Introduction

Warning and controlling the water invasion in water-driving reservoirs is significant because water invasion will seriously hamper well productivity and gas recovery (Kabir et al. 1983; Zendehboudi et al. 2014; Feng et al. 2015; Xu et al. 2019; Deng et al. 2020; Hu et al. 2021; Jiang et al. 2022, 2023; Zhi et al. 2022; Wang et al. 2023; Gao et al. 2023). High water production also gives rise to other problems, such as fine migration, the requirement for dividers, removal and management issues, and tube and surface tools corrosion (Karmakar and Chakraborty. 2006; Ali et al. 2011; Mohammad et al. 2023). The gas–water system of the reservoir in the western part of area B on the right bank of the Amu Darya is complex, and there are different degrees of water production problems in the early stage of production. Besides, the unique completion method makes it difficult to control water in the later stage of gas field development. Therefore, it is necessary to study the water invasion early warning and water control mode of water-driving wells for carbonate gas reservoirs in the western area of B.

Scholars have studied the identification method of water invasion in water-driving reservoirs. For example, Zhi et al. (2022) established a risk identification method for water invasion in deep bottom water reservoirs through a gas production profile test and three-dimensional water invasion simulation. Cheng et al. (2017) established the fluid physical property and water–gas ratio (WGR) method for the single-component conditions and the chloride conservation method for the multi-component conditions for water invasion in carbonate gas reservoirs and divided the water production law of gas wells into "type 1", "type 2" and "type 3" models. Ruan et al. (2021), based on the water invasion performance identification of MX gas reservoir, considered four water invasion modes: bottom water cone type, edge water finger type, edge water tongue type, and native movable water tongue type. Based on the principle of volume balance, Li et al. (2014) take the water invasion ring of the edge water gas reservoir as the research object and establish the dynamic early warning model of water invasion in the edge water gas reservoir. Luo et al. (2017) put forward the gas production index as a new sign of water invasion early warning. Deng et al. (2020) believe that the apparent geological storage method can find the water invasion characteristics of porous and relatively homogeneous weak water drive gas reservoirs earlier. In addition, there are some conventional methods, such as water-based chloride concentration monitoring and surface gas–water separation measurement. Most of these methods are based on water production and gas production data, and the water invasion characteristics of water wells still need to be considered (Shen et al. 2015; Li et al. 2016; Zou et al. 2017; Xu et al. 2021). Obviously, for the early warning of water invasion, it is necessary to consider the characteristics of water invasion.

Based on the water invasion characteristics of water-driving wells, we proposed a comprehensive water control workflow of early warning of water invasion, finding the location of invasion water, and plugging the perforation of priority water produced in water-driving reservoirs. First of all, the method calculates and distinguishes the water invasion characteristics based on the production data of water-driving wells, then obtains the early warning chart for the gas reservoir in the west of Amu Darya B area based on the proposed water invasion early warning method, and then finds the priority water-produced perforation by numerical simulation method. Finally, the water control effect after closing the priority water-produced perforation is studied. This work provides a practical and reliable method for water prevention and efficient water control in gas field development, which helps overcome the difficulty of water control in the Amu Darya.

Geology overview

The right bank of the Amu Darya gas field is located at the junction of Turkmenistan and Uzbekistan (Fig. 1) and belongs to the Amu Darya basin structurally (Cheng et al. 2017; Shan et al. 2022; Tang et al. 2023). By 2019, 21 gas fields and 76 gas wells had been operated in area B on the right bank of the Amu Darya. The gas field is mainly a marine carbonate gas reservoir. Middle-Upper Jurassic Callovian-Oxfordian's main gas-bearing intervals are complex in reservoir types, rich in fractures and cavities, and strong in heterogeneity. The gas field has bottom aquifer on the whole, active aquifer energy in local areas (Cheng et al. 2017). The above complex reservoir conditions lead to varying degrees of water production in some gas wells at the initial stage of production, which seriously reduces the productivity of gas wells.

Fig. 1
figure 1

Geographic location of the Right Bank of Amu Darya Gas Field (Cheng et al. 2017)

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Numerical simulation

Establishment of water invasion model

According to the actual reservoir characteristics and well layout, the water invasion model is established with reservoir 3D seismic prediction results as constraints. The stochastic modeling method is used to characterize the three-dimensional spatial distribution of reservoir physical properties. As shown in Fig. 2, the grid number of the water invasion model is 326,565 (= 123 × 59 × 45), and the grid size is 300 m × 300 m. The top depth of the model is 1891.15 m, and the bottom depth is 2437.87 m. The initial formation pressure is 22.7 MPa ~ 26.5 MPa, and the porosity is 0.0055–0.2745. There are ten production wells at present. Comparing the geological reserves calculated by the model and volumetric method, it is found that the error is less than 1%. In addition, the historical fitting results of water production well pressure show that the bottom hole pressure fits well (Fig. 3), which shows that the water invasion model is more reliable.

Fig. 2
figure 2

Water invasion model in study area

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Fig. 3
figure 3

Fitting result of bottom hole pressure in well A2

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Workflow of comprehensive water control

Early warning of water invasion

A new early warning method of water invasion is put forward. Based on the production data of water-driving wells, the method first judges the characteristics of water invasion and then determines the early warning pressure and the early warning values of level 1, level 2, and level 3 water–gas ratio. The method is applied to the gas reservoir in the west of B area, and the early warning index suitable for this reservoir is determined. The specific process is as follows.

  1. 1.

    Based on the actual geological reservoir, the water invasion model is established and verified.

  2. 2.

    According to the chart fitting method, the water volume coefficient, water invasion volume, water invasion rate, and water invasion replacement coefficient are calculated, and the water invasion characteristics are judged. The details are as follows.

First of all, calculate the dimensionless pseudo pressure and the recovery degree:

$$ p_{pD} = \frac{p/z}{{p_{i} /z_{i} }} $$
(1)
$$ R_{g} = \frac{{G_{p} }}{G} $$
(2)

where, \(p_{pD}\) is dimensionless pseudo pressure, MPa; \(p\) is resevior pressure, MPa; \(z\) is gas compression factor; \(p_{i}\) is initial resevior pressure, MPa; \(z_{i}\) is initial gas compression factor; \(R_{g}\) is recovery degree, \(G_{p}\) is cumulative gas production, m3; \(G\) is original gas reserves, m3。

According to the material balance equation of water-driving gas reservoir, there are:

$$ p_{pD} = \frac{{1 - R_{g} }}{1 - \omega } $$
(3)

where, \(\omega\) is the water volume coefficient. As shown in Fig. 4, a set of lines can be drawn on the axis by changing the values in Eq. 3. The recovery degree and dimensionless pseudo pressure of the gas reservoir are calculated by using the field production dynamic and static data, which are drawn in the chart of Fig. 4. The water volume coefficient is obtained from the distribution of the data points in the chart.

Fig. 4
figure 4

Gas reservoir water invasion board judged by recovery degree (Zhang et al. 2015)

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Calculate the water invasion volume:

$$ W_{e} = W_{p} B_{w} + GB_{gi} \omega $$
(4)

where, \(W_{e}\) is the water invasion invasion volume, m3; \(W_{p}\) is cumulative water production, m3; \(B_{w}\) is the volume coefficient of brine; \(B_{gi}\) is the volume coefficient of original gas.

The formula for calculating the replacement coefficient of water invasion is as follows:

$$ I = \frac{{W_{e} - W_{p} B_{w} }}{{G_{p} B_{gi} }} $$
(5)

For the water-driving gas reservoir, it is inactive water drive when the water invasion replacement coefficient is 0 ~ 0.15; it is subactive water drive when it is 0.15 ~ 0.4; it is active water drive when it is greater than 0.4.

  1. 3.

    Plot the variation curves of water invasion, daily water production, and water–gas ratio with formation pressure. Set the pressure at the maximum rising speed of water invasion as the early warning pressure and the corresponding water–gas ratio as the level 1 warning value of the water–gas ratio.

  2. 4.

    Finally, plot the variation curves of the water–gas ratio and water–gas ratio growth rate with production time. The first and second peak values of the water–gas ratio growth rate were taken as the level 2 and 3 warning values of the water–gas ratio, respectively.

Finding the location of invasion water

We propose a finding method of the location of invasion water based on a numerical simulation that aims at the multi-gas–water reservoir of carbonate rocks in the west of B area. First, the water production of different production schemes is simulated. In the simulation, the perforation of serious water production is automatically closed under a specific water cut by setting the keyword "WECON". Therefore, the automatic closing perforation parameters under different schemes are obtained, including perforation depth, perforation grid and closing time. The results of different schemes are compared to ensure the accuracy of perforation parameters. Finally, the priority perforation at the nearest end of the wellbore is selected, and the perforation parameters are simplified.

Plugging the perforation of priority water produced

Using the water invasion model, the water-plugging effect of closing the different numbers of water-produced perforations is studied using the numerical simulation method. Besides, the cumulative gas production of different schemes needs to be compared. Finally, the optimal water control scheme is obtained by comparing water and gas production.

Results

Early warning of water invasion

Based on the water invasion model, the production performance of 10 gas wells is simulated for 46 years, including field working schemes and different production systems. According to the proposed early warning method, the early warning indicators under different schemes are determined, and finally, the early warning chart is drawn. There, we give the early warning results when the gas production rate is 25 × 104 m3/d.

The results show that the calculated water volume coefficient is 0.154, and the water invasion volume is 10,788.15 × 104 m3. The water invasion volume of single well is 2697.04 × 104 m3, and water invasion replacement coefficient is 0.449, an active water drive. Figure 5 shows the change in water invasion volume, water–gas ratio, and daily water production with pressure. According to the proposed early warning method of water invasion, the early warning pressure is determined to be 11.4 MPa, and the corresponding level 1 early warning value of the water–gas ratio is 0.39 m3/104m3. Figure 6 shows the change of water–gas ratio and water–gas ratio growth rate with production time. It can be seen that the level 2 and level 3 water–gas ratio early warning values corresponding to the two peak values of the water–gas ratio growth rate curves are 0.85 m3/104m3 and 1.68 m3/104m3, respectively.

Fig. 5
figure 5

Change in water invasion volume, water–gas ratio, and daily water production with pressure

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Fig. 6
figure 6

Change in water–gas ratio and water–gas ratio growth rate with production time

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Simulates the early warning results of water invasion at different gas production rates (15 × 104 ~ 65 × 104 m3/d). Figure 7 shows the change in water invasion volume and water invasion replacement coefficient with gas production rate. With the increase in gas production rate, the larger the water invasion volume is, and the greater the water invasion replacement coefficient is, the more likely the water invasion is. When the gas production rate is 65 × 104 m3/d., compared with 15 × 104 m3/d., the water invasion volume has increased by 66.84%, and the water invasion replacement coefficient has increased by 54.33%. Although a high gas production rate can increase cumulative gas production, it will also increase the energy of water invasion, indicating an urgent need to study the water control strategy for this reservoir. Figure 8 shows the early warning pressure and early warning water–gas ratios with different gas production rates. It can be seen that the early warning pressure and water–gas ratio increase with the increase in gas production rate, which is because the higher gas production rate means a faster water invasion rate. Besides, the water–gas ratio of level 1, level 2, and level 3 of early warning increases step by step, which provides a theoretical basis for the early warning of field water-driving gas wells.

Fig. 7
figure 7

Change in water invasion volume and water invasion replacement coefficient with gas production rate

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Fig. 8
figure 8

Change in warning pressure and warning water–gas ratios with gas production rate

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Simulates the early warning results of water invasion under different bottom hole pressures (3 ~ 10 MPa) at constant pressure. Figure 9 shows the change in water invasion volume and replacement coefficient with bottom hole pressure. With the increase of bottom hole pressure during production, the water invasion volume decreases, and the water body activity decreases, making it less prone to water invasion. Figure 10 shows the early warning pressure and early warning water–gas ratio at different bottom hole pressures. The early warning pressure increases with the bottom hole pressure increase, while the early warning water–gas ratio is contrary. Besides, the water–gas ratio of level 1, level 2, and level 3 early warning increases step by step under the same bottom hole pressure. The results provide a theoretical basis for early warning of water-driving gas wells.

Fig. 9
figure 9

Change in water invasion volume and replacement coefficient with bottom hole pressure

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Fig. 10
figure 10

Change in warning pressure and warning water–gas ratios with bottom hole pressure

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Finding the location of invasion water

Water-finding technology is the premise of water plugging in water-driving wells. Only by accurately determining the water produced position can effectively plugging the water invasion. Besides, the water-finding technique can also obtain the production layer contribution profile and analyze the productivity contribution at different locations. Based on the proposed method of finding water, the water invasion model simulates different gas production rates and production methods. Among them, scheme 1 has a gas production rate of 25 × 104 m3/d, scheme 2 has a gas production rate of 65 × 104 m3/d, and scheme 3 has a constant pressure of 3 MPa. The three schemes are all set to automatically close the perforation with the most severe water production when the water content reaches 99%. The results show that there are four wells (well-A1 to well-A4).

Based on the results of scheme 1 and scheme 2, we draw the perforation depth and closing time of well A1 and A2, respectively, at different gas production rates, as shown in Figs. 11 and 12. Based on the results of scheme 2 and scheme 3, we draw the perforation depth and closing time of well A1 and A2 respectively under different production methods, as shown in Figs. 13 and 14.

Fig. 11
figure 11

The perforation depth and closing time of Well A1 due to serious water production at different gas production rates

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Fig. 12
figure 12

The perforation depth and closing time of Well A2 due to serious water production at different gas production rates

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Fig. 13
figure 13

The perforation depth and closing time of Well A1 due to serious water production at different production method

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Fig. 14
figure 14

The perforation depth and closing time of Well A2 due to serious water production at different production method

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It can be seen that the depth of the automatic closing perforation in the three schemes is the same, and the main difference lies in the change in closing time. Therefore, finding the perforation layer of most serious water production is the key to water finding. The results of Figs. 11 and 12 show that more perforation layers are closed at a high gas production rate because the high-pressure difference corresponding to a high gas production rate is more accessible to connect with the water layer. For any water-driving well, the position of the red point is higher than that of the black end at the same perforation depth, and the closing time of a low gas production rate is longer, which indicates that the water production with a high gas recovery rate is faster.

As can be seen in Figs. 13 and 14, more perforation layers are closed under the constant BHP of 3 MPa than in fixed production. For any water-driving well, the closing time of the same perforation layer in fixed production is longer than that in constant pressure of 3 MPa; that is, the same perforation layer closes later, which means that fixed production is slower than constant pressure in water production. Finally, the perforation parameters of four water-driving wells (A1−A4) under different production schemes are calculated. Because there is a sequence of water production by different perforations in the same layer, it is only necessary to block the nearest end of the wellbore, the perforation that prioritizes water produced. According to this method, 16 perforation layers that need to be closed are determined, and the specific parameters are shown in Table 1.

Table 1 Parameters of the perforation that needs to be closed most in the water finding study
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Plugging the perforation of priority water produced

The water invasion model is used to simulate the closure of different numbers of perforated layers in Table 1, and its water-plugging effect and cumulative gas production are studied to ensure sufficient gas production at the same time as successful water plugging. Figure 15 shows the distribution of water saturation around the wellbore of well A1 before and after water plugging. Blue is 1 for water saturation and red is 0. It can be seen that the water around well A1 decreases greatly after water plugging, which indicates that closing the perforation can isolate the flow channel of the water phase. Furthermore, Fig. 16 compares the water-plugging results of different schemes and their effects on cumulative gas production, including closing 4, 6, 8, and 12 perforated layers, respectively. The black number in the picture indicates the reduction of gas and water production after water plugging. The results show that the priority water produced perforation greatly influences water production; the more water produced perforation is, the better the water plugging effect is, but at the same time, it will also affect the total gas production of gas wells. After optimization, it is confirmed that the closure of 8 water-produced perforations (a total of 16) is the water plugging scheme for the gas reservoir west of area B. The details are shown in Table 2. At this time, water production decreased by 90.9%, while natural gas production decreased by only 9.7%.

Fig. 15
figure 15

The distribution of water saturation around the wellbore of well A1 before and after water plugging

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Fig. 16
figure 16

Cumulative gas production and cumulative water production when different numbers of perforations are closed, in which the percentage is the reduction of different schemes compared with the original scheme

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Table 2 Parameters for closing perforation in the study of water plugging
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Conclusions

Based on the water invasion characteristics of water-driving wells, the article developed a comprehensive water control workflow of early warning of water invasion, finding the location of invasion water, and plugging the perforation of priority water produced in water-driving reservoirs. The conclusions are as follows.

  1. 1.

    The water invasion model of the actual reservoir is established. The fitting results of model reserves and bottom hole pressure are good, which shows that the model is more reliable.

  2. 2.

    Proposes an early warning method of water invasion in the water-driving gas reservoir, and the characteristics of water invasion at fixed production and constant pressure are calculated. The relationship curve is drawn between the early warning value of water invasion, gas production rate, and bottom hole pressure. The results provide a theoretical basis for early warning of water-driving gas wells in the field.

  3. 3.

    A finding method of the location of invasion water based on numerical simulation is proposed. It is found that the perforation grid of water produced is similar at different gas production rates, and the model has the priority water-produced layer. Finding the invasion water location can be studied by identifying recurring perforations and prioritizing water-produced perforations among various water-driving wells.

  4. 4.

    The study of the invasion water plugging shows that the result of the finding method is accurate and the water plugging effect is successful; the more water produced perforation is, the better the water plugging effect is, but at the same time, it will also affect the total gas production and has an optimal scheme.