Condensate gas well wax precipitation prediction method and application thereof

Abstract

The invention belongs to the technical field of oil exploitation, and discloses a condensate gas well wax precipitation prediction method and application thereof.The method comprises the steps that a dynamic shaft gas-liquid wax precipitation prediction model is established through a basic diffusion deposition equation by considering the influence of an oil wax structure and gas high shear force, and the total model is shown in the formula (6); and the # imgabs0 # brings basic data of an oil and gas well into the model, calculation is carried out, and a wax precipitation chart is established. According to the invention, the paraffin precipitation position and the paraffin precipitation speed of the oil well can be predicted more accurately. According to the method, a gas-liquid two-phase wax deposition dynamic model is established by considering wax deposition mechanism influences such as flow patterns, gas high shear force and oil wax structures. The model is applied to establish a paraffin precipitation prediction chart of a certain condensate gas field, and has guiding significance on field paraffin precipitation problem treatment.

Description

Technical Field

[0001] The invention belongs to the technical field of petroleum exploitation and relates to a wax deposition prediction method for a condensate gas well and an application thereof. Background Art

[0002] During the development of high-wax condensate gas reservoirs, as the temperature and pressure decrease, the condensate gas overflows, and the precipitation and deposition of paraffin in the wellbore and surface pipelines will lead to increased pipeline back pressure, increased oil transportation resistance, wellbore blockage and reduced production, etc. In the past, the prediction of wax deposition in oil wells was generally carried out in oil wells, only considering the solid-liquid two phases. The method did not consider the influence of flow pattern and high shear force of gas on wax deposition, and did not better combine theoretical models with experimental data, so the prediction values ​​of previous wax deposition prediction models were not accurate enough.

[0003] Published literature clearly indicates that predictions of wax deposition in multiphase flow are very limited. In the past, wax deposition rates in multiphase flow conditions were generally considered to be lower than those in single-phase flow for the following reasons: (1) the higher solubility of wax in gaseous oil reduces the wax surface temperature; (2) the faster flow rate due to the presence of gas shortens the residence time, especially the heat capacity; (3) the faster flow rate increases the shear force on the pipe wall; and (4) the presence of gas reduces the contact between the oil and the pipe wall. However, the above assumptions have not been confirmed. Although the effects of various flow patterns on wax deposition vary, some have greater effects, such as transitional flow and slug flow, while others have less effects, such as bubbling flow and laminar flow, the wax deposition model under different flow patterns of gas-liquid two-phase flow should be further discussed. Summary of the invention

[0004] In order to overcome the deficiencies of the prior art, the present invention provides a method for predicting wax deposition in a condensate gas well and its application.

[0005] The technical solution of the present invention is as follows:

[0006] A wax deposition prediction method for condensate gas wells is proposed. Through the basic diffusion deposition equation, the influence of oil-wax structure and gas high shear force is considered to establish a dynamic prediction model for gas-liquid wax deposition in the wellbore. The overall model is shown in formula (6).

[0007]

[0008] D ow is the mass diffusion coefficient;

[0009] C1 C2 C3 are equal to 15.0, 0.055, 1.4 respectively;

[0010] C oil Related to the Reynolds number, N SR Used to evaluate wax oil surface;

[0011] ρg , L , m — gas, liquid, gas-liquid mixture density, ρ m =ρ L H L +ρ g (1-H L ), kg / m 3 ;

[0012] H L —Liquid holdup;

[0013] g—acceleration due to gravity, m / s 2 ;

[0014] f m —Two-phase friction coefficient;

[0015] G m —Mass flow rate of gas-liquid mixture, kg / s;

[0016] A—pipe flow cross-sectional area = πD 2 / 4,m 2 ;

[0017] D—inner diameter of the pipe, m;

[0018] T f —Wellbore fluid temperature, °C;

[0019] C pm —Specific heat of wellbore fluid at constant pressure, J / (kg·k);

[0020] A'—relaxation distance, m;

[0021] v—fluid velocity, m / s;

[0022] α H —Joule-Thomson coefficient, K / Pa;

[0023] Bring the basic data of oil and gas wells into the model, perform calculations, and establish a wax deposition chart.

[0024] Furthermore, the assumptions for establishing the dynamic prediction model of wellbore gas-liquid wax deposition are as follows:

[0025] (1) The fluid flow state is stable flow;

[0026] (2) The heat transfer in the wellbore is stable;

[0027] (3) Formation heat transfer is unstable and obeys the dimensionless time function recommended by Remay;

[0028] (4) Oil casing concentricity;

[0029] (5) Paraffin deposition is mainly based on two mechanisms: molecular diffusion and shear deposition;

[0030] (6) Ignore particle diffusion, gravity sedimentation, etc.;

[0031] (7) Ignore diffusion that is not caused by differences in wax molecule concentration.

[0032] Furthermore, In order to use DSC curve to fit the relationship between concentration and temperature,

[0033] When the temperature dT≤6℃, the temperature and concentration gradient have the relationship as shown in formula (24);

[0034] dw W =0.0058dT+0.3575 (24)

[0035] When the temperature is 6℃≤dT≤24.67℃, the temperature and concentration gradient exist as shown in equation (25);

[0036] dw W =-0.0006dT 2 +0.0118dT+0.3354 (25)

[0037] When the temperature dT ≥ 24.67 °C, the temperature and concentration gradient exist as shown in equation (26);

[0038] dw W =-0.0491dT+1.4926 (26).

[0039] Furthermore,

[0040]

[0041]

[0042] Furthermore,

[0043]

[0044] Where, T—oil flow temperature, K;

[0045] μ—viscosity, mPa·s;

[0046] V A —Molar volume of paraffin wax, cm 3 / mol;

[0047] γ—V A The function is expressed as:

[0048]

[0049] Furthermore,

[0050] In the foam flow,

[0051]

[0052] In transitional and slug flows,

[0053]

[0054] In annular flow,

[0055]

[0056] The beneficial effects of the present invention compared with the prior art are:

[0057] The present invention can more accurately predict the wax deposition location and wax deposition speed of oil wells. The present invention considers the influence of wax deposition mechanism such as flow pattern, high shear force of gas and oil-wax structure, and establishes a gas-liquid two-phase wax deposition dynamic model. The model is used to establish a wax deposition prediction chart for a condensate gas field, which has guiding significance for the treatment of on-site wax deposition problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is the temperature concentration fitting diagram;

[0059] Figure 2 It is the radial temperature distribution diagram of wax deposition wellbore;

[0060] Figure 3 This is the wax formation diagram with a daily output of 5t / d;

[0061] Figure 4 This is the wax formation diagram with a daily output of 3t / d;

[0062] Figure 5 This is the wax chart with a daily output of 10t / d. DETAILED DESCRIPTION

[0063] The present invention is described in detail below by specific examples, but the protection scope of the present invention is not limited. Unless otherwise specified, the experimental methods used in the present invention are all conventional methods, and the experimental equipment, materials, reagents, etc. used can be obtained from commercial channels.

[0064] Model Assumptions

[0065] The paraffin deposition process in crude oil is a very complex issue. On the one hand, the composition of the oil and gas system is very complex, and the influence of each component on paraffin deposition needs further study. On the other hand, the paraffin deposition process involves many theoretical issues, such as wax dissolution and crystallization, fluid dynamics, mass transfer dynamics and heat transfer. At present, the paraffin deposition mechanism in waxy reservoir fluids is not completely clear. Although the internal causes of the sedimentation law have been discussed, there is no consistent and unified understanding, and there are many explanatory theories.

[0066] This paper mainly considers diffusion deposition, interface diffusion and shearing to establish a dynamic prediction model for wellbore wax deposition. The main assumptions are as follows:

[0067] (1) The fluid flow state is stable flow;

[0068] (2) The heat transfer in the wellbore is stable;

[0069] (3) Formation heat transfer is unstable and obeys the dimensionless time function recommended by Remay;

[0070] (4) Oil casing concentricity;

[0071] (5) Paraffin deposition is mainly based on two mechanisms: molecular diffusion and shear deposition;

[0072] (6) Ignore particle diffusion, gravity sedimentation, etc.;

[0073] (7) Ignore diffusion that is not caused by concentration differences of wax molecules.

[0074] Basic equation

[0075] (1) Diffusion deposition equation

[0076] The prediction model of wax deposition in gas-liquid two-phase is based on molecular diffusion. The shear force reduces the deposition rate, while the wax structure increases the deposition rate. Therefore, the model must be considered from these aspects. The front deposition will increase with the flow process, and the wax will also peel off from the pipe wall.

[0077] The overall deposition rate model is expressed as formula (1).

[0078]

[0079] Π1 is the wax oil structure that increases the paraffin deposition rate. Therefore, Π1 has a sign of increasing paraffin deposition, which is consistent with D ow The mass diffusion coefficient has no relationship. Π2 is the relationship for the reduction of paraffin deposition due to shear forces.

[0080] (2) Shear deposition equation

[0081]

[0082] The empirical relationship C1 C2 C3 is obtained from single-phase and multi-phase deposition data and is equal to 15.0, 0.055, and 1.4.

[0083] (3) Oil wax structure equation

[0084]

[0085]

[0086] Coefficient C in the oil wax structure oil It is related to the Reynolds number. SR It is used to evaluate the wax surface.

[0087] (4) Pressure-temperature equation

[0088] Correctly predicting the pressure and temperature distribution of wax deposited wellbore fluid is the basis for accurately predicting wellbore wax deposition. Based on the Hagedorn-Brown vertical pipe two-phase flow pressure drop model and the Shiu-Beggs wellbore temperature calculation method, a comprehensive mathematical model for predicting the pressure and temperature distribution of wax deposited wellbore fluid is established.

[0089] Hagedorn and Brown (1965) proposed a pressure drop equation for two-phase vertical ascending pipe flow under various flow patterns based on the assumed pressure gradient model and the back calculation of liquid holdup based on a large amount of field experimental data. Shiu and Beggs introduced the relaxation distance A' and obtained the wellbore temperature calculation equation. In the wax-forming pipe section of the oil well, wax crystals precipitate and become gas-liquid-solid three-phase flow. For the convenience of calculation, the influence of wax crystals is ignored and two-phase flow is still considered, but it is corrected when calculating related parameters. The comprehensive mathematical model obtained by combining the pressure and temperature equations is as follows:

[0090]

[0091] In the formula, ρ g , L , m — gas, liquid, gas-liquid mixture density, ρ m =ρ L H L +ρ g (1-H L ), kg / m 3 ;

[0092] H L —Liquid holdup;

[0093] g—acceleration due to gravity, m / s 2 ;

[0094] f m—Two-phase friction coefficient;

[0095] G m —Mass flow rate of gas-liquid mixture, kg / s;

[0096] A—pipe flow cross-sectional area = πD 2 / 4,m 2 ;

[0097] D—inner diameter of the pipe, m;

[0098] T f —Wellbore fluid temperature, °C;

[0099] C pm —Specific heat of wellbore fluid at constant pressure, J / (kg·k);

[0100] A'—relaxation distance, m;

[0101] v—fluid velocity, m / s;

[0102] α H —Joule-Thomson coefficient, K / Pa.

[0103] Establishment of dynamic prediction model

[0104] Based on the basic diffusion deposition equation, taking into account the influence of oil-wax structure and high shear force of gas, a dynamic prediction model of gas-liquid wax deposition in wellbore is established. The overall model is shown in formula (6).

[0105]

[0106] The model can be used to accurately predict the wax deposition location, wax deposition speed and wax deposition amount in the wellbore. The model can also provide a theoretical basis for the injection amount of wellbore wax removal and prevention agent.

[0107] Solving the model

[0108] (1) Solution of radial temperature gradient and temperature

[0109] For a system of two homogeneous mixtures, there exist relations (7) to (8).

[0110] Q=U o (πd o L)ΔT LM (7)

[0111]

[0112] ΔT LM It is the logarithm of the temperature difference between two or one phase of oil and wax. ΔT mis the temperature difference between the inner wall and the outer wall. Mass transfer must be considered for two-phase mixing, except for laminar flow and wavy flow. For laminar flow and wavy flow, heat loss must be considered between the oil phase and the pipe wall. The heat loss of two-phase mixing in laminar flow and wavy flow can be expressed by Equation 9.

[0113] Q=U o (πd o S o L)ΔT LM (9)

[0114] Parameter S o S is the mass fraction of the oil phase on the surface area of ​​the tube wall. o It can be obtained experimentally from the fluid height fraction.

[0115] The temperature of the two-phase mixture is measured each time, based on the heat conductivity U outside the pipe wall. o Calculated from the thermodynamic equilibrium equation. The heat conduction expression for two-phase or single-phase including laminar flow can be obtained from the following equation.

[0116]

[0117] The radial temperature gradient and temperature of the oil-wax are obtained through thermodynamic equilibrium on the wax-oil surface and two-phase mass transfer.

[0118]

[0119]

[0120] Internal convection heat transfer coefficient α of two-phase pipe flow with different flow patterns m Obtained from the heat transfer relationship provided by Kim in 1997, 1999. For single-phase flow, the internal convection heat transfer coefficient is obtained by Sieder and Tate. However, the calculation of the heat transfer coefficient for two-phase flow is not a conduction relationship obtained from temperature data. Therefore, the temperature data must be added to make adjustments in each test. When calculating the heat transfer coefficient, the insignificant deposition of wax in the first 15 minutes should be ignored. The heat transfer exists only due to fluid heat conduction and tube wall heat conduction. External convection heat transfer coefficient α gl It is calculated by applying the Petukhov formula of 1970. The adjustment parameters are adjusted according to the convection in the tube.

[0121] (2) Solution of concentration gradient

[0122] Fit the experimental data to solve the concentration gradient, and use the previously made DSC curve to fit the relationship between concentration and temperature. Fit the heat release and temperature relationship data in DSC to calculate the amount of wax precipitation at different temperatures. The fitting results are as follows: Figure 1 shown.

[0123] When the temperature dT≤6℃, the temperature and concentration gradient have the relationship as shown in formula (24);

[0124] dw W =0.0058dT+0.3575 (24)

[0125] When the temperature is 6℃≤dT≤24.67℃, the temperature and concentration gradient exist as shown in equation (25);

[0126] dw W =-0.0006dT+0.0118dT+0.3354 (25)

[0127] When the temperature dT ≥ 24.67 °C, the temperature and concentration gradient exist as shown in equation (26);

[0128] dw W =-0.0491dT+1.4926 (26).

[0129] (3) Solution of diffusion coefficient

[0130] Obtained using the Hayduk-Minhas method.

[0131]

[0132] Where, T—oil flow temperature, K;

[0133] μ—viscosity, mPa·s;

[0134] V A —Molar volume of paraffin wax, cm 3 / mol;

[0135] γ—V A The function is expressed as:

[0136]

[0137] (4) Dimensional variable N SR Solution

[0138] N SR is a dimensionless variable, and each flow pattern is expressed in a different form:

[0139] 1) Bubble flow

[0140] In foam flow, due to the small amount of gas and uniform dispersion, and the pipe wall is completely wetted by the oil phase, the gas-liquid mixture can be regarded as a single-phase fluid, which is modified by the volumetric properties of gas and oil. In the foam flow form, due to the high fluid velocity and shear force on the pipe wall, the deposition rate is greatly reduced.

[0141]

[0142] 2) Transition flow, slug flow

[0143] In both flow regimes, the conditions at a point in the pipeline change with time. Over time, effective average rates of heat transfer and wax deposition are obtained. On shorter time scales, these rates are related to the composition of the material in contact with the pipe wall at a particular moment. When the oil is in contact with the surface, an estimate of the deposition rate requires an accurate average of the heat transfer rate. When severe turbulence occurs, foaming can cause the wax to flake off.

[42] This affects the deposition rate.

[0144]

[0145] 3) Annular flow

[0146] Annular flows include annular fog and annular wave. Since annular fog is mainly gas coexisting with an oil mist, if an oil film forms on the pipe wall, then wax deposition may form. The wax deposition rate in the oil film can be estimated according to the method of single-phase flow. Annular wave flow and annular fog flow morphology allow the pipe wall to be completely wetted by the oil film. The cooling and flow of the oil film on the pipe wall may be completed in the laminar layer. The conditions for wax deposition are more or less similar to those for single-phase flow, except that the gas core loses heat through the oil layer instead of the oil core through turbulence. The method for predicting wax deposition is similar to that for single-phase flow, but it is necessary to use modified pseudo-properties and consider the volume fraction of the pipe occupied by oil.

[0147]

[0148] The liquid holdup E is calculated by equations (32) to (33).

[0149]

[0150] E=1-(1-x l d w ) 2 (33)

[0151] According to the wax crystal growth theory, the substance in the supersaturated solution must be transferred from the fluid to the crystal surface by diffusion mechanism before it grows into a lattice. The growth rate is determined by the different concentrations of the boundary layer and the saturated solubility. The growth process of wax crystals is also an aging process. From the above, shear force control affects the aging of paraffin crystals but there is no direct model. However, it is assumed that the thickness of C2 and C3 wax deposition is included in the single-phase and multi-phase. The rate-decreasing model also controls the paraffin deposition rate. It can be imagined that the longer the deposition time, the stronger the deposition. While the wax deposition grows, the wax flakes are constantly falling. C2 and C3 continue to grow with the change of the paraffin deposition thickness. However, time is limited, and C2 and C3 are assumed to not change in the existing model.

[0152] (5) Solution of the pressure-temperature equation

[0153] For wax-deposited wells, when the HB model solves the wellbore pressure and temperature, due to the influence of the wax layer, the calculation of the friction coefficient and the total heat transfer coefficient in the wax-deposited pipe section is different from the conventional multiphase flow calculation. This paper uses the following method to calculate the friction coefficient and the total heat transfer coefficient of the wax-deposited oil well.

[0154] 1) Calculation of total heat transfer coefficient

[0155] There is a wax layer in the waxed pipe section of waxy oil wells. The appearance of the wax layer increases the heat conductivity layer and affects the radial heat transfer. For the waxed pipe section, the total heat transfer coefficient is calculated using the following method.

[0156] The heat transfer from wax-deposited wellbore fluid to the surrounding formation mainly goes through the following steps: Figure 2 As shown:

[0157] Formula for calculating the overall heat transfer coefficient:

[0158]

[0159] In the formula, h c —Convection heat transfer coefficient of annulus, W / (m 2 k);

[0160] h r —Annulus radiation heat transfer coefficient, W / (m 2 k);

[0161] h f —Fluid convection heat transfer coefficient, W / (m 2 k);

[0162] k wax —Thermal conductivity of wax layer, W / (m·k);

[0163] k cem —thermal conductivity of cement sheath, W / (m·k);

[0164] k cas —Thermal conductivity of casing, W / (m·k);

[0165] k tub —Thermal conductivity of oil pipe, W / (m·k);

[0166] r to —Outer diameter of the oil pipe, m;

[0167] r i —Radius of oil flow, m;

[0168] r ci —Inner diameter of casing, m;

[0169] r co —Outer diameter of casing, m;

[0170] r ti —Inner diameter of the oil pipe, m;

[0171] r ins —radius of the insulation layer, m;

[0172] T ti —Temperature of the inner wall of the oil pipe, °C;

[0173] T to —Temperature of the outer wall of the oil pipe, °C;

[0174] T ci —Temperature of the inner wall of the casing, °C;

[0175] T co —Temperature of the outer wall of the casing, ℃.

[0176] Formula (34) can be simplified as:

[0177]

[0178] 2) Calculation of friction coefficient

[0179] The inner wall of the oil pipe is generally not smooth, and its roughness is related to the pipe material, manufacturing method, corrosion and wax deposition, etc. Under a microscope, the roughness of the pipe wall is uneven, and the distance between the high and low points on the pipe wall surface varies greatly.

[0180] For wax-coated pipe sections, the presence of the wax layer affects the roughness of the pipe wall, thereby affecting the friction coefficient. During the calculation, a correction factor β is introduced based on the direct calculation formula proposed by Jain (1976).

[0181]

[0182] Where N Re —Fluid Reynolds number. The above formula can be used for all turbulent flow calculations.

[0183] Example calculation

[0184] Using the multiphase pipe flow wax deposition dynamic model and field experimental data, the relationship between wax thickness and time at different production rates was established. Figures 3 to 5 shown.

[0185] When the daily condensate oil production is 5t / d, it can be seen from the chart that the wax deposition position is about 500m, and the wax deposition thickness increases with time. When the production is reduced to 3t / d, the wax deposition thickness increases significantly, because the flow rate decreases and the temperature difference decreases; when the production increases to 10t / d, the wax deposition thickness decreases relatively. This is because, as the flow rate increases, the shear force increases and some paraffin is taken away; on the other hand, the flow rate increases and the temperature difference increases.

[0186] The above-described embodiments are only preferred embodiments of the present invention, but not all feasible embodiments of the present invention. For those skilled in the art, any obvious changes made thereto without departing from the principles and spirit of the present invention should be considered to be included in the scope of protection of the claims of the present invention.

Claims

1. A method for predicting wax deposition in a condensate gas well, characterized in that: Through the basic diffusion deposition equation, considering the influence of oil-wax structure and gas high shear force, a dynamic prediction model of wellbore gas-liquid wax deposition is established. The overall model is shown in formula (6); Among them, D ow is the mass diffusion coefficient; C1 C2 C3 are equal to 15.0, 0.055, 1.4 respectively; C oil Related to the Reynolds number, N SR Used to evaluate wax oil surface; ρ g , L , m — gas, liquid, gas-liquid mixture density, ρ m =ρ L H L +ρ g (1-H L ), kg / m 3 ; H L —Liquid holdup; g—acceleration due to gravity, m / s 2 ; f m —Two-phase friction coefficient; G m —Mass flow rate of gas-liquid mixture, kg / s; A—pipe flow cross-sectional area = πD 2 / 4,m 2 ; D—inner diameter of the pipe, m; T f —Wellbore fluid temperature, °C; C pm —Specific heat of wellbore fluid at constant pressure, J / (kg·k); A'—relaxation distance, m; v—fluid velocity, m / s; α H —Joule-Thomson coefficient, K / Pa; Bring the basic data of oil and gas wells into the model, perform calculations, and establish a wax deposition chart.

2. The method for predicting wax deposition in condensate gas wells according to claim 1, characterized in that: The assumptions for establishing the dynamic prediction model of wellbore gas-liquid wax deposition are as follows: (1) The fluid flow state is stable flow; (2) The heat transfer in the wellbore is stable; (3) Formation heat transfer is unstable and obeys the dimensionless time function recommended by Remay; (4) Oil casing concentricity; (5) Paraffin deposition is mainly based on two mechanisms: molecular diffusion and shear deposition; (6) Ignore particle diffusion, gravity sedimentation, etc.; (7) Ignore diffusion that is not caused by differences in wax molecule concentration.

3. The wax deposition prediction method for condensate gas wells according to claim 1, characterized in that: In order to use the DSC curve to fit the relationship between concentration and temperature, when the temperature dT≤6℃, the temperature and concentration gradient have the relationship as shown in formula (24); dw W =0.0058dT+0.3575 (24) When the temperature is 6℃≤dT≤24.67℃, the temperature and concentration gradient exist as shown in equation (25); dw W =-0.0006dT 2 +0.0118dT+0.3354 (25) When the temperature dT ≥ 24.67 °C, the temperature and concentration gradient exist as shown in equation (26); dw W =-0.0491dT+1.4926 (26)。 4. The method for predicting wax deposition in condensate gas wells according to claim 1, characterized in that:

5. The method for predicting wax deposition in condensate gas wells according to claim 1, characterized in that: Where, T—oil flow temperature, K; μ—viscosity, mPa·s; V A —Molar volume of paraffin wax, cm 3 / mol; γ—V A The function is expressed as:

6. The method for predicting wax deposition in condensate gas wells according to claim 1, characterized in that: In the foam flow, In transitional and slug flows, In annular flow,

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