Tight Gas Reservoir Dynamic Reserve Calculation with Modied Flowing Material Balance Method

: The determination of dynamic reserves of gas well is an important basis for 11 rational production allocation and development of a single well. The commonly used 12 flow material balance method (FMB method) uses the slope of the curve of wellhead 13 pressure and cumulative production after stable production of gas well to replace the 14 slope of the curve of average formation pressure and cumulative production to 15 calculate the controlled reserves of single well. However, based on the theoretical 16 calculation, the FMB method ignores the change of natural gas compression 17 coefficient, viscosity and deviation coefficient in the production process. After 18 considering these changes, the slope of the curve of the relationship between bottom 19 hole pressure and cumulative production and the slope of the curve of the relationship 20 between average formation pressure and cumulative production are not equal. In order 21 to solve this problem, the influence of pressure on each parameter is considered, and 22 the equation of modified flowing material balance method is derived. The application 23 of Yan'an gas field in Ordos Basin shows that: compared with the results of the 24 material balance method, the result of the flow material balance method is smaller, 25 and the maximum error is 58.816%. The consequence of the modified mobile material 26 balance method is more accurate, and the average error is 2.114%, which has good 27 applicability. This study provides technical support for an accurate evaluation of 28 dynamic reserves of tight gas wells in Yan'an gas field, and has important guiding 29 significance for economic and efficient development of gas reservoir.


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Yan'an gas field, located in the southeast of Yishan slope in Ordos Basin, is a typical 34 tight sandstone gas reservoir with the characteristics of low permeability, strong 35 heterogeneity, strong stress sensitivity and complex percolation mechanism (Li and 36 Qiao, 2012). Pressure measurement and variable production often occur in the process 37 of production test and development, so it is difficult to calculate the dynamic reserves 38 of gas wells in this gas field. 39 At present, the main methods for calculating dynamic reserves including material 40 balance method, the production decline method, production accumulation method, 41 elastic two-phase method and so on (Chen and Che, 2011;Shults, 2020). Among them, 42 the establishment of the material balance method is relatively easy, and only needs 43 high-pressure property data and production data, the calculation method is relatively  When there is no data such as bottom hole pressure, the material balance method 48 cannot calculate the dynamic reserves of gas wells. In order to solve this problem, 49 Mattar put forward the flowing material balance method, which is analyzed from the closed gas reservoir, after the gas well is produced relatively stable for a certain 52 period of time, the pressure wave is transmitted to the outer boundary of the formation, 53 and gas seepage enters a pseudo steady state (Huang et al., 2015). As showed in the  In order to solve the above problems, a modified FMB method is proposed in this 71 study, in which the influence of pressure on the viscosity and compression coefficient 72 of gas is considered, and the modified flowing material balance equation is derived.

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Taking the tight gas reservoir in Yanchang Oilfield in Ordos Basin as an example, the 74 flow material balance method before and after correction is compared and analyzed, 75 and the accuracy of the modified flow material balance method is verified. The viscosity of natural gas is different from that of liquid. Under the condition of low 80 pressure, the viscosity of natural gas increases with the increase of temperature (Yao et 81 al., 2015). However, when the pressure is greater than 10MPa, the viscosity of natural 82 gas decreases at first and then increases with the increase of temperature. However, 83 whether under low pressure or high pressure, the viscosity of natural gas increases 84 with the increase of pressure. When there is non-hydrocarbon gas in natural gas, the 85 viscosity often increases.

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The experimental determination of natural gas is difficult, so reservoir engineers 87 usually use relevant empirical formulas to calculate (Wei et al., 2017). Through 10 88 natural gas samples (Table. 1) under the condition of temperature 352 K and pressure   89 30MPa, the viscosity is calculated, and the pressure-viscosity diagram is drawn based 90 on the calculated results, as showed in figure (Fig. 2).       In the FMB method, it is assumed that the pressure has no effect on the viscosity and 126 compression coefficient of natural gas, that is: And then get: Therefore, when the gas reservoir reaches pseudo steady state,  The relationship between μgCg and pressure can be obtained from the experimental 143 data. As shown in figure (Fig. 6), it can be seen that the hypothetical formula (4) is not 144 valid, that is, the viscosity and compression coefficient of natural gas vary with 145 pressure.

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As can be seen from the figure (Fig. 6): Combined with the formula (3), (6), and then get: It can be seen that the absolute value of the slope of the line is greater 151 than that of the / p P Z G : line, and the lower the formation pressure is, the greater 152 the production pressure difference is, and the greater the difference between them is.
153 Therefore, reserves determined by the FMB method are smaller than the real reserves.

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In order to reduce the calculation error of gas well reserves, the FMB method must be 155 modified.

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By deforming the formula (3), and then get: It is assumed that in any short period at the initial stage of pseudo steady state, pss P And then get: Based on the above process, application steps of the modified FMB method are as 173 follows (Fig. 7).

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(1) according to the determined, the formula (3-13) is determined, and the R is calculated.

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(2) using the bottom hole flow pressure and cumulative production data, draw the   The initial production of type I wells in Yan'an gas field is high, the pressure drops 217 slowly, and the stable production time is long, so it has a good stable production 218 capacity under the condition of low pressure.

Calculation results of type Ⅱ wells 243
The test production of type II wells in the study area is between 4.0×10 4 m 3 /d and  S-5 well is a typical type Ⅱ well in Yan 128 high pressure well area (Fig. 11 to the large pressure fluctuation in the trial production process, the gas production is 252 difficult to be stable, and the working system is adjusted, the daily gas production is 253 gradually reduced to about 1×10 4 m 3 /d, and the daily water production is 0.1～1.8 254 m 3 /d. After the gas production is reduced to 1×10 4 m 3 /d, the oil pressure decreases 255 from 14.41MPa to 12.36MPa, a decrease of 2.05 MPa, and the oil pressure decreases 256 at a rate of 0.051MPa/d, which shows that the production is basically stable. Up to 257 April 2020, the cumulative gas production is 3471.62×10 4 m 3 and the cumulative 258 water production is 490.25m 3 .

Calculation results of type Ⅲ wells 270
The initial production of type Ⅲ wells in the study area is low, about 35×10 4 m 3 /m,   (Table. 3), using the measured formation pressure at different 303 stages of the production of the three wells, the scatter diagram between the cumulative 304 gas production and the measured Pzag Z is drawn (Fig. 15, Fig. 16, Fig. 17).

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By linear fitting these discrete data points, the dynamic reserves of single well   Fig. 18).

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Through the above calculation results (Fig. 18)   Combined with the production data of two wells, S-56 well was put into production in 336 June 2013 (Fig. 19), and the shut-in state appeared intermittently from June 2013 to 337 December 2016, the pressure recovery state was in a short time, which reflected that 338 the formation pressure and casing pressure drop in the early stage of production were 339 relatively small, and the gas production per unit pressure drop was relatively 340 large (Mattar et al., 2006). Because there is no intermittent shut-in in the later stage of 341 production, the law of monthly gas production verifies this theory. Therefore, it can be 342 concluded that the early shut-in leads to the large dynamic reserves of a single well.

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Similarly, the S-60-1 well was put into production in July 2015 (Fig. 20), and the 344 intermittent shut-in occurred in the later stage of production, and the production law 345 of the gas well could not fully reflect the real state of the gas well, resulting in a large 346 calculation error.

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It can be seen that the great change in the production system of gas wells will affect 348 the accuracy of the calculation results of the modified FMB method, especially the 349 shut-in for a long time before calculating the pressure drop gas production at a certain 350 time. Therefore, time data points with relatively stable production should be selected 351 as far as possible to calculate the dynamic reserves of a single well.

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(2) Through theoretical calculation and numerical simulation, it is found that the