Prediction method for constant production decline of water-producing gas well in highly heterogeneous reservoir

This patent application claims the benefit and priority of Chinese Patent Application No. 202110787098.X, filed on Jul. 13, 2021, the disclosure of which is incorporated by reference herein in its entirety as part of the present application.

The present disclosure belongs to the field of gas reservoir development, and in particular to a prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir.

Natural gas is considered to be a safer energy overall. There are various advantages of natural gas. For example, the use of natural gas can reduce the consumption of coal and petroleum, which alleviates environmental pollution to a great extent. Besides, it is helpful to cut down emissions of carbon dioxide, sulfur dioxide and dust, thereby reducing acid rain and fundamentally improving environmental quality. Therefore, natural gas exploitation has become particularly important. However, for a water-producing gas well in a highly heterogeneous reservoir, both strong heterogeneity and water production of the reservoir may cause changes in gas well production, resulting in the decline of natural gas well production different from conventional gas wells. Therefore, how to evaluate reservoir heterogeneity and decline of gas well production has become a breakthrough point in gas reservoir development.

At present, Chinese Patent CN201410638125.7 (entitled OIL AND GAS WELL PRODUCTION DECLINE ANALYSIS METHOD AND SYSTEM) provides an oil and gas well production decline analysis method and system that can be applied to production analysis and dynamic evaluation of shale gas wells and other types of oil and gas wells; however, this method is only intended to predict the production decline of gas wells without considering constant rate production in the process of actual gas well production, and the method fails to predict production of heterogeneous and water-producing gas wells. Chinese Patent CN201310314083.7 (entitled DYNAMIC ANALYSIS METHOD AND SYSTEM OF FRACTURE-CAVE CARBONATE GAS RESERVOIR) can predict the production performance of a fracture-cave heterogeneous gas reservoir in a mode of constant rate production, but cannot predict the production performance of a water-producing gas well. Therefore, in order to establish a better prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir, dynamic prediction is carried out on constant rate production of the water-producing gas well in the highly heterogeneous reservoir.

An objective of the present disclosure is to achieve production performance prediction of gas wells in highly-heterogeneous water-producing gas reservoirs under the condition of constant rate production, and to form a prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir, so as to lay a foundation for gas reservoir development.

The present disclosure adopts the technical solutions as follows.

S 100 , collecting from a target water-producing gas well an original formation pressure p i , a wellhead transmission pressure p t , point-measured static pressure data p j , a cumulative gas production G pj corresponding to the point-measured static pressure, a formation temperature T i , a wellhead temperature t, a middle depth h of a wellbore production layer, a wellbore radius r w , an open-flow capacity q AOF , a current cumulative gas production G p , a cumulative water production W p , a daily gas production q g , a daily water production q w , a relative density γ g of gas samples, a mole fraction y N2 of nitrogen, a mole fraction yC O2 of carbon dioxide, a mole fraction y H2S of hydrogen sulfide, a relative density γ w of water samples, and a mole fraction y Na C l of sodium chloride; S 200 , based on the daily cumulative water production and the daily cumulative gas production, obtaining a water-drive constant a and a water-drive constant b, and obtaining a type-A water-drive formula of a target water-producing gas well; S 300 , conducting fitting by a Blasingame plotting method to obtain dynamic reserves G of the target water-producing gas well, and obtaining a reserves recovery degree R j corresponding to the point-measured static pressure by dividing the dynamic reserves of the target water-producing gas well by the cumulative gas production corresponding to the point-measured static pressure; S 400 , collecting pressure recovery well testing data of the target water-producing gas well to carry out pressure recovery well testing analysis, and calculating a heterogeneity coefficient D of a reservoir at which the target water-producing gas well is located; where specific procedures are as follows: first, based on pressure data over well testing obtained by pressure recovery well testing on the target water-producing gas well, conducting data fitting by adopting a dual-medium model to obtain an elastic storativity ratio ω and an interporosity flow coefficient λ; second, substituting the elastic storativity ratio ω and the interporosity flow coefficient λ obtained through fitting into

According to the prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir, the Blasingame plotting method refers to a process of inputting, by F.A.S.T.RTA software, the production data, original formation pressure, formation temperature, middle depth of a wellbore production layer, and a wellbore radius of the target water-producing gas well, fitting an actual production curve on a theoretical curve plot, and then automatically calculating the dynamic reserves of the target water-producing gas well by the F.A.S.T.RTA software.

According to the prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir, the D-A-K method refers to a following process: based on relative density γ g of gas samples, calculating, by empirical formulas p pc =(46.7−32.1×(γ g −0.5))×0.09869 and T pc =171×(γ g −0.5)+182, pseudocritical pressure p pc and pseudocritical temperature T pc , then based on a formation pressure p k and a formation temperature T k , calculating, by P pr =p k /p pc and T pr =T k /T pc , a pseudoreduced pressure p pr and a pseudoreduced temperature T pr , calculating a deviation factor by simultaneous iteration of three formulas ρ pr =0.27p pr /(z k T pr ), F(ρ pr )=−0.27 p pr /T pr +ρ pr +(A 1 +A 2 /T pr +A 3 /T pr 3 +A 4 /T pr 4 +A 5 /T pr 5 )ρ pr 2 +(A 6 +A 7 /T pr +A 8 /T pr 2 )ρ pr 3 −A 9 (A 7 /T pr +A 8 /T pr 2 )ρ pr 6 +A 10 (1+A 11 ρ pr 2 )(p pr 3 /T pr 3 )exp(−A 11 ρ pr 2 ), and F′(ρ pr )=1+2(A 1 +A 2 /T pr +A 3 /T pr 3 +A 4 /T pr 4 +A 5 /T pr 5 )ρ pr +3(A 6 +A 7 /T pr +A 8 /T pr 2 ) ρ pr 2 −6A 9 (A 7 /T pr +A 8 /T pr 2 )ρ pr 5 +(A 10 +T pr 3 [3ρ pr 2 +A 11 (3ρ pr 4 −2A 11 ρ pr 6 )]exp(−A 11 ρ pr 2 ), where γ g denotes a unit-free relative density of gas samples; p pc denotes a pseudocritical pressure in MPa; T pc denotes a pseudocritical temperature in K; p k denotes a formation pressure in MPa; T k denotes a formation temperature in K; p pr denotes a pseudoreduced pressure in MPa; T pr denotes a pseudoreduced temperature in K; ρ pr denotes a unit-free pseudoreduced density; z k denotes a unit-free deviation factor corresponding to a formation pressure; F(ρ pr ) is a unit-free formula representing pseudoreduced density; A 1 =0.3265, free of unit; A 2 =−1.0700, free of unit; A 3 =−0.5339, free of unit; A 4 =0.01569, free of unit; A 5 =−0.05165, free of unit; A 6 =0.5475, free of unit; A 7 =−0.7361, free of unit; A 8 =0.1844, free of unit; A 9 =0.1056, free of unit; A 10 =0.6134, free of unit; A 11 =0.7210, free of unit; F′(ρ pr ) is a formula obtained after taking the derivative of ρ pr by F(ρ pr ), free of unit.

According to the prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir, Hagedom-Brown method refers to a process of calculating a flowing bottomhole pressure based on

Δ ⁢ p Δ ⁢ H = 10 - 6 ⁢ ( ρ m ⁢ g + f m ⁢ G mA 2 4 ⁢ r w 2 ⁢ ρ m ) , ρ m = ρ w ⁢ H L + ρ g ( 1 - H L ) , 1 / f m = 1.14 - 2 ⁢ lg ⁡ ( e / 2 / r w + 21.25 / N Re 0.9 ) , V sl = q w 86400 ⁢ π ⁢ r w 2 , V sg = q g 86400 ⁢ π ⁢ r w 2 , G mA 2 = V sl ⁢ ρ w + V sg ⁢ ρ g ⁢ and ⁢ N Re = ( V sl ⁢ ρ w + V sg ⁢ ρ g ) × 2 × r w μ w H L × μ g ( 1 - H L ) ,

where Δp denotes a well pipeline pressure increment in MPa; ΔH denotes a well pipeline depth increment in m; μ m denotes density of an air-water mixture in kg/m 3 ; g denotes a gravitational acceleration in m/s 2 ; f m denotes a two-phase friction coefficient free of unit; G mA denotes a mass flow rate of a mixture per pipeline sectional area in kg/s/m 2 ; r w denotes a wellbore radius in m; ρ w denotes water density of a target water-producing gas well, which, from physical property analysis, has a unit of kg/m 3 ; ρ g denotes gas density of a target water-producing gas well, which, from physical property analysis, has a unit of kg/m 3 ; H L denotes liquid holdup free of unit; e denotes an absolute roughness of a pipe wall, which, from pipe wall analysis, has a unit of m; Nre Re denotes a two-phase Reynolds number free of unit; q g denotes a daily gas production in m 3 ; q w denotes a daily water production in m 3 ; V s1 denotes an apparent liquid velocity in m/s; V sg denotes an apparent gas velocity in m/s; μ w denotes water viscosity, which, from physical property analysis, has a unit of mPa·s; and μ g denotes gas viscosity, which, from physical property analysis, has a unit of mPa·s.

According to the prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir, the one-point formula is

q AOF = 6 ⁢ q g 1 + 48 ⁢ p min 2 - p wfmin 2 p min 2 - 1 ,

where q g denotes a daily gas production in m 3 ; q AOF denotes an open-flow capacity in m 3 ; p mim denotes a formation pressure pmin at the end of stable production in MPa; and p wfmin denotes a flowing bottomhole pressure at the end of stable production in MPa.

The technical solution of the present disclosure has the advantages that reservoir heterogeneity can be quantitatively evaluated in combination with well test analysis, production prediction is carried out on the highly heterogeneous water-producing gas well in view of its constant production, thus a stable production period of the gas well is obtained, which allows for prediction of constant production decline of the water-producing gas well in the highly heterogeneous reservoir.

In the accompanying drawings:

FIG. 1 is a flowchart of a prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir.

FIG. 2 is a Type A water-drive curve of a highly heterogeneous water-producing gas well.

FIG. 3 is a Blasingame fitting plot of a highly heterogeneous water-producing gas well.

FIG. 4 is a dual-medium fitting diagram of a highly heterogeneous water-producing gas well.

FIG. 5 is a curve predicting constant production decline of a highly heterogeneous water-producing gas well.

The present disclosure will be explained in detail below with reference to the accompanying drawings.

The present disclosure provides a prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir. FIG. 1 is a flowchart of the method. The evaluation method includes the following steps:

S 100 , collecting from a target water-producing gas well an original formation pressure p i , a wellhead transmission pressure p t , point-measured static pressure data p j , a cumulative gas production G pj corresponding to the point-measured static pressure, a formation temperature T i , a wellhead temperature t, a middle depth h of a wellbore production layer, a wellbore radius r w , an open-flow capacity q AOF , a current cumulative gas production G p , a cumulative water production W p , a daily gas production q g , a daily water production q w , a relative density γ g of gas samples, a mole fraction y N2 of nitrogen, a mole fraction y CO2 of carbon dioxide, a mole fraction y H2S of hydrogen sulfide, a relative density γ w of water samples, and a mole fraction y NaCl of sodium chloride; S 200 , based on the daily cumulative water production and the daily cumulative gas production, obtaining a water-drive constant a and a water-drive constant b, and obtaining a type-A water-drive formula of a target water-producing gas well; S 300 , conducting fitting by a Blasingame plotting method to obtain dynamic reserves G of the target water-producing gas well, and obtaining a reserves recovery degree R j corresponding to the point-measured static pressure by dividing the dynamic reserves of the target water-producing gas well by the cumulative gas production corresponding to the point-measured static pressure; S 400 , collecting pressure recovery well testing data of the target water-producing gas well to carry out pressure recovery well testing analysis, and calculating a heterogeneity coefficient D of a reservoir at which the target water-producing gas well is located; where specific procedures are as follows: first, based on pressure data over well testing obtained by pressure recovery well testing on the target water-producing gas well, conducting data fitting by adopting a dual-medium model to obtain an elastic storativity ratio ω and an interporosity flow coefficient λ; second, substituting the elastic storativity ratio ω and the interporosity flow coefficient λ obtained through fitting into

Further, according to the prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir, the Blasingame plotting method refers to a process of inputting, by F.A.S.T.RTA software, the production data, original formation pressure, formation temperature, middle depth of a wellbore production layer, and a wellbore radius of the target water-producing gas well, fitting an actual production curve on a theoretical curve plot, and then automatically calculating the dynamic reserves of the target water-producing gas well by the F.A.S.T.RTA software.

Further, according to the prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir, the D-A-K method refers to a following process: based on relative density γ g of gas samples, calculating, by empirical formulas p pc =(46.7−32.1×(γ g −0.5)×0.09869 and T pc =171×(γ g −0.5)+182, pseudocritical pressure p pc and pseudocritical temperature T pc , then based on a formation pressure p k and a formation temperature T k , calculating, by p pr =p k /p pc and T pr =T k /T pc , a pseudoreduced pressure p pr and a pseudoreduced temperature T pr , calculating a deviation factor by simultaneous iteration of three formulas ρ pr =0.27p pr /(z k T pr ), F(ρ pr )=−0.27 p pr /T pr +ρ pr +(A 1 +A 2 /T pr +A 3 /T pr 3 +A 4 /T pr 4 +A 5 /T pr 5 )ρ pr 2 +(A 6 +A 7 /T pr +A 8 /T pr 2 )ρ pr 3 −A 9 (A 7 /T pr +A 8 /T pr 2 )ρ pr 6 +A 10 (1+A 11 ρ pr 2 )(p pr 3 /T pr 3 )exp(−A 11 ρ pr 2 ), and F′(ρ pr )=1+2(A 1 +A 2 /T pr +A 3 /T pr 3 +A 4 /T pr 4 +A 5 /T pr 5 )ρ pr +3(A 6 +A 7 /T pr +A 8 /T pr 2 ) ρ pr 2 −6A 9 (A 7 /T pr +A 8 /T pr 2 )ρ pr 5 +(A 10 +T pr 3 [3ρ pr 2 +A 11 (3ρ pr 4 −2A 11 ρ pr 6 )]exp(−A 11 ρ pr 2 ), where γ g denotes a unit-free relative density of gas samples; p pc denotes a pseudocritical pressure in MPa; T pc denotes a pseudocritical temperature in K; p k denotes a formation pressure in MPa; T k denotes a formation temperature in K; p pr denotes a pseudoreduced pressure in MPa; T pr denotes a pseudoreduced temperature in K; ρ pr denotes a unit-free pseudoreduced density; z k denotes a unit-free deviation factor corresponding to a formation pressure; F(ρ pr ) is a unit-free formula representing pseudoreduced density; A 1 =0.3265, free of unit; A 2 =−1.0700, free of unit; A 3 =−0.5339, free of unit; A 4 =0.01569, free of unit; A 5 =−0.05165, free of unit; A 6 =0.5475, free of unit; A 7 =−0.7361, free of unit; A 8 =0.1844, free of unit; A 9 =0.1056, free of unit; A 10 =0.6134, free of unit; A 11 =0.7210, free of unit; F′(ρ pr ) is a formula obtained after taking the derivative of ρ pr by F(ρ pr ), free of unit.

Further, according to the prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir, Hagedom-Brown method refers to a process of calculating a flowing bottomhole pressure based on

Δ ⁢ p Δ ⁢ H = 10 - 6 ⁢ ( ρ m ⁢ g + f m ⁢ G mA 2 4 ⁢ r w 2 ⁢ ρ m ) , ρ m = ρ w ⁢ H L + ρ g ( 1 - H L ) , 1 / f m = 1.14 - 2 ⁢ lg ⁡ ( e / 2 / r w + 21.25 / N Re 0.9 ) , V sl = q w 86400 ⁢ π ⁢ r w 2 , V sg = q g 86400 ⁢ π ⁢ r w 2 , G mA 2 = V sl ⁢ ρ w + V sg ⁢ ρ g ⁢ and ⁢ N Re = ( V sl ⁢ ρ w + V sg ⁢ ρ g ) × 2 × r w μ w H L × μ g ( 1 - H L ) ,

where Δp denotes a well pipeline pressure increment in MPa; ΔH denotes a well pipeline depth increment in m; μ m denotes density of an air-water mixture in kg/m 3 ; g denotes a gravitational acceleration in m/s 2 ; f m denotes a two-phase friction coefficient free of unit; G mA denotes a mass flow rate of a mixture per pipeline sectional area in kg/s/m 2 ; r w denotes a wellbore radius in m; ρ w denotes water density of a target water-producing gas well, which, from physical property analysis, has a unit of kg/m 3 ; ρ g denotes gas density of a target water-producing gas well, which, from physical property analysis, has a unit of kg/m 3 ; H L denotes liquid holdup free of unit; e denotes an absolute roughness of a pipe wall, which, from pipe wall analysis, has a unit of m; N Re denotes a two-phase Reynolds number free of unit; q g denotes a daily gas production in m 3 ; q w denotes a daily water production in m 3 ; V s1 denotes an apparent liquid velocity in m/s; V sg denotes an apparent gas velocity in m/s; μ w denotes water viscosity, which, from physical property analysis, has a unit of mPa·s; and μ g denotes gas viscosity, which, from physical property analysis, has a unit of mPa·s.

Further, according to the prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir, the one-point formula is

q AOF = 6 ⁢ q g 1 + 48 ⁢ p min 2 - p wfmin 2 p min 2 - 1 ,

where q g denotes a daily gas production in m 3 ; q AOF denotes an open-flow capacity in m 3 ; p min denotes a formation pressure pmin at the end of stable production in MPa; and p wfmin denotes a flowing bottomhole pressure at the end of stable production in MPa.

The steps of a prediction method for constant production decline of a water-producing gas well in a highly heterogeneous reservoir are described. Take a highly heterogeneous water-producing gas well as an example, predict production performance of the gas well in a condition of constant rate production so as to determine the stable production period of the gas well.

Collect production data, physical property analysis data and reservoir data of the highly heterogeneous water-producing gas well, and obtain water-drive constants a and b based on the type-A water-drive formula, where a=4.948, b=0.000000046, as shown in FIG. 2 ; by Blasingame plotting method, fit the dynamic reserves of the highly heterogeneous water-producing gas well to be 518000000 m 3 , as shown in FIG. 3 ; then based on buildup well testing, conduct data fitting using the dual-medium model to obtain elastic storativity ratio of 0.223, interporosity flow coefficient of 0.00000111, and reservoir heterogeneity coefficient of 3.4842, as shown in FIG. 4 ; by D-A-K, solve a deviation factor 1.71 under original formation pressure; and based on the mass balance equation of water-sealed gas, calculate a water invasion constant 2 using Newton's method. Then calculate flowing bottomhole pressure under wellhead transmission pressure as 36.918 MPa by using Hagedom-Brown method, and calculate the formation pressure as 44.862 MPa at the last stage of stable production corresponding to flowing bottomhole pressure at the last stage of stable production to be according to one-point formula. Through the iteration of time stride, obtain curve of flowing bottomhole pressure over time, and finally obtain the curve predicting constant production decline of the target water-producing gas well, as shown in FIG. 5 . According to the curve predicting constant production decline, it is concluded that the stable production period of a highly heterogeneous water-producing gas well is 1.115 years.

Compared with an existing prediction method for constant production of gas wells, the present disclosure has the following advantages: reservoir heterogeneity can be quantitatively evaluated in combination with well test analysis, production prediction is carried out on the highly heterogeneous water-producing gas well in view of its constant production, thus a stable production period of the gas well is obtained, which allows for prediction of constant production decline of the water-producing gas well in the highly heterogeneous reservoir.

Finally, it should be noted that the above examples are only intended to explain, rather than to limit the technical solutions of the present disclosure. Although the present disclosure is described in detail with reference to the preferred examples, those skilled in the art should understand that modifications or equivalent substitutions may be made to the technical solutions of the present disclosure without departing from the spirit and scope of the technical solutions of the present disclosure, and such modifications or equivalent substitutions should be included within the scope of the claims of the present disclosure.