Method for calculating daily gas production rate of methane hydrate deposit based on inflow performance relationship formulas

Abstract

A daily gas production rate of a methane hydrate deposit is calculated based on inflow performance relationship formulas. Step 1 determines the production stage, including the gas production rate trend of a production test and selecting an inflow performance relationship formula corresponding to the stage. Step 2 calculates basic coefficient terms related to energy conversion in the inflow performance relationship formula. Step 3 obtains other coefficient terms related to production in the inflow performance relationship formula. Step 4 predicts the gas production rate under other production pressure differences. Staged inflow performance relationship formulas characterize the complex methane hydrate deposit production performance. Gas production rate and deposit pressure under a large pressure differences are predicted through simple production tests under a small pressure difference, providing a basis for production design of the hydrate deposit and preventing accidents that may be caused by direct production under a large pressure difference.

Claims

1. A method for calculating the daily gas production rate of a methane hydrate deposit based on inflow performance relationship formulas, comprising: in a Step 1, determining a production stage, including determining the production stage according to a gas production rate trend of a production test of the methane hydrate deposit, and selecting an inflow performance relationship formula corresponding to the determined stage, wherein the production stage in Step 1 comprises a gas production rate ascent stage and a gas production rate decline stage; and when a gas production rate under a same production pressure continues to rise within a short production time, the production stage is in the ascent stage; otherwise the production stage is in the decline stage; in a Step 2, calculating basic coefficient terms related to energy conversion in the inflow performance relationship formula, including obtaining initial deposit parameters and fluid parameters of the methane hydrate deposit and substituting into related formula to calculate corresponding basic coefficient terms; in a Step 3, obtaining other coefficient terms related to production in the inflow performance relationship formula, including measuring production data of a single well through one or more sets of depressurization production tests under a small production pressure difference, and substituting these production data into the selected inflow performance relationship formula to obtain other pending coefficient terms under a same deposit condition and a same recovery percent; in a Step 4, predicting a gas production rate under other production pressure differences, comprising calculating production rates at other bottomhole production pressures based on the inflow performance relationship formula and parameters and the coefficients obtained in Steps 2-3; and thereby predicting the gas production rate of the methane hydrate deposit.

2. The method according to claim 1, wherein the methane hydrate deposit in Step 1 refers to a Class III natural gas methane hydrate deposit according to a geological type, only consists of a single hydrate layer, and is surrounded by impermeable mudstones at a top and bottom.

3. The method according to claim 1, wherein the inflow performance relationship formula of an ascent stage in Step 1 is: $\mathrm{Ln}\left(q_g\right)=A_1.Math.\mathrm{Ln}\left[{\left(B.Math.{\left(1-\frac{N_p}{N}\right)}^{\frac{P_{\max ,T=0}}{P_{\max }}}.Math.\left(P_i-P_r\right)+P_r\right)}^2-P_{\mathrm{wf}}^2\right]+A_2$ wherein q.sub.g is a gas production rate (m.sup.3/day), A.sub.1, A.sub.2, and B are coefficients, N.sub.p/N is a gas recovery percent, P.sub.i is an initial pressure (MPa) of the methane hydrate deposit, P.sub.r is an average deposit pressure (MPa) of the methane hydrate deposit, P.sub.wf is a bottomhole production pressure (MPa), and $\frac{P_{\max ,T=0}}{P_{\max }}$ is a ratio of a maximum production pressure difference under an initial deposit condition to a maximum production pressure difference during production.

4. The method according to claim 1, wherein the inflow performance relationship formula of a decline stage in Step 1 is: $\frac{q_g}{q_{\mathrm{gmax}}}=1-C\left(\frac{P_{\mathrm{wf}}-P_{\mathrm{ice}}}{P_r-P_{\mathrm{ice}}}\right)-\left(1-C\right){\left(\frac{P_{\mathrm{wf}}-P_{\mathrm{ice}}}{P_r-P_{\mathrm{ice}}}\right)}^2,$ wherein q.sub.gmax is a gas production rate (m.sup.3/day) corresponding to a minimum bottomhole production pressure, C is a coefficient, and P.sub.ice is a pressure (MPa) corresponding to a quadruple point of a hydrate.

5. The method according to claim 4, wherein the minimum bottomhole production pressure is set to the methane hydrate quadruple point pressure.

6. The method according to claim 1, wherein the parameters obtained through methods including well logging and production test in Step 2 comprise initial deposit pressure, initial deposit temperature, initial average hydrate saturation, fluid salinity, and thickness of the methane hydrate layer.

7. The method according to claim 1, wherein a related formula for calculating the basic coefficient terms related to energy conversion of an ascent stage in Step 2 is: $B=\left(2.056-0\mathrm{.254}.Math.\frac{{\left(0.0548+7\mathrm{.154}.Math.S_{\mathrm{irG}}\right)}^{3.97-0.795.Math.N_g}}{H^{-0.0847}-0.846}\right),$ wherein S.sub.irG is an irreducible gas saturation of a deposit fluid, N.sub.g is a gas index in calculation of gas relative permeability, and H is a thickness of a hydrate layer of the methane hydrate deposit.

8. The method according to claim 1, wherein a related formula for calculating the basic coefficient terms related to energy conversion of a decline stage in Step 2 is: $C=0.88-0\mathrm{.062}.Math.\frac{S_H^{0.38}.Math.\left(S+77.2\right)}{H^{1.27}}-0\mathrm{.012}.Math.\mathrm{Ln}\left(S_H^{-0.65}-1.3\right).Math.\left(S-4.61\right),$ wherein S.sub.H is a hydrate saturation of a hydrate layer of the methane hydrate deposit, and S is a salinity (%) of the methane hydrate deposit.

9. The method according to claim 1, wherein a production test of the single well in Step 3 is carried out by depressurization at a fixed bottomhole production pressure, and a difference between a bottomhole production pressure applied in the production test and a deposit pressure should not exceed half of an initial average deposit pressure.

10. The method according to claim 1, wherein parameters obtained in an ascent stage in Step 3 are pending coefficients A.sub.1 and A.sub.2, and is calculated by substituting gas production rate and deposit pressure data of no less than two sets of production tests into a corresponding inflow performance relationship formula.

11. The method according to claim 1, wherein a parameter obtained in a decline stage in Step 3 is a maximum gas production rate, and is calculated by substituting gas production rate and deposit pressure data of no less than one set of production tests into a corresponding inflow performance relationship formula.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a flow diagram of calculating a daily gas production rate of a methane hydrate deposit based on inflow performance relationship formulas according to an embodiment of the present disclosure.

DETAILED DESCRIPTION

(2) A detailed description of illustrative embodiments will now be described with reference to the various FIGURES. Although this description provides a detailed example of possible implementations, it should be noted that the details are intended to be exemplary and in no way limit the scope of the application. It should be noted that in this text, the terms methane hydrate deposit and deposit and can be used interchangeably.

(3) FIG. 1 depicts a method 100 for calculating the daily gas production rate of a methane hydrate deposit based on inflow performance relationship formulas is provided. FIG. 1 is a flow diagram of calculating a daily gas production rate of a methane hydrate deposit based on inflow performance relationship formulas according to an embodiment of the present disclosure. As shown in FIG. 1, the method includes:

(4) Step 1 105, determining production stage, including determining the production stage according to the gas production rate trend of a production test of the methane hydrate deposit, and selecting an inflow performance relationship formula corresponding to the determined stage;

(5) Step 2 110, calculating basic coefficient terms related to energy conversion in the inflow performance relationship formula, including obtaining initial deposit parameters and fluid parameters of the methane hydrate deposit and substituting into related formula to calculate corresponding basic coefficient terms;

(6) Step 3 115, obtaining other coefficient terms related to production in the inflow performance relationship formula, including measuring production data of a single well through one or more sets of depressurization production tests under a small production pressure difference, and substituting these production data into the selected inflow performance relationship formula to obtain other pending coefficient terms under the same deposit condition and the same recovery percent; and

(7) Step 4 120, predicting the gas production rate under other production pressure differences, including calculating production rates under other bottomhole production pressures based on the inflow performance relationship formulas and the parameters and coefficients obtained in Steps 2-3.

(8) The inventive concept will now be described with reference to the following two examples.

Example I

(9) There is a Class III methane hydrate deposit with an initial deposit pressure of 11.32 MPa, a hydrate saturation of 0.6, salinity of 0, a hydrate layer thickness of 20 m, an irreducible gas saturation of 0.05, and a gas index of 3. There is a production well in the center of the deposit. During the production test, the production pressure is 6 MPa, and the measured gas production rate is 2.01210.sup.4 m.sup.3/day. It is found that the gas production rate shows a downward trend. The corresponding deposit pressure during production is 6.429 MPa. Assuming the deposit pressure is constant, find out the corresponding gas production rate when the production pressure drops to 4 MPa under the same deposit condition. Specific solution steps are as follows:

(10) Step 1, since the gas production rate at the testing point shows a downward trend, the production is in a decline stage, the inflow performance relationship formula in the decline stage:

(11) $\frac{q_g}{q_{\mathrm{gmax}}}=1-C\left(\frac{P_{wf}-P_{\mathrm{ice}}}{P_r-P_{\mathrm{ice}}}\right)-\left(1-C\right){\left(\frac{P_{wf}-P_{\mathrm{ice}}}{P_r-P_{\mathrm{ice}}}\right)}^2\mathrm{is}\mathrm{adopted};$

(12) Step 2, coefficient C is calculated, and S.sub.H=0.6, H=20 m and Xs=0 (P.sub.ice=2.63 MPa) are substituted into formula:

(13) $C=0.88-0\mathrm{.062}.Math.\frac{S_H^{0.38}.Math.\left(S+77.2\right)}{H^{1.27}}-0\mathrm{.012}.Math.\mathrm{Ln}\left(S_H^{-0.65}-1.3\right).Math.\left(S-4.61\right)$
thereby, after calculation, C=0.643;

(14) Step 3, the maximum gas production rate is obtained, when P.sub.r=6.429 MPa, P.sub.wf=6 MPa, according to the inflow performance relationship formula, q.sub.gmax=13.59510.sup.4 m.sup.3/day, at this time the inflow performance relationship formula is:

(15) $\frac{q_g}{q_{g\max }}=1-0.648\left(\frac{P_{\mathrm{wf}}-2.63}{P_r-2.63}\right)-0.352{\left(\frac{P_{\mathrm{wf}}-2.63}{P_r-2.63}\right)}^2;$
and

(16) Step 4, P.sub.wf=4 MPa is substituted into the above formula to obtain that q.sub.g=9.78810.sup.4 m.sup.3/day.

Example II

(17) If the production pressure during the production test is 6 MPa, the gas production rate is 1.49210.sup.4 m.sup.3/day when recovery efficiency is 2.5%, and, after maintaining the production pressure for a period of time, the gas production rate tested again is 2.85410.sup.4 m.sup.3/day when recovery efficiency is 5%. It was found that the gas production rates show an upward trend during the two tests. The corresponding deposit pressures during production are 8.751 MPa and 7.995 MPa, respectively. Assuming the deposit conditions are the same, when the deposit pressure is 7.995 MPa and the recovery efficiency is 5%, find out the corresponding gas production rate when the production pressure drops to 4 MPa under the same deposit condition.

(18) Specific solution steps are as follows:

(19) Step 1, since the gas production rate at the testing point shows an upward trend, the production is in an ascent stage, the inflow performance relationship formula in the ascent stage:

(20) $\mathrm{Ln}\left(q_g\right)=A_1.Math.\mathrm{Ln}\left[{\left(B.Math.{\left(1-\frac{N_p}{N}\right)}^{\frac{P_{\max ,T=0}}{P_{\max }}}.Math.\left(P_i-P_r\right)+P_r\right)}^2-P_{\mathrm{wf}}^2\right]+A_2$
is adopted;

(21) Step 2, coefficient B is calculated, and S.sub.irG=0.05, Ng=3.0 and H=20 m are substituted into formula:

(22) 0$B=\left(2.056-0\mathrm{.254}.Math.\frac{{\left(0.0548+7\mathrm{.154}.Math.S_{\mathrm{irG}}\right)}^{3.97-0.795.Math.N_g}}{H^{-0.0847}-0.846}\right)$
thereby, after calculation, B=2.946;

(23) $P_r=8.751\mathrm{MPa},P_{wf}=6\mathrm{MPa},\frac{N_p}{N}=0.025,q_g=2.01210^4$
Step 3, coefficients A.sub.1 and A.sub.2 are calculated, and P.sub.i=11.32 MPa, m.sup.3/day are substituted into the formula to obtain that

(24) $9.610=5.395A_1+A_2;P_i=11.32\mathrm{MPa},P_r=7.995\mathrm{MPa},P_{\mathrm{wf}}=6\mathrm{MPa},\frac{N_p}{N}=0.05,q_g=2.85410^4$
m.sup.3/day are substituted into the formula to obtain that 10259=5.5338A.sub.1+A.sub.2; the two formulas adopt a simultaneous solution to obtain that A.sub.1=4.8505, A.sub.2=16.5827 by a regression method, at this time the inflow performance relationship formula is:

(25) $\mathrm{Ln}\left(q_g\right)=4.8505.Math.\mathrm{Ln}\left[{\left(2.946.Math.{\left(1-\frac{N_p}{N}\right)}^{\frac{P_{\max ,T=0}}{P_{\max }}}.Math.\left(P_i-P_r\right)+P_r\right)}^2-P_{\mathrm{wf}}^2\right]-16.5827;$
and

(26) Step 4,

(27) $P_i=11.32\mathrm{MPa},P_{\mathrm{wf}}-4\mathrm{MPa},P_r=7.995\mathrm{MPa},\frac{N_p}{N}=0.05$
are substituted into the above formula to obtain that q.sub.g=4.64010.sup.4 m.sup.3/day.

(28) Although features and elements are described above in particular combinations, one of ordinary skill in the art will appreciate that each feature or element can be used alone or in any combination with the other features and elements. In addition, the methods described herein may be implemented in a computer program, software, or firmware incorporated in a computer-readable medium for execution by a computer or processor. Examples of computer-readable media include electronic signals (transmitted over wired or wireless connections) and computer-readable storage media. Examples of computer-readable storage media include, but are not limited to, a read only memory (ROM), a random access memory (RAM), a register, cache memory, semiconductor memory devices, magnetic media such as internal hard disks and removable disks, magneto-optical media, and optical media such as CD-ROM disks, and digital versatile disks (DVDs).

(29) The foregoing description of the embodiments of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of this disclosure. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto.