Single well water invasion simulation and water breakthrough time prediction method for bottom water gas reservoir

Abstract

The application discloses a method for simulating water invasion of a single well in a bottom water gas reservoir and predicting water breakthrough time, which solves the productivity of micro-element sections at different positions of a wellbore under the premise of considering the influence of wellbore pressure drop, and then obtains a mathematical model of water coning and water crest in the bottom water gas reservoir according to the mirror reflection principle and the superposition principle of velocity; the technical scheme is as follows: in an infinite homogeneous gas reservoir, a point sink is produced, the seepage thereof can be regarded as a spherical centripetal flow, and the movement velocity is calculated; in the point sink distance gas reservoir, other parameters remain unchanged, a point sink production in the bottom water gas reservoir is equivalent to the arrangement mode in the infinite gas reservoir, and the movement velocity is calculated; in the straight well and horizontal well production in the bottom water gas reservoir, the production is equivalent to a plurality of point sinks, and according to the mirror reflection principle and the superposition principle of velocity, a mathematical model of production time and water crest height can be obtained; the above mathematical model and parameters are used, and a MATLAB calculation is combined to solve a water breakthrough time prediction model of the horizontal well and the straight well; the solving speed is fast, and the method has strong generalization.

Description

TECHNICAL FIELD

[0001] The application relates to a single-well water invasion simulation and water breakthrough time prediction method for a bottom water gas reservoir and belongs to the oil and gas field development field. BACKGROUND

[0002] In the development process of a bottom water gas reservoir, no matter whether a vertical well or a horizontal well is used for production, with continuous extraction of natural gas in the reservoir, a pressure drawdown funnel will be formed in the reservoir according to the distribution of the well, the bottom water will enter the reservoir, and finally the water breakthrough will occur in the gas well, leading to the vertical well water cone breakthrough and the horizontal well water ridge breakthrough. The vertical well and the horizontal well have the advantages of large oil control area and high yield, but once the water breakthrough occurs in the horizontal well, the yield will decrease rapidly and the water plugging measure will be difficult. In the development of a low water gas reservoir, the water breakthrough in the horizontal well will not only increase the development and exploitation difficulty of the gas reservoir but also cause the loss of the gas well productivity, reduce the gas reservoir recovery ratio and finally affect the development benefit of the gas reservoir. Many scholars have made researches on the vertical well water cone and the horizontal well water ridge, mainly considering the influence of the water breakthrough time and the critical parameters of the bottom water oil and gas reservoir, and the research on the water cone and water ridge process is less, which needs to be further deepened.

[0003] The bottom water coning is a key problem in the development of the bottom water gas reservoir and is of great significance to the accurate prediction of the water breakthrough time and the development of the bottom water gas reservoir. Under the influence of the opening degree of the gas reservoir, the gas-water mobility ratio, the non-Darcy law and the skin factor, the simulation of the single-well water invasion and the prediction of the water breakthrough time of the bottom water gas reservoir are easy to affect the accuracy of the calculation result, and therefore the influence of the wellbore internal pressure drop and the bottom water on the productivity needs to be considered. Under the premise of considering the influence of the wellbore pressure drop, the productivity of the microelement segment at different positions of the wellbore is solved, and then the mathematical model of the water cone and the water ridge of the bottom water gas reservoir is obtained according to the mirror reflection principle and the superposition principle of velocity. SUMMARY

[0004] The application aims at accurately predicting the water breakthrough time and the development of the bottom water gas reservoir, and based on the mirror reflection principle and the superposition principle of velocity, the three-dimensional relationship between the production days and the water cone and water ridge height is solved, and the application has the characteristics of high solution accuracy, fast solution speed and strong generalizability.

[0005] To achieve the above-mentioned purpose, the application provides a single-well water invasion simulation and water breakthrough time prediction method for a bottom water gas reservoir, which comprises the following steps.

[0006] S100: the influence of the wellbore pressure drop is considered to solve the productivity of the microelement segment at different positions of the wellbore, and then the mathematical model of the water cone and the water ridge of the bottom water gas reservoir is obtained according to the mirror reflection principle and the superposition principle of velocity, and the main steps are as follows.

[0007] S1001: in an infinite homogeneous gas reservoir, a point sink is regarded as a spherical centripetal flow, a particle in the gas reservoir moves at a velocity v z, the distance of motion dz is calculated;

[0008] S1002: In the bottom water gas reservoir, the distance of point sink to the top of gas reservoir is h p , the distance to the bottom water is z w , other parameters are unchanged, according to the top and bottom boundary characteristics of the bottom water gas reservoir, a point sink in the bottom water gas reservoir is equivalent to the arrangement mode in the infinite gas reservoir, and an arbitrary water quality point in the gas reservoir moves at a speed v z , the distance of motion dz is calculated;

[0009] S1003: In the bottom water gas reservoir, a straight well is produced, the straight well is equivalent to a plurality of point sinks, according to the mirror reflection principle and the superposition principle of speed, a mathematical model of production time t and water ridge height z1 can be obtained;

[0010] S1004: In the bottom water gas reservoir, a horizontal well is produced, the horizontal well is equivalent to a plurality of point sinks, according to the mirror reflection principle and the superposition principle of speed, a mathematical model of production time t and water ridge height z1 can be obtained;

[0011] S1005: The prediction time model of water cone and water ridge of single horizontal well and straight well is obtained, according to the superposition principle of speed and the mirror reflection principle, a mathematical model of production time t and water ridge height z1 can be obtained;

[0012] S1006: The prediction time model of water cone and water ridge of single horizontal well and straight well is obtained, and the water breakthrough time model of interwell interference is derived;

[0013] S200: The water breakthrough time prediction model of horizontal well and straight well is solved;

[0014] The above-mentioned bottom water gas reservoir point sink water breakthrough time prediction method specifically includes the following steps;

[0015] S2001: First, in the bottom water gas reservoir, before the water body ridge advances or coned due to the production of the gas well, in the infinite homogeneous gas reservoir, a point sink, the seepage is spherical centripetal flow, the equation of the relationship between the velocity of point B to the point sink and the distance is established:

[0016]

[0017] In the formula, q g is the point sink production; r is the distance of the point to the point sink, m; z is the vertical distance of point B to the point sink, m; S wi is the irreducible water saturation; S gr is the residual gas saturation; is the porosity;

[0018] S2002: Second, in the bottom water gas reservoir, the distance of point sink to the top of gas reservoir is h p, the distance from the bottom water is z w , other parameters remain unchanged, to establish any water quality point velocity v z and the distance dz of the equation:

[0019]

[0020] In the formula, z w is the distance from the point sink to the bottom boundary, m; q g is the point sink yield; r i is the distance from the point to the point sink, m; z i is the vertical distance from point B to the point sink, m; S wi is the irreducible water saturation; S gr is the residual gas saturation; is the porosity;

[0021] S300: the above-mentioned water-influx time prediction method for a vertical well in a bottom water gas reservoir, specifically comprising the following steps:

[0022] S3001: in the production of a vertical well in a bottom water gas reservoir, after the vertical well is equivalent to a plurality of point sinks, a mathematical model of production time t and water ridge height z1 is established according to the mirror reflection principle and the superposition principle of velocity;

[0023]

[0024] In the formula, z w is the distance from the point sink to the bottom boundary, m; q g is the point sink yield; r i is the distance from the point to the point sink, m; z i is the vertical distance from point B to the point sink, m; S wi is the irreducible water saturation; S gr is the residual gas saturation; is the porosity; N is the number of micro-segments, q gi is the yield of the i-th micro-segment studied, m 3 / d;

[0025] S300: the above-mentioned water-influx time prediction method for a horizontal well in a bottom water gas reservoir, specifically comprising the following steps:

[0026] In the production of a horizontal well in a bottom water gas reservoir, after the horizontal well is equivalent to a plurality of point sinks, a mathematical model of production time t and water ridge height z1 is established according to the mirror reflection principle and the superposition principle of velocity;

[0027]

[0028] In the formula, z w is the distance from the point sink to the bottom boundary, m; q g is the point sink yield; ri is the distance from the point to the point sink, m; z i is the vertical distance from point B to the point sink, m; S wi is the irreducible water saturation; S gr is the residual gas saturation; is the porosity; N is the number of micro-segments, q gi is the production of the i-th micro-segment under study, m 3 / d;

[0029] S400: The water breakthrough time prediction model of the above interwell interference, specifically comprising the following steps;

[0030] Based on the above obtained prediction time model of the water cone and water ridge of the single horizontal well and the vertical well, the interference existing between the multi-well production is considered, and a mathematical model of the production time t and the water ridge height z l is established according to the superposition principle of velocity and the mirror reflection principle;

[0031]

[0032] In the formula, z w is the distance from the point to the bottom boundary, m; q g is the point sink production; r i is the distance from the point to the point sink, m; z i is the vertical distance from point B to the point sink, m; S wi is the irreducible water saturation; S gr is the residual gas saturation; is the porosity; N is the number of micro-segments, q gi is the production of the i-th micro-segment under study, m 3 / d; M is the number of wells.

[0033] S500: Solving the water breakthrough time prediction model of the horizontal well and the vertical well, specifically comprising the following steps;

[0034] First, there is a horizontal well production in the X-Z plane, and the distance from the horizontal well to the bottom water is z w After the horizontal well is opened for production, the water particle motion law in the Y-Z plane is analyzed, and at a certain time, a water particle a in the Y-Z plane is obtained. The velocity generated by the horizontal well to the particle a, the vertical velocity and the vertical velocity generated by the entire micro-segment are obtained;

[0035] Second, considering the influence of the bottom water gas reservoir, the vertical velocity, vertical displacement and the distance S from the water particle to the bottom water of the particle a are obtained according to the mirror reflection principle;

[0036] S t = v z2 x Δt

[0037] S = S + S t

[0038] In the formula, the vertical point velocity generated by the point a, S is the vertical distance of the water point from the bottom water;

[0039] Compared with the prior art, the present application has the following beneficial effects: (1) using the mirror reflection principle and the superposition principle of velocity, the superposition effect is good; (3) programming to realize time step calculation, saving time and effort; (3) strong generalizability. BRIEF DESCRIPTION OF DRAWINGS

[0040] In the drawings:

[0041] Figure 1 is the technical roadmap for solving the water breakthrough time.

[0042] Figure 2 is the schematic diagram of point sink seepage in an infinite gas reservoir.

[0043] Figure 3 is the schematic diagram of point sink in a bottom water gas reservoir.

[0044] Figure 4 is the schematic diagram of point sink in a bottom water gas reservoir.

[0045] Figure 5 is the schematic diagram of mirror superposition principle for determining seepage velocity in a bottom water gas reservoir.

[0046] Figure 6 is the schematic diagram of mirror superposition principle for determining seepage velocity in a bottom water gas reservoir.

[0047] Figure 7 is the schematic diagram of mirror superposition principle for determining seepage velocity considering multi-well interference.

[0048] Figure 8 is the schematic diagram of solving velocity in different time periods. DETAILED DESCRIPTION

[0049] The present application will be further described below in combination with embodiments and drawings.

[0050] The present application provides a bottom water gas reservoir single well water invasion simulation and water breakthrough time prediction method, Figure 1 The technical roadmap for solving the water breakthrough time of the present method comprises the following steps:

[0051] The influence of wellbore pressure drop is considered to solve the productivity of microelement segment at different positions of the wellbore, and then the bottom water gas reservoir water cone and water ridge mathematical model is obtained according to the mirror reflection principle and the superposition principle of velocity, and the main steps are:

[0052] In infinite homogeneous gas reservoir, a point sink, its seepage is regarded as a spherical centripetal flow, a particle in the gas reservoir moves with velocity v z , and the motion distance dz is calculated; the seepage model is established;

[0053] In the point sink, the distance from the top of the gas reservoir is h p , the distance from the bottom water is z w , and other parameters remain unchanged, according to the top and bottom boundary characteristics of the bottom water gas reservoir, the point sink in the bottom water gas reservoir is equivalent to the arrangement mode in the infinite gas reservoir, and any water particle in the gas reservoir moves with velocity v z , and the motion distance dz is calculated;

[0054] In the bottom water gas reservoir, a vertical well is equivalent to a plurality of point sinks, according to the mirror reflection principle and the superposition principle of velocity, the mathematical model of production time t and water ridge height z1 can be obtained;

[0055] In the bottom water gas reservoir, a horizontal well is equivalent to a plurality of point sinks, according to the mirror reflection principle and the superposition principle of velocity, the mathematical model of production time t and water ridge height z1 can be obtained;

[0056] Using the above-mentioned prediction time model of water cone and water ridge of single horizontal well and vertical well, the water breakthrough time model of interwell interference is derived;

[0057] The above-mentioned point sink water breakthrough time prediction method for bottom water gas reservoir specifically includes the following steps;

[0058] In the bottom water gas reservoir, before the water body ridge advances or coned due to gas well production, in the infinite homogeneous gas reservoir, a point sink, its seepage is spherical centripetal flow, the equation of the relationship between the velocity of particle B to the point sink and the distance is established:

[0059]

[0060] In the formula, q g is the point sink production; r is the distance of the particle from the point sink, m; z is the vertical distance of the particle B to the point sink, m; S wi is the irreducible water saturation; S gr is the residual gas saturation; is the porosity;

[0061] Secondly, in the bottom water gas reservoir, the distance from the point sink to the top of the gas reservoir is h p , the distance from the bottom water is z w , and other parameters remain unchanged, the schematic diagram of the point sink in the bottom water gas reservoir is shown in Figure 3 . According to the top and bottom boundary characteristics of the bottom water gas reservoir, the point sink in the bottom water gas reservoir is equivalent to the arrangement mode in the infinite gas reservoir as shown in Figure 4 , the velocity v zEquation with motion dz:

[0062]

[0063] In the formula, z w q is the distance from the bottom boundary of the point sink, in meters; g For point exchange rate output; r i Z is the distance from point B to the sink, in meters; Z is the perpendicular distance from point B to the sink, in meters; S wi S represents the bound water saturation. gr Residual gas saturation; Porosity;

[0064] The above-mentioned method for predicting the water breakthrough time of a vertical well in a bottom-water gas reservoir specifically includes the following steps;

[0065] In bottom-water gas reservoirs, vertical well production involves treating the vertical well as several point sinks. Based on the principles of mirror reflection and velocity superposition, a schematic diagram illustrating the determination of seepage velocity using the mirror superposition principle is shown below. Figure 5 As shown, a mathematical model is established for the relationship between production time t and water ridge height z1;

[0066]

[0067] In the formula, z w q is the distance from the bottom boundary of the point sink, in meters; g For point exchange rate output; r i The distance from the point mass to the sink is m; z i S is the perpendicular distance from point B to the sink point, in meters (m). wi S represents the bound water saturation. gr Residual gas saturation; Porosity; N is the number of micro-segments, q gi The output of the i-th infinitesimal segment under study, m 3 / d;

[0068] The above-mentioned method for predicting the water breakthrough time of horizontal wells in bottom-water gas reservoirs specifically includes the following steps;

[0069] In horizontal well production within bottom-water gas reservoirs, the horizontal well is equivalent to several point sinks. Based on the mirror reflection principle and the velocity superposition principle, a schematic diagram illustrating the determination of seepage velocity using the mirror superposition principle is obtained, as shown below. Figure 6 As shown, a mathematical model is established for the relationship between production time t and water ridge height z1;

[0070]

[0071] In the formula, z w q is the distance from the bottom boundary of the point sink, in meters; g For point exchange rate output; r iis the vertical distance from the point B to the point sink, m; S i is the vertical distance from the point B to the point sink, m; S wi is the irreducible water saturation; S gr is the residual gas saturation; is the porosity; N is the number of micro-segments, q gi is the production of the i-th micro-segment under study, m 3 / d;

[0072] The water breakthrough time prediction model of the above interwell interference specifically includes the following steps.

[0073] Based on the above obtained prediction time model of the water cone and the water ridge of the single horizontal well and the vertical well, the interference between multiple wells is considered, and the mirror image superposition principle of the multiple well interference is obtained according to the superposition principle of velocity and the mirror image reflection principle. The schematic diagram of the seepage velocity is shown in Figure 7 , and the mathematical model of the production time t and the water ridge height z1 is established.

[0074]

[0075] In the formula, z w is the distance from the point sink to the bottom boundary, m; q g is the production of the point sink; r i is the vertical distance from the point B to the point sink, m; S i is the vertical distance from the point B to the point sink, m; S wi is the irreducible water saturation; S gr is the residual gas saturation; is the porosity; N is the number of micro-segments, q gi is the production of the i-th micro-segment under study, m 3 / d; M is the number of wells.

[0076] Solving the water breakthrough time prediction model of the horizontal well and the vertical well specifically includes the following steps.

[0077] First, there is a horizontal well production in the X-Z plane, and the distance from the horizontal well to the bottom water is z w After the horizontal well is opened for production, the water particle motion law in the Y-Z plane is analyzed, and at a certain time, a water particle a in the Y-Z plane is obtained. The water particle motion relationship is shown in Figure 8 , the velocity generated by the arbitrary micro-segment of the horizontal well to the particle a, the vertical velocity and the vertical velocity generated by the whole micro-segment are obtained.

[0078] Second, considering the influence of the bottom water gas reservoir, the vertical velocity, the vertical displacement and the distance S from the water particle to the bottom water of the particle a are obtained according to the mirror image reflection principle.

[0079] S t = vz2 x delta t

[0080] S = S + S t

[0081] In the formula, the vertical point velocity generated by the mass point a, S is the vertical distance of the water mass point from the bottom water;

[0082] Compared with the prior art, the present application has the following beneficial effects: (1) using the mirror reflection principle and the superposition principle of velocity, the superposition effect is good; (3) programming realizes time step calculation, saving time and effort; (3) strong generalizability.

[0083] Finally, it should be explained that: the above examples are only used to illustrate but not to limit the technical solutions of the present application, although the present application has been described in detail with reference to the above examples, those skilled in the art should understand that: the present application can still be modified or replaced equivalently without departing from the spirit and scope of the present application Any modification or partial replacement should be covered in the scope of the claims of the present application.

Claims

1. A method for single well water invasion simulation and water breakthrough time prediction of a gas reservoir with bottom water, characterized in that, The method comprises the following steps: S100: Deriving the productivity of the microelement section at different positions of the wellbore by considering the influence of the wellbore pressure drop, and then obtaining a mathematical model of a water crest and a water cone in the bottom water gas reservoir according to the mirror reflection principle and the superposition principle of velocity, and the main steps are as follows: S1001: In an infinite homogeneous gas reservoir, a point sink, the seepage is regarded as a spherical centripetal flow, a particle in the gas reservoir moves at a speed v z , the distance dz is calculated; S1002: the distance between the point sink and the top of the gas reservoir is h p , the distance from the bottom water is z w , other parameters remain unchanged, according to the top and bottom boundary characteristics of the bottom water gas reservoir, a point sink in the bottom water gas reservoir is equivalent to the arrangement mode in the infinite gas reservoir, and the motion distance dz of any water quality point in the gas reservoir is calculated at the speed v z . S1003: In the bottom water gas reservoir, the straight well is equivalent to several point sinks. According to the mirror reflection principle and the velocity superposition principle, the mathematical model of production time t and water ridge height z can be obtained. l ​ S1004: In the production of horizontal wells in bottom water gas reservoirs, the horizontal well is equivalent to several point sinks. According to the mirror reflection principle and the superposition principle of velocity, the mathematical model of production time t and water ridge height z l can be obtained. S1005: Using the above-obtained single-port horizontal and straight well water crest and water cone prediction time model, the water breakthrough time model of interwell interference is derived; S200: Solving the water breakthrough time prediction model of the horizontal well and the straight well; The step S200 specifically comprises the following steps: S2001: Before the well is opened for production, the gas reservoir has a unified gas-water interface; as the development proceeds, the water quality point will gradually move to the opened section of the gas well, and the velocity is constantly changing; the velocity of the water quality point movement in this period is selected as the average value of the initial velocity and the final velocity in the step length Δt. S2002: The horizontal well produces in the X-Z plane, and the distance between the horizontal well and the bottom water is z w After the horizontal well is opened for production, the motion law of the water quality point in the Y-Z plane is analyzed to obtain the velocity v gi and the vertical velocity v giz of an arbitrary microelement section of a water quality point a in the Y-Z plane at a certain moment of the horizontal well z1 ; S2003: According to the mirror reflection principle, the vertical velocity v generated by the particle a is obtained in consideration of the influence of the bottom water gas reservoir z2 ; S2004: vertical velocity v generated from the mass point a z2 , the vertical displacement S of the water mass point in the time Δt is calculated t ; S2005: obtaining the distance S of the water quality point from the bottom water according to the vertical displacement S of the water quality point t ; S2006: the distance between the horizontal well and the bottom water is z w The iterative calculation is performed, if the distance between the water particle and the bottom water is less than the distance between the horizontal well and the bottom water, the iterative calculation is continued until the distance between the water particle and the bottom water is greater than or equal to the distance between the horizontal well and the bottom water; finally, the positions of all water particles in the Y-Z plane and the corresponding water cone and water ridge breakthrough time are output, and the calculation is ended; wherein the water breakthrough time model of the interwell interference is: where q gi is the production of the ith microelement segment of study, m 3 / d; z w is the distance from the point sink to the bottom boundary; z i is the vertical distance from the point B to the point sink; v z1 is the moving velocity of the point; S wi is the irreducible water saturation; S gr is the residual gas saturation; is the porosity, and M is the number of wells.

2. The method according to claim 1, wherein the method is characterized in that: In the production of a vertical well in a gas reservoir with bottom water, the mathematical model for the production time t and the water cresting height z l is where q gi Production of the i-th microelement segment under study, m 3 / d; z w Distance from the point sink to the bottom boundary; z i Vertical distance from the point B to the point sink; v z1 Particle moving velocity; S wi Irreducible water saturation; S gr Residual gas saturation; Porosity.

3. The method of claim 1, wherein the method further comprises: In the production of horizontal wells in gas reservoirs with bottom water, the mathematical model of the production time t and the water crest height z l is given where q gi Production of the i-th microelement segment under study, m 3 / d; z w Distance from the point sink to the bottom boundary; z i Vertical distance from the point B to the point sink; v z1 Particle moving velocity; S wi Irreducible water saturation; S gr Residual gas saturation; Porosity.

4. The method of claim 1, wherein the method further comprises: The water quality point distance from the bottom water is S = S + S t where S is the vertical distance of the water quality point from the bottom water; S t Water quality point vertical displacement.

Images