaluating the critical production of sand production in gas wells can obtain the critical flow rate and critical flow rate in the production process according to different wellhead pressure changes, thereby formulating a reasonable oil and gas well working system to prevent sand production in the formation.

[0005] The technical solution of the present invention is: a numerical simulation method for evaluating the critical production of sand production in a gas well, characterized by comprising the following steps:

[0006] S1. Based on the mechanical analysis of the critical sand production characteristic position of the gas well, combined with the stress state of the reservoir rock and the rock failure criterion used to judge the failure conditions of the reservoir rock, a critical mathematical model of sand production in the gas well is established;

[0007] S2. Considering the fluid pressure in the pores of the formation rock, when the rock at the critical position begins to fail, the bottom hole flow pressure obtained is the critical bottom hole flow pressure for sand production;

[0008] S3. Based on the Darcy flow equation of gas in the fracture and the non-Darcy flow equation of gas in the propped fracture, and combined with the inertial resistance coefficient formula in the proppant reflux mechanics model under the gas test system, the equation for the critical flow velocity of gas in the propped fracture under the critical state is obtained;

[0009] S4. Obtain the critical gas production equation on the ground from the crack width, crack height and natural gas volume coefficient;

[0010] S5. Calculate the critical bottom hole flow pressure, critical production pressure difference, critical gas flow rate and critical gas production of the gas well according to the wellhead pressure change and gas production.

[0011] Furthermore, in step S1, the critical mathematical model of gas well sand production is a proppant reflux mechanics model. When establishing the proppant reflux mechanics model in the production process, the following assumptions are made:

[0012] (1) The supporting crack is a vertical crack, and the crack width is constant at every height;

[0013] (2) The flow state in the fracture is a gas-liquid two-phase linear flow;

[0014] (3) The proppant particles are uniform in size, the particles are in point contact, and particle deformation is not considered;

[0015] (4) During the production process, the cracks close and the vertical forces cancel each other out.

[0016] In the horizontal direction, the critical condition for sand production in gas wells is

[0017] F≥f (1)

[0018] In the formula: F is the sand discharge power, f is the sand discharge resistance.

[0019] Furthermore, in the formula (1), the sand production force F includes the drag force strength P of the gas on the proppant. drag and capillary force strength σ c , the sand production resistance f includes the closing stress resistance strength f c , shear stress intensity T and tensile strength σ r , then the mathematical expression of the critical condition of sand production in gas wells is:

[0020] P drag +σ c ≥T+σ r +f c (2)

[0021] Where: P drag is the drag strength, MPa; σ c is the capillary strength, MPa; T is the shear stress, MPa; σ r Tensile strength, MPa; fc is the closing stress resistance strength, MPa.

[0022] Furthermore, in step S2, when the rock at the critical position begins to break, the following conditions are satisfied:

[0023] σ max -β·P≥2C0tanα+(σ min -β·P)·tan 2 α (3)

[0024] Where: max is the maximum horizontal stress, MPa; σ min is the horizontal minimum stress, MPa; β is the Bitau constant, dimensionless; P is the fluid pressure in the rock pores, MPa; C0 is the rock compressive strength, MPa; α is the failure angle, rad.

[0025] Furthermore, in step S2, at the critical position, the maximum and minimum stresses are functions of the bottom hole flow pressure, and thus the equilibrium equation for the bottom hole flow pressure is obtained:

[0026] F(P wf )=σ max (P wf )-β·P(P wf )-2C0tanα-[σ min (P wf )-β·P(P wf )]·tan 2 α≥0 (4)

[0028] Where P wf is the bottom hole flowing pressure, MPa.

[0029] Furthermore, in the formula (4), P wf As a variable, solve the equation, and the bottom hole flowing pressure obtained is the critical bottom hole flowing pressure for sand production, which can be converted to the critical production pressure difference for sand production:

[0030] ΔP c =P r -P wfc (5)

[0031] Where ΔP c is the critical production pressure difference of sand production, MPa; P r is the formation static pressure, MPa; P wfc is the critical bottom hole flowing pressure for sand production, MPa.

[0032] Furthermore, in step S3, the Darcy flow equation of the gas in the crack is:

[0033]

[0034] Where: L pf is the proppant fracture length, m; P is the fluid pressure in the rock pores, MPa; P r is the formation static pressure, MPa; P wf is the bottom hole flowing pressure, MPa;

[0035] Non-Darcy flow equation for gas in propped fractures:

[0036]

[0037] Where: R is the gas Proctor constant, dimensionless; μ gi is the viscosity of natural gas in the formation, mPa·s; Z is the natural gas deviation factor, dimensionless; T i is the formation temperature, K; ρ a is the air density, kg / m 3 ;δ is the inertial resistance coefficient, 1 / m;γ g is the relative density of natural gas, dimensionless; P wf is the bottom hole flow pressure, MPa; k g is the absolute permeability of the fracture, mD; is the fracture equivalent porosity, dimensionless; v is the gas flow rate, m / s.

[0038] Furthermore, the formula for the inertial resistance coefficient in the proppant reflux mechanics model under the gas test system is

[0039]

[0040] Where: δ is the inertial resistance coefficient, 1 / m; L pt is the proppant fracture length, m; d p is the proppant diameter, m; is the fracture equivalent porosity, dimensionless.

[0041] Furthermore, the equation for the critical velocity of gas in the critical state in the propped fracture is obtained from equations (6), (7), and (8):

[0042]

[0043] Where: V c is the critical gas velocity, m / s.

[0044] Further, in step S4, the critical gas production equation on the ground is obtained from the fracture width, fracture height and natural gas volume coefficient:

[0045]

[0046] Where: W pfj is the crack width, m; Hpfj is the support crack height, m; B g is the natural gas volume coefficient; n is the number of fracturing stages, dimensionless; Q is the natural gas production, m 3 / d;V j is the gas flow rate in the current fracturing section, m / s. The present invention has the following beneficial effects: Due to the adoption of the above scheme, the present invention is based on the early prevention of critical sand production in gas wells, and obtains the critical flow rate and critical flow rate in the production process according to different wellhead pressure changes. A reasonable oil and gas well working system is formulated according to the critical flow rate and critical flow rate to prevent sand production in the formation, thereby solving the problem of sand production in the gas well caused by excessive production pressure difference and gas production rate during gas testing and production after fracturing of deep gas wells; at the same time, based on the critical flow rate for sand production, the maximum gas testing capacity can be obtained while preventing sand production. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of the present invention;

[0048] Figure 2 It is a schematic diagram of the mathematical model of proppant return;

[0049] Figure 3 It is the XS32 well simulation parameter input interface in Example 1;

[0050] Figure 4 This is the XS32 well simulation output interface in Example 1. DETAILED DESCRIPTION

[0051] The present invention will be further described below in conjunction with the accompanying drawings:

[0052] Depend on Figure 1 As shown, a numerical simulation method for evaluating the critical production of sand production in a gas well comprises the following steps:

[0053] S1. Based on the mechanical analysis of the critical sand production characteristic position of the gas well, combined with the stress state of the reservoir rock and the rock failure criterion used to judge the failure conditions of the reservoir rock, a critical mathematical model of sand production in the gas well is established.

[0054] The critical mathematical model for sand production in gas wells is the proppant reflux mechanics model. When establishing the proppant reflux mechanics model in the production process, the following assumptions are made:

[0055] (1) The supporting crack is a vertical crack, and the crack width is constant at every height;

[0056] (2) The flow state in the fracture is a gas-liquid two-phase linear flow;

[0057] (3) The proppant particles are uniform in size, the particles are in point contact, and particle deformation is not considered;

[0058] (4) During the production process, the cracks close and the forces in the vertical direction cancel each other out.

[0059] During the production process, the critical condition for sand production in the gas well in the horizontal direction is (see Figure 2 ):

[0060] F≥f (1)

[0061] In the formula: F is the sand discharge power, f is the sand discharge resistance.

[0062] Among them, the sand production power F includes the drag force strength P of the gas on the proppant drag and capillary force strength σ c , the sand production resistance f includes the closing stress resistance strength f c , shear stress intensity T and tensile strength σ r , then the mathematical expression of the critical condition of sand production in gas wells is:

[0063] P drag +σ c ≥T+σ r +f c (2)

[0064] Where: P drag is the drag strength, MPa; σ c is the capillary strength, MPa; T is the shear stress, MPa; σ r Tensile strength, MPa; f c is the closing stress resistance strength, MPa.

[0065] S2. According to the analysis of sand production characteristics and the rock failure criterion, when the rock at the critical position begins to fail, the gas well begins to produce sand. Considering the fluid pressure in the pores of the formation rock and the Mohr-Coulomb criterion expressed by the principal stress, when the rock at the critical position begins to fail, the bottom hole pressure obtained is the critical bottom hole pressure for sand production.

[0066] When the rock begins to fail at the critical position, the following conditions are met:

[0067] σ max -β·P≥2C0tanα+(σ min -β·P)·tan 2 α (3)

[0068] Where: max is the maximum horizontal stress, MPa; σ min is the horizontal minimum stress, MPa; β is the Bitau constant, dimensionless; P is the fluid pressure in the rock pores, MPa; C0 is the rock compressive strength, MPa; α is the failure angle, rad.

[0069] At the critical position, the maximum and minimum stresses are functions of the bottom hole pressure, and the equilibrium equation for the bottom hole pressure is obtained:

[0070] F(P wf )=σ max (P wf )-β·P(P wf )-2C0tanα-[σ min (P wf )-β·P(P wf )]·tan 2 α≥0 (4)

[0072] Where P wf is the bottom hole flowing pressure, MPa.

[0073] In the formula (4), P wf As a variable, solve the equation, and the bottom hole flowing pressure obtained is the critical bottom hole flowing pressure for sand production, which can be converted to the critical production pressure difference for sand production:

[0074] ΔP c =P r -P wfc (5)

[0075] Where ΔP c is the critical production pressure difference of sand production, MPa; P r is the formation static pressure, MPa; P wfc is the critical bottom hole flowing pressure for sand production, MPa.

[0076] S3. Based on the Darcy flow equation for gas in fractures and the non-Darcy flow equation for gas in propped fractures, combined with the inertial resistance coefficient formula in the proppant reflux mechanics model under the gas test system, the equation for the critical flow velocity of gas in propped fractures under the critical state is solved.

[0077] Darcy flow equation for gas in a crack:

[0078]

[0079] Where: L pf is the proppant fracture length, m; P is the fluid pressure in the rock pores, MPa; P r is the formation static pressure, MPa; P wf is the bottom hole flowing pressure, MPa.

[0080] Non-Darcy flow equation for gas in propped fractures:

[0081]

[0082] Where: R is the gas Proctor constant, dimensionless; μgi is the viscosity of natural gas in the formation, mPa·s; Z is the natural gas deviation factor, dimensionless; T i is the formation temperature, K; ρ a is the air density, kg / m 3 ;δ is the inertial resistance coefficient, 1 / m;γ g is the relative density of natural gas, dimensionless; P wf is the bottom hole flow pressure, MPa; k g is the absolute permeability of the fracture, mD; is the fracture equivalent porosity, dimensionless; v is the gas flow rate, m / s.

[0083] Formula of inertial resistance coefficient in proppant reflux mechanical model under gas testing system

[0084]

[0085] Where: δ is the inertial resistance coefficient, 1 / m; L pt is the proppant fracture length, m; d p is the proppant diameter, m; is the fracture equivalent porosity, dimensionless.

[0086] The equation for the critical velocity of gas in the critical state in the propped fracture is obtained from equations (6), (7) and (8):

[0087]

[0088] Where: V c is the critical gas velocity, m / s.

[0089] S4. The critical gas production equation on the ground is obtained from the crack width, crack height and natural gas volume coefficient:

[0090]

[0091] Where: W pfj is the crack width, m; H pfj is the support crack height, m; B g is the natural gas volume coefficient; n is the number of fracturing stages, dimensionless; Q is the natural gas production, m3 / d; V j is the gas flow rate in the current fracturing stage, m / s.

[0092] S5. Based on the critical sand production characteristic parameters of gas wells (critical bottom hole flowing pressure, critical flow rate, critical production), an information file for numerical simulation of sand production and critical production is derived, input parameters (reservoir parameters, fracture parameters, gas production parameters, production parameters) are set, and a critical sand production simulation program for gas wells is compiled. Through program calculations, the critical bottom hole flowing pressure, critical production pressure difference, critical gas flow rate and critical gas production of the gas well can be calculated according to different wellhead pressure changes and different gas productions. This can be used to determine whether deep gas wells are producing sand, and to guide the formulation of a reasonable gas test system for different wellhead pressures and test gas productions.

[0093] (1) Set input parameters:

[0094] ① Reservoir parameters: including reservoir porosity, reservoir permeability, reservoir temperature, reservoir depth, rock internal friction angle, uniaxial compressive strength, minimum principal stress, etc.

[0095] ② Crack parameters: including closure stress within the crack, crack width, crack height, crack length, etc.

[0096] ③ Gas parameters: including natural gas relative density, natural gas deviation factor, natural gas viscosity, natural gas volume coefficient, etc.

[0097] ④ Production parameters: including wellhead pressure, daily production of gas wells corresponding to different wellhead pressures, etc.

[0098] (2) Output results

[0099] The critical bottom hole flowing pressure, critical gas flow rate and critical gas production corresponding to different wellhead pressure changes.

[0100] Embodiment 1

[0101] The numerical simulation method of critical production of sand production in gas wells was applied to the gas production test of XS32 well in Songliao deep gas formation. The reservoir parameters, fracture parameters, gas production parameters and production parameters of XS32 well were input into the simulation program. Figure 3 .

[0102] Run the simulation program to obtain the critical flow rate and critical production under different wellhead pressure conditions, see Figure 4 The simulation results show that the critical production of proppant backflow in Well XS32 is 20.734×10 4 m 3 / d, in order to prevent the sand from being produced by the proppant reflux test, the production should be controlled below 20.734×10 4 m 3 / d. Based on the results, a production system for XS32 well was formulated. An 11.91 mm oil nozzle was used on site to produce 19.8 × 10 4 m 3 / d, with a total production of 200 days, no sand production at the wellhead, and the gas test production situation was consistent with the critical sand production prediction.

Claims

1. A numerical simulation method for evaluating the critical production of sand production in gas wells, characterized in that The following steps are involved: S1. Based on the mechanical analysis of the critical sand production characteristic position of the gas well, combined with the stress state of the reservoir rock and the rock failure criterion used to judge the failure conditions of the reservoir rock, a critical mathematical model of sand production in the gas well is established; S2. Considering the fluid pressure in the pores of the formation rock, when the rock at the critical position begins to fail, the bottom hole flow pressure obtained is the critical bottom hole flow pressure for sand production; S3. Based on the Darcy flow equation of gas in the fracture and the non-Darcy flow equation of gas in the propped fracture, and combined with the inertial resistance coefficient formula in the proppant reflux mechanics model under the gas test system, the equation for the critical flow velocity of gas in the propped fracture under the critical state is obtained; S4. Obtain the critical gas production equation on the ground from the crack width, crack height and natural gas volume coefficient; S5. Calculate the critical bottom hole flow pressure, critical production pressure difference, critical gas flow rate and critical gas production of the gas well according to the wellhead pressure change and gas production.

2. The numerical simulation method for evaluating the critical production of sand production in a gas well according to claim 1, characterized in that: In step S1, the critical mathematical model for sand production in gas wells is a proppant reflux mechanics model. When establishing the proppant reflux mechanics model in the production process, the following assumptions are made: (1) The supporting crack is a vertical crack, and the crack width is constant at every height; (2) The flow state in the fracture is a gas-liquid two-phase linear flow; (3) The proppant particles are uniform in size, the particles are in point contact, and particle deformation is not considered; (4) During the production process, the cracks close and the vertical forces cancel each other out. In the horizontal direction, the critical condition for sand production in gas wells is F≥f (1) In the formula: F is the sand discharge power, f is the sand discharge resistance.

3. The numerical simulation method for evaluating the critical production of sand production in a gas well according to claim 2, characterized in that: In the formula (1), the sand production force F includes the drag force strength P of the gas on the proppant drag and capillary force strength σ c , the sand production resistance f includes the closing stress resistance strength f c , shear stress intensity T and tensile strength σ r , then the mathematical expression of the critical condition of sand production in gas wells is: P drag +s c ≥T+σ r +f c (2) Where: P drag is the drag strength, MPa; σ c is the capillary strength, MPa; T is shear stress, MPa; σ r Tensile strength, MPa; f c is the closing stress resistance strength, MPa.

4. The numerical simulation method for evaluating the critical production of sand production in a gas well according to claim 1, characterized in that: In step S2, when the rock at the critical position begins to break, the following conditions are met: s max -β·P≥2C0tanα+(σ min -β·P)·tan 2 a (3) Where: max is the maximum horizontal stress, MPa; σ min is the minimum horizontal stress, MPa; β is the Biteau constant, dimensionless; P is the fluid pressure in the rock pores, MPa; C0 is the rock compressive strength, MPa; α is the failure angle, rad.

5. The numerical simulation method for evaluating the critical production of sand production in a gas well according to claim 4, characterized in that: In step S2, at the critical position, the maximum and minimum stresses are functions of the bottom hole flow pressure, and the equilibrium equation for the bottom hole flow pressure is obtained: F(P wf )6σ max (P wf )-β·P(P). wf )-2C0tanα-[σ min (P wf )-β·P(P). wf )]·tan 2 α≥0 (4) Where P wf is the bottom hole flowing pressure, MPa.

6. The numerical simulation method for evaluating the critical production of sand production in a gas well according to claim 5, characterized in that: In the formula (4), P wf As variables, solve the equation, and the bottom hole flowing pressure obtained is the critical bottom hole flowing pressure for sand production, which can be converted to the critical production pressure difference for sand production: ΔP c =P r -P wfc (5) Where ΔP c is the critical production pressure difference of sand production, MPa; P r is the formation static pressure, MPa; P wfc is the critical bottom hole flowing pressure for sand production, MPa.

7. The numerical simulation method for evaluating the critical production of sand production in a gas well according to claim 1, characterized in that: In step S3, the Darcy flow equation of gas in the crack is: Where: L pf is the proppant fracture length, m; P is the fluid pressure in the rock pores, MPa; P r is the formation static pressure, MPa; P wf is the bottom hole flowing pressure, MPa; Non-Darcy flow equation for gas in propped fractures: Where: R is the gas Proctor constant, dimensionless; μ gi is the viscosity of natural gas in the formation, mPa·s; Z is the natural gas deviation factor, dimensionless; T i is the formation temperature, K; ρ a is the air density, kg / m 3 ;δ is the inertial resistance coefficient, 1 / m;γ g is the relative density of natural gas, dimensionless; P wf is the bottom hole flow pressure, MPa; k g is the absolute permeability of the fracture, mD; is the fracture equivalent porosity, dimensionless; v is the gas flow rate, m / s.

8. The numerical simulation method for evaluating the critical production of sand production in a gas well according to claim 7, characterized in that: Formula of inertial resistance coefficient in proppant reflux mechanical model under gas testing system Where: δ is the inertial resistance coefficient, 1 / m; L pt is the proppant fracture length, m; d p is the proppant diameter, m; is the fracture equivalent porosity, dimensionless.

9. The numerical simulation method for evaluating the critical production of sand production in a gas well according to claim 8, characterized in that: The equation for the critical velocity of gas in the critical state in the propped fracture is obtained from equations (6), (7) and (8): Where: V c is the critical gas velocity, m / s.

10. The numerical simulation method for evaluating the critical production of sand production in a gas well according to claim 1, characterized in that: In step S4, the critical gas production equation on the ground is obtained from the crack width, crack height and natural gas volume coefficient: Where: W pfj is the crack width, m; H pfj is the support crack height, m; B g is the natural gas volume coefficient; n is the number of fracturing stages, dimensionless; Q is the natural gas production, m 3 / d;V j is the gas flow rate in the current fracturing stage, m / s.

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