Method for adjusting gas injection and production profile through variable perforation density of gas storage

Abstract

The invention belongs to the technical field of oil and gas production, and provides a method for adjusting a gas injection and production profile through variable perforation density of a gas storage. The method comprises the following steps: constructing a gas reservoir model; calculating a skin coefficient S by adopting a group of uniformly distributed perforation densities; calculating a flow profile according to the skin coefficient, and repeatedly calculating the skin coefficient and the flow profile by adjusting the perforation density until the flow profile calculation requirement is met; and variable-density perforation is completed. According to the method, the flow profile of gas injection and production can be effectively improved, the gas injection and production difference of the heel end and the toe end is reduced, and uniform propelling of the flow profile is achieved; after perforation parameter design is carried out through the method, the gas injection speed distribution from the heel end to the toe end in the gas injection and production process of the horizontal well of the gas storage can be more uniform, the water control capacity is enhanced, a flow profile meeting the gas injection and production requirements is formed, and the method can be used for simulating the process from an unsteady state to a steady state and is more suitable for actual production field application.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas production, and relates to a method for adjusting a gas injection and production profile by changing the perforation density of a gas storage reservoir. Background Art

[0002] Building underground gas storage is a relatively advanced method to regulate the seasonal supply and demand contradictions in the natural gas market. It is to form a closed space deep underground, inject natural gas into it in the form of pumping on the ground and store it, and then extract the natural gas to the ground through production wells and transport it to users as needed. It has the advantages of large gas storage capacity, high safety factor and low cost, and has now become a very important link in the natural gas supply and marketing chain.

[0003] When the gas storage is injected with a large flow rate, the gas pressure in the horizontal well is higher at the root end and gradually decreases with the gas flow direction. When the reservoir pressure remains unchanged and the perforation density is consistent everywhere on the horizontal well, the pressure difference between different positions of the horizontal well and the reservoir is larger at the heel end of the horizontal well and smaller at the toe end, resulting in a large gas injection rate at the heel end of the horizontal well and a small gas injection rate at the toe end. During gas production, due to the presence of bottom water, water is easily seen at the heel end and toe end. In order to adjust the flow profile, the perforation construction needs to be adjusted. The adjustable construction parameters of perforation include: bullet type, hole density, hole depth, hole diameter, etc. Different parameter combinations will produce different perforation resistances. For example, deep penetration and large hole density can greatly reduce the seepage resistance of the wellbore, while low hole density and small hole depth can introduce a large seepage resistance near the wellbore; based on this, the seepage resistance can be increased in the high permeability layer, and high hole density and deep penetration can be used in the low permeability layer to reduce the skin coefficient near the oil well, thereby reducing the interference of the high permeability layer on the low permeability layer and improving the overall recovery rate of the reservoir. Without adding any process and investment, better results can be achieved than general perforation.

[0004] In "Analysis and Optimization of Inflow Profile of Perforated Completion Horizontal Well Based on Coupling Model", Journal of Chongqing University of Science and Technology (Natural Science Edition), Vol. 23, No. 3, Jiang Lifu calculated the productivity of perforated completion horizontal wells and optimized the inflow profile by coupling the deep flow model of the reservoir in the far well area, the segmented near-well heterogeneous zone and the perforation zone flow model, and the relationship between pressure and flow of the wellbore pipe flow model; the calculation and analysis of the horizontal section inflow profile under the influence of multiple parameters and the optimization design of completion parameters can be realized; at the same time, the change of local perforation density produces a diversion effect, which can reduce the influence of the near-well zone heterogeneity on the inflow profile. In order to ensure the production capacity and reduce the profile fluctuation, the ideal inflow profile when the homogeneous reservoir and the pressure drop of the pipe flow can be used as the standard inflow profile. However, this calculation method for horizontal well perforation design is relatively complicated and has a large amount of calculation. The analytical solution is only for the flow profile that has entered the steady state, and it cannot simulate the process from unsteady state to steady state.

[0005] With the country's growing energy demand, gas storage has received high attention for its advantages of strong mobility, large storage capacity, and wide peak-shaving range. For depleted oil and gas reservoir-type gas storage, the perforation process must meet the requirements of removing the pollution of the formation during the drilling and cementing process, minimizing the secondary pollution of the formation during the perforation process, meeting the requirements of balanced advancement of the gas injection and production front, and ensuring the maximum reservoir utilization capacity. By calculating the skin coefficient of the wellbore and using mathematical calculations to obtain the corresponding flow profile, the perforation density of the horizontal well is optimized. According to different gas storages, a set of optimal parameters for variable perforation density can be obtained to make the flow profile more uniform. The variable perforation density to adjust the flow profile technology effectively controls the speed and pressure changes of gas injection and production during operation, further improving the operational stability of the gas storage. Summary of the invention

[0006] In view of the problems of large amount of calculation and inability to simulate the process from non-steady state to steady state in the prior art, the present invention provides a method for adjusting the injection and production gas profile by changing the perforation density of a gas storage reservoir, which can effectively improve the flow profile of gas injection and production, reduce the difference between the heel end and the toe end of gas injection and production, and achieve uniform advancement of the flow profile. After using the present invention to design the perforation parameters, the gas injection velocity distribution from the heel end to the toe end during the gas injection and production of the horizontal well of the gas storage reservoir can be made more uniform, the water control ability can be enhanced, and a flow profile that meets the requirements of gas injection and production can be formed.

[0007] The technical solution of the present invention is as follows:

[0008] A method for adjusting a gas injection and production profile by changing the perforation density of a gas storage reservoir comprises the following steps:

[0009] S1: Construct gas reservoir model: including wellbore flow model;

[0010] S2: Use a set of uniformly distributed perforation densities to calculate the skin factor S;

[0011] S3: Calculate flow profile: Calculate the flow profile based on the skin factor and determine whether the flow profile calculation requirements are met; if not, use a set of variable perforation densities from the heel end to the toe end of the horizontal well to repeatedly calculate the skin factor and flow profile until the flow profile calculation requirements are met;

[0012] S4: Calculate perforation pressure loss: The friction pressure loss is calculated by using the skin factor S and the wellbore flow model;

[0013] S5: Complete variable density perforating.

[0014] Furthermore, in step (1), the wellbore flow model is constructed using the coupling relationship between the horizontal well and the matrix fluid flow, as follows:

[0015]

[0016] In the formula, is the flow rate, m3 / s; λ α is the fluidity of the α phase, cp·D,; ρ α is the density of α phase, kg / m3; J w is the well index, m3 / (s·Pa); P bh is the horizontal well pressure, Pa; P α is the reservoir pressure, Pa; ΔZ is the height difference, m; α phase is the gas phase or water phase;

[0017] In the rectangular coordinate system, for the well index J w for:

[0018]

[0019] Where kh is the product of effective permeability and net thickness, D·m; r w is the radius of the horizontal well, m; r e is the equivalent radius, m; S is the skin factor, dimensionless; θ is a parameter related to the well position relative to the grid position in the numerical model, dimensionless parameter;

[0020] Considering friction resistance and gravity, the energy conservation equation for flow in a horizontal well is:

[0021]

[0022] Where: △P α is the pressure loss, Pa; u α is the phase velocity, m / s;

[0023] Ignoring local pressure losses, the friction pressure loss is:

[0024]

[0025] Where f is the Fanning friction coefficient, dimensionless; L is the flow length, m; D is the wellbore diameter, m.

[0026] Furthermore, ΔP α Represents the grid P α When the bottom hole pressure is fixed, all other P α It can be determined by △P α To obtain.

[0027] Furthermore, in step S2, the skin coefficient S is obtained by the two-dimensional flow skin coefficient S 2D , Wellbore plugging skin coefficient S wb and the three-dimensional flow skin coefficient S 3D constitute.

[0028] Furthermore, the skin coefficient S and the two-dimensional flow skin coefficient S 2D , Wellbore plugging skin coefficient S wb and the three-dimensional flow skin coefficient S 3D The relationship is as follows:

[0029] S=S 2D +S sw +S 3D (5).

[0030] Furthermore, the two-dimensional flow skin S 2D for:

[0031] When the number of perforations m in the same plane is 1 or 2,

[0032]

[0033] When the number of perforations m in the same plane is 3 or 4,

[0034]

[0035] Where k represents permeability, subscripts x, y and z represent three directions, mD; α represents phase angle, °; l pD is the perforation length, which is the ratio of the perforation length to the horizontal well radius and is dimensionless; a m is a constant related to m.

[0036] Furthermore, the wellbore plugging surface S wb for:

[0037] S wb =b m ln{c m / l pD,eff +exp[-c m / l pD,eff ]} (8)

[0038] Where l pD，eff is the effective perforation length, dimensionless, and related to the perforation length, phase angle, and permeability ratio; b m and c m is a constant related to m.

[0039] Furthermore, the three-dimensional flow skin S 3D for:

[0040]

[0041] β1=d m logr pD +e m (10)

[0042] β2=f m r pD +g m (11)

[0043] Where d m , e m , f m and g m is a constant related to m;

[0044] When m = 1 or 2, the dimensionless perforation spacing h D and dimensionless perforation radius r pD for:

[0045]

[0046]

[0047] Where h represents the perforation spacing, m; r p represents the perforation radius, m; α' and α" are:

[0048]

[0049]

[0050] When m = 3 or 4, the dimensionless perforation density h D and dimensionless perforation radius r pD for:

[0051]

[0052]

[0053] Furthermore, in step S3, the flow profile calculation is to substitute the skin coefficient S calculated by formulas (5)-(17) into formula (2), and calculate the profile using formulas (1)-(4).

[0054] Furthermore, in step S3, the flow profile calculation requirement is that the standard deviation of the normalized flow rate at the beginning and end of production is not higher than 0.3 and 0.2 respectively.

[0055] Furthermore, in step S3, the basis for changing the perforation density is that the perforation density ranges from 1 to 20 holes / m, and the gradient is adjusted from 0.5 to 1 hole / m each time.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. The present invention overcomes the problem of uneven flow profile caused by perforating gas injection and production in the past, and proposes a technical method of using skin coefficient to guide the adjustment of perforation density. Compared with the common steady-state analytical method, the present invention adopts numerical solution, which can simulate the process from unsteady state to steady state. Compared with the method of using analytical solution in the prior art, the numerical solution of the present invention takes more comprehensive considerations for guiding the adjustment of perforation density, is based on the complex situation of the real oil and gas reservoir geological model, and is closer to the actual situation on site;

[0058] 2. Use the skin coefficient to replace the pressure loss caused by perforation, including the 2D flow skin S 2D , wellbore plugging skin S wb and 3D flow skin S 3D According to the calculated skin coefficient, the perforation density from the heel to the toe is adjusted accordingly, and the skin coefficient is calculated repeatedly. The flow profile under the corresponding perforation scheme is obtained, and the optimal perforation scheme is obtained, achieving the purpose of adjusting the flow profile by changing the perforation density. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 A flow chart of a method for adjusting the gas injection and production profile by changing the perforation density of a gas storage reservoir according to the present invention;

[0060] Figure 2 The gas production profile when the perforations are evenly distributed in Example 2 of the present invention;

[0061] Figure 3 The gas production profile when the two ends are compressed and distributed in Example 2 of the present invention;

[0062] Figure 4 This is the gas production profile when the two-end pressing distribution is gradually changed in Example 2 of the present invention. DETAILED DESCRIPTION

[0063] The following non-limiting examples can enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. The following content is merely an exemplary description of the scope of the present invention, and those skilled in the art can make various changes and modifications to the present invention based on the disclosed content, which should also fall within the scope of the present invention.

[0064] Example 1

[0065] The following is combined with Figure 1 The flow chart of the method for adjusting the injection and production gas profile of a gas storage by changing the perforation density is shown to explain the method of the present invention;

[0066] The specific design steps are as follows:

[0067] S1: According to the method in Wang J, Dai J, Xie B, et al. Gas Injection Capacity of Slotted Liner and Perforation Completion in Underground Natural Gas Storage Reservoirs [J]. Processes, 2023, 11 (5): 1471. (Gas injection capacity of slotted liner and perforation completion in underground natural gas storage reservoirs), the gas reservoir model was constructed using MATLAB Reservoir Simulation Toolbox, a discrete well model was adopted, and a wellbore flow model was specified;

[0068] S2: A set of uniformly distributed (h constant) perforation densities is used; the corresponding skin factor S is calculated using formulas (5) to (17). The specific calculation process is as follows:

[0069] (S2-1) The skin coefficient S is derived from the two-dimensional flow skin coefficient S 2D , Wellbore plugging skin coefficient S wb and the three-dimensional flow skin coefficient S 3D The relationship is as follows:

[0070] S=S 2D +S sw +S 3D (5).

[0071] (S2-2) Two-dimensional flow skin S 2D for:

[0072] When the number of perforations m in the same plane is 1 or 2,

[0073]

[0074] When the number of perforations m in the same plane is 3 or 4,

[0075]

[0076] Where k represents permeability, subscripts x, y and z represent three directions, respectively, %; α represents phase angle, °; l pD is the perforation length, which is the ratio of the perforation length to the horizontal well radius and is dimensionless; a m is a constant related to m.

[0077] (S2-3) Wellbore plugging skin S wb for:

[0078] S wb =b m ln{c m / l pD,eff +exp[-c m / l pD,eff ]} (8)

[0079] Where l pD，eff is the effective perforation length, dimensionless, and related to the perforation length, phase angle, and permeability ratio; b m and c m is a constant related to m.

[0080] (S2-4) Three-dimensional flow skin S 3D for:

[0081]

[0082] β1=d m logr pD +e m (10)

[0083] β2=f m r pD +g m (11)

[0084] Where d m , e m , f m and g m is a constant related to m;

[0085] When m = 1 or 2, the dimensionless perforation spacing h D and dimensionless perforation radius r pD It can be expressed as:

[0086]

[0087]

[0088] Where h represents the perforation spacing, m; r p represents the perforation radius, m; α' and α" are:

[0089]

[0090]

[0091] When m = 3 or 4, the dimensionless perforation density h D and dimensionless perforation radius r pD for:

[0092]

[0093]

[0094] S3: Substitute the skin factor into formula (2) and use formulas (1) to (4) to calculate the flow profile: The specific calculation process is as follows:

[0095] (S3-1) The wellbore flow model is constructed by using the coupling relationship between the horizontal well and the matrix fluid flow, as follows:

[0096]

[0097] In the formula, is the flow rate, m 3 / s;λ α is the fluidity of the α phase, cp·D,; ρ α is the density of the α phase, kg / m 3 ; J w is the well index, m 3 / (s·Pa);P bh is the horizontal well pressure, Pa; P α is the reservoir pressure, Pa; ΔZ is the height difference, m; α phase is the gas phase or water phase;

[0098] (S3-2) In the rectangular coordinate system, for the well index J w for:

[0099]

[0100] Where kh is the product of effective permeability and net thickness, D·m; r w is the radius of the horizontal well, m; r e is the equivalent radius, m; S is the skin factor, dimensionless; θ is a parameter related to the well position relative to the grid position in the numerical model, dimensionless parameter;

[0101] (S3-3) Considering friction resistance and gravity, the energy conservation equation for flow in a horizontal well is:

[0102]

[0103] Where: △P α is the pressure loss, Pa; u α is the phase velocity, m / s;

[0104] Ignoring local pressure losses, the friction pressure loss is:

[0105]

[0106] Where f is the Fanning friction coefficient, dimensionless; L is the flow length, m; D is the wellbore diameter, m.

[0107] S4: Determine whether the flow profile meets the calculation requirements. If not, use a set of perforation densities that gradually increase (h decreases) from the heel section to the toe end of the horizontal well. During this process, the perforation density ranges from 1 to 20 holes / m, and the gradient is adjusted to 0.5 to 1 hole / m each time. Repeat the calculation of the skin coefficient and flow profile until the flow profile calculation requirements are met (i.e., the standard deviation of the normalized flow rate at the beginning and end of production is not higher than 0.3 and 0.2, respectively).

[0108] Example 2

[0109] This embodiment is based on the A parameters of a gas storage reservoir (see Table 1) to demonstrate how to adjust the flow profile by changing the perforation density.

[0110] Table 1 Physical parameters of fluids in horizontal wells

[0111]

[0112] Keeping the bottom hole pressure of the horizontal well constant, the calculation time is 1 year (Note: the hole density ns and the hole spacing h are reciprocals of each other).

[0113] For the values ​​of parameters related to m in the calculation process of the skin coefficient S, please refer to the reference Furui KA comprehensiveskin factor model for well completions based on finite element simulations [M]. The University of Texas at Austin, 2004.

[0114] (1) For the convenience of construction, the hole density is usually kept constant. Taking 16 holes / m evenly distributed as an example, the inflow profiles at the early and late stages of production are: Figure 1 As shown in the figure, due to the influence of wellbore pressure loss and end effect, the flow rate near the heel and toe of the horizontal well is relatively large. The non-uniformity of the flow rate is measured by the node standard deviation. The standard deviation of the flow rate at the beginning and end of production is 0.4119 and 0.1884 respectively. Therefore, consider reducing the perforation density near the heel and toe. At this time, due to uneven injection and production, the recovery rate is only 21.3%.

[0115] (2) The 100 m near the heel and toe are reduced to 8 holes / m, and the front and rear gas production profiles become Figure 2 , it can be seen that the gas production at both ends is reduced, and the standard deviation of flow rate at the beginning and end of production is 0.3044 and 0.1665 respectively. However, this method is too rigid, and the recovery rate is only increased to 24.6%.

[0116] (3) Consider a gradual change scheme in which the perforation rate increases linearly from 2.5 holes / m to 13.6 holes / m for 100 m near the heel and toe ends. The total number of perforations in this scheme remains unchanged from the former. The standard deviations of flow rates at the beginning and end of production are 0.2631 and 0.1378, respectively, indicating that the gas production profile has been significantly improved in both the early and late stages of production, and the recovery factor has been increased to 29.1%.

[0117] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, rather than to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions of the technical solution of the present invention by ordinary technicians in this field do not deviate from the essence and scope of the technical solution of the present invention.

Claims

1. A method for adjusting the gas injection and production profile by changing the perforation density of a gas storage reservoir, characterized in that: The following steps are involved: S1: Construct gas reservoir model: including wellbore flow model; S2: Use a set of uniformly distributed perforation densities to calculate the skin factor S; S3: Calculate flow profile: Calculate the flow profile based on the skin factor and determine whether the flow profile calculation requirements are met; if not, use a set of variable perforation densities from the heel end to the toe end of the horizontal well to repeatedly calculate the skin factor and flow profile until the flow profile calculation requirements are met; S4: Calculate perforation pressure loss: The friction pressure loss is calculated by using the skin factor S and the wellbore flow model; S5: Complete variable density perforating.

2. The method according to claim 1, characterized in that In step (1), the wellbore flow model is constructed by using the coupling relationship between the horizontal well and the matrix fluid flow, as follows: In the formula, is the flow rate, m 3 / s;λ α is the mobility of the α phase, cp·D,; ρ α is the density of the α phase, kg / m 3 ; J w is the well index, m 3 / (s·Pa);P bh is the horizontal well pressure, Pa; P α is the reservoir pressure, Pa; ΔZ is the height difference, m; α phase is the gas phase or water phase; In the rectangular coordinate system, for the well index J w for: Where kh is the product of effective permeability and net thickness, D·m; r w is the radius of the horizontal well, m; r e is the equivalent radius, m; S is the skin factor, dimensionless; θ is a parameter related to the well position relative to the grid position in the numerical model, dimensionless parameter; Considering friction resistance and gravity, the energy conservation equation for flow in a horizontal well is: Where: △P α is the pressure loss, Pa; u α is the phase velocity, m / s; Ignoring local pressure losses, the friction pressure loss is: Where f is the Fanning friction coefficient, dimensionless; L is the flow length, m; D is the wellbore diameter, m.

3. The method according to claim 1, characterized in that In step S2, the skin coefficient S is obtained by the two-dimensional flow skin coefficient S 2D , Wellbore plugging skin coefficient S wb and the three-dimensional flow skin coefficient S 3D constitute.

4. The method according to claim 3, characterized in that The skin coefficient S and the two-dimensional flow skin coefficient S 2D , Wellbore plugging skin coefficient S wb and the three-dimensional flow skin coefficient S 3D The relationship is as follows: S=S 2D +S sw +S 3D (5)。 5. The method according to claim 3, characterized in that: The two-dimensional flow skin S 2D for: When the number of perforations m in the same plane is 1 or 2, When the number of perforations m in the same plane is 3 or 4, Where k represents permeability, subscripts x, y and z represent three directions, mD; α represents phase angle, °; l pD is the perforation length, which is the ratio of the perforation length to the horizontal well radius and is dimensionless; a m is a constant related to m.

6. The method according to claim 3, characterized in that The wellbore plugging epidermis S wb for: S wb =b m ln{c m / l pD,eff +exp[-c m / l pD,eff ]} (8) Where l pD，eff is the effective perforation length, dimensionless, and related to the perforation length, phase angle, and permeability ratio; b m and c m is a constant related to m.

7. The method according to claim 3, characterized in that The three-dimensional flow skin S 3D for: β1=d m achieve pD +e m (10) β2=f m r pD +g m (11) Where d m , e m , f m and g m is a constant related to m; When m = 1 or 2, the dimensionless perforation spacing h D and dimensionless perforation radius r pD for: Where h represents the perforation spacing, m; r p represents the perforation radius, m; α' and α" are: When m = 3 or 4, the dimensionless perforation density h D and dimensionless perforation radius r pD for:

8. The method according to claim 1, characterized in that In step S3, the flow profile is calculated by substituting the skin coefficient S calculated by formulas (5)-(17) into formula (2), and calculating the profile using formulas (1)-(4).

9. The method according to claim 1, characterized in that: In step S3, the flow profile calculation requirement is that the standard deviation of the normalized flow rate at the beginning and end of production is not higher than 0.3 and 0.2 respectively.

10. The method according to claim 1, characterized in that In step S3, the basis for changing the perforation density is that the perforation density ranges from 1 to 20 holes / m, and the gradient is adjusted from 0.5 to 1 hole / m each time.

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