Calculation method of imbibition time and imbibition velocity of variable diameter capillary tube in two-liquid system

Abstract

The present invention relates to the technical field of tight oil reservoir exploitation, and in particular to the method for calculating the imbibition time and imbibition speed of a variable diameter capillary under a dual liquid phase system, and includes the following steps: determining the variable diameter capillary structural parameters, fluid parameters, and the pressure at the inlet and outlet ends of the variable diameter capillary; solving the structural integral variable for each section of the variable diameter capillary separately; correcting the viscosity value by considering the solid-liquid wall effect; determining the discrete steps and the discrete steps; solving the intermediate integral variable; calculating the imbibition time and the imbibition speed at any position of the variable diameter capillary. The present invention establishes a basic microscopic theoretical model for the seepage characteristics of non-uniform diameter capillaries under liquid-liquid systems, takes into account the influence of the pressure difference and the solid-liquid wall effect on the imbibition displacement during the imbibition displacement process, and provides an analytical method for the displacement imbibition calculation of complex pore structures.

Description

Technical Field

[0001] The invention relates to the technical field of tight oil reservoir exploitation, in particular to a method for determining a study on microscopic seepage law of tight oil reservoirs, and in particular to a method for calculating the imbibition time and imbibition velocity of a variable diameter capillary in a dual liquid phase system. Background Art

[0002] After the tight oil reservoirs are converted to water injection development, they generally face the dilemma of rapid decline in production due to water flooding caused by artificial or natural fractures. The concept of fine water injection development guided by the imbibition theory is beneficial to avoid the opening of fractures and reduce water flooding; reduce the low water injection rate, increase the oil-water exchange time, give full play to the imbibition effect, and produce more matrix crude oil, but this concept is still in the field experimental exploration stage.

[0003] Through theoretical research and field practice, it is found that the imbibition effect of matrix-fracture can effectively mobilize crude oil that cannot be mobilized by conventional water injection in the matrix, and the development practice of tight oil reservoirs based on this idea has also achieved relatively ideal results. Studying the influence of fractures and imbibition is to understand and optimize the tight water injection development strategy from both macro and micro dimensions. In microscopic theory, straight tube equal-diameter capillaries, non-equal-diameter capillaries, double capillaries, etc. all have a certain research basis. Among them, non-equal-diameter capillaries are often used for theoretical and numerical research. The current work mainly focuses on gas-liquid systems, while the imbibition process of non-equal-diameter capillaries in liquid-liquid systems suitable for oilfield development environments is still lacking. Summary of the invention

[0004] In order to solve the problem of insufficient research on the imbibition process of non-uniform diameter capillaries in liquid-liquid systems in the prior art, the present invention provides a method for calculating the imbibition time and imbibition velocity of variable diameter capillaries in a two-liquid phase system.

[0005] The method for calculating the imbibition time and imbibition velocity of a variable diameter capillary in a two-liquid phase system of the present invention comprises the following steps:

[0006] (1) Determining the structural parameters of the variable diameter capillary, the fluid parameters, and the inlet and outlet pressures of the variable diameter capillary;

[0007] (2) solving the structural integral variables for each section of the variable diameter capillary separately according to the structural parameters of the variable diameter capillary determined in step (1);

[0008] (3) According to the fluid parameters determined in step (1), the viscosity value is corrected by considering the solid-liquid wall effect;

[0009] (4) determining the number of discrete steps and the length of discrete steps according to the variable diameter capillary structure parameters determined in step (1);

[0010] (5) solving the intermediate integral variable according to the variable diameter capillary structure parameters and fluid parameters determined in step (1) combined with the corrected viscosity value and the structure integral variable;

[0011] (6) Based on the results of steps (2), (3), (4), and (5), calculate the imbibition time and imbibition velocity at any position of the variable diameter capillary.

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

[0013] The structural parameters of the variable diameter capillary include: the number of variable diameter capillary sections n, the radius of each section of the variable diameter capillary r, the length of each section of the variable diameter capillary l, and the ratio of the difference between the inlet and outlet radius of the variable diameter capillary to the section length is less than 2;

[0014] Fluid parameters include: Wetting phase viscosity μ w , non-wetting phase viscosity μ nw , surface tension γ; contact angle θ e ;

[0015] Capillary inlet pressure P si , capillary outlet pressure P so .

[0016] Preferably, step (2) calculates the structural integral variable of each section of the variable diameter capillary according to the following formula:

[0017] Assumption: n represents the total number of segments of the multi-segment capillary, and k represents one of the segments, then the structural integral variable C k for;

[0018] In formula (1), r k is the radius of the kth section of the variable diameter capillary, m;

[0019] l k is the length of the kth section of the variable diameter capillary, m.

[0020] Preferably, step (3) corrects the viscosity value according to the following formula:

[0021] Where: b is the viscosity coefficient caused by the interaction between the tube wall and the fluid molecules, Pa·s·m;

[0022] A s is the Hamaker constant of the tube wall, J;

[0023] A w is the fluid Hamaker constant, J;

[0024] μ0 is the viscosity of the fluid without considering the solid-liquid wall effect, Pa·s.

[0025] Preferably, step (4) determines the discrete step number P and the structural parameters under any step number in the following manner: take the discrete step number P = n ~ 10n, the step length Δx = ∑l k / P, when calculating, determine the current segment number k according to the current calculation step number, and the position l in the segment where the current calculation step is located k，x And the radius r at the current calculation step k，x .

[0026] Preferably, step (5) solves the intermediate integral variable according to the following formula:

[0027] Where: e k,x is the intermediate integral variable at x in the kth section of the variable diameter capillary;

[0028] b w is the viscosity coefficient caused by the interaction between the tube wall and the wetting phase fluid molecules, Pa·s·m;

[0029] μ w0 is the viscosity of the wetting phase fluid when the solid-liquid wall effect is not considered, Pa·s;

[0030] b nw is the viscosity coefficient caused by the interaction between the tube wall and the non-wetting phase fluid molecules, Pa·s·m;

[0031] μ nw0 is the viscosity of the non-wetting phase fluid when the solid-liquid wall effect is not considered, Pa·s;

[0032] A s is the Hamaker constant of the tube wall, J;

[0033] A w is the fluid Hamaker constant, J;

[0034] A nw is the Hamaker constant of the non-wetting phase fluid, J;

[0035] l k is the length of the kth section of the variable diameter capillary, m;

[0036] l k，x is the length at x in the kth section of the variable diameter capillary, m;

[0037] r k，x is the radius at point x in the kth section of the variable diameter capillary, m.

[0038] Preferably, step (6) calculates the imbibition time and the imbibition speed at any position of the variable diameter capillary according to the following formula:

[0039] The imbibition velocity v at any position in the tube k，xThe solution process is:

[0040] The solution process of the imbibition time t is:

[0041] In the formula, v k，x is the imbibition velocity at point x in the kth section of the variable diameter capillary, m / s;

[0042] r k，x is the radius at x in the kth section of the variable diameter capillary, m;

[0043] P si is the inlet pressure, MPa;

[0044] P so is the outlet pressure, MPa;

[0045] γ is the surface tension, N / m;

[0046] θ e Contact angle.

[0047] The technical effects of the present invention are:

[0048] The present invention establishes a basic microscopic theoretical model for the seepage characteristics of non-uniform diameter capillaries in a liquid-liquid system, takes into account the influence of pressure difference and solid-liquid wall action on the imbibition displacement during the imbibition displacement process, and provides an analytical method for the displacement imbibition calculation of complex pore structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 The calculation data in the literature is compared and verified with the calculation results of this method.

[0050] Figure 2 It is a schematic diagram of the theoretical model of the expanded diameter capillary tube of the present invention.

[0051] Figure 3 It is a schematic diagram of the expansion-contraction capillary theory model of the present invention.

[0052] Figure 4 Schematic diagrams of six structures of the three-section capillary of the present invention.

[0053] Figure 5 This is a graph showing the calculation results of the imbibition time of the liquid-liquid system of the present invention. DETAILED DESCRIPTION

[0054] The method for calculating the imbibition time and imbibition velocity of a variable diameter capillary in a two-liquid phase system of the present invention comprises the following steps:

[0055] (1) Determining the structural parameters of the variable diameter capillary, the fluid parameters, and the inlet and outlet pressures of the variable diameter capillary;

[0056] (2) solving the structural integral variables for each section of the variable diameter capillary separately according to the structural parameters of the variable diameter capillary determined in step (1);

[0057] (3) According to the fluid parameters determined in step (1), the viscosity value is corrected by considering the solid-liquid wall effect;

[0058] (4) determining the number of discrete steps and the length of discrete steps according to the variable diameter capillary structure parameters determined in step (1);

[0059] (5) solving the intermediate integral variable according to the variable diameter capillary structure parameters and fluid parameters determined in step (1) combined with the corrected viscosity value and the structure integral variable;

[0060] (6) Based on the results of steps (2), (3), (4), and (5), calculate the imbibition time and imbibition velocity at any position of the variable diameter capillary.

[0061] The parameters to be determined in step (1) are as follows:

[0062] The structural parameters of the variable diameter capillary include: the number of variable diameter capillary sections n, the radius of each section of the variable diameter capillary r, the length of each section of the variable diameter capillary l, and the ratio of the difference between the inlet and outlet radius of the variable diameter capillary to the section length is less than 2;

[0063] Fluid parameters include: Wetting phase viscosity μ w , non-wetting phase viscosity μ nw , surface tension γ; contact angle θ e ;

[0064] Capillary inlet pressure P si , capillary outlet pressure P so .

[0065] The structural integral variable in step (2) is an important parameter for calculating the friction resistance of a single section of a variable diameter capillary. This value is only related to the radius and length of the i-th section of the pipeline. The structural integral variable of each section of the variable diameter capillary is calculated according to the following formula:

[0066] Assumption: n represents the total number of segments of the multi-segment capillary, and k represents a segment, then the integral variable of any segment structure is;

[0067] In formula (1), r k is the radius of the kth section of the variable diameter capillary, m;

[0068] l k is the length of the kth section of the variable diameter capillary, m.

[0069] In step (3), the viscosity value is corrected by considering the solid-liquid wall effect. Since the viscosity of the displacing phase fluid and the viscosity of the displaced phase fluid are both assumed to be constant, this assumption is more reasonable in macroscopic flow, but has certain defects in the micro-nano scale. Since viscosity is a measure of the resistance encountered by fluid molecules during fluid flow, its essence is a representation of the intermolecular attraction. In microscopic flow, due to the small size of the flow channel, some fluid molecules are affected by the van der Waals force of the solid molecules on the tube wall, thereby generating additional viscosity. This effect can be calculated by the following formula:

[0070] Where: b is the viscosity coefficient caused by the interaction between the tube wall and the fluid molecules, Pa·s·m;

[0071] A s is the Hamaker constant of the tube wall, J;

[0072] A w is the fluid Hamaker constant, J;

[0073] μ0 is the viscosity of the fluid without considering the solid-liquid wall effect, Pa·s;

[0074] The Hamaker constant is a key parameter for characterizing van der Waals gravity. From formula (2), it can be seen that the size of the additional viscosity is related to the size of the flow channel. The smaller the flow channel, the more obvious the additional viscosity effect. In micro-nano flow, the influence of this additional viscosity on fluid flow cannot be ignored. In the process of solving the multi-segment capillary absorption velocity, due to the size difference of each capillary segment, the additional viscosity is also different. When the number of calculated segments is large or the size difference is obvious, the accumulated calculation error will lead to obvious deviation in the calculation result. Therefore, when calculating the interface movement rate, the viscosity of each segment needs to be corrected.

[0075] Step (4) Determine the discrete number of steps P and the structural parameters under any number of steps: Take the discrete number of steps P = n ~ 10n, the step length Δx = ∑l k / P, when calculating, determine the current segment number k according to the current calculation step number, and the position l in the segment where the current calculation step is located k，x And the radius r at the current calculation step k，x ; Before each calculation, the position of the current step needs to be judged. For example, when calculating the Pth step, the moving path of the phase interface in the variable diameter capillary is PΔx. At this time, it is judged that PΔx is at x in the kth section of the variable diameter capillary, where the value range of x is 0 to the length of the kth section l k .

[0076] Step (5) calculates the intermediate integral variable, where the displacement phase intermediate integral variable e k,x (μ w) is the product of the sum of the structural integral variables of the displacement phase before the kth segment and the structural integral variables within the length range occupied by the kth segment of the displacement phase and the viscosity of the displacement phase. The intermediate integral variable of the non-displacement phase, e k,x (μ nw ) is the product of the sum of the structural integral variables of the non-displacement phase after the kth segment and the structural integral variables within the length range occupied by the kth segment of the non-displacement phase and the viscosity of the non-displacement phase.

[0077] Then the total intermediate integral variable e k,x The calculation is done using the following formula:

[0078] Where: e k,x is the intermediate integral variable at x in the kth section of the variable diameter capillary;

[0079] b w is the viscosity coefficient caused by the interaction between the tube wall and the wetting phase fluid molecules, Pa·s·m;

[0080] μ w0 is the viscosity of the wetting phase fluid when the solid-liquid wall effect is not considered, Pa·s;

[0081] b nw is the viscosity coefficient caused by the interaction between the tube wall and the non-wetting phase fluid molecules, Pa·s·m;

[0082] μ nw0 is the viscosity of the non-wetting phase fluid when the solid-liquid wall effect is not considered, Pa·s.

[0083] Step (6) calculates the imbibition time and imbibition speed at any position of the variable diameter capillary according to the following formula:

[0084] The imbibition velocity v at any position in the tube k，x The solution process is:

[0085] The solution process of the imbibition time t is:

[0086] In the formula, v k，x is the imbibition velocity at point x in the kth section of the variable diameter capillary, m / s;

[0087] r k，x is the radius at x in the kth section of the variable diameter capillary, m;

[0088] P si is the inlet pressure, MPa;

[0089] P so is the outlet pressure, MPa;

[0090] γ is the surface tension, N / m;

[0091] θ e Contact angle.

[0092] Example:

[0093] According to step (1), the parameters of the variable diameter capillary structure are determined, and six types of variable diameter capillary structures are defined as follows: Figure 4 Its structural parameters are shown in Table 1:

[0094] Table 1 Structural parameters of variable diameter capillary

[0095] According to step (1), assume that the fluid parameters and the capillary inlet pressure P si , capillary outlet pressure P so They are:

[0096] μ w =1mPa·s,μ nw =4mPa·s, γ=0.03N / m, θ e =30°, P si =100Kpa, P so =0Kpa, A s =4.2×10 -20 J.A w =1.2×10 -20 J.A nw =2.07×10 -20 J.

[0097] Based on the data in Table 1, the structural integral variable of each section of the variable diameter capillary is solved according to formula (1) in step (2). Taking capillary a as an example: C1 = 3 × 10 -18 , C2=1.97×10 -17 , C3=1.87×10 -17 , C4=2.56×10 -16 , C5=3.7×10 -16 ;

[0098] B. According to the fluid parameters and formula (2) in step (3), the position of the phase interface is determined and then the viscosity value after considering the solid-liquid wall effect is corrected;

[0099] C discretizes the capillary a according to step (4), setting the discrete steps P = 100 and the step length Δx = 1.1 mm;

[0100] D determines the segment number and position within the segment of any step. Take the 50th step as an example: Since P 50Δx=55mm. According to Table 1, when the interface moves to the 50th step, it is located in the third section of the variable diameter capillary, at a position of 15mm in the section, that is, k=3, l k =30mm, l k，x =15mm, r k，x =30μm;

[0101] E According to formula (3) in step (5), solve the intermediate integral variable of each step of the variable diameter capillary. Taking the solution of step 50 as an example, substitute the relevant parameters in A, B, and C into formula (2) to obtain e 3，15 =4.24×10 18 ;

[0102] F solves the imbibition velocity v and the imbibition time t according to equations (4) and (5) in step (6). Taking the solution of step 50 as an example, it is calculated that the fluid imbibition velocity is 0.55 mm / s and the imbibition time is 28.86 s;

[0103] G Substitute the remaining variable diameter capillary parameters shown in Table 1 into the above steps for calculation, and the calculation results are shown in Figure 5 .

[0104] The results of numerical solutions are closer to the real situation, and their prediction effect is enhanced as the simulation grid size is reduced. Therefore, in the absence of physical experiments, the correctness of the prediction results of analytical solutions is usually compared with numerical results. Figure 1 The comparison of the imbibition characteristics predicted by the present invention in the expanding-contracting capillary with the prediction results of the previous numerical simulation and analytical solution is shown. It is worth noting that the geometric parameters and fluid parameters used in the present invention are the same as those set by Erickson et al in the simple expanding-contracting capillary imbibition study. The results show that the prediction results of the present method in complex capillaries are not significantly different from the previous numerical results, and the fitting effect is excellent, indicating that the derivation of the analytical model is correct.

Claims

1. A method for calculating the imbibition time and imbibition velocity of a variable diameter capillary in a two-liquid phase system, characterized in that: The steps include: (1) Determine the variable diameter capillary structure parameters, fluid parameters and the variable diameter capillary inlet pressure P si and outlet pressure P so ; The structural parameters of the variable diameter capillary include: the number of variable diameter capillary sections n, the radius of each section of the variable diameter capillary r, the length of each section of the variable diameter capillary l, and the ratio of the difference between the inlet and outlet radius of the variable diameter capillary to the section length is less than 2; (2) solving the structural integral variables for each section of the variable diameter capillary separately according to the structural parameters of the variable diameter capillary determined in step (1); (3) According to the fluid parameters determined in step (1), the viscosity value is corrected by considering the solid-liquid wall effect; (4) determining the number of discrete steps and the length of discrete steps according to the variable diameter capillary structure parameters determined in step (1); (5) solving the intermediate integral variable according to the variable diameter capillary structure parameters and fluid parameters determined in step (1) combined with the corrected viscosity value and the structure integral variable; (6) Based on the results of steps (2), (3), (4), and (5), calculate the imbibition time and imbibition velocity at any position of the variable diameter capillary; The step (6) calculates the imbibition time and the imbibition speed at any position of the variable diameter capillary according to the following formula: The imbibition velocity v at any position in the tube k，x The solution process is: The solution process of the imbibition time t is: In the formula, v k，x is the imbibition velocity at point x in the kth section of the variable diameter capillary, m / s; r k,x is the radius at x in the kth section of the variable diameter capillary, m; P si is the inlet pressure, MPa; P so is the outlet pressure, MPa; γ is the surface tension, N / m; θ e Contact angle; e k,x is the intermediate integral variable at x in the kth section of the variable diameter capillary; k is a section among the number n of variable diameter capillary sections.

2. The method for calculating the imbibition time and imbibition velocity of a variable diameter capillary in a two-liquid phase system according to claim 1, characterized in that: The parameters to be determined in step (1) are as follows: Fluid parameters include: Wetting phase viscosity μ w , non-wetting phase viscosity μ nw , surface tension γ; contact angle θ e .

3. The method for calculating the imbibition time and imbibition velocity of a variable diameter capillary in a two-liquid phase system according to claim 2, characterized in that: The step (2) calculates the structural integral variable of each section of the variable diameter capillary according to the following formula: Assumption: n represents the total number of segments of the multi-segment capillary, and k represents one of the segments, then the structural integral variable C k for; In formula (1), r k is the radius of the kth section of the variable diameter capillary, m; l k is the length of the kth section of the variable diameter capillary, m.

4. The method for calculating the imbibition time and imbibition velocity of a variable diameter capillary in a two-liquid phase system according to claim 3, characterized in that: The step (3) corrects the viscosity value according to the following formula: Where: b is the viscosity coefficient caused by the interaction between the tube wall and the fluid molecules, Pa·s·m; A s is the Hamaker constant of the tube wall, J; A w is the fluid Hamaker constant, J; μ0 is the viscosity of the fluid without considering the solid-liquid wall effect, Pa·s.

5. The method for calculating the imbibition time and imbibition velocity of a variable diameter capillary in a two-liquid phase system according to claim 4, characterized in that: The step (4) determines the discrete step number P and the structural parameters under any step number in the following manner: the discrete step number P = n ~ 10n, the step length Δx = ∑l k / P, when calculating, determine the current segment number k according to the current calculation step number, and the position l in the segment where the current calculation step is located k，x And the radius r at the current calculation step k，x .

6. The method for calculating the imbibition time and imbibition velocity of a variable diameter capillary in a two-liquid phase system according to claim 5, characterized in that: The step (5) solves the intermediate integral variable according to the following formula: Where: b w is the viscosity coefficient caused by the interaction between the tube wall and the wetting phase fluid molecules, Pa·s·m; μ w0 is the viscosity of the wetting phase fluid when the solid-liquid wall effect is not considered, Pa·s; b nw is the viscosity coefficient caused by the interaction between the tube wall and the non-wetting phase fluid molecules, Pa·s·m; μ nw0 is the viscosity of the non-wetting phase fluid when the solid-liquid wall effect is not considered, Pa·s; A s is the Hamaker constant of the tube wall, J; A w is the fluid Hamaker constant, J; A nw is the Hamaker constant of the non-wetting phase fluid, J; l k is the length of the kth section of the variable diameter capillary, m; l k，x is the length at x in the kth section of the variable diameter capillary, m; r k，x is the radius at point x in the kth section of the variable diameter capillary, m.

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