CN111305825B - Gas well pressure dynamic simulation method with variable control reserves - Google Patents

Abstract

The invention discloses a dynamic simulation method of gas well pressure with variable control reserves. Based on the principle of material balance, by correcting the virtual original formation pressure and virtual cumulative production in different control reserves stages, the unstable flow pressure calculation method of a single fixed reserves system is used. The single-well pressure dynamics with multi-stage controlled reserve variation is generated, which is used to track and fit the actual single-well production performance. The calculation results show that the calculated pressure is continuous at the junction of variable reserves, showing and maintaining the dynamic characteristics of the reserves in stages. This method is as follows: Using the existing single-well seepage model in closed-boundary gas reservoirs provides a convenient method to analyze the dynamics of variable reserve systems.

Description

A dynamic simulation method of gas well pressure with variable control reserves

technical field

The invention relates to the field of dynamic simulation, in particular to a dynamic simulation method for gas well pressure for variable control reserves.

Background technique

In traditional single-well dynamic analysis, such as modern productivity decline analysis theoretical models and interpretation methods, it is assumed that the controlled reserves of a single well are fixed, and the drop of flow pressure is regarded as two components: one is the flow pressure drop of fluid migration to the well. , and the second is the formation pressure drop due to energy depletion; the flow pressure drop is related to the instantaneous production, and the formation pressure drop is related to the cumulative production.

The prior art has the following defects:

(1) To directly develop the analytical solution of the seepage mathematical model of the new variable reserve system, it is necessary to establish the seepage model separately for different well types, different boundaries, and different number of reserve sections for analytical solutions. This method is complex and inefficient, and cannot utilize the existing Some seepage model results, some problems are still difficult to solve;

(2) Contribution of new reserves. The heterogeneity of gas reservoirs leads to a certain threshold pressure difference between different reservoirs. When the pressure difference is greater than the threshold pressure difference, the reservoir starts to contribute, showing a trend of increasing reserves;

(3) There is the influence of inter-well interference. In a system with strong connectivity, the production of new wells and the production changes of adjacent adjacent wells lead to changes in the control reserves of gas wells.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a dynamic simulation method of gas well pressure for variable control reserves in view of the above problems.

The invention object of the present invention is realized by the following technical scheme: a kind of gas well pressure dynamic simulation method for variable control reserves, is characterized in that, comprises the following steps:

S1: Correction of material balance, including the following steps:

S101: Iteratively calculate the formation pressure through the gas reservoir material balance equation according to the total cumulative production, wherein the gas reservoir material balance equation is:

表示累积有效压缩系数，Q_p表示总累积产量，G表示控制储量，p_i表示原始地层压力，z_i表示压力p_i下的天然气偏差因子，p表示目前地层压力，z表示压力p下的天然气偏差因子；in,

Indicates the cumulative effective compressibility coefficient, Q _p represents the total cumulative production, G represents the control reserve, pi represents the original formation pressure, _{zi represents} the natural gas deviation factor at the pressure _pi , p represents the current formation pressure, and z represents the natural gas under the pressure p bias factor;

The total cumulative output described is:

Q _p =G _p +W _p B _w /B _g

Among them, G _p represents the cumulative gas production, W _p represents the cumulative water production, B _w represents the volume factor under formation water pressure p, and B _g represents the volume factor under natural gas pressure p;

S102: Comparing the end state of the first stage with the start state of the second stage, obtain the virtual total cumulative production of the second stage reserves;

产生等效的状态，所述的第1阶段结束的状态方程和第2阶段开始的状态方程为：The end state of stage 1 is equal to the start state of stage 2, and the virtual total cumulative production of the beginning of stage 2 when the reserves of stage 2 act as an isolated system

The equivalent state is generated, the state equation at the end of the first stage and the state equation at the beginning of the second stage are:

Among them, G ₁ represents the controlled reserves of the gas reservoir in the first stage, G ₂ represents the controlled reserves of the second stage, Q _p,1 represents the total cumulative production at the end of the first stage, and p ₁ represents the formation pressure at the end of the first stage , z ₁ represents the natural gas deviation factor under pressure p ₁ ;

Among them, _G1 is the controlled reserve of the gas reservoir in the first stage, G2 is the controlled reserve of the _second stage, Q _{p,1 is} the total cumulative production at the end of the first stage, p1 is the formation pressure at the end of the first stage, z ₁ represents the natural gas bias factor at pressure p ₁ .

Comparing the equations of state at the end of stage 1 and the beginning of stage 2, we get:

which is:

To get the virtual total cumulative production of the Phase 2 reserves:

S103: When the control reserves of the gas reservoir change, update the virtual cumulative production of gas and water at the beginning of the new reserve system, and the virtual cumulative production of gas and water is:

为第2阶段开始的虚拟累积产气量，

为第2阶段开始的虚拟累积产水量，G_p,1为第1阶段结束时的真实累积产气量、W_p,1为第1阶段结束时的真实累积产水量；in,

is the virtual cumulative gas production at the beginning of the second stage,

is the virtual cumulative water production at the beginning of the second stage, G _p,1 is the real cumulative gas production at the end of the first stage, and W _p,1 is the real cumulative water production at the end of the first stage;

计算，其中所述的累积产气量和累积产水量为：S104: After entering the second stage, the cumulative gas production _Gp and the cumulative water production _Wp are corrected to be based on the virtual cumulative production

Calculated, where the cumulative gas production and cumulative water production are:

Among them, q _sc (t) represents the gas production, q _w (t) represents the water production, t ₁ represents the end time of the first stage, and t represents the current production time;

Substitute the calculated corrected cumulative production G _p , W _p into the total cumulative production to calculate the virtual total cumulative production Q _p , take the second-stage controlled reserve G ₂ as the current reserve G, and iteratively calculate the second stage’s The formation pressure p changes with the total cumulative production, and then the pressure p is converted into the pseudo-pressure ψ form required for the dynamic calculation of the gas well pressure.

S2: Stage initial pressure correction:

When S103 occurs, the virtual initial formation pressure of the first stage is updated, and the cumulative gas production in the previous period is injected into the new reserve system, and the pseudo pressure for calculating the virtual initial pressure is:

Among them, ψ _i,2 represents the pseudo pressure of the new reserve system, that is, the virtual initial pressure of the second stage, G _p1 represents the cumulative gas production in the early stage, that is, the end point of the first stage, ψ ₁ represents the pseudo pressure of the formation pressure at the end point of the previous stage, and c _t represents the The overall compressibility of the system.

S3: Dynamic calculation of bottom hole pressure:

Using the pseudo pressure of the virtual initial formation pressure, the bottom hole flow pressure pseudo pressure under the action of the variable flow rate in the second stage is calculated by the superposition principle:

In the formula, t is time, hour; q is flow rate, m ³ /d; q _j =q(t _j ), q ₀ =0, q(t _j ) is flow sequence, j=1,2,...,N ; P _D is the dimensionless pressure solution of any reservoir model with skin and well reservoir, B is the gas volume coefficient at the original pressure; μ is the gas viscosity at the original pressure, mPa.s; k is the reservoir permeability , um ² ; h represents the thickness of the reservoir, m.

The pseudo pressure ψ _wf (t) calculated by the bottom hole flow pressure pseudo pressure formula is then inversely transformed into the bottom hole flow pressure P _wf (t), which is used for dynamic fitting of the measured pressure. When the change of the controlled reserves exceeds 2 stages, the treatment method is similar to that of the 2 stage.

Beneficial effects of the invention: The method provides a convenient method for analyzing the dynamics of a variable reserve system by using the existing single-well seepage model of a closed boundary gas reservoir.

Description of drawings

Fig. 1 is the method flow chart of the present invention;

Fig. 2 is the analysis curve of pressure index of well xc1;

Fig. 3 is the fitting diagram of the Blasingame diagnostic curve of variable reserves in well xc1;

Fig. 4 is the fitting curve of double logarithmic pressure of variable reserves in well xc1;

Fig. 5 is the gas injection production curve diagram of well xc1;

Fig. 6 is the fitting curve of bottom hole flow pressure in xc1 well;

Fig. 7 is the prediction curve of formation pressure of well xc1.

Detailed ways

In order to have a clearer understanding of the technical features, purposes and effects of the present invention, the specific embodiments of the present invention are first described with reference to the accompanying drawings.

A method for dynamic simulation of gas well pressure for variable control reserves, characterized in that it comprises the following steps:

S1: Correction of material balance, including the following steps:

S101: Iteratively calculate the formation pressure through the gas reservoir material balance equation according to the total cumulative production, wherein the gas reservoir material balance equation is:

表示累积有效压缩系数，Q_p表示总累积产量，G表示控制储量，p_i表示原始地层压力，z_i表示压力p_i下的天然气偏差因子，p表示目前地层压力，z表示压力p下的天然气偏差因子；in,

Indicates the cumulative effective compressibility coefficient, Q _p represents the total cumulative production, G represents the control reserve, pi represents the original formation pressure, _{zi represents} the natural gas deviation factor at the pressure _pi , p represents the current formation pressure, and z represents the natural gas under the pressure p bias factor;

The total cumulative output described is:

Q _p =G _p +W _p B _w /B _g

Among them, G _p represents the cumulative gas production, W _p represents the cumulative water production, B _w represents the volume factor under formation water pressure p, and B _g represents the volume factor under natural gas pressure p;

S102: Comparing the end state of the first stage with the start state of the second stage, obtain the virtual total cumulative production of the second stage reserves;

产生等效的状态，所述的第1阶段结束的状态式和第2阶段开始的状态方程为：The end state of stage 1 is equal to the start state of stage 2, and the virtual total cumulative production of the beginning of stage 2 when the reserves of stage 2 act as an isolated system

To generate an equivalent state, the state equation at the end of the first stage and the state equation at the beginning of the second stage are:

Among them, G ₁ represents the controlled reserves of the gas reservoir in the first stage, G ₂ represents the controlled reserves of the second stage, Q _p,1 represents the total cumulative production at the end of the first stage, and p ₁ represents the formation pressure at the end of the first stage , z ₁ represents the natural gas bias factor at pressure p ₁ .

Comparing the equations of state at the end of stage 1 and the beginning of stage 2, the virtual total cumulative production of reserves in stage 2 is obtained as:

S103: When the control reserves of the gas reservoir change, update the virtual cumulative production of gas and water at the beginning of the new reserve system, and the virtual cumulative production of gas and water is:

为第2阶段开始的虚拟累积产气量，

为第2阶段开始的虚拟累积产水量，G_p,1为第1阶段结束时的真实累积产气量、W_p,1为第1阶段结束时的真实累积产水量；in,

is the virtual cumulative gas production at the beginning of the second stage,

is the virtual cumulative water production at the beginning of the second stage, G _p,1 is the real cumulative gas production at the end of the first stage, and W _p,1 is the real cumulative water production at the end of the first stage;

计算，其中所述的累积产气量和累积产水量为：S104: After entering the second stage, the cumulative gas production _Gp and the cumulative water production _Wp are corrected to be based on the virtual cumulative production

Calculated, where the cumulative gas production and cumulative water production are:

Among them, q _sc (t) represents the gas production, q _w (t) represents the water production, t ₁ represents the end time of the first stage, and t represents the current production time.

Substitute the calculated corrected cumulative production G _p , W _p into the total cumulative production to calculate the virtual total cumulative production Q _p , take the second-stage controlled reserve G ₂ as the current reserve G, and iteratively calculate the second stage’s The formation pressure p changes with the total cumulative production, and then the pressure p is converted into the pseudo-pressure ψ form required for the dynamic calculation of the gas well pressure.

S2: Stage initial pressure correction:

When S103 occurs, the virtual initial formation pressure of the first stage is updated, and the cumulative gas production in the previous period is injected into the new reserve system, and the pseudo pressure for calculating the virtual initial pressure is:

Among them, ψ _i,2 represents the pseudo pressure of the new reserve system, that is, the virtual initial pressure of the second stage, G _p1 represents the cumulative gas production in the early stage, that is, the end point of the first stage, ψ ₁ represents the pseudo pressure of the formation pressure at the end point of the previous stage, and c _t represents the The overall compressibility of the system.

S3: Dynamic calculation of bottom hole pressure:

Using the pseudo pressure of the virtual initial formation pressure, the bottom hole flow pressure pseudo pressure under the action of the variable flow rate in the second stage is calculated by the superposition principle:

In the formula, t is time, hour; q is flow rate, m ³ /d; q _j =q(t _j ), q ₀ =0, q(t _j ) is flow sequence, j=1,2,...,N ; P _D is the dimensionless pressure solution of any reservoir model with skin and well reservoir, B is the gas volume coefficient at the original pressure; μ is the gas viscosity at the original pressure, mPa.s; k is the reservoir permeability , um ² ; h represents the thickness of the reservoir, m.

The pseudo pressure ψ _wf (t) calculated by the bottom hole flow pressure pseudo pressure formula is then inversely transformed into the bottom hole flow pressure P _wf (t), which is used for dynamic fitting of the measured pressure. When the change of the controlled reserves exceeds 2 stages, the treatment method is similar to that of the 2 stage.

The present embodiment is an analysis result provided by a gas well in a certain gas storage, and the details are as follows:

The gas well xc1 of a gas storage shows the phenomenon of variable controlled reserves during the second round of gas injection. As shown in Figure 2, the pressure index curve presents a 2-stage slope, reflecting that the initial controlled reserves are small and the later controlled reserves are large. The results are shown in Table 1.

Table 1. Analysis results of controlled reserves in Well xc1

A change in controlled reserves occurred around August 20, 2014. The fitting curve of the Blasingame chart for the constant production pressure drop of variable control reserves is shown in Figure 3, and the fitting curve of the double logarithmic pressure drop chart is shown in Figure 4. According to the gas injection production curve of Well xc1 as shown in Figure 5, the bottom hole flow pressure fitting curve is calculated as shown in Figure 6. It can be seen that the simulated curve can better track the gas injection pressure dynamics, and the formation pressure change is predicted as shown in Figure 7. Around August 20, 2014, the calculated flow pressure and formation pressure were continuous, and after this date, the formation pressure increased slowly, which corresponds to the phenomenon of controlled reserves increasing.

In this embodiment, the specific method principle is analyzed as follows:

By revising the virtual original formation pressure and virtual cumulative production in different control reserve stages, the unstable flow pressure calculation mode of the fixed reserve system can be maintained;

The calculation results show that the pressure calculated by the method in this case is continuous at the junction of variable reserves, showing and maintaining the dynamic characteristics of the reserves in stages, which can be used to track and fit the actual gas well production performance.

The basic principles and main features of the present invention and the advantages of the present invention have been shown and described above. Those skilled in the art should understand that the present invention is not limited by the above-mentioned embodiments, and the descriptions in the above-mentioned embodiments and the description are only to illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have Various changes and modifications fall within the scope of the claimed invention. The claimed scope of the present invention is defined by the appended claims and their equivalents.

Claims (4)

1. A dynamic simulation method for gas well pressure with variable control reserves is characterized by comprising the following steps:

s1: correcting the material balance state, calculating the virtual total accumulated yield by using the corrected accumulated yield, and calculating the formation pressure by using a gas reservoir material balance equation and the current reserve;

s2: correcting the initial pressure of the stage, namely calculating virtual initial pressure pseudo pressure by using the accumulated gas production rate of the 1 st stage end point calculated in the step S1;

s3: and (4) dynamically calculating the bottom hole pressure, namely calculating the bottom hole flow pressure simulated pressure under the variable flow action in the 2 nd stage by using the simulated pressure of the virtual initial pressure obtained in the step S2 and a superposition principle, and then inversely transforming the bottom hole flow pressure into the bottom hole flow pressure.

2. The method for dynamically simulating the pressure of a gas well with variable control reserve as claimed in claim 1, wherein the step S1 specifically comprises the following steps:

s101: and (3) iteratively calculating the formation pressure through a gas reservoir material balance equation according to the total accumulated yield, wherein the gas reservoir material balance equation is as follows:

wherein,

representing the cumulative effective compression factor, Q_pRepresenting the total cumulative yield, G representing the control reserve, p_iRepresenting the original formation pressure, z_iDenotes the pressure p_iA natural gas deviation factor below, p represents the current formation pressure, and z represents the natural gas deviation factor under the pressure p;

the total cumulative yield is:

Q_p＝G_p+W_pB_w/B_g

wherein G is_pRepresents cumulative gas production, W_pIndicating cumulative water production, B_wRepresents the volume coefficient under the formation water pressure p, B_gRepresents the volume coefficient under the pressure p of the natural gas;

s102: comparing the ending state of the 1 st stage with the starting state of the 2 nd stage to obtain the virtual total accumulated yield of the reserves of the 2 nd stage;

the ending state of stage 1 is equal to the starting state of stage 2, and when the stage 2 reserves are taken as the isolated system, the virtual total cumulative production of stage 2 is started

Generating equivalent states, wherein the state equation at the end of the 1 st stage and the state equation at the beginning of the 2 nd stage are as follows:

wherein G is₁Indicating the gas reservoir control reserve, G, of stage 1₂Indicating the control reserve, Q, of stage 2_p,1Denotes the total cumulative yield at the end of stage 1, p₁Denotes the formation pressure at the end of phase 1, z₁Denotes the pressure p₁A natural gas deviation factor of;

comparing the state equations at the end of stage 1 and the beginning of stage 2 to obtain the virtual total cumulative yield of stage 2 reserves as:

s103: when the control storage amount of the gas reservoir changes, updating the virtual accumulated yield of the gas and the water when a one-time new storage amount system starts, wherein the virtual accumulated yield of the gas and the water is as follows:

wherein,

for the virtual cumulative gas production beginning at stage 2,

for the virtual cumulative water production starting at stage 2, G_p,1Is the true cumulative gas production, W, at the end of stage 1_p,1Is the true cumulative water production at the end of stage 1;

s104: after entering stage 2, the gas production is accumulated G_pCumulative water production W_pModified to be based on virtual cumulative yield

Calculating, wherein the cumulative gas production and the cumulative water production are as follows:

wherein q is_sc(t) gas production, q_w(t) represents the water yield, t₁Represents the end time of the 1 st stage, t represents the current production time;

using calculated modificationsPositive cumulative yield G_p、W_pCalculating a virtual total cumulative yield Q by substituting the total cumulative yield_pWith control of reserves G in stage 2₂And (3) iteratively calculating the change of the formation pressure p in the 2 nd stage along with the total accumulated production through a gas reservoir material balance equation for the current reserve G, and converting the formation pressure p into a pseudo pressure psi form required by the dynamic calculation of the gas well pressure.

3. A method for dynamically simulating pressure in a gas well with variable control reserve as claimed in claim 2 wherein step S103 further comprises step S2 of updating the initial virtual formation pressure in a first stage, injecting the previous cumulative gas production into the new reserve system, and calculating the pseudo pressure of the initial virtual pressure as:

wherein psi_i,2Pseudo pressure, G, representing the virtual initial pressure of the new reserve system, phase 2_p1Cumulative gas production, # indicating the end of the early, i.e. phase 1₁Pseudo pressure representing formation pressure at the previous end point, c_tRepresenting the overall compression factor of the system.

4. The method for dynamically simulating gas well pressure with variable control reserves according to claim 3, wherein the step S3 specifically comprises:

and calculating the bottom hole flow pressure simulation pressure under the variable flow effect of the 2 nd stage by using the simulation pressure of the virtual initial formation pressure through a superposition principle:

wherein t represents time, hour; q represents a flow rate, m³/d；q_j＝q(t_j)，q₀＝0，q(t_j) Represents the flow sequence, j ═ 1,2, …, N;P_Dthe method is a dimensionless pressure solution of any oil reservoir model containing the skin and the well reservoir, and B represents a gas volume coefficient under the original pressure; μ represents the gas viscosity at the original pressure, mpa.s; k denotes reservoir permeability, um²(ii) a h represents reservoir thickness, m;

pseudo pressure psi calculated from bottom hole flowing pressure pseudo pressure formula_wf(t) reconversion to bottom hole flow pressure P_wf(t) dynamic fitting of measured pressure; when the control storage amount changes more than 2 sections, the processing mode is similar to the 2-stage condition.

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