Construction method of drag coefficient model of sedimentation of proppant in non-Newtonian carbon dioxide

Abstract

The invention discloses a construction method of a drag coefficient model of sedimentation of a proppant in non-Newtonian carbon dioxide, and relates to the field of oil and gas reservoir yield increase transformation. The method specifically comprises the following steps: S1, performing non-Newtonian carbon dioxide rheological mode pipe flow tests at different temperatures, pressures and flow velocities; s2, establishing a non-Newtonian carbon dioxide rheological model; s3, carrying out proppant particle sedimentation tests under different temperatures, pressures and proppant properties; s4, calculating a numerical value of a propping agent sedimentation drag coefficient; and S5, numerically constructing a function model of the motion Reynolds number of the proppant and the drag coefficient. According to the method, rheological characteristics of the non-Newtonian carbon dioxide under different temperatures and pressures and interaction between the non-Newtonian carbon dioxide and the proppants are considered, and a drag coefficient calculation model of sedimentation of the proppants with different properties in the non-Newtonian carbon dioxide is constructed. The method provides a basis for sand transportation design and optimization of carbon dioxide fracturing, and is of great significance to effective application of carbon dioxide fracturing and unconventional resource development.

Description

Technical Field

[0001] The invention relates to the field of oil and gas reservoir production enhancement and transformation, and in particular to a method for constructing a drag coefficient model of proppant settling in non-Newtonian carbon dioxide. Background Art

[0002] With the continuous growth of my country's energy demand, the development of unconventional resources (such as shale oil, shale gas, coalbed methane and tight gas) has become an important task in the field of energy development. Unconventional reservoirs are characterized by strong heterogeneity, low porosity and low permeability, making it difficult to effectively develop these resources using traditional hydraulic fracturing technology. It is necessary to adopt advanced production stimulation technology to effectively develop unconventional oil and gas. As an emerging unconventional oil and gas resource development technology, carbon dioxide fracturing involves injecting anhydrous carbon dioxide mixed with proppants as working fluid into the fracturing fractures in the reservoir. Under the action of carbon dioxide fluid and gravity, the proppant settles in the fracturing fracture to form a high conductivity propped fracture. In this process, the drag coefficient between carbon dioxide and proppant controls the fluid-solid two-phase momentum exchange, and also quantitatively characterizes the migration ability of the self-proppant in the fracture. The drag coefficient model is the basis for the numerical simulation of proppant transport in the fracture, which is of great significance for the optimization of fracturing pumping parameters. The smaller the drag coefficient value, the less resistance the proppant movement encounters from the fluid. The proppant can move with the fluid to the depth of the fracture, improving the fracturing operation effect. However, the low viscosity of carbon dioxide leads to its weak ability to carry proppant migration, which limits the effective transportation of proppant in the fracture, thus affecting the effect of fracturing operation. In order to improve the ability of carbon dioxide to carry proppant migration, a thickener is usually mixed with pure carbon dioxide and pumped into the reservoir with the proppant. When carbon dioxide is mixed with additives, its fluid properties change from Newtonian fluid to non-Newtonian fluid, which will change the interaction between the fluid and the proppant particles. The drag coefficient between conventional Newtonian fluids and solid particles can be quantitatively characterized by empirical formulas. For non-Newtonian carbon dioxide, the effective viscosity of the fluid is determined by the properties of the thickener, shear rate, temperature and pressure, and the proppant sedimentation velocity and interphase drag coefficient are different from those of pure carbon dioxide. It is difficult for conventional drag coefficient calculation models to accurately characterize the drag coefficient of proppant sedimentation in non-Newtonian carbon dioxide. However, there is currently no method for constructing a drag coefficient calculation model for proppant sedimentation in non-Newtonian carbon dioxide. Therefore, the present invention considers the rheological properties of non-Newtonian carbon dioxide and the interaction with the proppant, and invents a method for constructing a drag coefficient model for proppant sedimentation in non-Newtonian carbon dioxide, which is of great significance for optimizing carbon dioxide fracturing operations and unconventional resource development. Summary of the invention

[0003] In view of the above-mentioned vacancy in the construction of the drag coefficient model in the prior art, the purpose of the present invention is to provide a method for constructing a drag coefficient model for proppant sedimentation in non-Newtonian carbon dioxide. Considering the rheological properties of non-Newtonian carbon dioxide at different temperatures and pressures and the interaction between proppant and proppant, constructing a drag coefficient calculation model for proppant sedimentation of different properties in non-Newtonian carbon dioxide is of great significance for optimizing carbon dioxide fracturing operations and unconventional resource development. The method of the present invention comprises the following steps:

[0004] S1. Conduct non-Newtonian carbon dioxide rheological mode pipe flow test at different temperatures, pressures and flow rates;

[0005] S2. Establish a non-Newtonian rheological model for carbon dioxide;

[0006] S3. Conduct proppant particle sedimentation tests under different temperatures, pressures, and proppant properties;

[0007] S4, numerical calculation of proppant settling drag coefficient;

[0008] S5. Numerically construct a functional model of the proppant motion Reynolds number and drag coefficient.

[0009] Further, the non-Newtonian carbon dioxide rheological mode pipe flow test device in S1 is shown in Figure 1 , physically simulate the flow velocity and flow pressure difference of carbon dioxide mixed with thickener in a circular tube under different temperatures and pressures. The experimental test device consists of four parts: a carbon dioxide injection module, an electric heating module, a cooling cycle test module and a data acquisition control system. It can physically simulate the flow of carbon dioxide in the temperature range of -20 to 80°C and the pressure range of 0 to 20MPa. It is equipped with a horizontal flow test pipe section with a diameter of 10mm and a length of 4m. The test system is connected to an additive container to mix pure carbon dioxide and thickener to form a non-Newtonian carbon dioxide fluid. During the test, the data acquisition system records the fluid velocity, fluid temperature, fluid pressure and test pipe section pressure difference. The main test steps include:

[0010] (1) Add the corresponding proportion of thickener according to the pipeline volume;

[0011] (2) Start the vacuum pump to evacuate the entire test pipeline;

[0012] (4) Start the carbon dioxide injection module, turn on the high-pressure injection pump, and inject carbon dioxide into the test pipeline;

[0013] (5) starting the cooling device to liquefy the carbon dioxide gas into liquid carbon dioxide;

[0014] (6) Turn on the control system and the circulation pump, turn on the electric heating module, adjust the test temperature, pressure and fluid flow rate to the target values, and allow the carbon dioxide to circulate in the pipeline;

[0015] (7) If the temperature and pressure exceed the target value, a venting operation can be performed to discharge part of the carbon dioxide to reduce the fluid temperature and pressure;

[0016] (8) Observe the dissolution of the thickener in carbon dioxide through the additive container;

[0017] (9) When the viscosity enhancer is completely dissolved and the temperature, pressure and flow rate are stabilized at the target values, record the temperature, flow rate and pressure drop data;

[0018] (10) After the test at the target temperature, pressure, and flow rate is completed, check and store the data in the control system computer;

[0019] (11) Change the test temperature, pressure, flow rate and other conditions, repeat steps (6) to (10), and carry out rheological mode pipe flow tests under other conditions.

[0020] Furthermore, a non-Newtonian carbon dioxide rheological model is established in the above S2, and its main contents include:

[0021] (1) When the flow in the test tube is in a stable laminar state, the velocity of the pipe section is linearly distributed, and the fluid shear stress is linearly distributed on the pipe section. The relationship between the pipe wall shear stress, the flow pressure difference and the test tube size parameters can be obtained:

[0022]

[0023] In the formula, τ w is the wall shear stress; ΔP is the non-Newtonian carbon dioxide flow pressure difference in the test pipe section; d is the test pipe diameter; L is the length of the test pipe section.

[0024] (2) After the wall shear stress is calculated by the flow pressure, the non-Newtonian carbon dioxide wall shear velocity can be further calculated in combination with the flow rate in the pipe:

[0025]

[0026] In the formula, γ w is the wall shear velocity; Q is the non-Newtonian carbon dioxide flow rate in the test pipe section, which can be calculated by the fluid velocity.

[0027] (3) Combining the carbon dioxide wall shear velocity and shear stress, the non-Newtonian carbon dioxide effective viscosity under different test conditions is calculated:

[0028]

[0029] In the formula, μ eff is the effective viscosity of non-Newtonian carbon dioxide.

[0030] (4) Non-Newtonian carbon dioxide mostly follows a power law rheological model, which is controlled by the continuity index and manifold index. The continuity index and manifold index under different test conditions can be further determined by the effective viscosity of the fluid:

[0031] μ eff =Kγ n-1 (4)

[0032] Where K is the continuity index of non-Newtonian carbon dioxide; γ is the flow shear velocity; n is the manifold index of non-Newtonian carbon dioxide, and its value is less than 1.

[0033] Further, the proppant particle settling test device in the above S3 is shown in Figure 2 , physically simulate the sedimentation process of proppant particles in non-Newtonian carbon dioxide at different temperatures and pressures. The experimental test device consists of five parts: particle sedimentation channel, carbon dioxide injection module, heat exchange module, booster module and data acquisition and control system. By opening the top valve to release the proppant particles into the sedimentation channel, the sedimentation channel is connected to the high-temperature and high-pressure reactor to provide a 2-meter-long vertical sedimentation channel for the proppant particles. Use a high-speed camera to record the motion trajectory of the proppant in the visual window, read the motion displacement of the proppant particles at different time intervals, and further calculate the sedimentation velocity of the proppant particles. The main test steps include:

[0034] (1) Fix the position of the camera and light source and adjust relevant parameters so that the observation window is fully presented in the shooting picture;

[0035] (2) adding the viscosity enhancer into the reactor and calculating the volume based on the mass of carbon dioxide at the target experimental temperature and pressure;

[0036] (3) Turn on the booster pump and heat exchanger to inject liquid carbon dioxide into the tank and mix it with the viscosity enhancer;

[0037] (4) Set the test temperature and pressure to target values;

[0038] (5) placing the proppant into a particle container;

[0039] (6) Control the top valve system to release the pressure in the lower part of the particle container and balance the pressure in the upper flow path and the reactor;

[0040] (7) releasing proppant particles to allow them to fall freely in the channel and recording the settling velocity using a high-speed camera;

[0041] (8) Changing the test temperature, pressure, proppant properties and other conditions, repeating steps (4) to (6), and further conducting proppant particle sedimentation tests under other test conditions.

[0042] Furthermore, the numerical calculation of the proppant settling drag coefficient in the above S4 is obtained by analyzing the force on the proppant particles in the gravity direction, and the main contents include:

[0043] (1) The drag force on the proppant in the fluid is controlled by the fluid-solid relative velocity and the drag coefficient, and the calculation expression is as follows:

[0044]

[0045] Where F is the drag force on the proppant; C d is the drag coefficient; ρ f is the fluid density; A p is the cross-sectional area of ​​the proppant; u f is the fluid velocity; u p is the proppant movement speed.

[0046] (2) When the approximately spherical proppant particles reach a uniform sedimentation state, the gravity they are subjected to is balanced with the fluid drag force, and the drag coefficient numerical calculation formula is obtained:

[0047]

[0048] In the formula, ρ p is the proppant particle density; d p is the proppant particle diameter; u e is the uniform settling velocity of the proppant particles; g is the gravitational acceleration.

[0049] Furthermore, the drag coefficient calculation model constructed in the above S5 is obtained by numerically fitting the functional relationship between the proppant motion Reynolds number and the drag coefficient. The numerical calculation of the proppant motion Reynolds number is involved:

[0050]

[0051] Wherein, the values ​​of manifold index and continuity index involved are obtained from the Newtonian carbon dioxide rheological model in S2. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Schematic diagram of the non-Newtonian carbon dioxide rheological model test device;

[0053] Figure 2 Schematic diagram of the proppant sedimentation test apparatus in non-Newtonian carbon dioxide;

[0054] Figure 3 Non-Newtonian carbon dioxide continuity index at different temperatures and pressures;

[0055] Figure 4 Non-Newtonian carbon dioxide manifold index at different temperatures and pressures;

[0056] Figure 5 Proppant drag coefficient as a function of Reynolds number. DETAILED DESCRIPTION

[0057] The present invention will be further described below in conjunction with the examples and drawings. The specific examples herein are constructed for a proppant drag coefficient model in a specific formulation of non-Newtonian carbon dioxide, and are used to demonstrate the use method and principle of the present invention. The drag coefficient model for other non-Newtonian carbon dioxide, proppant properties, test temperature and test pressure conditions can be similarly constructed using the method of the present invention. This example does not limit the scope of use of the present invention. Simple modifications and equivalent changes made based on the technical essence of the present invention without departing from the content of the present invention are all within the scope of protection of the present invention.

[0058] This example constructs a proppant settling drag coefficient model for non-Newtonian carbon dioxide formed by a formula of "2wt% siloxane polymer + 98wt% pure carbon dioxide". The main steps are as follows:

[0059] S1. Conduct non-Newtonian carbon dioxide rheological mode pipe flow test at different temperatures, pressures and flow rates;

[0060] S2. Establish a non-Newtonian rheological model for carbon dioxide;

[0061] S3. Conduct proppant particle sedimentation tests under different temperatures, pressures, and proppant properties;

[0062] S4, numerical calculation of proppant settling drag coefficient;

[0063] S5. Numerically construct a functional model of the proppant motion Reynolds number and drag coefficient.

[0064] Specifically, the test temperature is set at 0-70°C, the pressure is set at 5-20MPa, and the flow velocity is set at 0.1-1m / s to simulate the laminar flow under the temperature and pressure conditions of the on-site fracturing injection. The specific steps are as follows: First, add the corresponding proportion of siloxane polymer to the adjacent Figure 1 Additive container in the device; start the vacuum pump to evacuate the entire test pipeline so that carbon dioxide can be smoothly sucked into the test device; start the carbon dioxide injection module, turn on the high-pressure injection pump, and inject carbon dioxide into the test pipeline; start the cooling device to liquefy the carbon dioxide gas into liquid; turn on the control system and the circulation pump, turn on the electric heating module, adjust the test temperature, pressure and fluid flow rate to the target values, so that carbon dioxide circulates in the pipeline, prompting the siloxane polymer to dissolve rapidly in the carbon dioxide; when the siloxane polymer is completely dissolved and the temperature, pressure and flow rate are stabilized at the target values, record the flow temperature, flow rate and pressure drop data.

[0065] Specifically, the non-Newtonian carbon dioxide rheological model in S2 is established using the temperature, flow rate and pressure drop data measured in S1. The continuity index and manifold index of non-Newtonian carbon dioxide at different temperatures and pressures are calculated by equations (2), (3) and (4). The results are shown in the attached Figure 3 and attached Figure 4 Furthermore, the rheological model of non-Newtonian carbon dioxide under this formula can be obtained by functional fitting in combination with formula (4):

[0066]

[0067] Specifically, the proppant settling test in S3 was carried out on the Figure 2 The specific steps are as follows: fix the position of the camera and the light source so that the observation window is fully presented in the shooting picture; add the corresponding proportion of siloxane polymer to the reactor; turn on the booster pump and the heat exchanger, inject liquid carbon dioxide into the tank, and mix it with the siloxane polymer; set the test temperature and pressure; put the proppant into the particle container; control the top valve system to release the pressure at the bottom of the particle container and balance the pressure in the upper flow path and the reactor; release the proppant particles to make them fall freely in the sedimentation channel, and use a high-speed camera to record the sedimentation velocity. In order to have a larger numerical range of the Reynolds number of the proppant sedimentation movement and a stronger applicability of the subsequent fitted drag coefficient calculation model, the test temperature, pressure and proppant properties (density, size) are set to cover the application range of fracturing construction as much as possible. The specific setting parameters are as follows:

[0068]

[0069] Specifically, the proppant drag coefficient in S4 is numerically calculated by substituting the settling velocity obtained from the S3 test into equation (6).

[0070] Specifically, the construction of the function model of the proppant motion Reynolds number and the drag coefficient in S5 mainly includes the following steps:

[0071] (1) Based on the non-Newtonian CO2 rheological model established in S2, the proppant settling Reynolds number at different temperatures and pressures is calculated by equation (7);

[0072] (2) The mathematical function relationship between the proppant motion Reynolds number and the drag coefficient is established by numerical fitting, as shown in the attached figure. Figure 5 As shown, the established drag coefficient calculation model is as follows:

[0073] logC d =0.729-0.67logRe p +0.0604(logRe p ) 2 ,R 2 =0.94 (9).

Claims

1. A method for constructing a drag coefficient model for proppant sedimentation in non-Newtonian carbon dioxide, taking into account the rheological properties of non-Newtonian carbon dioxide and the interaction between the proppant and the non-Newtonian carbon dioxide at different temperatures and pressures, comprising the following steps: S1. Conduct non-Newtonian carbon dioxide rheological mode pipe flow test at different temperatures, pressures and flow rates; S2. Establish a non-Newtonian rheological model for carbon dioxide; S3. Conduct proppant particle sedimentation tests under different temperatures, pressures, and proppant properties; S4, numerical calculation of proppant settling drag coefficient; S5. Numerically construct a functional model of the proppant motion Reynolds number and drag coefficient.

2. Non-Newtonian carbon dioxide refers specifically to a fluid formed by mixing a viscosity enhancer with pure carbon dioxide in a specific proportion.

3. The non-Newtonian carbon dioxide rheological model in S2 above is obtained based on the non-Newtonian carbon dioxide pipeline laminar flow experimental simulation under different temperatures, pressures and flow rates in S1, and further provides a non-Newtonian carbon dioxide effective viscosity calculation model for the subsequent model construction of the drag coefficient calculation model.

4. The proppant particle sedimentation test in the above S3 is achieved by means of a high temperature, high pressure closed system with a vertical sedimentation channel.

5. The numerical calculation of the proppant sedimentation drag coefficient in S4 above is obtained by analyzing the force on the proppant particles in the S3 sedimentation test. The drag force on the proppant in the fluid is controlled by the relative velocity of the fluid and solid phases and the drag coefficient. For the approximately spherical proppant particles, when they reach a uniform sedimentation state, the gravity they are subjected to is balanced with the fluid drag force, and the drag coefficient numerical calculation formula is obtained: In the formula, C d is the drag coefficient; ρ p is the proppant particle density; ρ f is the fluid density; d p is the proppant particle diameter, u e is the uniform settling velocity of the proppant particles, and g is the gravitational acceleration.

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