CN115060875A - Method for determining hydrate reservoir production pressure interval based on Darcy's law - Google Patents
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Abstract
The invention belongs to the technical field of hydrate exploitation, and discloses a method for determining a hydrate reservoir production pressure interval based on Darcy's law, which comprises the following steps of firstly determining the temperature T of a reservoir; then determining the phase equilibrium pressure P of the hydrate reservoir according to the phase equilibrium condition of the hydrate 1 (ii) a The hydrate saturation S is then determined again h (ii) a Secondly, calculating the permeability K of the hydrate reservoir according to Darcy's law of coupling effective stress; then bringing the Darcy law into the process and solving the production pressure P o (ii) a Finally comparing the phase equilibrium pressure P of the hydrate reservoir 1 And the production pressure P o The size of (d); and finally, determining an optimal production pressure interval of the hydrate reservoir. The method has the advantages that the influence of effective stress on the exploitation process of the hydrate can be fully considered, the classic Darcy's law is corrected, the optimal production pressure interval of the hydrate reservoir is determined, and the hydrate is improved to the maximum extentGas recovery from the reservoir.
Description
Technical Field
The invention belongs to the technical field of hydrate exploitation, and relates to a method for determining a hydrate reservoir production pressure interval based on Darcy's law.
Background
The natural gas hydrate is the largest unknown energy bank which is not developed on the earth as a potential energy source in the future. Natural gas hydrates, also known as clathrate hydrates, are crystalline compounds composed of water and methane under certain conditions (low temperature, high pressure). According to the data of hydrate exploration technology, the natural gas hydrate is widely distributed in the natural world, and is mainly distributed in the slope zone of continents and islands, the rising part of the continental margin, and the deep water environment of polar continental frames and inland lakes. The natural gas hydrate has the characteristics of wide distribution, large resource quantity, shallow burial, high energy density, cleanness and the like. Under standard conditions, 1 unit volume of natural gas hydrate can be decomposed to produce 184 units volume of natural gas at most.
The principle of natural gas hydrate exploitation is that the phase equilibrium condition (low temperature and high pressure) of the hydrate is broken through external injection, and then the decomposed substances in the hydrate are obtained. Physical parameters such as salt ion concentration of a reservoir at a hydrate, sediment pore size and the like have certain influence on phase equilibrium conditions, a phase equilibrium expression of the reservoir of the hydrate is determined, and further the solution of the phase equilibrium pressure has important significance on hydrate exploitation. Confining pressure is an indispensable condition for researching hydrate generation and decompression decomposition characteristics in an in-situ state. Exploration data from in situ hydrate deposits indicate that there is a radial stress-confining pressure exerted on the hydrate layer in the in situ reservoir. The confining pressure is mainly related to the depth of water, the density and the thickness of the upper covering layer and the lower covering layer. At present, the exploitation method of the hydrate mainly comprises an injection heating method, a depressurization method, a chemical reagent injection method, a carbon dioxide replacement method and an exploitation method combining a plurality of methods.
The depressurization method is the most common extraction method, and is to reduce the pressure of an extraction well of a hydrate reservoir to be below phase balance so as to form pressure difference or cause great decomposition of the hydrate, if the set production pressure difference is too large, the damage of effective stress on the hydrate reservoir is caused so as to cause blockage of the reservoir, and if the set production pressure is too small, the flow rate of hydrate extraction is too small so as to cause low extraction benefit of the hydrate reservoir. The influence of permeability stress sensitivity on the productivity of the coal-bed gas well is disclosed by anybody and the like, and if the production pressure difference is small, although the influence of the stress sensitivity on the gas production efficiency of the coal-bed gas is not obvious, the gas production rate is low, and the formation energy is wasted due to overlarge production pressure difference. Based on this, it can be found that a reasonable production pressure is of great significance for the economy of reservoir production. However, research on relevant aspects such as production pressure of a hydrate reservoir and the like is lacked, and an optimal production pressure interval is determined based on coupling effective stress. Therefore, the optimal production pressure interval of the hydrate reservoir is determined based on Darcy's law of coupling effective stress.
Disclosure of Invention
The invention aims to provide a method for determining a production pressure interval of a hydrate reservoir based on Darcy's law.
The technical scheme of the invention is as follows:
a method for determining a hydrate reservoir production pressure interval based on Darcy's law is based on Darcy's law of fluid flow, and meanwhile, adverse effects of effective stress on hydrate production and fluid flow around the reservoir production process are considered, and a suitable hydrate reservoir production pressure interval is determined, so that on one hand, the stress-strain effect of the effective stress on the hydrate reservoir is reduced, on the other hand, the production pressure of the reservoir can be optimized to obtain the maximum flow, the positive control on the final hydrate reservoir production pressure interval is of specific main significance, and the maximum efficiency and economy of hydrate production are finally realized. The method comprises the following steps:
the method comprises the following steps: measuring basic physical conditions of the hydrate reservoir, including temperature T and pore pressure P of the hydrate reservoir i Confining pressure P u Absolute permeability K o Saturation of hydrate S h The length L of the seepage channel of the hydrate reservoir and the cross-sectional area A of the seepage channel of the hydrate reservoir;
step two: determining the phase equilibrium pressure condition of the hydrate reservoir, selecting the phase equilibrium calculation formula of the hydrate reservoir, and calculating the phase equilibrium pressure P of the hydrate reservoir according to the phase equilibrium condition of the hydrate 1 ；
Step three: establishing a Darcy's law of deformation, calculating the permeability K of the coupling effective stress hydrate reservoir, and establishing the Darcy's law of coupling effective stress;
step 3.1, determining the effective stress sigma
After the effective stress is applied to the hydrate reservoir, the flow of fluid in the reservoir is actually influenced; according to the principle of effective stress at confining pressure P u Under the action of (3), the effective stress sigma of the hydrate reservoir is as follows:
σ＝P u -(P i +P o )/2 (2)
in the formula: p u Is the confining pressure around the hydrate reservoir, P o Is the production pressure of a hydrate reservoir, P i The pore pressure of the hydrate reservoir is MPa;
and 3.2, directly influencing the flow of the fluid in the hydrate reservoir by the hydrate permeability. The actual reservoir environment of the hydrate is considered as comprehensive as possible, and particularly effective stress around the hydrate reservoir has certain guiding significance on the exploitation of the hydrate reservoir. Establishing the permeability K of the hydrate reservoir coupled with the effective stress, wherein the specific process is as follows:
K＝K o *σ -b (3)
in the formula: k o Is the absolute permeability of the hydrate reservoir,the unit is mD; sigma is the effective stress of the hydrate reservoir, and the unit is MPa; b is a fitted dimensionless parameter;
step 3.3, determining dimensionless parameter b of the hydrate reservoir
b＝aS h +b o (4)
In the formula: s. the h The hydrate saturation of the reservoir of the hydrate; a is a fitting parameter of the hydrate reservoir; b o Coefficient of deposit for the hydrate reservoir;
step 3.4 Darcy's law for establishing coupling effective stress
In the formula: p is atmospheric pressure, the unit is MPa, and the value is 0.1 MPa; q is the flow under the standard condition, and the unit is mL/s; l is the length of a seepage channel of the hydrate reservoir, and the unit is cm; u is a gas viscosity coefficient, and the unit is MPa.S; a is the cross-sectional area of the seepage passage of the hydrate reservoir, cm 2 ；
Step four: solving for the production pressure P of the hydrate reservoir o And determining its pore pressure P with the hydrate reservoir i Relative size of (a);
step 4.1, establishing flow Q and production pressure P o The relation between
The working conditions of the hydrate reservoir include temperature T and pore pressure P i Confining pressure P u Absolute permeability K o Length L of seepage channel, cross-sectional area A of seepage channel and hydrate saturation S h And performing constant processing, and further establishing the following relational expression:
Q＝f(P o ) (6)
step 4.2, mixing the flow Q with the production pressure P o Make a derivation
First derivative of
Step 4.3, solving the production pressure P of the hydrate reservoir o
Let the right side of the formula (7) be 0, bring the working condition of the reservoir of the hydrate into the formula (7), and further solve out P o ；
Step 4.4, comparing the pressure
Solving the production pressure P of the hydrate reservoir o Determining the pore pressure P between the hydrate reservoir and the reservoir i The calculated rationality and the accuracy of the values are further determined, and the production pressure P of the hydrate reservoir is obtained according to the actual exploitation process o Should be less than the pore pressure P of its reservoir i . If the production pressure P of the hydrate reservoir is obtained o Greater than the pore pressure P of its reservoir i And the calculation proceeds to step 3.3, and the coefficient b of the deposit of the hydrate reservoir is continuously adjusted o ；
Step five: determining an optimal hydrate reservoir production pressure interval P 1 -P o
The condition for exploiting the hydrate is to break the high-pressure and low-temperature environment in which the hydrate stably exists, and the production pressure P obtained under the actual working condition o Will certainly be less than the hydrate phase equilibrium pressure P of the reservoir 1 The obtained hydrate reservoir production pressure P o The pressure P of the hydrate phase equilibrium of the reservoir 1 Determining an optimal hydrate reservoir production pressure interval (P) of the hydrate reservoir 1 -P o )。
The invention has the beneficial effects that:
1. the effect of effective stress on permeability was first quantified. According to the method, a permeability K model of the coupling effective stress is established, so that the structure measured by the method is more fit with the actual reservoir of the hydrate and more accurate. The effect of the effective stress on the affiliated hydrate reservoir stratum is quantified, the practicability and the scientificity of the method operation are improved, and accurate calculation description is realized.
2. The method has wide application range of hydrate reservoirs and can accurately regulate and control parameters. The method can use various hydrate reservoir types, has wide applicable temperature and pressure range, and can accurately regulate and control the coefficient of the deposit of the hydrate reservoir according to the property and physical parameters of the deposit of the hydrate reservoir.
3. The method has the advantages of less related parameters, simple operation and high feasibility. The method can better guide the actual exploitation site of the hydrate, and maximally improve the economic benefit of hydrate exploitation.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not intended to limit the present invention in any way, and all simple modifications, equivalent variations and modifications made to the above embodiments according to the technical spirit of the present invention are within the scope of the present invention.
Drawings
FIG. 1 is a schematic illustration of hydrate reservoir production.
Figure 2 is a phase equilibrium diagram for hydrates.
Fig. 3 is a production pressure-flow diagram.
Fig. 4 is a production pressure versus effective stress diagram.
Fig. 5 is a production pressure interval diagram.
FIG. 6 is a flow chart of a method for determining a hydrate reservoir production pressure interval based on Darcy's law.
Note: FIGS. 1-5 show a working condition temperature T of 279.15K and a pore pressure P i Is 10MPa and confining pressure P u 18MPa, coefficient of deposit b o 0.1546, an experimental fitting parameter a of 2.6, and an absolute permeability K o 20mD, the length L of the seepage channel is 1000cm, and the cross-sectional area A of the seepage channel is 1000cm 2 And hydrate saturation S h The 35% operating condition is exemplified.
Detailed Description
The present invention will be described in detail with reference to the following embodiments.
One environment in which the present invention may be practiced is shown in FIG. 1 and includes sea level 1, upper overburden 2, hydrate reservoir 3, lower overburden 4, production wellbore 5, hydrates 6, sediments 7, pore gas 8, and pore water 9. The method for determining the optimal production pressure interval of the hydrate reservoir is shown in figures 2-6 and comprises the following implementation steps:
The fundamental physical conditions of a hydrate reservoir are the decisive parameters for determining the properties of the hydrate reservoir. Firstly, measuring the temperature T and the pore pressure P of a hydrate reservoir i Confining pressure P u Absolute permeability K o Saturation of hydrate S h Basic physical property conditions such as the length L of the seepage channel of the hydrate reservoir and the cross section area A of the seepage channel of the hydrate reservoir. Wherein in step 1, the working condition temperature T is 279.15K and the pore pressure P i Is 10MPa and confining pressure P u 18MPa, absolute permeability K o 20mD, the length L of the seepage channel is 1000cm, and the cross-sectional area A of the seepage channel is 1000cm 2 And hydrate saturation S h Is 35% for example.
Determining the phase equilibrium pressure of a hydrate reservoir is of great significance in setting the production pressure of the hydrate reservoir. When the pressure reduction method is adopted to exploit the hydrate, the production pressure must be lower than the phase equilibrium pressure of a hydrate reservoir stratum so that the hydrate is decomposed. Selecting a phase equilibrium calculation formula of the hydrate reservoir according to the basic physical property conditions of the hydrate reservoir measured in the step 1, and calculating the phase equilibrium pressure P of the hydrate reservoir according to the phase equilibrium conditions of the hydrate 1 . The phase equilibrium pressure P of the hydrate reservoir can be determined by searching the hydrate phase equilibrium graph of fig. 2 based on the temperature and other physical conditions of the hydrate reservoir determined in step 1 1 The pressure was 4.9 MPa.
Step 3.1 determining the effective stress σ
The surrounding of the hydrate reservoir has acting force of confining pressure on the hydrate reservoir, the confining pressure acts on the hydrate reservoir, the reservoir is inevitably deformed, and further fluid seepage channels in the hydrate reservoir are adversely affected. Pore pressure is generated by a large amount of pore gas in the hydrate reservoir. Effective stress is generated under the interaction of confining pressure and pore pressureThe effective stress is the actual force of the confining pressure on the hydrate reservoir. Therefore, the concrete quantification of the effective stress on the hydrate reservoir has an important role in analyzing the seepage behavior of the fluid. According to the principle of effective stress at a confining pressure P u Under the action of (3), the effective stress sigma of the hydrate reservoir is as follows:
σ＝P u -(P i +P o )/2 (1)
in the formula: p u To confining pressure, P o To production pressure, P i The pore pressure is in MPa.
Determining the pore pressure P of the hydrate reservoir according to the measurement in the step 1 i Is 10MPa and confining pressure P u Is 18MPa, i.e. an effective stress sigma of (13-P) obtained according to formula (1) o And/2) MPa. Set different production pressures P o Wherein the specific effective stress versus production pressure relationship is shown in figure 4.
Step 3.2 establishing permeability K of hydrate reservoir coupled with effective stress
The effective stress around the hydrate reservoir firstly influences the deformation of the hydrate reservoir, further influences the seepage behavior of fluid in the hydrate reservoir, and the establishment of the dynamic permeability of the hydrate containing the effective stress has significance for actually guiding the optimized production and exploitation of the hydrate. By combining the physical property and seepage characteristic of the hydrate reservoir, the dynamic permeability K of the hydrate under the effective stress is coupled.
K＝K o *σ -b (2)
In the formula: k is the permeability K of the hydrate reservoir coupled with the effective stress, and the unit is mD;
K o absolute permeability of the hydrate reservoir in mD;
sigma is the effective stress of the hydrate reservoir, MPa;
b is dimensionless parameters of experimental fitting;
the absolute permeability K of the hydrate reservoir measured according to the step 1 o To 20mD, step 3.1 determines the different production pressuresEffective stress σ, where the dimensionless parameter b of the experimental fit needs to be determined according to step 3.3.
Step 3.3 determining dimensionless parameter b of the reservoir to which it belongs
Hydrates are ice-like crystals, with impermeability. The flow of the fluid in the hydrate reservoir is adversely affected due to the impermeability characteristic of the hydrate, and the saturation of the hydrate reservoir is specifically quantified, so that the method has important significance in establishing the permeability which is closer to the actual hydrate reservoir.
b＝aS h +b o (3)
In the formula: s h The hydrate saturation of the reservoir of the hydrate;
a is an experiment fitting parameter;
b o is the coefficient of the deposit of the hydrate reservoir.
Determining the hydrate saturation S of the determined hydrate reservoir according to step 1 h At 35%, establishing parameters between the reservoir hydrate saturation (determining the reservoir hydrate saturation at 35% and 0%) and dimensionless parameter b under different saturations, and establishing a fitting curve equation for the determined points to obtain the coefficient b of the deposit of the reservoir of the hydrate o To 0.1546, the parameter a of the experimental fitting 1 Is 2.6.
Step 3.4 Darcy's law for establishing coupling effective stress
The seepage behavior of the hydrate reservoir accords with Darcy's law, and the Darcy's law of coupling effective stress can be obtained by substituting the established permeability K into the Darcy's law of the hydrate reservoir
In the formula: p is atmospheric pressure, the unit is MPa, and the value is 0.1 MPa;
q is the flow under the standard condition (STP) and the unit is mL/s;
l is the length of a seepage channel of the hydrate reservoir, and the unit is cm;
u is a gas viscosity coefficient, and the unit is MPa.S;
a is the cross-sectional area of the seepage passage of the hydrate reservoir, cm 2 ；
The remaining parameter names can refer to steps 3.3, 3.2 and 3.1.
The experimental parameters and physical property condition parameters measured in the above steps are substituted into the formula (4), so that a production pressure-flow diagram under different production pressures can be obtained, and particularly, as shown in fig. 3, a non-positive correlation linear relation between the production pressure and the flow can be obviously found. But rather there is a certain extreme point.
Step 4.1 establish flow Q and production pressure P o The relation between
And (4) establishing a relational expression of the flow Q of the hydrate reservoir and the working condition of the hydrate reservoir according to the formula (4). The working conditions (temperature T, pore pressure P) of the hydrate reservoir are measured i Confining pressure P u Absolute permeability K o Length L of seepage channel, cross-sectional area A of seepage channel and hydrate saturation S h ) Performing constant processing, and further establishing the following functional relation:
Q＝f(P o ) (5)
step 4.2 relating the flow Q to the production pressure P o Make a derivation
According to flow Q and production pressure P o The functional relationship between the two is obviously found to be that an extreme point (the production pressure P) necessarily exists o ) And the flow Q of the hydrate reservoir stratum is maximized. To determine the flow under effective stress and the production pressure P o The first derivative derivation is performed on the formula (4), and the specific result is as follows:
step 4.3 of solving the production pressure P of the hydrate reservoir o
Let the right side of the formula (6) be 0, bring the working condition of the reservoir of the hydrate into the formula (6), and furtherCan solve out P o . The calculated production pressure P under the determined operating conditions o Is 1.93 MPa.
Step 4.4 size of contrast pressure
Solving the production pressure P of the hydrate reservoir o Determining the pore pressure P between the hydrate reservoir and the reservoir i The calculated reasonableness and the accuracy of the values are determined, and according to the actual exploitation process, the production pressure P of the hydrate reservoir is obtained o Should be less than the pore pressure P of its reservoir i . If the production pressure P of the hydrate reservoir is obtained o Greater than the pore pressure P of its reservoir i And the calculation proceeds to step 3.3, and the coefficient b of the deposit of the hydrate reservoir is continuously adjusted o And the like.
The determined production pressure P of the hydrate reservoir determined in step 4.3 o 1.93MPa, the phase equilibrium pressure of the determined hydrate reservoir is 4.9MPa, the value range of the pressure is met, and the production pressure is met, namely the optimal production pressure P solved under the determined working condition o Is 1.93 MPa.
Step 5.1 determining the optimal hydrate reservoir production pressure interval
The condition for exploiting the hydrate is to break the high-pressure and low-temperature environment in which the hydrate stably exists, and the production pressure P obtained under the actual working condition o Will be less than the hydrate phase equilibrium pressure P of the reservoir 1 The obtained hydrate reservoir production pressure P o The pressure P of the hydrate phase equilibrium of the reservoir 1 Determining an optimal hydrate reservoir production pressure interval (P) of the hydrate reservoir 1 -P o )。
Optimum production pressure P solved under the conditions determined in step 4.4 o The pressure is 1.93MPa, the phase equilibrium pressure of the determined hydrate reservoir is 4.9MPa, namely the optimal production pressure interval of the hydrate reservoir is 1.93-4.9MPa, and the specific result is shown in FIG. 5. In the determined optimal production pressure interval of the hydrate reservoir, the positive phase between the flow and the production pressure can be obviously foundThe relation is concerned, and in the non-optimal production pressure interval of the hydrate reservoir, the relation of negative correlation between the flow rate and the production pressure can be obviously found.
Claims (4)
1. A method for determining a hydrate reservoir production pressure interval based on Darcy's law is characterized by comprising the following steps of:
the method comprises the following steps: measuring basic physical conditions of the hydrate reservoir, including temperature T and pore pressure P of the hydrate reservoir i Confining pressure P u Absolute permeability K o Saturation of hydrate S h The length L of the seepage channel of the hydrate reservoir and the cross-sectional area A of the seepage channel of the hydrate reservoir;
step two: determining the phase equilibrium pressure condition of the hydrate reservoir, selecting the phase equilibrium calculation formula of the hydrate reservoir, and calculating the phase equilibrium pressure P of the hydrate reservoir according to the phase equilibrium condition of the hydrate 1 ；
Step three: establishing a Darcy law of deformation, calculating the permeability K of the coupling effective stress hydrate reservoir, and establishing the Darcy law of coupling effective stress;
step four: solving for the production pressure P of the hydrate reservoir o And determining its pore pressure P with the hydrate reservoir i The relative size of (d);
step five: determining an optimal hydrate reservoir production pressure interval P 1 -P o 。
2. The determination method according to claim 1, wherein the specific steps of step three are as follows:
step 3.1, determining the effective stress σ
After the effective stress is applied to the hydrate reservoir, the flow of fluid in the reservoir is actually influenced; according to the principle of effective stress at a confining pressure P u Under the action of (3), the effective stress sigma of the hydrate reservoir is as follows:
σ＝P u -(P i +P o )/2 (2)
in the formula: p u Is the confining pressure around the hydrate reservoir, P o Is the production pressure of a hydrate reservoir, P i The pore pressure of the hydrate reservoir is MPa;
3.2, the hydrate permeability is an important parameter which directly influences the flow of the fluid in the hydrate reservoir; establishing the permeability K of the hydrate reservoir coupled with the effective stress, wherein the specific process is as follows:
K＝K o *σ -b (3)
in the formula: k o Absolute permeability of the hydrate reservoir in mD; sigma is the effective stress of the hydrate reservoir, and the unit is MPa; b is a fitted dimensionless parameter;
step 3.3, determining dimensionless parameter b of the hydrate reservoir
b＝aS h +b o (4)
In the formula: s h The hydrate saturation of the reservoir of the hydrate; a is a fitting parameter of the hydrate reservoir; b is a mixture of o Coefficient of deposit for the hydrate reservoir;
step 3.4 Darcy's law for establishing coupling effective stress
In the formula: p is atmospheric pressure, the unit is MPa, and the value is 0.1 MPa; q is the flow under the standard condition, and the unit is mL/s; l is the length of a seepage channel of the hydrate reservoir, and the unit is cm; u is a gas viscosity coefficient, and the unit is MPa.S; a is the cross-sectional area of the seepage passage of the hydrate reservoir, cm 2 。
3. The determination method according to claim 2, wherein the specific steps of step four are as follows:
step 4.1, establishing flow Q and production pressure P o The relation between
Will be describedThe working conditions of the hydrate reservoir comprise temperature T and pore pressure P i Confining pressure P u Absolute permeability K o Length L of seepage channel, cross-sectional area A of seepage channel and hydrate saturation S h And performing constant processing, and further establishing the following relational expression:
Q＝f(P o ) (6)
step 4.2, mixing the flow Q with the production pressure P o Make a derivation
First derivative of
Step 4.3, solving the production pressure P of the hydrate reservoir o
The right side of the formula (7) is set to be 0, the working condition of the reservoir of the hydrate is brought into the formula (7), and then P is solved o ；
Step 4.4, comparing the pressure
Solving the production pressure P of the hydrate reservoir o Determining the pore pressure P between the hydrate reservoir and the reservoir i The calculated rationality and the accuracy of the values are further determined, and the production pressure P of the hydrate reservoir is obtained according to the actual exploitation process o Should be less than the pore pressure P of its reservoir i (ii) a If the production pressure P of the hydrate reservoir is obtained o Greater than pore pressure P of its reservoir i And the calculation proceeds to step 3.3, and the coefficient b of the deposit of the hydrate reservoir is continuously adjusted o 。
4. The method of claim 1, wherein step five comprises determining an optimal hydrate reservoir production pressure interval P 1 -P o The method comprises the following specific steps:
the conditions for exploiting the hydrate are breaking the high-pressure and low-temperature environment where the hydrate stably exists, and the production pressure P obtained under the actual working condition o Will certainly be less than the hydrate phase equilibrium pressure P of the reservoir 1 The obtained hydrate reservoir production pressure P o The pressure P of the hydrate phase equilibrium of the reservoir 1 Determining an optimal hydrate reservoir production pressure interval (P) of the hydrate reservoir 1 -P o )。
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