A characterization method for imbibition displacement based on a variable-diameter capillary bundle model

Abstract

The present invention relates to the field of tight oil reservoir exploitation technology, specifically to a method for characterizing capillary bundles based on variable diameter capillaries and imbibition displacement, comprising the following steps: determining variable diameter capillary generation parameters based on real core experiments, establishing a core-scale random variable diameter capillary bundle using a random algorithm; calculating the spatial coordinates of each capillary segment in the capillary bundle; solving the imbibition rate based on the obtained random variable diameter capillary structural parameters; and solving the recovery degree and water content of the random variable diameter capillary bundle based on the calculated results. The present invention establishes a complex random variable diameter capillary bundle model. The model uses the real core pore structure as a basic parameter, can randomly generate complex pore structures, construct a more realistic flow space, and calculate core displacement experiment results such as recovery rate and water content. Compared with the real core displacement experiment, it has a better prediction effect.

Description

Technical Field

[0001] The present invention relates to the technical field of tight oil reservoir exploitation, and in particular to a method for characterizing capillary bundles based on a variable-diameter capillary tube model and imbibition displacement. Background Art

[0002] Ultra-low permeability reservoirs feature diverse pore types and well-developed microfractures. Large-scale volume fracturing further complicates the network of pores, microfractures, and artificial fractures, leading to significant heterogeneity. The significant difference in seepage capacity between fractures and the matrix leads to injected water channeling and flooding along the fractures, resulting in the accumulation of significant residual oil within the matrix and poor waterflooding effectiveness. With the continued advancement of experimental research on medium exchange flow between fractures and the matrix, effectively leveraging imbibition has become a key approach to improving waterflooding effectiveness in ultra-low permeability reservoirs. In recent years, domestic and international researchers have conducted extensive laboratory experiments on the mechanisms of imbibition, achieving a certain understanding of its modes, models, and influencing factors.

[0003] In order to simplify the study of porous media, some scholars have used the interacting capillary bundle model to study the oil-water two-phase seepage law in tight oil reservoirs, and established an oil-water two-phase seepage model suitable for tight oil reservoirs based on the pressure balance and flow conservation laws. This model can be used to analyze the influence of factors such as permeability, wettability, and interfacial tension changes in the two-phase flow process on the seepage law.

[0004] However, actual shale is a porous medium with a complex spatial structure. The traditional capillary bundle model uses capillaries of equal diameter, which is quite different from the actual pore flow space of the formation. As a result, the calculated results of indicators such as water content and recovery rate are quite different from the actual core test results. Summary of the Invention

[0005] In order to solve the above problems, the present invention provides a more realistic calculation method of oil-water flow law in porous media based on a variable diameter capillary bundle model and an imbibition displacement characterization method.

[0006] The present invention provides a method for characterizing imbibition displacement based on a variable diameter capillary bundle model, comprising the following steps:

[0007] (1) Determine the capillary formation parameters of variable diameter capillaries based on real core experiments, including capillary length L, radius distribution dataset r, and tortuosity range τ;

[0008] (2) Based on the parameters in step (1), a random algorithm is used to establish a core-scale capillary bundle with random variable diameters;

[0009] (3) calculating the spatial coordinates of each capillary segment in the capillary bundle according to the randomly variable diameter capillary bundle obtained in step (2);

[0010] (4) solving the imbibition rate according to the randomly variable diameter capillary structure parameters obtained in steps (2) and (3);

[0011] (5) Based on the calculation results of step (4), the extraction degree and water content of the randomly variable diameter capillary bundle are solved.

[0012] Preferably, the variable diameter capillary generation parameters to be determined in step (1) are as follows:

[0013] Determine the capillary length L based on the actual core length;

[0014] The number of capillary segments is k, where k = (L, 5L);

[0015] According to the real core mercury injection or nuclear magnetic resonance data, the radius distribution data set r is determined, and the sum of the generation frequencies of the data set r is 1;

[0016] Determine the tortuosity range τ based on real core experimental data;

[0017] The actual capillary flow path L is calculated using the following formula: e ;

[0018]

[0019] Preferably, step (2) establishes a core-scale variable diameter capillary bundle according to the following method:

[0020] (a) Generate a segment list K based on the number of capillaries n and the number of capillary segments k L ={k1,k2,k3…k n}, where k i ∈K L , then the capillary bundle has n k =∑k i microtubule segments;

[0021] (b) Generate a tortuosity list τ based on the capillary number n and the tortuosity range τ L ={τ1,τ2,τ3…τ n}, where τ i ∈τ L ;

[0022] (c) Generate a radius list R based on the radius distribution data set r and nk values L ={r1,r2,r3…r nk}, where r i ∈R L ;

[0023] (d) For any capillary i, from the segment number list τ L Assign a τ to it i , from the segment number list KL Specify a k for it i and from the radius list R L Take k i By assigning a value to each segment, a random variable diameter capillary bundle model with spatial coordinates and random distribution of segment number and radius can be obtained.

[0024] Preferably, step (3) determines the spatial coordinates of each segment of each random variable diameter capillary in the random variable diameter capillary bundle model according to the following method:

[0025] Perform the following calculations for all variable diameter capillaries, dividing the capillary length L into k segments to obtain the single segment forward length L k , the current capillary real flow path L e Divide into k segments to obtain a single segment length L e，k , use the following formula to calculate the longitudinal deflection L corresponding to each section p，k ;

[0026]

[0027] Let the single segment increment Δx of the variable diameter capillary in the x-axis direction be i =L k , the single-segment increment Δy of the variable diameter capillary in the y-axis direction i =L p，k The coordinates of the ends of each section of the reducer are shown below. The corresponding capillary structure can be drawn according to the obtained coordinates. Figure 3 :

[0028]

[0029] Preferably, step (4) solves the variable diameter capillary bundle according to the following formula to solve the variable diameter capillary bundle infiltration velocity v k，x With time t:

[0030]

[0031]

[0032] in,

[0033]

[0034] Where, v kx is the imbibition velocity at point x in the kth section, m / s; r kx is the radius of the pipeline at the kth section x, m; l k is the length of the kth section pipeline, m; t is the imbibition displacement time, s; μ w0 is the viscosity of the wetted phase, Pa·s; μ nw0 is the non-wetting phase viscosity, Pa·s; P siis the inlet pressure, MPa; P so is the outlet pressure, MPa; C i is an intermediate integral variable; γ is the surface tension, N / m; θ e is the contact angle; A s is the Hamaker constant of the tube wall, J.

[0035] Preferably, step (5) is to solve the recovery degree and water content of the randomly variable diameter capillary bundle according to the following formula:

[0036] The extraction rate R of the capillary bundle is calculated by the following formula:

[0037]

[0038] Where, R is the recovery degree, %; r k is the radius of the kth section of pipeline, m; l k is the length of the kth section of pipeline, m; r kT is the radius of the pipeline where the interface is located at time T, m; l kT is the length of the pipeline where the interface is located at time T, m; n is the number of capillaries; k is the number of capillary segments; k T is the pipeline section where the interface is located at time T.

[0039] The water content f of the capillary bundle is calculated by the following formula: w :

[0040]

[0041] in,

[0042]

[0043] Where, f w is the moisture content, %; r i，end is the end pipe radius of the i-th capillary, m; v i，end is the end imbibition displacement velocity of the i-th capillary, m / s; A i is the state parameter at the end of the i-th capillary, and the time for complete absorption of the i-th capillary is t i，end The relative size with the current time t is determined, A i =1 indicates that water is produced at the end of the i-th capillary, A i =0 indicates that oil is produced at the end of the i-th capillary.

[0044] The technical effects of the present invention are:

[0045] Based on the microscopic theoretical model of non-uniform capillary imbibition, the present invention establishes a complex random variable diameter capillary bundle model. This model uses the real core pore structure as the basic parameter. Under the premise of considering factors such as the real core pore distribution and tortuosity, it can randomly generate complex pore structures and construct a more realistic flow space. Based on the above random variable diameter capillary bundle model, under the conditions of considering the effect of the variable diameter section and the additional viscosity, the imbibition rate and imbibition time can be calculated, and the core displacement experiment results such as recovery rate and water content can be further calculated. Compared with the real core displacement experiment, it has a good prediction effect and provides a new analytical method for displacement imbibition calculation. This model can be used to analyze the influence of factors such as permeability, wettability, and interfacial tension changes on the core seepage law in the two-phase flow process. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of radius distribution.

[0047] Figure 2 This is the geometric relationship of a single section of a variable diameter capillary.

[0048] Figure 3 Schematic diagram of a randomly variable diameter capillary.

[0049] Figure 4 The calculation results of recovery degree and water content. DETAILED DESCRIPTION

[0050] The present invention provides a method for characterizing imbibition displacement based on a variable diameter capillary bundle model, comprising the following steps:

[0051] (1) Determine the capillary formation parameters of variable diameter capillaries based on real core experiments, including capillary length L, radius distribution dataset r, and tortuosity range τ;

[0052] (2) Based on the parameters in step (1), a random algorithm is used to establish a core-scale capillary bundle with random variable diameters;

[0053] (3) calculating the spatial coordinates of each capillary segment in the capillary bundle according to the randomly variable diameter capillary bundle obtained in step (2);

[0054] (4) solving the imbibition rate according to the randomly variable diameter capillary structure parameters obtained in steps (2) and (3);

[0055] (5) Based on the calculation results of step (4), the extraction degree and water content of the randomly variable diameter capillary bundle are solved.

[0056] The parameters for generating the variable diameter capillary tube to be determined in step (1) are as follows:

[0057] Determine the capillary length L based on the actual core length;

[0058] The number of capillary segments is k, where k = (L, 5L);

[0059] According to the real core mercury injection or nuclear magnetic resonance data, the radius distribution data set r is determined, and the sum of the generation frequencies of the data set r is 1;

[0060] Determine the tortuosity range τ based on real core experimental data;

[0061] The actual capillary flow path L is calculated using the following formula: e ;

[0062]

[0063] Step (2) establishes a core-scale variable diameter capillary bundle according to the following method:

[0064] (a) Generate a segment list K based on the number of capillaries n and the number of capillary segments k L ={k1,k2,k3…k n}, where k i ∈K L , then the capillary bundle has n k =∑k i microtubule segments;

[0065] (b) Generate a tortuosity list τ based on the capillary number n and the tortuosity range τ L ={τ1,τ2,τ3…τ n}, where τ i ∈τ L ;

[0066] (c) Generate a radius list R based on the radius distribution data set r and nk values L ={r1,r2,r3…r nk}, where r i ∈R L ;

[0067] (d) For any capillary i, from the tortuosity list τ L Assign a τ to it i , from the segment number list K L Specify a k for it i and from the radius list R L Take k i By assigning a value to each segment, a random variable diameter capillary bundle model with spatial coordinates and random distribution of segment number and radius can be obtained.

[0068] Step (3) determines the spatial coordinates of each segment of each random variable diameter capillary in the random variable diameter capillary bundle model according to the following method:

[0069] Perform the following calculations for all variable diameter capillaries, dividing the capillary length L into k segments to obtain the single segment forward length L k , the current capillary real flow path L e Divide into k segments to obtain a single segment length L e，k , and L e，k ≥L k , calculate the longitudinal deflection L corresponding to each segment p，k , and set the random deflection direction coefficient B, the schematic diagram is attached Figure 2 ;

[0070]

[0071] Let the single segment increment Δx of the variable diameter capillary in the x-axis direction be i =L k , the single-segment increment Δy of the variable diameter capillary in the y-axis direction i =L p，k The coordinates of the ends of each section of the reducer are shown below. The corresponding capillary structure can be drawn according to the obtained coordinates. Figure 3 :

[0072]

[0073] Step (4) solve the variable diameter capillary bundle imbibition velocity v according to the following formula: k，x With time t:

[0074]

[0075] in,

[0076]

[0077] Where, v kx is the imbibition velocity at point x in the kth section, m / s; r kx is the radius of the pipeline at the kth section x, m; l k is the length of the kth section pipeline, m; t is the imbibition displacement time, s; μ w0 is the viscosity of the wetted phase, Pa·s; μ nw0 is the non-wetting phase viscosity, Pa·s; P si is the inlet pressure, MPa; P so is the outlet pressure, MPa; C i is an intermediate integral variable; γ is the surface tension, N / m; θ e is the contact angle; A s is the Hamaker constant of the tube wall, J.

[0078] Step (5) When solving the extraction degree and water content of the random variable diameter capillary bundle according to the following formula, it is necessary to first determine the position of the phase interface in each capillary. For time T, the phase interface in the i-th capillary is at the k-th T The corresponding pipeline radius is r kT , then the volume of the wetting phase in the i-th capillary at time T is approximately The sum of the wetted phase volumes of the variable diameter tube bundle is Then the recovery degree at time T is equal to the ratio of the sum of the wetting phase volume to the sum of the volume of the variable diameter tube bundle at time T;

[0079] The extraction rate R of the capillary bundle is calculated by the following formula:

[0080]

[0081] Where, R is the recovery degree, %; r k is the radius of the kth section of pipeline, m; l k is the length of the kth section of pipeline, m; r kT is the radius of the pipeline where the interface is located at time T, m; l kT is the length of the pipeline where the interface is located at time T, m; n is the number of capillaries; k is the number of capillary segments; k T is the pipeline section where the interface is located at time T.

[0082] Moisture content f w It is defined as the ratio of the volume flow rate of the wetting phase at the outlet of the pipeline to the total flow rate. The phase interface in the i-th capillary at time t is calculated using step (4). t The imbibition velocity v i,kt Then, according to the law of continuity The volume flow rate at the end of the i-th capillary at time T can be obtained by judging t and the time t required for the i-th capillary to completely absorb. i,end The relative size of can be used to determine whether the terminal flow at the current moment is a wetting phase;

[0083] The water content f of the capillary bundle is calculated by the following formula: w :

[0084]

[0085] in,

[0086]

[0087] Where, f w is the moisture content, %; r i，end is the end pipe radius of the i-th capillary, m; v i，end is the end imbibition displacement velocity of the i-th capillary, m / s; A iis the state parameter at the end of the i-th capillary, and the time for complete absorption of the i-th capillary is t i，end The relative size with the current time t is determined, A i =1 indicates that water is produced at the end of the i-th capillary, A i =0 indicates that oil is produced at the end of the i-th capillary.

[0088] Example 1

[0089] (1) Determine the parameters for generating variable diameter capillaries. A conventional 50 mm core is used to define the capillary length L = 50 mm, the number of segments k = (50 to 250), and the tortuosity range τ = 1 to 2. Core mercury injection data should be used for calculations of different core tortuosity ranges.

[0090] The radius distribution data set r is determined based on the core mercury injection data, as follows: Figure 1 As shown, {1μm: 1%, 1.6μm: 1%, 2.5μm: 1%, 4.0μm: 2%, 6.3μm: 5%, 10μm: 10%, 16μm: 13%, 25μm: 18%, 40μm: 33%, 63μm: 15%, 100μm: 1%};

[0091] (2) Establish a variable diameter capillary bundle model with n = 10,000 and determine a list K of segments containing 10,000 data points and each element belonging to k. L ={k1,k2,k3…k n}; Determine the tortuosity list τ containing 10,000 data and each element belongs to τ L ={τ1,τ2,τ3…τ n};

[0092] According to the total number of segments n of all capillaries k =∑k i , and generate a list R that matches the true radius distribution L ={r1,r2,r3…r nk};

[0093] According to the above data, the structure and segment coordinates of each capillary are determined. Taking the first capillary as an example: k1 = 60, τ1 = 1.1, L = 50 mm, then according to formula (1) in step (1), L can be obtained. e =55mm;

[0094] (3) Calculate the spatial coordinates of each segment of the randomly variable diameter capillary. Taking the first capillary as an example, divide L = 50 mm into k1 parts to obtain the single segment forward length list L k , L e =55mm is divided into k1 parts to get the single segment length list L e，k, then according to formula (2) and formula (3), the coordinate value of each section of the first capillary can be obtained;

[0095] Assign a radius list of segment length to each capillary. Take the first capillary as an example, from the radius distribution list R L Take k1 elements from the list to form the radius list R of the first capillary k1 ;

[0096] (4) List the single segment forward length L in the previous step k , Single segment length list L e，k Substituting the radius list into equations (4) and (5) to solve them, we can get the relationship between the infiltration rate and time at any time;

[0097] (5) Substitute the calculated results of the imbibition velocity and time obtained in (3) into equations (7) and (8) to solve them, and the recovery degree R and water content f of the random variable diameter capillary bundle can be obtained. w , the calculation results are shown in Figure 4 .

Claims

1. A method for characterizing imbibition displacement based on a variable diameter capillary bundle model, characterized in that: The following steps are involved: (1) Determine the capillary formation parameters of variable diameter capillaries based on real core experiments, including capillary length L, radius distribution dataset r, and tortuosity range τ; (2) Based on the parameters in step (1), a random algorithm is used to establish a core-scale capillary bundle with random variable diameters; (3) calculating the spatial coordinates of each capillary segment in the capillary bundle according to the randomly variable diameter capillary bundle obtained in step (2); (4) solving the imbibition rate according to the random variable diameter capillary structure parameters obtained in steps (2) and (3); (5) According to the calculation results of step (4), the extraction degree and water content of the randomly variable diameter capillary bundle are solved; The step (4) is to solve the variable diameter capillary bundle imbibition velocity v according to the following formula: k，x With time t: in, Where, v kx is the imbibition velocity at point x in the kth section, m / s; r kx is the radius of the pipeline at the kth section x, m; l k is the length of the kth section pipeline, m; t is the imbibition displacement time, s; μ w0 is the viscosity of the wetted phase, Pa·s; μ nw0 is the non-wetting phase viscosity, Pa·s; P si is the inlet pressure, MPa; P so is the outlet pressure, MPa; C i is an intermediate integration variable; γ is the surface tension, N / m; θ e is the contact angle; A s is the Hamaker constant of the tube wall, J.

2. A method for characterizing imbibition displacement based on a variable diameter capillary bundle model according to claim 1, characterized in that: The parameters for generating the variable diameter capillary tube to be determined in step (1) are as follows: Determine the capillary length L based on the actual core length; The number of capillary segments is k, where k = (L, 5L); According to the real core mercury injection or nuclear magnetic resonance data, the radius distribution data set r is determined, and the sum of the generation frequencies of the data set r is 1; Determine the tortuosity range τ based on real core experimental data; The actual capillary flow path L is calculated using the following formula: e ; 3. A method for characterizing imbibition displacement based on a variable diameter capillary model according to claim 2, characterized in that: The step (2) is to establish a core-scale variable diameter capillary bundle according to the following method: (a) Generate a segment list K based on the number of capillaries n and the number of capillary segments k L ={k1,k2,k3…k n }, where k i ∈K L , then the capillary bundle has n k =∑k i microtubule segments; (b) Generate a tortuosity list τ based on the capillary number n and the tortuosity range τ L ={τ1,τ2,τ3…τ n }, where τ i ∈τ L ; (c) Generate a radius list R based on the radius distribution data set r and nk values L ={r1,r2,r3…r nk }, where r i ∈R L ; (d) For any capillary i, from the tortuosity list τ L Assign a τ to it i , from the segment number list K L Specify a k for it i and from the radius list R L Take k i By assigning a value to each segment, a random variable diameter capillary bundle model with spatial coordinates and random distribution of segment number and radius can be obtained.

4. A method for characterizing imbibition displacement based on a variable diameter capillary model according to claim 3, characterized in that: The step (3) determines the spatial coordinates of each segment of each random variable diameter capillary in the random variable diameter capillary bundle model in the following manner: perform the following calculation on all variable diameter capillaries, divide the capillary length L into k segments to obtain the single segment forward length L k , the current capillary real flow path L e Divide into k segments to obtain a single segment length L e，k , use the following formula to calculate the longitudinal deflection L corresponding to each section p，k Let the single segment increment Δx of the variable diameter capillary in the x-axis direction be i =L k , the single-segment increment Δy of the variable diameter capillary in the y-axis direction i =L p，k , the coordinates of the ends of each section of the reducer are expressed as follows:

5. The imbibition displacement characterization method based on the variable diameter capillary bundle model according to claim 4, characterized in that: The step (5) is to solve the extraction degree and water content of the randomly variable diameter capillary bundle according to the following formula: The extraction rate R of the capillary bundle is calculated by the following formula: Where, R is the recovery degree, %; r k is the radius of the kth section of pipeline, m; l k is the length of the kth section of pipeline, m; r kT is the radius of the pipeline where the interface is located at time T, m; l kT is the length of the pipeline where the interface is located at time T, m; n is the number of capillaries; k is the number of capillary segments; k T is the pipeline section where the interface is located at time T; The water content f of the capillary bundle is calculated by the following formula: w : in, Where, f w is the moisture content, %; r i，end is the end pipe radius of the i-th capillary, m; v i，end is the end imbibition displacement velocity of the i-th capillary, m / s; A i is the state parameter at the end of the i-th capillary, and the time for complete absorption of the i-th capillary is t i，end The relative size with the current moment T is determined, A i =1 indicates that water is produced at the end of the i-th capillary, A i =0 indicates that oil is produced at the end of the i-th capillary.

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