A method for calculating the amount of accumulated fluid and flow pressure in a high-pressure gathering and transportation gas well

Abstract

The present application relates to a kind of high-pressure gathering and transferring gas well wellbore fluid volume and flow pressure calculation method, belong to gas production engineering field.The method first carries out calculation basis data preparation;Second, set the initial value H1 of tubing fluid volume equivalent liquid column height, annulus fluid volume equivalent liquid column height H2 is calculated according to proportionality coefficient k;According to the tubing model, the pressure p1 of tubing liquid level and flow pressure p wf1 , the pressure p2 of annulus fluid surface and flow pressure p wf2 Are calculated according to static gas column model;If p wf1 =p wf2 , determine the tubing fluid volume equivalent liquid column height H1, and flow pressure p wf , wellbore fluid volume Q are calculated according to gas well basis data, if p wf1 =p wf2 Not established, then adjust H1 setting value and carry out iterative operation.The present application only needs to use gas well production report data, low in cost, strong in logic, after being converted into computer program, can automatically realize fast cycle iteration, real-time monitoring wellbore fluid volume and flow pressure, timely guide drainage gas recovery process matching, reduce gas well fluid production reduction risk, improve gas well development benefit.

Description

TECHNICAL FIELD

[0001] The application relates to a high-pressure gathering and transportation gas well wellbore liquid loading and flow pressure calculation method and belongs to the field of gas production engineering. BACKGROUND

[0002] Dense low-permeability gas reservoirs are generally water-bearing and gas-water is not separated, and gas wells show gas-water co-production as soon as they are put into production. At the same time, the average pressure coefficient of the gas reservoir is less than 1, and the liquid carrying capacity of the gas well is insufficient, so liquid loading and production reduction or even water flooding and well shut-in are prone to occur during production. Therefore, identifying liquid loading wells and matching reasonable foam displacement and injection systems according to wellbore liquid loading are the keys to realizing stable production of gas wells.

[0003] There are nearly 2000 high-pressure gathering and transportation gas wells in the Ordos Basin. Due to the restriction of production cost, it is not realistic to use periodic flow pressure testing or to install annular liquid level testing equipment in gas wells to monitor wellbore liquid loading and flow pressure. Therefore, a method for quantitatively calculating wellbore liquid loading and flow pressure through production data is established, which is of great significance for reducing the cost of judging gas well flow pressure and liquid loading, improving the calculation speed, and thus identifying liquid loading gas wells in a timely manner and matching foam displacement technology.

[0004] For high-pressure gathering and transportation gas wells, there are two methods to determine the liquid loading and flow pressure in the wellbore. The first method is to use infrasound or echo instrument to monitor, such as the Chinese invention patent document with the publication number CN108678729A which discloses a high-pressure gas well wellbore liquid loading automatic monitoring device and method, and the Chinese invention patent document with the publication number CN208564538U which discloses a high-pressure gas well wellbore liquid loading automatic monitoring device, both of which use infrasound generated by wellhead high-pressure gas to detect annular liquid loading; such as the Chinese invention patent document with the publication number CN105649603A which discloses a method for real-time testing of gas well wellbore liquid loading, which uses an echo instrument to monitor the annular liquid level height; the second method is similar to the present application, which uses a theoretical model to calculate the wellbore liquid loading and flow pressure, such as the Chinese invention patent document with the publication number CN113338915A which discloses a method for judging whether a gas well is liquid loading and predicting liquid loading height, which assumes that there is no liquid loading in the annulus, calculates the wellbore bottom hole flow pressure and the non-liquid loading pressure profile in the tubing by static gas column, and compares it with the actual tubing pressure profile to determine the liquid loading in the tubing, but it cannot calculate the liquid loading in the annulus; such as the Chinese invention patent document with the publication number CN103590812A which discloses a gas well liquid loading calculation method, calculation device and determination method, which calculates the annular liquid loading and tubing liquid loading, but it confuses the flow pressure under different conditions, equates the flow pressure under non-liquid loading conditions to that under liquid loading conditions, and then calculates the annular liquid loading and tubing liquid loading, which is not perfect in method. SUMMARY

[0005] The application aims to provide a high-pressure gathering and transportation gas well wellbore liquid loading amount and flow pressure calculation method to solve the problem of not discovering liquid loading gas well in time and guiding the implementation of the matching drainage gas recovery process.

[0006] To achieve the above-mentioned purpose, the steps of the high-pressure gathering and transportation gas well wellbore liquid loading amount and flow pressure calculation method of the application are as follows:

[0007] 1) Complete the preparation of calculation basis data;

[0008] 2) Set the initial value H1 of the equivalent liquid column height of the tubing liquid loading amount, and calculate the equivalent liquid column height H2 of the annulus liquid loading amount according to the proportional coefficient k of H2 and H1;

[0009] 3) Use the basis data in step 1) to calculate the tubing liquid surface pressure p1 by the tubing pressure p tf According to the pipe flow model, the tubing liquid surface pressure p1 is calculated, and the casing pressure p ts According to the static gas column model, the annulus liquid surface pressure p2 is calculated;

[0010] 4) The tubing liquid surface pressure p1 plus the equivalent liquid column gravity ρgH1 of the tubing obtains the flow pressure P wf1 , and the annulus liquid surface pressure p2 plus the equivalent liquid column gravity ρgH2 of the annulus obtains the flow pressure p wf2 ;

[0011] 5) If p wf1 =p wf2 , the set value is the equivalent liquid column height H1 of the tubing liquid loading amount, and the flow pressure p wf and the wellbore liquid loading amount Q are calculated according to the gas well basis data, if p wf1 ≠p wf2 , the H1 set value is adjusted for iterative operation.

[0012] The high-pressure gathering and transportation gas well wellbore liquid loading amount and flow pressure calculation method established by the application does not rely on a certain testing device, and has the characteristics of low calculation cost; compared with other methods for calculating the wellbore liquid loading amount and flow pressure through theoretical models, the application can simultaneously include the tubing liquid loading and the annulus liquid loading in the iterative calculation by simplifying the wellbore gas-liquid two-phase distribution model and introducing the ratio of the equivalent liquid column height in the annulus to the equivalent liquid column height in the tubing, and there is no problem of ignoring the annulus liquid loading or confusing the flow pressure under different states, which is consistent with the actual production situation.

[0013] Further, the calculation basis data in step 1) includes: wellbore vertical height H, wellbore measured length H m , wellbore vertical depth and measured depth comparison table, casing inner diameter Φ c (multiple inner diameter values are used for combined casing, denoted as Φc-1 , …, Φ c-n ), oil pipe outer diameter Φ o1 , oil pipe inner diameter Φ o2 (Refer to casing conditions in combination of oil pipe conditions respectively as Φ o1-1 , …, Φ o1-n , Φ o2-1 , …, Φ o2-n ), casing pressure p of gas well ts , oil pressure p tf , daily gas production q g and liquid gas ratio WGR.

[0014] The present application provides comprehensive and complete data support for subsequent calculation process by collecting basic data required for calculation.

[0015] Further, in the step 2), k=H2 / H1, wherein H1 is the equivalent liquid column height of oil pipe liquid loading, m; and H2 is the equivalent liquid column height of annular liquid loading, m. The calculation steps of H2 are as follows: according to a large amount of flow pressure measurement data of gas well with pressure profile inflection point in wellbore, an empirical formula for calculating k value through casing pressure is established:

[0016] k=-0.000005p ts 5 +0.000297p ts 4 -0.007437p ts 3 +0.091081p ts 2 -0.559651p ts +1.633512;

[0017] In the formula, p ts is the casing pressure at wellhead, MPa.

[0018] On the basis of setting the initial value of H1, k is calculated from the casing pressure p ts in the basic data, and the value of H2 is obtained, i.e. H2=kH1.

[0019] The present application can calculate the equivalent liquid column height H2 of annular liquid loading according to the equivalent liquid column height H1 of oil pipe liquid loading by establishing the calculation formula of k value, which avoids direct measurement of H2 and the calculation result is more accurate.

[0020] Further, in the step 3), on the basis of setting the initial value of H1, the pressure p1 at the oil pipe liquid surface can be calculated according to Beggs & Brill gas-liquid two-phase pipe flow model from the oil pressure p tf , daily gas production q g and liquid gas ratio WGR:

[0021]

[0022] Wherein: z is the distance of axial flow, m, wherein the integral total length of z value is the vertical height H-H1 from the equivalent liquid column liquid surface of the tubing to the wellhead on the basis of setting the initial value of H1; p is the average pressure of the pipeline, MPa; p l is the liquid density, kg / m 3 ; p g is the gas density, kg / m 3 ; H l is the liquid holdup, m 3 / m 3 ; g is the acceleration of gravity, m / s 2 , theta is the angle between the pipeline and the horizontal, °; lambda is the along-path resistance coefficient of two-phase flow, dimensionless; G is the mass flow rate of the mixture, m / s; v is the average flow rate of the mixture, m / s; v sg is the reduced speed of the gas, m / s; D is the diameter of the pipe, m; A is the cross-sectional area of the pipe, m 2 .

[0023] The application provides a specific tubing liquid surface pressure calculation method.

[0024] Further, in the step 3), the tubing liquid surface pressure p ts According to the static gas column model, the annular liquid surface pressure p2 can be calculated:

[0025]

[0026] Wherein: p2 is the pressure at the annular liquid surface position, MPa; H is the vertical height of the wellbore, m; H-H2 is the vertical height from the equivalent liquid column liquid surface of the annulus to the wellhead, m; gamma g is the relative density of natural gas, dimensionless; T is the average thermodynamic temperature of the wellbore static gas column, K; Z is the average compression factor of the wellbore static gas column, dimensionless.

[0027] The application provides a specific annular liquid surface pressure calculation method.

[0028] Further, in the step 4), the flowing pressure P wf1 , p wf2 is calculated by the formula:

[0029] p wf1 =p1+ρgH1

[0030] p wf2 =p2+ρgH2

[0031] In the formula: p1 is the pressure at the liquid surface when the equivalent liquid column height in the tubing is H1, MPa; p2 is the pressure at the liquid surface when the equivalent liquid column height in the annulus is H2, MPa; ρ is the density of water, 1000 kg / m3; g is the acceleration due to gravity, 9.8 N / kg.

[0032] In order to improve the fluid carrying capacity of the wellbore during gas well production, the end of the tubing is as close as possible to the middle depth of the reservoir. The vertical height between the end of the tubing and the middle of the reservoir is generally <50m, corresponding to a pressure <0.5MPa. Therefore, the vertical distance from the end of the tubing to the reservoir is ignored in the calculation of this invention.

[0033] This invention provides a specific flow pressure p wf1 p wf2 The calculation method.

[0034] Furthermore, in step 5), it is determined that P wf1 =p wf2 When it is established, the flowing pressure P needs to be calculated. wf Wellbore fluid accumulation Q:

[0035] P wf =(p wf1 +P wf2 ) / 2

[0036] Flow pressure p wf The calculation formula needs to consider the case where the gas well does not accumulate fluid, i.e., H1 = 0, in which case it is equivalent to the oil pressure p. tf The bottom-hole flowing pressure p is directly calculated based on the gas-liquid two-phase pipe flow model. wf1 , sleeve pressure p ts The bottom-hole flowing pressure p is directly calculated based on the static gas column model. wf2 Considering the model calculation error, there exists p wf1 With p wf2 If they are not equal, then take the average of the two.

[0037]

[0038] In the formula: Q is the volume of fluid accumulated in the wellbore, in meters. 3 ; Φc is the inner diameter of the casing, m; Φo1 is the outer diameter of the tubing, m; Φo2 is the inner diameter of the tubing, m; H m2 When the equivalent fluid column height in the annulus is H2, according to the wellbore vertical depth and depth measurement comparison table, the equivalent fluid column length in the annulus is (m); H m1 When the equivalent fluid column height in the tubing is H1, the equivalent fluid column length in the tubing is calculated in meters according to the wellbore vertical depth and depth measurement comparison table.

[0039] This invention provides a specific flow pressure p wf The calculation method for the amount of liquid accumulated in the wellbore, Q.

[0040] Further, the wellbore liquid loading Q is calculated, and when the combined casing or combined tubing is used, the wellbore liquid loading is calculated in sections and summed.

[0041] The application provides a high-pressure gathering and transportation gas well wellbore liquid loading and flow pressure calculation method, which is beneficial to timely find the high-pressure gathering and transportation gas well with wellbore liquid loading, and calculate the wellbore liquid loading and flow pressure, can accurately guide the optimization of gas well drainage gas recovery process and parameter design, eliminate the wellbore liquid loading state, avoid the liquid loading of the gas well, improve the development benefit of the gas well. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is a wellbore liquid loading and flow pressure calculation flowchart in the method embodiment of the application;

[0043] Figure 2 is a gas-liquid two-phase distribution mode schematic diagram of the high-pressure gathering and transportation gas well in the method embodiment of the application;

[0044] Figure 3 is a k value and casing pressure intersection diagram in the method embodiment of the application;

[0045] Figure 4 is a first measured tubing pressure profile diagram in the method embodiment of the application;

[0046] Figure 5 is a third measured tubing pressure profile diagram in the method embodiment of the application. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical scheme and advantages of the application more clear and obvious, the application will be further described in detail below with reference to the drawings and embodiments.

[0048] Method embodiment:

[0049] The embodiment provides a high-pressure gathering and transportation gas well wellbore liquid loading and flow pressure calculation method, and takes well A as an example, the well is guided by three rounds of wellbore liquid loading and flow pressure calculation, and the process is as shown in the figure. Figure 1

[0050] Step 1) complete the preparation of basic data;

[0051] Specifically, the basic data of well A at three time points are prepared, as shown in Table 1; and the wellbore vertical depth and depth contrast table is as shown in Table 2.

[0052] Table 1 wellbore liquid loading and flow pressure calculation basic data preparation table

[0053]

[0054] Table 2 wellbore vertical depth and depth contrast table ​

[0055]

[0056] Step 2) Set the initial value H1 of the equivalent liquid column height of the tubing liquid accumulation amount, and calculate the equivalent liquid column height H2 of the annulus liquid accumulation amount according to the proportional coefficient k of H2 and H1;

[0057] Define the equivalent liquid column height H1 of the tubing liquid accumulation amount and the equivalent liquid column height H2 of the annulus liquid accumulation amount in step 2). For a gas well that has appeared wellbore liquid loading, the tubing and the casing annular space (referred to as annulus) are in a static state during production, the lower part is a static liquid column, and the upper part is a static gas column; the inside of the tubing does not have a pure liquid column under the disturbance of the gas flow, but a heterogeneous distribution pattern of gas-liquid two-phase mixture with an inflection point of pressure gradient. The lower pressure gradient of the inflection point reflects the dispersed distribution of the tubing liquid accumulation amount under the disturbance of the gas flow, and this part of the liquid amount cannot reach the wellhead and slips at the inflection point; the upper pressure gradient of the inflection point reflects the daily gas production and daily liquid production that can reach the ground and be metered. The gas-liquid two-phase distribution in the tubing is simplified in the present application as the lower part is the equivalent pure liquid column formed by the tubing liquid accumulation amount, and the upper part is the uniform distribution of daily gas production and daily liquid production; similarly, the lower part of the annulus is the equivalent pure liquid column formed by the annulus liquid accumulation amount, and the upper part is a static gas column, as shown in Figure 2 Therefore, the vertical height of the equivalent pure liquid column formed by the tubing liquid accumulation amount is defined as the equivalent liquid column height H1 of the tubing liquid accumulation amount; and the vertical height of the equivalent pure liquid column formed by the annulus liquid accumulation amount is defined as the equivalent liquid column height H2 of the annulus liquid accumulation amount.

[0058] The algorithm of the present application needs to calculate the k value first, and then calculate H2, so the k value calculation formula needs to be established. As shown in Figure 3 Based on a large amount of flow pressure measurement data of gas wells with pressure profile inflection points in wellbores, an empirical formula for calculating the k value from casing pressure is established.

[0059] Specifically, in actual production, the initial value H1 of the equivalent liquid column height of the tubing liquid accumulation amount ranges from 0 to 3127 m. In order to better demonstrate the iteration process of the calculation method and prove that the algorithm has a unique solution, 0-3127 m is divided into 150 parts in each round of calculation, and the calculation process of steps 2) to 5) is completed in turn as the initial value of H1, as shown in Table 3. For example, the 80th group on March 29, 2022, is assigned an initial value of 601 m for H1, and the k value is calculated as 0.27 according to the k value calculation equation, corresponding to a calculated H2 of 162 m.

[0060] Step 3) Use the basic data in step 1) to calculate the pressure p tf According to the pipe flow model, the pressure p1 at the liquid level of the tubing is calculated, and the casing pressure p ts According to the static gas column model, the pressure p2 at the liquid level of the annulus is calculated;

[0061] Specifically, according to the basic data on March 29, 2022, under the condition of the 80th group H1 assignment, p1 is 7.3 MPa, and p2 is 8.0 MPa.

[0062] Step 4) The pressure p1 at the oil pipe liquid level is added to the equivalent liquid column gravity ρgH1 of the oil pipe to obtain the flow pressure p wf1 ; the pressure p2 at the annulus liquid level is added to the equivalent liquid column gravity ρgH2 of the annulus to obtain the flow pressure p wf2 .

[0063] Specifically, according to the basic data on March 29, 2022, under the condition of the 80th group H1 assignment, ρgH1 is 6.0 MPa, p wf1 is 13.3 MPa; ρgH2 is 1.6 MPa, and P wf2 is 9.6 MPa.

[0064] Step 5) If p wf1 =p wf2 , the set value is the equivalent liquid column height H1 of the oil pipe liquid accumulation, and the flow pressure p wf and the wellbore liquid accumulation Q are calculated according to the basic data of the gas well; if p wf1 ≠p wf2 , the H1 set value is adjusted for iterative operation.

[0065] Specifically, according to the basic data on March 29, 2022, under the condition of the 80th group H1 assignment, P wf1 is 13.3 MPa, and p wf2 is 9.6 MPa, which are not equal, and the H1 set value needs to be adjusted for calculation again.

[0066] Specifically, according to the calculation steps of steps 2) to 5), three rounds of 144 times each are completed on March 29, 2022, May 25, 2022, and October 23, 2022, and a total of 432 times of iterative calculation are completed, as shown in Table 3. From the calculation results, the wellbore liquid accumulation and the flow pressure calculated by the algorithm of the application have a unique solution, in which the wellbore liquid accumulation on March 29, 2022 is 0 m3, and the flow pressure is 8.2 MPa; the wellbore liquid accumulation on May 25, 2022 is 1.8 m3, and the flow pressure is 7.5 MPa; the wellbore liquid accumulation on October 23, 2022 is 3.5 m3, and the flow pressure is 7.4 MPa, and the degree of wellbore liquid accumulation gradually increases, and a matching drainage process is required.

[0067] Specifically, in order to verify the reliability of the calculation results, wellbore flow pressure profile tests were carried out on March 29, 2022 and October 23, 2022, respectively, as shown in Figure 4 , Figure 5The calculation error of the flow pressure on March 29, 2022 is 2.6%, and the calculation error of the liquid accumulation amount is 0%; the calculation error of the flow pressure on October 23, 2022 is 5.3%, and the calculation error of the liquid accumulation amount is 12%, as shown in Table 4.

[0068] The established high-pressure gathering and transportation gas well wellbore liquid accumulation amount and flow pressure calculation method of the present application does not rely on a certain test device, only needs to use gas well production report data, has the characteristics of low calculation cost; by simplifying the gas-liquid two-phase distribution mode of the wellbore and introducing the ratio of the equivalent liquid column height in the annulus to the equivalent liquid column height in the tubing, the tubing liquid accumulation and the annulus liquid accumulation can be simultaneously included in the iterative calculation, there is no problem of ignoring the annulus liquid accumulation or confusing the flow pressure under different states, which conforms to the actual production situation, after being converted into a computer program, it can automatically realize rapid cyclic iteration, real-time monitoring of wellbore liquid accumulation amount and flow pressure, timely guidance of drainage gas recovery process matching, reduction of gas well liquid accumulation and production reduction risk, and improvement of gas well development benefit.

[0069] Table 3 Wellbore liquid accumulation amount and flow pressure calculation basis data preparation table

[0070]

[0071] Table 4 Wellbore liquid accumulation amount and flow pressure calculation basis data preparation table

[0072]

Claims

1. A method for calculating the amount of accumulated fluid and the flow pressure in the wellbore of a high-pressure gathering and transmission gas well, characterized in that, The method comprises the following steps: 1) completing the calculation of the basic data preparation; 2) Set the initial value of the tubing liquid loading equivalent liquid column height , and according to and the proportional coefficient k of , calculate the annulus liquid loading equivalent liquid column height ; The calculation steps are as follows: according to the gas well mass flow pressure measurement data of the wellbore pressure profile inflection point, an empirical formula for calculating k value through casing pressure is established: ; in setting initial value basis, and by the basis data in the set pressure k, get value, that is ; 3) Using the base data from step 1), the oil pressure According to the pipe flow model, the pressure at the tubing fluid level is calculated According to the static gas column model, the pressure at the annular fluid level is calculated According to the static gas column model, the pressure at the annular fluid level is calculated ; 4) pressure at tubing fluid level plus tubing equivalent fluid column gravity to get flow pressure ; annulus fluid level pressure plus annulus equivalent fluid column gravity to get flow pressure where is the density of water, is the acceleration due to gravity; 5) If If true, the set value is the equivalent height of the fluid column for the tubing accumulation. The flowing pressure was calculated based on the gas well baseline data. , wellbore fluid accumulation Q; if If not, then adjust. Perform iterative calculations on the set value; determine... If it is established, then the flowing pressure is calculated. Wellbore fluid accumulation Q: ， ， wherein: Q is the wellbore fluid accumulation volume; Φ c is the casing internal diameter; Φ o1 is the tubing external diameter; Φ o2 is the tubing internal diameter; H m2 is the annulus internal equivalent fluid column height; and is the tubing internal equivalent fluid column height. m1 is the tubing internal equivalent fluid column length according to the wellbore depth versus depth measured table when H is the tubing internal equivalent fluid column length.

2. The method according to claim 1, wherein, The calculation basis data in the step 1) includes: wellbore vertical height H, wellbore measured length H m , wellbore vertical depth and measured depth comparison table, casing inner diameter Ф c , tubing outer diameter Ф o1 , tubing inner diameter Ф o2 , gas well casing pressure , oil pressure , daily gas production q g and liquid gas ratio WGR.

3. The method according to claim 1, wherein, In step 3), in setting Based on the initial value, from the oil pressure p tf Daily gas production q g Based on the liquid-to-gas ratio WGR and the Beggs & Brill gas-liquid two-phase pipe flow model, the pressure p1 at the liquid surface in the tubing can be calculated. where: is the distance of axial flow; is the average pressure of the pipe; is the liquid density; is the gas density; is the liquid holdup; is the gravitational acceleration, is the angle of the pipe from horizontal; is the frictional resistance coefficient for two-phase flow; is the mass flow rate of the mixture; is the average flow rate of the mixture; is the gas slip velocity; is the diameter of the pipe; is the cross-sectional area of the pipe.

4. The method for calculating the liquid loading and flow pressure in the wellbore of a high-pressure gathering gas well according to claim 1, characterized in that, In step 3), the pressure at the annular liquid level is calculated based on the calculated value of the casing pressure According to the static gas column model, the pressure at the annular liquid level can be calculated as According to the static gas column model, the pressure at the annular liquid level can be calculated as : where: P is annulus fluid level position pressure; H is wellbore vertical height; P is annulus fluid level position pressure; H is wellbore vertical height; P is annulus fluid level position pressure; H is wellbore vertical height; 5. The method for calculating the liquid loading and flow pressure in the wellbore of a high-pressure gathering gas well according to claim 1, characterized in that, In step 4), the flow pressure , The calculation formula is as follows: ， where: is the equivalent fluid column height in the tubing of is the pressure at the fluid level; and is the equivalent fluid column height in the annulus of is the pressure at the fluid level; and is the density of water; and is the acceleration due to gravity.

6. The method for calculating the liquid loading and flow pressure in the wellbore of a high-pressure gathering gas well according to claim 1, characterized in that, Calculating the wellbore liquid loading Q, when using a combination of casing or tubing, the wellbore liquid loading is calculated in sections and summed up.

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