Shale gas well dynamic production allocating method

Abstract

The present invention provides a shale gas well dynamic production allocating method. The steps comprise: step 1, constructing a single well material balance equation of a shale gas well; step 2, according to the actual shale gas well related reservoir properties, establishing the relationship function between the cumulative gas production and the formation pressure in combination with constructing a single well actual material balance equation in step 1; step 3, calculating the cumulative gas production according to the current formation pressure; step 4, through the productivity test, establishing a binomial productivity equation, and allocating production according to the open flow; step 5, according to the production allocating result obtained in step 4, drawing a chart of cumulative gas production and formation pressure and single well production allocation; and step 6, according to the cumulative gas production of different reservoirs of a shale gas well, searching for the resulting chart for production allocation. The solution of the present invention can not only quickly allocate production. In the production process of a gas well, according to the current cumulative gas production of the well, a reasonable production allocation amount can be quickly determined by searching for the chart, and there is no need to consider time factors in the production allocating process, which is very convenient, efficient, and practical.

Claims

1. A shale gas well dynamic production allocating method, wherein the steps comprise: step 1, constructing a single well material balance equation of a shale gas well, wherein when the adsorbed gas is not desorbed, the material balance equation refers to formula (I); $\begin{matrix} G_{pg} B_{g} + G_{pw} B_{w} = G_{m} (B_{g} - B_{gi}) + G_{m} B_{gi} \frac{c_{w} S_{mwi}}{1 - S_{mwi}} (P_{i} - P) + G_{m} B_{gi} \frac{c_{m}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{m} B_{gi}}{(1 - S_{mwi}) B_{w}} S_{mwi} (R_{si} - R_{s}) B_{g} + G_{f} (B_{g} - B_{gi}) + G_{f} B_{gi} \frac{c_{w} S_{fwi}}{1 - S_{fwi}} (P_{i} - P) + G_{f} B_{gi} \frac{c_{f}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{f} B_{gi}}{(1 - S_{fwi}) B_{w}} S_{fwi} (R_{si} - R_{s}) B_{g} & (I) \end{matrix}$ when the adsorbed gas is desorbed, the material balance equation refers to formula (II); $\begin{matrix} G_{p g} B_{g} + C_{pw} B_{w} = G_{m} (B_{g} - B_{gi}) + G_{m} B_{gi} \frac{c_{w} S_{mwi}}{1 - S_{mwi}} (P_{i} - P) + G_{m} B_{gi} \frac{c_{m}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{m} B_{gi}}{(1 - S_{mwi}) B_{w}} S_{mwi} (R_{si} - R_{s}) B_{g} + G_{f} (B_{g} - B_{gi}) + G_{f} B_{gi} \frac{c_{w} S_{fwi}}{1 - S_{fwi}} (P_{i} - P) + G_{f} B_{gi} \frac{c_{f}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{f} B_{gi}}{(1 - S_{fwi}) B_{w}} S_{fwi} (R_{si} - R_{s}) B_{g} + ρ_{s} V_{S} V_{m} (\frac{P_{c d}}{P_{L} + P_{c d}} - \frac{P}{P_{L} + P}) & (II) \end{matrix}$ in formula (I) and formula (II): G.sub.m represents the surface free gas volume of shale gas reservoir matrix, G.sub.f represents the surface free gas volume of shale gas reservoir fractures, B.sub.gi represents the original volume coefficient of shale gas, C.sub.w represents the groundwater compression coefficient of a shale gas reservoir, C.sub.m represents the compression coefficient of shale matrix, R.sub.si represents the original groundwater solubility coefficient of a shale gas reservoir, P.sub.i represents the original formation pressure, S.sub.wf represents the fracture water saturation of a shale gas reservoir, C.sub.f represents the fracture rock compressibility coefficient, B.sub.w represents the formation water volume coefficient, ρ.sub.s represents the shale density, V.sub.m represents the Langmuir's volume, P.sub.L represents the Langmuir's pressure, P.sub.cd represents the critical desorption pressure, V.sub.s represents the single well controlled shale volume, B.sub.g represents the natural gas volume coefficient, R.sub.s represents the formation water solubility coefficient, R.sub.s represents the original groundwater solubility coefficient, P represents the formation pressure, G.sub.pg represents the cumulative gas production, G.sub.pw represents the cumulative water production, S.sub.mwi represents the original water saturation of the matrix, and S.sub.fwi represents the original water saturation of the fracture; step 2, according to the actual shale gas well related reservoir properties, establishing the relationship function between the cumulative gas production and the formation pressure in combination with constructing a single well actual material balance equation in step 1; step 3, calculating the cumulative gas production according to the current formation pressure; step 4, according to the current formation pressure, through the productivity test, establishing a binomial productivity equation, and allocating production according to the open flow; step 5, according to the production allocating result obtained in step 4, drawing a chart of cumulative gas production and formation pressure and single well production allocation; and step 6, according to the cumulative gas production of different reservoirs of a shale gas well, searching for the resulting chart for production allocation.

2. The shale gas well dynamic production allocating method according to claim 1, wherein: the chart drawn in step 5 comprises a double-logarithmic diagram of pressure and cumulative gas production before desorption, a double-logarithmic diagram of production allocation and cumulative gas production before desorption, a double-logarithmic diagram of pressure and cumulative gas production after desorption, a double-logarithmic diagram of production allocation and cumulative gas production after desorption, and the full life cycle production allocating chart of a shale gas well is drawn based on these four charts.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] FIG. 1 is a double-logarithmic diagram of pressure and cumulative gas production before desorption in the embodiment;

[0022] FIG. 2 is a double-logarithmic diagram of production allocation and cumulative gas production before desorption in the embodiment;

[0023] FIG. 3 is a double-logarithmic diagram of pressure and cumulative gas production after desorption in the embodiment;

[0024] FIG. 4 is a double-logarithmic diagram of production allocation and cumulative gas production after desorption in the embodiment;

[0025] FIG. 5 is a double-logarithmic diagram of pressure and cumulative gas production in the embodiment;

[0026] FIG. 6 is a double-logarithmic diagram of production allocation and cumulative gas production in the embodiment;

[0027] FIG. 7 is a double-logarithmic implementation diagram of actual production allocation in the embodiment.

DESCRIPTION OF THE EMBODIMENTS

[0028] The technical solutions of the present invention will be further described hereinafter in combination. It is pointed out that the following embodiments cannot be understood as limiting the scope of protection of the present invention. Those skilled in the art make some non-essential improvements and adjustments based on the claims of the present invention, all of which fall within the protection scope of the present invention.

Embodiment

[0029] A shale gas well dynamic production allocating method is provided, wherein the steps are as follows.

[0030] The obtained relevant parameters of a certain shale gas well are shown in Table 1.

TABLE-US-00001 TABLE 1 Parameters of a certain shale gas well Parameter Parameter name Symbol Unit Parameter value classification surface free gas volume of G.sub.m m.sup.3 G.sub.m + G.sub.f = 1.97 × 10.sup.7 gas reservoir shale gas reservoir matrix geological surface free gas volume of G.sub.f m.sup.3 parameters shale gas reservoir fractures original volume coefficient B.sub.gi m.sup.3/m.sup.3 0.0069 of shale gas groundwater compression C.sub.w Mpa.sup.−1 0.000453 coefficient of a shale gas reservoir compression coefficient of C.sub.m Mpa.sup.−1 0.000419 shale matrix original groundwater R.sub.si m.sup.3/m.sup.3 0.647887 solubility coefficient of a shale gas reservoir original formation pressure P.sub.i m.sup.3/m.sup.3 48.6 fracture water saturation of a S.sub.wf % 45 shale gas reservoir fracture rock compressibility C.sub.f Mpa.sup.−1 0.000419 coefficient formation water volume B.sub.w m.sup.3/m.sup.3 0.993262 coefficient shale density ρ .sub.s g/cm.sup.3 2.65 Langmuir's volume V.sub.m m.sup.3 3.24 Langmuir's pressure P.sub.L MPa 2.69 critical desorption pressure P.sub.cd MPa 8.67 single well controlled shale V.sub.s M.sup.3 4382 × 104 volume natural gas volume B.sub.g m.sup.3/m.sup.3 variable coefficient formation water solubility Rs m.sup.3/m.sup.3 variable coefficient Binomial productivity A dimensionless 1.8633 × 10.sup.−8 gas well test equation coefficient parameters Binomial productivity B dimensionless 5.78 × 10.sup.−3 equation coefficient

[0031] Step 1, a single well material balance equation of a shale gas well is constructed, wherein

[0032] when the adsorbed gas is not desorbed, the material balance equation refers to formula (I);

[00003] $\begin{matrix} G_{pg} B_{g} + G_{pw} B_{w} = G_{m} (B_{g} - B_{gi}) + G_{m} B_{gi} \frac{c_{w} S_{mwi}}{1 - S_{mwi}} (P_{i} - P) + G_{m} B_{gi} \frac{c_{m}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{m} B_{gi}}{(1 - S_{mwi}) B_{w}} S_{mwi} (R_{si} - R_{s}) B_{g} + G_{f} (B_{g} - B_{gi}) + G_{f} B_{gi} \frac{c_{w} S_{fwi}}{1 - S_{fwi}} (P_{i} - P) + G_{f} B_{gi} \frac{c_{f}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{f} B_{gi}}{(1 - S_{fwi}) B_{w}} S_{fwi} (R_{si} - R_{s}) B_{g} & (I) \end{matrix}$

[0033] when the adsorbed gas is desorbed, the material balance equation refers to formula (II);

[00004] $\begin{matrix} G_{p g} B_{g} + C_{pw} B_{w} = G_{m} (B_{g} - B_{gi}) + G_{m} B_{gi} \frac{c_{w} S_{mwi}}{1 - S_{mwi}} (P_{i} - P) + G_{m} B_{gi} \frac{c_{m}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{m} B_{gi}}{(1 - S_{mwi}) B_{w}} S_{mwi} (R_{si} - R_{s}) B_{g} + G_{f} (B_{g} - B_{gi}) + G_{f} B_{gi} \frac{c_{w} S_{fwi}}{1 - S_{fwi}} (P_{i} - P) + G_{f} B_{gi} \frac{c_{f}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{f} B_{gi}}{(1 - S_{fwi}) B_{w}} S_{fwi} (R_{si} - R_{s}) B_{g} + ρ_{s} V_{S} V_{m} (\frac{P_{c d}}{P_{L} + P_{c d}} - \frac{P}{P_{L} + P}) & (II) \end{matrix}$

[0034] in formula (I) and formula (II):

[0035] G.sub.m represents the surface free gas volume of shale gas reservoir matrix, G.sub.f represents the surface free gas volume of shale gas reservoir fractures, B.sub.gi represents the original volume coefficient of shale gas, C.sub.w represents the groundwater compression coefficient of a shale gas reservoir, C.sub.m represents the compression coefficient of shale matrix, R.sub.si represents the original groundwater solubility coefficient of a shale gas reservoir, P.sub.i represents the original formation pressure, S.sub.wf represents the fracture water saturation of a shale gas reservoir, C.sub.f represents the fracture rock compressibility coefficient, B.sub.w represents the formation water volume coefficient, ρ.sub.s represents the shale density, V.sub.m represents the Langmuir's volume, P.sub.L represents the Langmuir's pressure, Pea represents the critical desorption pressure, V.sub.s represents the single well controlled shale volume, B.sub.g represents the natural gas volume coefficient, R.sub.s represents the formation water solubility coefficient, R.sub.s represents the original groundwater solubility coefficient, P represents the formation pressure, G.sub.pg represents the cumulative gas production, G.sub.pw represents the cumulative water production, S.sub.mwi represents the original water saturation of the matrix, and S.sub.fwi represents the original water saturation of the fracture;

[0036] Step 2, according to the actual shale gas well related reservoir properties, the relationship function between the cumulative gas production and the formation pressure is established in combination with constructing a single well actual material balance equation in step 1.

[0037] Because the value of accumulated underground water production is too small, the value of accumulated underground water production is ignored. Therefore, when the adsorbed gas is not desorbed (before desorption), the actual material balance equation for a single well is established as formula (III):

[00005] $\begin{matrix} G_{pg} B_{g} = G_{m} (B_{g} - B_{gi}) + G_{m} B_{gi} \frac{c_{w} S_{mwi}}{1 - S_{mwi}} (P_{i} - P) + G_{m} B_{gi} \frac{c_{m}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{m} B_{gi}}{(1 - S_{mwi}) B_{w}} S_{mwi} (R_{si} - R_{s}) B_{g} + G_{f} (B_{g} - B_{gi}) + G_{f} B_{gi} \frac{c_{w} S_{fwi}}{1 - S_{fwi}} (P_{i} - P) + G_{f} B_{gi} \frac{c_{f}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{f} B_{gi}}{(1 - S_{fwi}) B_{w}} S_{fwi} (R_{si} - R_{s}) B_{g} & (III) \end{matrix}$

[0038] text missing or illegible when filed

[0039] text missing or illegible when filed

[0040] text missing or illegible when filed

[0041] text missing or illegible when filed

[0042] where B.sub.g=0.22919P.sup.−0.902

[0043] From the high-pressure physical property parameter test of shale gas in this block, the function relationship between the volume coefficient of natural gas and the formation pressure is obtained by linear regression.

[0044] According to Empirical Formula For Formation Water-Related Physical Property Parameters from Chen Yuanqian (Chen Yuanqian, Empirical Formula For Formation Water-Related Physical Property Parameters [J]. Trial Mining Technology, 1990,11 (3):31-33.)

R.sub.s=(T,M,P)=−3.1670×10.sup.−10T.sup.2.Math.M+1.997×10.sup.−8T.Math.M+1.0635×10.sup.−10P.sup.2.Math.M−9.7764×10.sup.−8P.Math.M+2.9745×10.sup.−10T.Math.P.Math.M+1.6230×10.sup.−4T.sup.2−2.7879×10.sup.−2T− . . . 2.0587×10.sup.−5P.sup.2+1.7323×10.sup.−2P+9.5233×10.sup.−6T.Math.P+1.1937 (IV)

[0045] In formula (IV): R.sub.s—the solubility of natural gas in formation water, m.sup.3/m.sup.3; T-temperature, ° C.; P-pressure, MPa×10; M-formation water mineralization, mg/L.

[0046] Formula (IV) is substituted into the material balance equation (III), and the cumulative gas production is calculated according to different pressures, as shown in Table 2.

TABLE-US-00002 TABLE 2 Various parameter values of material balance before desorption Natural Formation Formation gas water water Rock Cumulative elasticity elasticity dissolution elasticity Formation gas gas gas gas gas pressure production production production production production (MPa) (m.sup.3) (m.sup.3) (m.sup.3) (m.sup.3) (m.sup.3) 42 2560459.20 19126.88 332.66 10.15 683.46 40 3336274.03 26103.11 433.46 13.82 890.56 38 4112330.29 33775.96 534.27 17.83 1097.67 36 4888812.02 42257.42 635.08 22.26 1304.78 34 5665925.73 51685.15 735.88 27.16 1511.89 32 6443904.57 62230.28 836.69 32.61 1719.00 30 7223013.61 74108.31 937.49 38.73 1926.10 28 8003556.54 87594.61 1038.30 45.65 2133.21 26 8785884.37 103046.90 1139.10 53.54 2340.32 24 9570406.94 120938.80 1239.91 62.64 2547.43 22 10357608.40 141911.19 1340.72 73.27 2754.53 21 10752390.42 153817.76 1391.12 79.28 2858.09 20 11148068.55 166853.94 1441.52 85.85 2961.64 19 11544735.14 181191.83 1491.92 93.05 3065.20 18 11942493.03 197040.76 1542.33 101.01 3168.75 17 12341457.31 214657.93 1592.73 109.82 3272.30 16 12741757.64 234363.14 1643.13 119.67 3375.86 15 13143541.06 256559.08 1693.54 130.73 3479.41 14 13546975.68 281760.31 1743.94 143.27 3582.97 13 13952255.33 310635.31 1794.34 157.60 3686.52 12 14359605.84 344069.08 1844.74 174.15 3790.07 11 14769293.37 383259.25 1895.15 193.52 3893.63 10 15181635.92 429868.63 1945.55 216.50 3997.18 9 15597019.69 486277.36 1995.95 244.25 4100.74

[0047] According to the current formation pressure, the binomial productivity equation (V) is constructed through the productivity test, and production is allocated according to the open flow.

P.sup.2−P.sub.wf=Aq.sup.2+Bq (V)

[0048] In the formula, P-formation pressure, MPa; P.sub.wf-shaft bottom flowing pressure, MPa; q-single well production, m.sup.3/d, A is 1.9633×10.sup.−8, B is 5.78×10.sup.−3;

[0049] In combination with the formula of the open flow,

[00006] $\frac{- B + \sqrt{B^{2} + 4 A (P^{2} - 0 . 1^{2})}}{2 A}$

[0050] According to production allocation of ⅕ of the open flow, it is obtained that:

[00007] $\begin{matrix} \frac{- B + \sqrt{B^{2} + 4 A (P^{2} - 0 . 1^{2})}}{2 A} & (VI) \end{matrix}$

[0051] Therefore, before desorption of shale gas, the corresponding cumulative gas production and formation pressure and the corresponding production allocation results are shown in Table 3.

TABLE-US-00003 TABLE 3 Production allocation results of shale gas before desorption Formation Cumulative gas production pressure (MPa) production (m.sup.3) allocation (m.sup.3) 42 2560459.197 68913.45 40 3336274.032 66309.87 38 4112330.293 63734.68 36 4888812.023 61191.45 34 5665925.73 58684.34 32 6443904.573 56218.18 30 7223013.614 53798.60 28 8003556.54 51432.18 26 8785884.367 49126.59 24 9570406.94 46890.82 22 10357608.4 44735.33 21 10752390.42 43691.43 20 11148068.55 42672.30 19 11544735.14 41679.76 18 11942493.03 40715.76 17 12341457.31 39782.38 16 12741757.64 38881.82 15 13143541.06 38016.41 14 13546975.68 37188.60 13 13952255.33 36400.97 12 14359605.84 35656.17 11 14769293.37 34956.94 10 15181635.92 34306.07 9 15597019.69 33706.35

[0052] According to Table 3, the charts of cumulative gas production and formation pressure and single well allocation are drawn, as shown in FIG. 1 and FIG. 2;

[0053] When the formation pressure P<P.sub.cd=8.67 MPa, shale gas begins to desorb, ignoring the surface volume corresponding to the cumulative water production on the left side of the equation. At this time, the actual material balance equation for a single well is established as equation (VII):

[00008] $\begin{matrix} C_{pg} B_{g} = G_{m} (B_{g} - B_{gi}) + G_{m} B_{gi} \frac{c_{w} S_{mwi}}{1 - S_{mwi}} (P_{i} - P) + G_{m} B_{gi} \frac{c_{m}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{m} B_{gi}}{(1 - S_{mwi}) B_{w}} S_{mwi} (R_{si} - s) B_{g} + G_{f} (B_{g} - B_{gi}) + G_{f} B_{gi} \frac{c_{w} S_{fwi}}{1 - S_{fwi}} (P_{i} - P) + G_{f} B_{gi} \frac{c_{f}}{1 - S_{mwi}} (P_{i} - P) + \frac{G_{f} B_{gi}}{(1 - S_{fwi}) B_{w}} S_{fwi} (R_{s i} - R_{s}) B_{g} + ρ_{s} V_{S} V_{m} (\frac{P_{c d}}{P_{L} + P_{c d}} - \frac{P}{P_{L} + P}) & (VII) \end{matrix}$

[0054] In the same way, the relevant parameters of shale gas are substituted into equation (VII), and the cumulative gas production is calculated according to different pressures, as shown in Table 4.

TABLE-US-00004 TABLE 4 Various parameter values of material balance after desorption Formation Natural gas water Rock elasticity Formation dissolution elasticity Adsorption Cumulative gas gas water elasticity gas gas gas Formation production production gas production production production production pressure(MPa) (m.sup.3) (m.sup.3) (m.sup.3) (m.sup.3) (m.sup.3) (m.sup.3) 8 483265353.97 556020.01 2046.36 278.48 4204.29 16411840.12 7.8 619871708.87 572003.66 2056.44 286.32 4225.00 21696963.85 7.6 754941375.89 588786.30 2066.52 294.54 4245.71 27177110.59 7.4 888361045.29 606430.54 2076.60 303.18 4266.42 32863277.88 7.2 1020007633.86 625005.73 2086.68 312.28 4287.13 38767305.99 7 1149747248.76 644588.96 2096.76 321.86 4307.84 44901960.20 6.8 1277434018.47 665266.15 2106.84 331.98 4328.55 51281022.94 6.6 1402908770.93 687133.35 2116.92 342.67 4349.27 57919397.18 6.4 1525997534.83 710298.32 2127.00 353.99 4369.98 64833222.63 6.2 1646509836.21 734882.36 2137.08 366.00 4390.69 72040006.79 6 1764236756.94 761022.54 2147.16 378.77 4411.40 79558772.94 5.8 1878948715.47 788874.30 2157.24 392.36 4432.11 87410227.86 5.6 1990392922.42 818614.74 2167.32 406.87 4452.82 95616952.23 5.4 2098290454.22 850446.51 2177.40 422.39 4473.53 104203617.55 5.2 2202332875.90 884602.58 2187.48 439.04 4494.24 113197233.83 5 2302178330.19 921352.26 2197.56 456.95 4514.95 122627433.43

[0055] According to the current formation pressure, production is allocated in combination with the binomial productivity equation (V) and according to the open flow, referring to Table 5 for the results.

TABLE-US-00005 TABLE 5 Production allocation results after desorption Formation production pressure Cumulative gas allocation (MPa) production (m.sup.3) (m.sup.3) 8 2560459.197 33160.58 7.8 619871708.9 33058.14 7.6 754941375.9 32957.98 7.4 888361045.3 32860.13 7.2 1020007634 32764.61 7 1149747249 32671.44 6.8 1277434018 32580.64 6.6 1402908771 32492.23 6.4 1525997535 32406.22 6.2 1646509836 32322.65 6 1764236757 32241.52 5.8 1878948715 32162.86 5.6 1990392922 32086.68 5.4 2098290454 32013.00 5.2 2202332876 31941.84 5 2302178330 31873.21

[0056] According to Table 5, the charts of cumulative gas production and formation pressure and single well allocation are drawn, as shown in FIG. 3 and FIG. 4;

[0057] The full life cycle production allocating chart of the shale gas well is finally established in combination with the above charts, as shown in FIG. 5 and FIG. 6.

[0058] Finally, in the production process of a gas well, according to the current cumulative gas production of the well and the above charts, a reasonable production allocation amount is quickly determined.

[0059] For example: the current cumulative gas production volume of the shale gas well is 0.14×10.sup.8 m.sup.3, and the cumulative gas production logarithm is 7.15. It can be known that the production allocation logarithm of the shale gas well is 4.56 by checking the chart (as shown in FIG. 7), so that the reasonable production allocation of the shale gas well is 36286 m.sup.3.

Shale gas well dynamic production allocating method

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Abstract

Claims

Description