Accumulated water-gas ratio chart determination method and gas reservoir endogenous water yield prediction method

Abstract

The invention discloses a cumulative water-gas ratio chart determination method and a gas reservoir internal source water yield prediction method.The cumulative water-gas ratio chart determination method comprises the steps that according to the material balance principle, the ratio of the maximum output of formation water to the maximum output of natural gas serves as a first cumulative water-gas ratio, and the first cumulative water-gas ratio serves as a second cumulative water-gas ratio; obtaining a relational expression between different water saturations and the first accumulated water-gas ratio in the formation pressure reduction process; obtaining an instantaneous water-gas ratio according to a gas-water two-phase seepage theory in the reservoir; in combination with a relational expression between the accumulated water-gas ratio and the instantaneous water-gas ratio, obtaining a relational expression between different water saturations and a second accumulated water-gas ratio in the formation pressure drop process; and comparing the second accumulated water-gas ratio with the first accumulated water-gas ratio, determining the smaller one as the accumulated water-gas ratio, and establishing a chart of the accumulated water-gas ratio changing along with the formation pressure and the water saturation. The maximum accumulated water-gas ratio of the gas reservoir in the production process is determined through the accumulated water-gas ratio chart, and the internal source water yield of the gas reservoir is calculated according to the maximum accumulated water-gas ratio.

Description

Technical Field

[0001] This invention relates to the field of natural gas development technology, and in particular to a method for determining the cumulative water-gas ratio map and a method for predicting the internal water production of a gas reservoir. Background Technology

[0002] Most gas reservoirs produce water to varying degrees at different development stages. This formation water may originate from external edge and bottom water sources within the reservoir, or from internal sources such as interlayer water or pore water. Typically, low-permeability, tight, or highly heterogeneous gas reservoirs exhibit complex gas-water distributions, with no water layer indications in well logging or geological data, and no signs of water production during gas testing. However, some gas wells still produce formation water. The formation water volume calculated using volumetric and water intrusion dynamic methods is relatively small (water volume ratio less than 1), making it difficult to explain water intrusion and water production in gas wells when the formation water flow velocity and expansion energy are much lower than those of natural gas and the water volume ratio is small. This complicates the accurate assessment of water production risk, the determination of water production sources, and the prediction of water production trends. Therefore, predicting the amount of water produced from internal reservoir sources is crucial for inferring the source of gas reservoir water production and developing reasonable and effective development plans.

[0003] In the derivation of the material balance equation for conventional waterless gas reservoirs, it is assumed that both reservoir water intrusion and water production are zero. It is assumed that for gas reservoirs without edge or bottom water, the main source of water production from gas wells is the pore-source water within the reservoir. Some studies have proposed using movable water saturation to characterize the water production characteristics of gas wells through statistical analysis of the relationship between gas well water production characteristics and movable water saturation. Other studies have revealed the relationship between reservoir movable water saturation and water production characteristics through gas-driven water and nuclear magnetic resonance experiments. Still other studies, combining gas-water phase permeability curves and seepage theory, have established a relationship between the production water-to-gas ratio and movable water saturation, finding that the movable water saturation of gas reservoirs in the western South China Sea is less than 25%, and the calculated water-to-gas ratio is approximately below 2.3 cubic meters per 10,000 cubic meters. However, these studies only consider the production of the original movable water portion and do not consider the water produced from all primary water sources, including bound water, due to elastic expansion energy, leading to inaccurate predicted water production. Therefore, there is an urgent need to research methods for predicting the intrinsic water production of gas reservoirs. Summary of the Invention

[0004] The purpose of this invention is to overcome the problem of inaccurate water production predictions obtained by existing technologies, and to provide a method for determining the cumulative water-gas ratio based on water saturation and formation pressure, and a method for predicting the internal water production of gas reservoirs.

[0005] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0006] The method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure includes the following steps:

[0007] Based on the principle of material balance, the ratio of the maximum production of formation water to the maximum production of natural gas, determined by fluid expansion and storage space compression, is taken as the first cumulative water-gas ratio, and the relationship between different water saturation and the first cumulative water-gas ratio during the formation pressure decline process is obtained.

[0008] Based on the theory of gas-water two-phase flow in the reservoir, the instantaneous water-gas ratio controlled by the gas-water two-phase flow is obtained; combined with the relationship between the cumulative water-gas ratio and the instantaneous water-gas ratio, the cumulative water-gas ratio converted from the instantaneous water-gas ratio is used as the second cumulative water-gas ratio, and the relationship between different water saturation and the second cumulative water-gas ratio during the formation pressure decrease process is obtained.

[0009] By comparing the second cumulative water-gas ratio with the first cumulative water-gas ratio, the smaller one is the cumulative water-gas ratio determined by elastic expansion energy and flow conditions. The relationship between different water saturation and cumulative water-gas ratio during the formation pressure decrease process is obtained, and a chart is established to show the changes of cumulative water-gas ratio with formation pressure and water saturation.

[0010] In the technical solution of this invention, the cumulative water-gas ratio from the gas reservoir source is analyzed from the two aspects of material balance principle and gas-water two-phase flow. It is determined by elastic expansion energy and flow conditions. This is to predict the water production from gas reservoir source water such as interlayer water or pore primary water, and to provide a reference for predicting the production water-gas ratio and inferring the source of water production. At the same time, it explains why gas reservoirs without obvious edge and bottom water have a large water production and a high water-gas ratio.

[0011] In this invention, the material balance principle is based on the material balance equation of a homogeneous, closed gas reservoir without boundary or bottom water intrusion. Fluid expansion includes the expansion of natural gas and formation water, while reservoir space compression refers to the reduction of pore volume caused by the expansion of the rock skeleton volume. Specifically, to demonstrate the changes in the physical properties of natural gas and formation water, as well as pore volume, with pressure during the formation pressure decrease process, it is necessary to utilize the experimental results of high-pressure physical properties of natural gas and formation water in the gas reservoir and the rock compressibility coefficient. The gas-water two-phase flow theory refers to the two-phase flow theory of simultaneous gas-water flow that obeys Darcy flow, reflecting the flow conditions of simultaneous gas-water flow.

[0012] As a preferred embodiment of the present invention, the formula for calculating the first cumulative water-air ratio is as follows:

[0013]

[0014] In the formula R fwg For the first cumulative water-gas ratio, S wi The initial water saturation is expressed in %; S w The current water saturation level is expressed in %; P i P represents the original formation pressure of the gas reservoir, in MPa; B represents the current formation pressure, in MPa;g B represents the natural gas volume factor under current conditions. w C is the formation water volume factor under current conditions. p Rock compressibility coefficient, in MPa -1 C w The formation water compressibility coefficient is expressed in MPa. -1 C g The compressibility coefficient of natural gas, measured in MPa. -1 .

[0015] As a preferred embodiment of the present invention, based on the experimental results of high-pressure physical properties of natural gas in the gas reservoir, the relationship between the volume coefficient of natural gas and formation pressure and the relationship between the compressibility coefficient of natural gas and formation pressure are established by regression method; based on the experimental results of high-pressure physical properties of formation water in the gas reservoir, the relationship between the compressibility coefficient of formation water and formation pressure is established by regression method.

[0016] As a preferred embodiment of the present invention, the formula for calculating the rock compressibility coefficient is as follows:

[0017]

[0018] In the formula, φ represents porosity, expressed as a percentage (%); E s ν is the elastic modulus, measured in MPa; ν is Poisson's ratio.

[0019] As a preferred embodiment of the present invention, the formula for calculating the instantaneous water-air ratio is:

[0020]

[0021] In the formula R wg S represents the instantaneous water-to-air ratio. w A represents water saturation. kr B kr μ is the regression parameter for the gas-water phase permeability ratio and water saturation. g The viscosity of natural gas is μ. w B represents the viscosity of formation water. g B represents the natural gas volume factor under current conditions. w This represents the formation water volume factor under current conditions.

[0022] As a preferred embodiment of the present invention, the regression parameters of the gas-water phase permeability ratio and water saturation are obtained by simulation based on the gas-water phase permeability experimental results. The simulated regression relationship between the gas-water phase permeability ratio and water saturation is as follows:

[0023]

[0024] In the formula K rg K represents the relative permeability of natural gas. rw This represents the relative permeability of formation water.

[0025] As a preferred embodiment of the present invention, the formula for calculating the viscosity of formation water is as follows:

[0026]

[0027] In the formula μ wi This represents the viscosity of the original formation water.

[0028] As a preferred embodiment of the present invention, the viscosity of natural gas is obtained by regression analysis based on the results of natural gas high-pressure tests. The formula for calculating the viscosity of natural gas is as follows:

[0029] μ g =A μ P+B μ

[0030] In the formula A μ B μ The regression parameter is the viscosity of natural gas.

[0031] As a preferred embodiment of the present invention, when converting the instantaneous water-gas ratio into the cumulative water-gas ratio, for the sake of simplification, it is based on the assumption that the daily gas production is constant, that is, assuming a fixed gas production rate, to obtain the calculation formula for the second cumulative water-gas ratio:

[0032]

[0033] In the formula r swg For the second cumulative water-gas ratio, r wg is the instantaneous water-to-air ratio, and n is the production time.

[0034] Another aspect of the present invention provides a system for determining a cumulative water-gas ratio map based on water saturation and formation pressure, comprising at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the aforementioned method for determining a cumulative water-gas ratio map based on water saturation and formation pressure.

[0035] This invention also provides a method for predicting the endogenous water production of a gas reservoir, comprising:

[0036] Using the above-mentioned method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure, a chart showing the changes in cumulative water-gas ratio with formation pressure and water saturation is obtained. The maximum cumulative water-gas ratio of the gas reservoir during the production process is determined based on the water saturation of the gas reservoir, and the internal water production of the gas reservoir is calculated based on the maximum cumulative water-gas ratio.

[0037] As a preferred embodiment of the present invention, the cumulative water production is calculated based on the maximum cumulative water-gas ratio. The cumulative water production is the same as the internal water production of the gas reservoir. The formula for calculating the cumulative water production is as follows:

[0038] W P =R rwg G P

[0039] In the formula W P To accumulate water production, R rwg For the maximum cumulative water-to-gas ratio, G P To accumulate gas production.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] This invention provides a quantitative analysis method for predicting endogenous water production in gas reservoirs based on water saturation. It considers both the principle of mass balance and the two-phase flow of gas and water, simultaneously taking into account the cumulative water-to-gas ratio originating from within the gas reservoir, determined by elastic expansion energy (such as fluid expansion and reservoir space compression) and flow conditions. This method provides a reference for predicting the production water-to-gas ratio and inferring the source of water production in gas reservoirs where no obvious edge or bottom water has been identified. This method comprehensively considers both the source and quantity of water production to analyze the possible production water-to-gas ratio of a gas reservoir, and can, to some extent, explain why the production water-to-gas ratio of gas reservoirs where no obvious edge or bottom water has been identified remains relatively high. Attached Figure Description

[0042] Figure 1 This is a flowchart of the method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure according to the present invention;

[0043] Figure 2 The figure shows the regression curves of the natural gas volume factor for the YBCX and HBJ gas reservoirs in the examples.

[0044] Figure 3 This is a regression curve of the natural gas compressibility coefficient for the YBCX and HBJ gas reservoirs in the example;

[0045] Figure 4 The above is a regression curve of the formation water compressibility coefficient of the YBCX and HBJ gas reservoirs in the example.

[0046] Figure 5 This is a graph showing the relationship between different water saturations and the first cumulative water-gas ratio during the formation pressure decrease process of the YBCX gas reservoir in the example;

[0047] Figure 6 This is a graph showing the relationship between different water saturations and the first cumulative water-gas ratio during the formation pressure decrease process of the HBJ gas reservoir in the example;

[0048] Figure 7 This is a graph showing the relationship between different water saturations and the second cumulative water-gas ratio during the formation pressure decrease process of the YBCX gas reservoir in the example;

[0049] Figure 8This is a graph showing the relationship between different water saturations and the second cumulative water-gas ratio during the formation pressure decrease process of the HBJ gas reservoir in the example;

[0050] Figure 9 This is a comparison curve of the actual and theoretical cumulative water-gas ratio of well CX1021 in the YBCX gas reservoir in the example.

[0051] Figure 10 This is a comparison curve of the actual and theoretical cumulative water-gas ratio of well HJ3 in the HBJ gas reservoir in the embodiment.

[0052] Figure 11 This example compares the actual cumulative water-to-gas ratio of four producing wells in the YBCX gas reservoir with the theoretical chart.

[0053] Figure 12 This example compares the actual cumulative water-to-gas ratio of six producing wells in the HBJ gas reservoir with the theoretical chart.

[0054] Table 1 shows the logging interpretation and cumulative water-gas ratio statistics of four water-producing wells in the YBCX gas reservoir that do not have non-pure gas layers. Detailed Implementation

[0055] To more clearly describe the inventive objectives, technical solutions, and advantages of the specific embodiments of this invention, the solutions in the specific embodiments will be described in detail below with reference to the accompanying drawings. The specific technical solutions involved in the following embodiments are merely for the purpose of clearly and completely describing the innovative technical solutions of this invention. They are only a part of the specific implementation methods that this invention can adopt, not all embodiments, and should not be construed as limiting the innovative solutions of this invention. Any solution that adopts the same inventive concept as this invention should be included within the protection scope of this invention.

[0056] Secondly, the descriptions in the accompanying drawings of the specific embodiments of this invention are merely for the convenience of those skilled in the art to understand the invention. The details shown in the drawings are for the purpose of clearly presenting the technical solution, and should not be construed as including all technical features in the drawings in the specific implementation examples, nor should the details in the drawings be considered as additional limitations on the innovative technical solution of this invention. The components in the various embodiments described and shown in the drawings can be combined and arranged in different configurations. These variations in combination and arrangement should be considered as part of all embodiments of the innovative solution of this invention and included within the scope of protection of this invention.

[0057] In summary, the solutions or descriptions presented in the specific embodiments and accompanying drawings of this invention are not intended to limit the scope of protection claimed, but merely to illustrate selected embodiments / examples to help those skilled in the art understand the relevant innovative solutions. All other equivalent or parallel embodiments obtained by those skilled in the art based on these embodiments without inventive effort are within the scope of protection claimed by this invention.

[0058] Example 1

[0059] Methods for determining the cumulative water-gas ratio based on water saturation and formation pressure, such as... Figure 1 As shown, it includes the following steps:

[0060] Based on the principle of material balance, the ratio of the maximum production of natural gas formation water to the maximum production, which is determined by fluid expansion and storage space compression, is taken as the first cumulative water-gas ratio. The relationship between different water saturation and the first cumulative water-gas ratio during the formation pressure decline process is obtained.

[0061] Based on the theory of gas-water two-phase flow in the reservoir, the instantaneous water-gas ratio controlled by the gas-water two-phase flow is obtained; the cumulative water-gas ratio converted from the instantaneous water-gas ratio is taken as the second cumulative water-gas ratio; and by combining the relationship between the cumulative water-gas ratio and the instantaneous water-gas ratio, the relationship between different water saturation and the second cumulative water-gas ratio during the formation pressure decrease process is obtained.

[0062] By comparing the second cumulative water-gas ratio with the first cumulative water-gas ratio, the smaller one is the cumulative water-gas ratio determined by elastic expansion energy and flow conditions. The relationship between different water saturation and cumulative water-gas ratio during the formation pressure decrease process is obtained, and a chart is established to show the changes of cumulative water-gas ratio with formation pressure and water saturation.

[0063] The principle of mass balance is based on the mass balance equation of a homogeneous, closed gas reservoir without boundary or bottom water intrusion. Fluid expansion includes the expansion of natural gas and formation water, while reservoir compression refers to the reduction of pore volume caused by the expansion of the rock skeleton. Assume a homogeneous, closed gas reservoir without boundary or bottom water intrusion, with the initial formation pressure P. i The pore volume is V Pi V gi The original natural gas volume is S, and the original water saturation of the gas reservoir is S. wi The volume of the primary water in the gas reservoir is V. wi =V Pi S wi When the reservoir pressure drops to P,

[0064] The reduction in pore volume of the gas reservoir:

[0065] ΔV p =V pi C p (Pi -P)ΔV p =V Pi C P (P i -P)

[0066] Expansion of the primary water volume in the gas reservoir:

[0067] ΔV w =V wi C w (P i -P)ΔV w =V wi C w (P i -P)

[0068] Expansion of natural gas in the gas reservoir:

[0069] ΔV g =V gi C g (P i -P)ΔV g =V gi C g (P i -P)

[0070] Normally, natural gas mobility is much greater than formation water mobility. If only gas is produced and no water is produced, the initial water saturation S... wi Gradually increase to the current water saturation S w If the increased formation water is produced at the surface, the first cumulative water-to-gas ratio can be calculated using the principle of mass balance. The produced natural gas volume is denoted as G. P The volume of formation water extracted is denoted as W. P The underground volumes are C respectively. P B g W P B w According to the principle of mass balance, the underground volume of the produced fluid = original volume + expansion volume - remaining volume.

[0071] The underground volume of the produced gas: G p ·B g =V gi +ΔV g -(1-S w (V) pi -ΔV p )

[0072] The underground volume of the produced water: W p ·B w =V wi +ΔV w -S w (Vpi -ΔV p )

[0073] Based on the principle of material balance, the maximum production of natural gas and formation water in a closed gas reservoir, determined by fluid expansion and storage space compression, is obtained. The ratio of the maximum production of natural gas and formation water to the maximum production is taken as the first cumulative water-gas ratio. Based on the above, the expressions for the expansion of natural gas and formation water, the reduction of pore volume caused by the expansion of the rock skeleton, and the first cumulative water-gas ratio are established as follows:

[0074]

[0075] In the formula R fwg For the first water-to-air ratio, S wi The initial water saturation is expressed in %; S w Current water saturation, in %; P i P represents the original formation pressure of the gas reservoir, in MPa; B represents the current formation pressure, in MPa; g B represents the natural gas volume factor under current conditions. w W is the formation water volume factor under current conditions. P Cumulative water production, in m³ 3 G P Cumulative gas production, in m³ 3 C p Rock compressibility coefficient, in MPa -1 C w The formation water compressibility coefficient is expressed in MPa. -1 C g The compressibility coefficient of natural gas, measured in MPa. -1 .

[0076] This embodiment takes the YBCX and HBJ gas reservoirs in northeastern Sichuan as examples, and uses their production dynamics and other relevant data to estimate the production of primary water. The YBCX bioherm gas reservoir belongs to the bioherm deposits on the edge of the platform. It is a tectonic-lithologic gas reservoir with localized edge (bottom) water and controlled by the reef-shoal body. It was put into development in 2014. Currently, 12 out of 38 producing wells produce formation water; among them, the logging interpretation of 4 water-producing wells shows no non-pure gas layers and the tests do not produce water, but the current water-to-gas ratio is 0.5 m³ / 10,000 m³ to 3 m³ / 10,000 m³ (converted to a cumulative water-to-gas ratio of 0.47 m³ / 10,000 m³ to 1.09 m³ / 10,000 m³). The HBJ gas reservoir is a tight-low permeability, ultra-high pressure, medium-sulfur, elastic gas drive, tectonic lithology gas reservoir. It underwent trial production in 2010. Logging interpretation of the six production wells revealed no non-pure gas layers, and testing showed no water production; all production wells produced formation water. Currently, the water-to-gas ratio is 0.5 m³ / 10,000 m³ to 5 m³ / 10,000 m³ (equivalent to a cumulative water-to-gas ratio of 0.8 m³ / 10,000 m³ to 4.6 m³ / 10,000 m³). The following section, using the two gas reservoirs mentioned above, explains the method for determining the cumulative water-to-gas ratio chart based on water saturation and formation pressure.

[0077] Based on the high-pressure physical property test results of natural gas and formation water in the gas reservoir, the relationship between the volume coefficient of natural gas and formation pressure, the relationship between the compressibility coefficient of natural gas and formation pressure, and the relationship between the compressibility coefficient of formation water and formation pressure are established respectively. At the same time, based on the rock compressibility coefficient, the changes in the physical properties of natural gas and formation water and pore volume with pressure during the formation pressure decrease process are reflected.

[0078] Based on the high-pressure physical property test results of natural gas in the YBCX gas reservoir, the regression equation for the relationship between the natural gas volume factor and formation pressure is B. g =0.0881P -0.828 The relationship between the compressibility coefficient of natural gas and the formation pressure is C. g =1.7745P -1.279 The YBCX gas reservoir is primarily composed of dolomite. Using the elastic modulus of dolomite (34000), Poisson's ratio (0.26), and porosity (4.6%), the rock compressibility coefficient is calculated to be 0.02 × 10⁻⁶. -4 MPa -1 Based on the empirical formula for formation water compressibility, the formation water compressibility in the middle of the YBCX gas reservoir at a temperature of 152.5℃ was calculated, and the relationship between formation water compressibility and formation pressure was derived as C. w = -2×10 -6 P+0.0008, such as Figure 2 , 3 As shown in Figure 4, the formation water volume factor was obtained through high-pressure physical property experiments on formation water.

[0079] Rock compressibility formula:

[0080] Where: φ is porosity, in %; E s ν is the elastic modulus, MPa; ν is Poisson's ratio.

[0081] Based on the high-pressure physical property test results of natural gas in the BHJ gas reservoir, the regression equation for the relationship between the natural gas volume factor and formation pressure is B. g =0.087P -0.813 The relationship between the compressibility coefficient of natural gas and the formation pressure is C. g =1.872P -1.318 The BHJ gas reservoir is primarily composed of dolomite. Using the elastic modulus of dolomite (34000), Poisson's ratio (0.26), and porosity (4.46%), the rock compressibility coefficient is calculated to be 0.02 × 10⁻⁶. -4 MPa -1 Based on the empirical formula for formation water compressibility, the formation water compressibility in the middle of the BHJ gas reservoir at a temperature of 110℃ was calculated, and the relationship between formation water compressibility and formation pressure was derived as C. w = -2×10 -6 P+0.0006, as Figure 2 , 3 As shown in Figure 4.

[0082] Substituting these regression equations reflecting the changes in fluid and pore volume with pressure (with the formation water volume factor approximated as 1) into the first cumulative water-air ratio calculation formula, we obtain:

[0083] The first cumulative water-gas ratio of the YBCX gas reservoir:

[0084]

[0085] The first cumulative water-gas ratio of the BHJ gas reservoir:

[0086]

[0087] Taking the YBCX gas reservoir CX1021 well and the HBJ gas reservoir HJ3 well as examples, in the calculation process, the formation pressure P is considered to decrease gradually from 0.95Pi to 0.15Pi, and the water saturation S is considered to be... w The values ​​are taken as 0.05-0.95, and substituted into the calculation formula for the first cumulative water-gas ratio, respectively, to obtain the relationship between different water saturation levels and the first cumulative water-gas ratio during the formation pressure decrease process, as follows: Figure 5 , Figure 6The curve reflects the variation of the first cumulative water-gas ratio with formation pressure under ideal conditions where the water saturation of the gas reservoir does not change with space and time. As shown in the figure, in the initial stage of production, if the water saturation is 5%, the cumulative water-gas ratios of the YBCX gas reservoir at 0.95 Pi and 0.05 Pi are 0.11 m³ / 10,000 m³ and 0.05 m³ / 10,000 m³, respectively, and those of the HBJ are 0.10 m³ / 10,000 m³ and 0.05 m³ / 10,000 m³, respectively. If the water saturation is 95%, the cumulative water-gas ratios of the YBCX gas reservoir at 0.95 Pi and 0.15 Pi are 37.95 m³ / 10,000 m³ and 19.01 m³ / 10,000 m³, respectively, and those of the HBJ are 36.78 m³ / 10,000 m³ and 18.92 m³ / 10,000 m³, respectively. Under the same water saturation, the cumulative water-gas ratio decreases as formation pressure decreases; under the same formation pressure, the cumulative water-gas ratio increases as water saturation increases.

[0088] Based on Darcy's formula for gas-water two-phase flow, the ratio f of the water phase flow rate to the total flow rate in the formation can be derived. w :

[0089]

[0090] In the formula f w The water phase dispersal rate in the formation; μ g The viscosity of natural gas is μ. w Formation water viscosity, in mP a ·s;K rg K represents the relative permeability of natural gas. rw This represents the relative permeability of formation water.

[0091] Meanwhile, the water phase separation rate f in the formation w The instantaneous water-to-air ratio R can also be used. wg Represented as:

[0092]

[0093] f w By combining and transforming the two expressions, the instantaneous water-air ratio can be obtained:

[0094]

[0095] Based on the gas-water phase infiltration experiment, the regression relationship between the gas-water phase infiltration ratio and the water saturation level was obtained as follows:

[0096]

[0097] Combining the two equations yields the expression for the instantaneous water-to-gas ratio, which is controlled by the mobility ratio of the water phase to the gas phase:

[0098]

[0099] In the formula: Sw f represents water saturation; A represents the degree of saturation. kr B kr The regression parameters are the ratio of gas-water interpenetration to water saturation.

[0100] The formation water viscosity is calculated using an empirical formula (with an accuracy of 96% when the formation pressure is less than 68.95 MPa):

[0101]

[0102] Based on the results of natural gas high-pressure tests, the relationship between natural gas viscosity and formation pressure can be derived:

[0103] μ g =A μ P+B μ

[0104] In the formula A μ B μ The regression parameter is the viscosity of natural gas.

[0105] The formula for calculating the instantaneous water-air ratio can then be obtained as follows:

[0106]

[0107] Using the relative permeability curves of well CX1021 in the YBCX gas reservoir and well HJ3 in the HBJ gas reservoir, the instantaneous water-gas ratios were obtained as follows:

[0108] YBCX:

[0109]

[0110] HBJ:

[0111]

[0112] Based on the relationship between the cumulative water-gas ratio and the instantaneous water-gas ratio, the second cumulative water-gas ratio is calculated from the instantaneous water-gas ratio.

[0113] The second cumulative water-gas ratio is compared with the first cumulative water-gas ratio, and the smaller one is the cumulative water-gas ratio determined by the elastic expansion energy and flow conditions under these conditions.

[0114] The cumulative water-gas ratio calculated from the instantaneous water-gas ratio is defined as the second cumulative water-gas ratio, R. swg The instantaneous water-gas ratio R is the ratio of cumulative gas production to cumulative water production. wg The ratio of daily gas production to daily water production is given, where n is the production time (number of days for gas production) and j is the number of days in n.

[0115]

[0116] In the initial stage of production, a fixed gas production rate is generally adopted. To simplify the formula, the daily gas production rate is assumed to remain constant. Therefore, the above formula simplifies to the calculation formula for the second cumulative water-gas ratio:

[0117]

[0118] In the formula (R) wg ) j Let be the instantaneous water-gas ratio on day j. In actual gas well production, after deducting the flowback fluid, the instantaneous water-gas ratio of a gas well tends to increase in the early stages. The increase varies among different gas wells, but generally, the instantaneous water-gas ratio and the second cumulative water-gas ratio do not exceed one order of magnitude.

[0119] Based on the gas-water phase permeability test results of the YBCX and HBJ gas reservoirs, due to the strong heterogeneity of the reservoirs, the ratio of water phase permeability to gas phase permeability varies significantly among the core samples. The regression parameter A of the ratio of water phase to gas phase permeability and water saturation is... kr B kr The variation range is relatively large, among which the regression parameter A of the YBCX gas reservoir is... kr From 1×10 -10 Up to 4×10 -5 The regression parameter A of the HBJ gas reservoir kr From 1×10 -10 Up to 3×10 -6 Calculations revealed that the instantaneous water-to-gas ratio increases with decreasing formation pressure and increasing water saturation. The influence of water saturation is particularly significant. Under different initial water saturation conditions (0.05-0.95), when the formation pressure decreases to P (with values ​​ranging from (0.15-0.95)Pi), the instantaneous water-to-gas ratio of the YBCX gas reservoir is 0.0004-540 m³ / 10,000 m³, and that of the HBJ gas reservoir is 0.000003-320 m³ / 10,000 m³.

[0120] Using the formula for calculating the second cumulative water-gas ratio, the instantaneous water-gas ratios of the two wells during the formation pressure decrease process were converted into cumulative water-gas ratios. The resulting charts showing the relationship between different water saturations and the second cumulative water-gas ratio during the formation pressure decrease process in the YBCX and HBJ gas reservoirs are shown below. Figure 7 , Figure 8 As shown.

[0121] By comparing the second cumulative water-gas ratio with the first cumulative water-gas ratio, the smaller one is the cumulative water-gas ratio determined by elastic expansion energy and flow conditions. This yields the relationship between different water saturation levels and the cumulative water-gas ratio during the formation pressure decrease process, and a chart is established to show the changes in the cumulative water-gas ratio as a function of formation pressure and water saturation. Figures 9-10These are comparison charts showing the theoretical and actual cumulative water-gas ratios of produced water from wells CX1021 in the YBCX gas reservoir and HJ3 in the HBJ gas reservoir, categorized by their effects on elastic expansion and two-phase flow control. The logging interpretation for the horizontal well CX1021 shows a completely pure gas layer, but the average water saturation over its entire effective section is 22.1%, with a 27.43-meter section exhibiting a high water saturation of 28.5% on average. From... Figure 9 It can be seen that when the water saturation is 20%-30%, the cumulative water-gas ratio caused by elastic expansion energy can reach as high as 0.5 m³ / 10,000 m³-0.8 m³ / 10,000 m³. The well began producing water after 262 days of actual production, and the current cumulative water-gas ratio is 0.71 m³ / 10,000 m³, indicating that more areas with high water saturation are involved in the flow. From... Figure 10 It can be seen that the HJ3 well in the HBJ gas reservoir produced water immediately upon commissioning, and the actual cumulative water-gas ratio showed a decreasing trend, initially at 1.7 m³ / 10,000 m³, and currently at 1.41 m³ / 10,000 m³. This is consistent with the theoretical first cumulative water-gas ratio in both magnitude and trend. The second cumulative water-gas ratio, determined by the two-phase flow conditions, is always greater than the first, indicating that the well's water production is entirely determined by elastic expansion energy. Furthermore, this suggests that the initial water saturation distribution within the well's affected area is relatively uniform and stable. Since there are no logging curves for this well, the estimated average water saturation is approximately 48.2%.

[0122] In actual gas reservoirs, due to the heterogeneity of reservoir development, the spatial distribution of water saturation and relative permeability curves varies. Furthermore, water saturation changes over time during production, making it difficult to obtain the instantaneous water-to-gas ratio controlled by flow conditions using relative permeability curves. Therefore, for highly heterogeneous gas reservoirs, only a rough prediction based on reservoir maps can be made to obtain the maximum cumulative water-to-gas ratio during production, thus providing a basis for preliminary prediction of well water production and determining its source.

[0123] Example 2

[0124] This embodiment provides a method for predicting the endogenous water production of a gas reservoir, including:

[0125] Using the cumulative water-gas ratio chart determination method based on water saturation and formation pressure from Example 1, a chart showing the cumulative water-gas ratio changing with formation pressure and water saturation is obtained. The maximum cumulative water-gas ratio during the gas reservoir's production process is determined based on the reservoir's water saturation. The cumulative water production is then calculated based on this maximum cumulative water-gas ratio, and this cumulative water production is the reservoir's internal water production. The formula for calculating the cumulative water production is as follows:

[0126] W P =R rwg G P

[0127] In the formula W P To accumulate water production, R rwg For the maximum cumulative water-to-gas ratio, G P To accumulate gas production.

[0128] According to Example 1, due to the strong heterogeneity of the YBCX and HBJ gas reservoirs, in addition to the spatial and temporal variations in water saturation, the relative permeability curves also show significant differences, making it difficult to obtain the instantaneous water-gas ratio controlled by flow conditions using the relative permeability curves. Therefore, for gas reservoirs with strong heterogeneity, the maximum value of the cumulative water-gas ratio during the actual gas reservoir's production process is predicted based on the cumulative water-gas ratio chart of the gas reservoir.

[0129] The cumulative water-gas ratios of the actual producing wells in the YBCX and HBJ gas reservoirs are projected onto the corresponding gas reservoir charts. Figures 11-12 The source of water production from gas wells can be inferred by combining well logging interpretation results.

[0130] The YBCX gas reservoir currently has 38 producing wells, including 12 water-producing wells. Early geological assessments of 8 wells revealed non-pure gas layers, while 4 wells did not. From... Figure 11 It can be seen that the cumulative water-gas ratio curves of the four wells in the YBCX gas reservoir that did not develop non-pure gas layers and produced water are all within the cumulative water-gas ratio curve chart of the gas reservoir, and the actual production cumulative water-gas ratio shows an upward trend. This reflects that during actual production, as the formation pressure decreases, more and more pores with high water saturation or initial water saturation greater than bound water saturation in the complex porous media within the pressure drop range participate in the flow, which is consistent with the phenomenon of non-uniform distribution of fluid saturation in actual reservoirs. The current cumulative water-gas ratio of the four wells is 0.47 m³ / 10,000 m³-1.09 m³ / 10,000 m³, and the estimated average water saturation is about 18%-39%. This understanding can be confirmed by the well logging interpretation results. As can be seen from Table 1, although the well logging interpretation of these four wells did not show gas-water co-layers or gas-water layers, and the tests did not produce water, the well logging interpretation showed a relatively high water saturation.

[0131] Of the six producing wells in the HBJ gas reservoir, well HJ3 was the first to commence production in November 2010, while the remaining five wells were put into production after 2020. All five experienced an initial pressure drop exceeding 20 MPa. The cumulative water-to-gas ratio shows an upward trend; except for well HJ1, which had a 40-day waterless gas production period, the other four wells produced water immediately upon commissioning, and all have large cumulative water-to-gas ratios. Initially, the cumulative water-to-gas ratio was 0.5 m³ / 10,000 m³ to 0.66 m³ / 10,000 m³, suggesting an average pore water saturation of approximately 25%-28% during the initial production phase. Currently, the cumulative water-to-gas ratio is 0.8 m³ / 10,000 m³ to 4.6 m³ / 10,000 m³, indicating that more areas with high water saturation are participating in the flow, with an average water saturation of approximately 33%-71%. The analysis suggests that the gas reservoir has a relatively small volume, resulting in a large impact area for the HJ3 well. Furthermore, since the formation water mobility is much lower than the natural gas mobility, only the natural gas in other well areas is utilized, while the original water is retained in the formation, leading to an increase in water saturation. Therefore, the cumulative water-to-gas ratio of the wells put into production later is relatively large. On the other hand, the HJ4 well, which is furthest from HJ3, is relatively less affected, resulting in the smallest cumulative water-to-gas ratio (0.79 cubic meters per 10,000 cubic meters).

[0132] Table 1 Well Logging Interpretation Results

[0133]

[0134] Example 3

[0135] This embodiment provides a system for determining the cumulative water-gas ratio chart based on water saturation and formation pressure, including at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, characterized in that the instructions are executed by the at least one processor to enable the at least one processor to execute the method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure of Embodiment 1.

[0136] For those skilled in the art, when understanding the solutions described in the specific embodiments of the present invention, conventional technical manuals in the field can be consulted. At the same time, appropriate understandings or adjustments can be made to the above-mentioned terms to deduce the same or similar technical solutions without creative effort.

[0137] The above embodiments describe only the basic principles, main features and / or advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and the description of the invention content in the specification are only the principles or specific cases of the present invention. Without departing from the essence of the innovative idea of ​​the present invention, there are various changes and improvements to the innovative solution of the present invention, and all such changes and improvements fall within the scope of protection claimed by the present invention.

Claims

1. A method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure, characterized in that, Includes the following steps: Based on the principle of material balance, the ratio of the maximum production of formation water to the maximum production of natural gas is taken as the first cumulative water-gas ratio, and the relationship between different water saturation and the first cumulative water-gas ratio during the formation pressure decline process is obtained. Based on the theory of two-phase gas-water flow in the reservoir, the instantaneous water-gas ratio is obtained. Combining the relationship between the cumulative water-gas ratio and the instantaneous water-gas ratio, the cumulative water-gas ratio converted from the instantaneous water-gas ratio is used as the second cumulative water-gas ratio, and the relationship between different water saturation and the second cumulative water-gas ratio during the formation pressure decrease process is obtained. By comparing the second cumulative water-gas ratio with the first cumulative water-gas ratio, the smaller one is the cumulative water-gas ratio determined by elastic expansion energy and flow conditions. The relationship between different water saturation and cumulative water-gas ratio during the formation pressure decrease process is obtained, and a chart is established to show the changes of cumulative water-gas ratio with formation pressure and water saturation.

2. The method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure according to claim 1, characterized in that, The formula for calculating the first cumulative water-air ratio is as follows: In the formula R fwg For the first cumulative water-gas ratio, S wi The initial water saturation; S w This represents the current water saturation level; P i P represents the original formation pressure of the gas reservoir; B represents the current formation pressure. g B represents the natural gas volume factor under current conditions. w C is the formation water volume factor under current conditions. p C is the rock compressibility coefficient. w C is the formation water compressibility coefficient. g This is the compressibility coefficient of natural gas.

3. The method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure according to claim 2, characterized in that, Based on the high-pressure physical property test results of natural gas in the gas reservoir, the relationship between the volume coefficient of natural gas and formation pressure and the relationship between the compressibility coefficient of natural gas and formation pressure were established by regression method; based on the high-pressure physical property test results of formation water in the gas reservoir, the relationship between the compressibility coefficient of formation water and formation pressure was established by regression method.

4. The method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure according to claim 2, characterized in that, The formula for calculating the rock compressibility coefficient is: In the formula, φ represents porosity; E s ν is the elastic modulus; ν is Poisson's ratio.

5. The method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure according to claim 1, characterized in that, The formula for calculating the instantaneous water-air ratio is: In the formula R wg S represents the instantaneous water-to-air ratio. w A represents water saturation. kr B kr μ is the regression parameter for the gas-water phase permeability ratio and water saturation. g The viscosity of natural gas is μ. w B represents the viscosity of formation water. g B represents the natural gas volume factor under current conditions. w This represents the formation water volume factor under current conditions.

6. The method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure according to claim 5, characterized in that, The regression parameters for the gas-water permeability ratio and water saturation were obtained through simulation based on the gas-water permeability experimental results. The simulated regression relationship between the gas-water permeability ratio and water saturation is as follows: In the formula K rg K represents the relative permeability of natural gas. rw This represents the relative permeability of formation water.

7. The method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure according to claim 1, characterized in that, The formula for calculating the second cumulative water-air ratio is as follows: In the formula R swg R is the second cumulative water-gas ratio. wg is the instantaneous water-to-air ratio, and n is the production time.

8. A system for determining the cumulative water-gas ratio map based on water saturation and formation pressure, comprising at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, characterized in that, The instructions are executed by at least one processor to enable the at least one processor to perform the method for determining the cumulative water-gas ratio chart based on water saturation and formation pressure as described in any one of claims 1-7.

9. A method for predicting endogenous water production in a gas reservoir, characterized in that, include: Using the cumulative water-gas ratio chart determination method based on water saturation and formation pressure as described in any one of claims 1-7, a chart showing the cumulative water-gas ratio changing with formation pressure and water saturation is obtained. The maximum cumulative water-gas ratio of the gas reservoir during the production process is determined based on the water saturation of the gas reservoir, and the internal water production of the gas reservoir is calculated based on the maximum cumulative water-gas ratio.

10. The method for predicting endogenous water production in a gas reservoir according to claim 9, characterized in that, The cumulative water production is calculated based on the maximum cumulative water-gas ratio. The cumulative water production is the same as the internal water production of the gas reservoir. The formula for calculating the cumulative water production is as follows: W P =R rwg G P In the formula W P For cumulative water production, R rwg For the maximum cumulative water-to-gas ratio, G P To accumulate gas production.

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