CN110132818B - Method and system for obtaining permeability of sediments containing natural gas hydrate - Google Patents

Abstract

The invention discloses a method and a system for obtaining the permeability of sediments containing natural gas hydrates. The system comprises: a pore network model building module; a pore-filling hydrate model addition module; a permeability conduction equation establishing module; a permeability calculation module; the method can be made by secondary development on the basis of an open source computing tool OpenPNM of a pore network model. The invention can calculate the permeability when the pore network model contains the hydrate and the hydrate does not completely block the pore throat, provides the selection of the positions of various hydrates and solves the problem that the permeability of the deposit containing the hydrate changes along with the change of the saturation of the hydrate.

Description

A method and system for obtaining permeability of natural gas hydrate-bearing sediments

technical field

The invention belongs to the technical field of accumulation and development of hydrate reservoirs, relates to a method for obtaining the permeability of hydrate sediments, and in particular relates to a method and system for obtaining the permeability of gas hydrate-bearing sediments based on a pore network model numerical simulation algorithm .

Background technique

Natural gas hydrates are a class of clathrate compounds formed by water molecules connected by hydrogen bonds to envelop small gas molecules [Sloan E D, Koh C A. Clathrate hydrates of natural gas[M].Third Edition ed.BocaRaton:CRC Press,2007] , when the gas component is methane-based natural gas, it is also called "flammable ice" because it is flammable. Because of its large reserves, it is a promising energy source, so in the past few decades, major energy consuming countries have invested heavily in hydrate exploration and development technology research [Li J F, Ye J L, Qin X W, et al. al.The first offshorenatural gas hydrate production test in South China Sea[J].China Geology,2018,1(1):5–16.], during development, physical properties of hydrate sediments, including permeability, porosity Degree, saturation, is a prerequisite for establishing an appropriate production strategy [Waite WF, Santamarina J C, Cortes D D, et al.Physical properties of hydrate-bearing sediments[J].Reviews of Geophysics,2009,47(4):465–84 .]. Among the above properties, the permeability of sediment cores from methane hydrate deposits in the eastern nankai trough is a key parameter for studying water and gas behavior during production [Konno Y, Yoneda J, Egawa K, et al. [J]. Marine and Petroleum Geology, 2015, 66: 487–95.].

When hydrates are formed in sediment pores, they occupy the space of pores and throats, reducing the permeability of sediments; when hydrates are decomposed, the pore space is released to increase the permeability of sediments. Therefore, the permeability of hydrate-bearing reservoirs will change with the hydrate saturation (the ratio of the hydrate volume in the sediment pores to the total sediment pore volume). Accurately predicting the permeability change of the hydrate-bearing sediments is the key to the successful development of hydrates. key factor. Since it is difficult to carry out laboratory experiments under the condition of hydrate thermodynamic stability, numerical simulation is a more feasible method to study the effect of hydrate formation and decomposition on sediment permeability.

In the prior art, the pores described in the literature [1] (Blunt M J. Flow in porous media–pore-network models and multiphase flow [J]. Current Opinion in Colloid & Interface Science, 2001, 6(3): 197–207.) The Pore Network Model (PNM) is a mature method for simulating the permeability of multiphase flow in porous media, and it is also widely used in the numerical simulation of hydrate saturation and permeability properties. Seol Y. Water permeability in hydrate-bearing sediments: A pore-scale study [J]. Geophysical Research Letters, 2014, 41(12): 4176–84.), literature [3] (Jang J, Santamarina J C. Recoverable gas from hydrate-bearing sediments:Pore networkmodel simulation and macroscale analyses[J].Journal of Geophysical Research:Solid Earth,2011,116(B8)), literature[4](Mahabadi N,Jang J.Relative water and gaspermeability for gas production from hydrate-bearing sediments[J].Geochemistry,Geophysics,Geosystems,2014,15(6):2346–53.), literature[5](Mahabadi N,Dai S,Seol Y,et al.The water retention curve and Relative permeability forgas production from hydrate-bearing sediments: Pore–network model simulation [J]. Geochemistry, Geophysics, Geosystems, 2016, 17(8): 3099–110.) have documented the related applications of pore network models. At present, in the numerical simulation study of the relationship between hydrate saturation and permeability using PNM, it is assumed that once the hydrate is formed, the pore will be completely blocked (the pores only have two states of being completely free of hydrate and completely blocked by hydrate). The increased saturation is simulated by increasing the number of blocked pores. However, the actual process of hydrate growth in the pores is a gradual process (the hydrate gradually plugs the pores), and the existing methods are difficult to reflect this gradual process in the simulation process, and it is difficult to accurately describe the synthesis and decomposition of hydrates in the pores. Therefore, the existing technology applied to the numerical simulation of hydrate saturation and permeability has low accuracy, and it is difficult to solve the problem that the permeability of hydrate-containing sediments changes with the change of hydrate saturation.

SUMMARY OF THE INVENTION

In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a method and system for obtaining the permeability of natural gas hydrate-containing sediments. By adding a pore-filling hydrate model to the calculation method of the pore network model, and giving the hydrated pores of the pores According to the permeability conduction equation under gas filling, the permeability of natural gas hydrates can be calculated to solve the problem that the permeability of hydrate-containing sediments changes with the change of hydrate saturation.

For the convenience of explanation, this article agrees:

Hydrate saturation: the ratio of hydrate volume in sediment pores to the total volume of sediment pores, dimensionless.

Hydrate: Abbreviation for natural gas hydrate. It is a type of clathrate compound formed by water molecules connecting and enveloping small gas molecules by hydrogen bonds. When the gas component is natural gas mainly composed of methane, it is also called "flammable ice" because of its flammability.

Pore space: The non-solid portion of a sediment.

Pore: The larger independent space in the pore space.

Throat: A narrow section of pore space that connects two pores.

Node: The geometric center point of the pore.

Conduit: the connecting part between two adjacent nodes of a pore, including: a half-pore at the left node, a throat between two nodes, and a half-pore at the right node.

The steps of calculating sediment permeability by pore network model method (PNM) are as follows:

1. Establish a geometric model of the pore network.

2. Calculate the permeability conductivity of pores and throats in the network model.

3. The volume of all nodes of the network model is conserved.

4. Assign value to import and export pressure.

5. Calculate the pressure at each node.

6. Calculate the inlet flow and outlet flow.

7. Apply Darcy's law to calculate permeability.

Based on the pore network model method, the invention adds a pore hydrate model to the pore network geometric model, and provides a calculation method for the permeability and conductivity of the pores and throats in the pore network model under the condition of hydrate, so as to make the Pore network model method is suitable for permeability calculation of hydrate-bearing sediments. In the implementation process of the present invention, the pore network model method adopts the open source calculation tool of pore network model—OpenPNM as the bottom layer, and performs secondary development on the basis.

The technical scheme provided by the present invention is as follows:

(1) A method for obtaining the permeability of gas hydrate-containing sediments. In the state where the pores of the sediment are filled with gas hydrates, the pore-filling hydration type is added to the pore-throat space of the pore network model that has been established and completed. The gas hydrate-bearing pore network model is obtained by calculating the permeability of the gas hydrate-containing pore network model, and the permeability conduction equation is established in this state. The following steps are included:

A. Establish a pore network model, and add a pore-filled hydrate model to the pore throat space of the pore network model;

The nodes in the established pore network model represent the center points of pores in the sediment; the conduits in the pore network geometric model represent the connection between two adjacent pore center points in the sediment. The conduit includes: a left node half-pore in two adjacent pore nodes, a throat between the two nodes, and a right node half-pore.

In specific implementation, adding a pore-filled hydrate model to the pore-throat space of the pore network model is to add the pore-hydrate geometric feature representation array parameters in the geometry class in OpenPNM, including:

A1. The added pore hydrate geometric characteristic characterization array parameters include: the diameter array h _i of the hydrate generated in the center of the pore, the thickness array h _p of the hydrate generated on the pore surface, and the thickness array h _t of the hydrate generated on the throat surface;

A2. Set the pore diameter array in the pore network model as D, the throat length array as L, and the throat diameter array as T. When the hydrate grows on the surface of the pore, the pore diameter array is: Dh _p , and when the hydrate grows on the throat surface, the throat diameter is recorded as the array Th _t .

B. Derive the permeability conduction equation of the hydrate-containing conduit, and calculate the inter-conduit permeability of the gas hydrate-containing pore network model;

In the specific implementation, in the calculation class in OpenPNM, the calculation method of inter-node permeability when the pores contain hydrates is added, including the following operations:

B1. For the hydrates generated in the center of the pores, the internode conduits are divided into 5 segments (numbered ④～⑧ in Fig. 2b). By simplifying the geometry of the conduits (as shown in Fig. 2d), each conduit The morphology becomes a shape that simplifies the calculation of permeability. Among them, the sections numbered ⑤～⑦ in the figure are cylindrical, and the sections ④ and _⑧ are ring-shaped.

where D is the outer diameter of the annular section (pore diameter), hi is the inner diameter of the annular section (hydrate diameter), L is the length of the section (=0.5h _{i )} , and μ is the pore fluid viscosity.

The formula for calculating the permeability (g _c ) of the cylindrical section is as shown in Equation 2:

The permeability (g) of the entire conduit is expressed as Equation 3 according to the Hagen-Poiseuille equation:

Among them, g _zone1 to g _zone5 represent the 5 segments into which the conduit between nodes is divided;

B2. For the hydrates generated on the surface of pores and throats, the inter-node conduits are divided into three sections (①～③ in Figure 2a). By simplifying the shape of the conduits (Figure 2c), the three sections of conduits are all simplified into cylinders shape (①～③ in Fig. 2c). The permeability formula of the cylindrical section has been given by Equation 2. It is only necessary to replace the diameter D in Equation 2 with: Dh _p (①, ③ in Fig. 2c) and Th _t (② in Fig. 2c) for calculation to obtain the conduit interpenetration;

C. Calculate the permeability of the sample using the pore network model method.

It is assumed that the fluid flow in the conduit between nodes is laminar. The fluid seepage flow Qij in the throat has the following form:

Among them, p is the pressure of the fluid, rij and lij are the radius and length of the throat, respectively, μ is the viscosity coefficient of the fluid, and gij is the backflow rate of the throat.

Assuming that the fluid in the formation pores is incompressible, for a single pore, the sum of the flow rates of all the throats connected to it should be zero, namely:

∑Q _ij =0 (Equation 5)

From this, a linear equation system with the pressure as the unknown can be obtained, and the pressure distribution of the formation pores can be obtained after the solution. Finally, the inlet flow and outlet flow of the formation are calculated, and Darcy's law is used to solve the absolute permeability of the formation.

Through the above steps, the permeability of natural gas hydrate-containing hydrate is calculated.

In specific implementation, the above calculation process can execute the calculation method provided by the tool OpenPNM, and then the permeability of natural gas hydrates can be obtained.

(2) A device for obtaining the permeability of natural gas hydrate-containing sediments, comprising a memory and a processor; the memory is used to store a computer program; the processor is used to implement the above-mentioned computer program when executing the computer program Methods for obtaining permeability of gas hydrate-bearing sediments.

(3) A computer-readable storage medium, where a computer program is stored on the storage medium, and when the computer program is executed by a processor, the above-mentioned method for obtaining the permeability of a gas hydrate-containing sediment is realized.

(4) A system for acquiring the permeability of natural gas hydrate-bearing sediments, characterized in that the system is developed on the basis of the open source computing tool OpenPNM for pore network model; it includes the following modules:

The pore network model building module is used to establish the pore network model of sediments;

Pore-filled hydrate model add-on module, used to add a pore-filled hydrate model to the pore throat space of the pore network model;

a permeability conduction equation establishment module, the permeability includes the permeability of the annular columnar annular section and the permeability of the cylindrical section;

The permeability calculation module of the gas hydrate-containing pore network model is used to calculate the permeability of the gas hydrate-containing pore network model by using the inter-node permeability calculation method when the pores contain hydrate.

Beneficial effects of the present invention:

The invention provides a method for obtaining the permeability of natural gas hydrate-containing sediments. By adding a pore-filled hydrate model to the calculation method of the pore network model, and giving the permeability conduction equation in this state, the natural gas hydrate can be calculated. permeability of the substance. The present invention adopts the improved pore network model and simplified formula for the first time to realize the continuous simulation of hydrate permeability. Using the solution provided by the present invention, the permeability of the pore network model containing hydrate and the hydrate does not completely block the pore throat can be calculated, and a variety of hydrate location options are provided to solve the problem of hydrate-containing sediment permeation. rate changes with hydrate saturation.

Description of drawings

Figure 1 shows the custom hydrate geometric parameters added to the geometry class in OpenPNM by the present invention; including: the diameter array hi of the hydrate generated in the center of the pore; hp is the thickness array of the hydrate generated on the pore surface; ht is the hydrate generated Array of thicknesses on the throat surface.

Fig. 2 is the calculation model of the conduit between nodes established by the present invention;

Among them, (a) is the inter-node conduit model when the hydrate grows on the pore surface; (b) is the inter-node conduit model when the hydrate grows in the center of the pore; (c) The inter-node conduit model when the hydrate grows on the pore surface Simplified calculation model of permeability; (d) Calculation model of conduit permeability between nodes when hydrate grows in the center of the pore; ①～③ represent the left node semi-porous section and node of conduit 3 segment when hydrate grows on the pore surface, respectively The inter-nodal throat segment and the right-node semi-porous segment, ④～⑧ respectively represent the left-nodal ring cylindrical segment, left-nodal cylindrical segment, and inter-nodal throat segment in the 5 segment of the inter-nodal conduit when the hydrate grows in the center of the pore , right node cylindrical segment, right node ring cylindrical segment.

FIG. 3 is a flow chart of the implementation of the method of the present invention.

Detailed ways

Below in conjunction with the accompanying drawings, the present invention is further described by means of embodiments, but the scope of the present invention is not limited in any way.

The invention provides a method and system for obtaining the permeability of natural gas hydrate-containing sediments. By adding a pore-filled hydrate model to the calculation method of the pore network model, and giving the permeability conduction equation in this state, the calculation method of Permeability of natural gas hydrates.

Fig. 2 is the calculation model of the conduit between nodes established by the present invention; wherein, (a) is the conduit model between nodes when hydrates grow on the surface of pores; (b) is conduit model between nodes when hydrates grow in the center of pores; ( c) Simplified calculation model of inter-node conduit permeability when hydrates grow on the pore surface; (d) Calculation model of inter-node conduit permeability when hydrates grow in the center of pores; ①～③ represent when hydrates grow on the pore surface, respectively The left-node semi-porous section, the inter-node throat section, and the right-node semi-porous section in the conduit 3 segment, ④～⑧ respectively represent the left nodal ring column in the inter-node conduit 5 segment when the hydrate grows in the center of the pore. Segment, Left Node Cylindrical Segment, Internode Throat Segment, Right Node Cylindrical Segment, Right Node Ring Cylindrical Segment.

Figure 3 shows the implementation flow of the method of the present invention, comprising the following steps:

A. In the geometry class in OpenPNM, an open source computing tool for pore network models, add a pore hydrate geometric feature representation array, including:

A1. The diameter array hi generated by adding hydrate in the center of the pore, the thickness array h _p generated by adding hydrate on the pore surface _{, and the thickness array h t generated} by adding hydrate on the throat surface;

A2. Set the pore diameter array in the pore network model as D, the throat length array as L, and the throat diameter array as T. When the hydrate grows on the surface of the pore, the pore diameter array is: Dh _p , and when the hydrate grows on the throat surface, the throat diameter is recorded as the array Th _t .

B. In the calculation class in OpenPNM, an open source calculation tool for the pore network model, the calculation method of inter-node permeability when the pores contain hydrates is added:

B1. For hydrates generated in the center of pores, the internode conduit is divided into 5 segments (see Figure 2),

As shown in b in Figure 2, the sections numbered ⑤ to ⑦ in the figure are cylindrical, and the sections ④ and ⑧ are annular columns. The formula for calculating the permeability (permeability, g _loop ) of the annular section of the annular column is:

where D is the outer diameter of the annular section, d is the inner diameter of the annular section, L is the length of the section, and μ is the pore fluid viscosity.

The formula for calculating the permeability (g _c ) of the cylindrical section is as shown in Equation 2:

The permeability (g) of the entire conduit is expressed as Equation 3 according to the Hagen-Poiseuille equation:

B2. For the hydrates generated on the surface of pores and throats, replace the pore diameter and throat diameter with Dh _p and Th _t in the calculation formula of inter-conduit permeability, and execute according to the calculation method of the tool OpenPNM. The main calculation method is;

It is assumed that the fluid flow in the conduit between nodes is laminar. The fluid seepage flow Qij in the throat has the following form:

Among them, p is the pressure of the fluid, rij and lij are the radius and length of the throat, respectively, μ is the viscosity coefficient of the fluid, and gij is the backflow rate of the throat.

Assuming that the fluid in the formation pores is incompressible, for a single pore, the sum of the flow rates of all the throats connected to it should be zero, namely:

∑Q _ij =0 (Equation 5)

From this, a linear equation system with the pressure as the unknown can be obtained, and the pressure distribution of the formation pores can be obtained after the solution. Finally, the inlet flow and outlet flow of the formation are calculated, and Darcy's law is used to solve the absolute permeability of the formation. Through the above steps, the permeability of natural gas hydrate-containing hydrate is calculated.

The following embodiment specifically describes the implementation of the method of the present invention by taking the generation of a pore network of a cubic grid with a scale of 100×100×100 in three directions under Cartesian coordinates as an example. The pore node interval is set to 0.63mm, the pore diameter (D) distribution is normal distribution, the distribution median is 0.42mm, and the standard deviation is 0.1mm, and the diameters of all 1,000,000 pores are generated by a random algorithm. The throat diameter is 0.7 times the diameter of the adjacent smaller pores. The geometric features of the above pore network model are recorded in the form of a dictionary.

Enter the hydrate model, here it is assumed that the hydrate is generated at the center of the pore, and the number of hydrate growth steps is set to 10 steps, then the hydrate diameter in each step is [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 ,0.9]×D (pore diameter).

Calculate the permeability of the hydrate-containing pore network model. When using OpenPNM to calculate the permeability, call the inter-node conduit permeability calculation model in step B. Substitute [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] × D (pore diameter) as the hydrate diameter into the calculation in turn to obtain the permeability under different hydrate sizes, and then the following formula Obtain the hydrate saturation _Sh :

In the formula, ΣV _hydrate is the volume sum of all hydrates, and ΣV _pore is the volume sum of all pore spaces.

It should be noted that the purpose of publishing the embodiments is to help further understanding of the present invention, but those skilled in the art can understand that various replacements and modifications are possible without departing from the spirit and scope of the present invention and the appended claims of. Therefore, the present invention should not be limited to the contents disclosed in the embodiments, and the scope of protection of the present invention shall be subject to the scope defined by the claims.

Claims (4)

1. A method for obtaining the permeability of the sediments containing the natural gas hydrate comprises the steps of establishing a pore network model under the condition that the pores of the sediments are filled with the natural gas hydrate, adding a pore filling type hydrate model into the pore throat space of the pore network model, establishing a permeability conduction equation under the condition, and calculating to obtain the permeability of the pore network model containing the natural gas hydrate;

the method comprises the following steps:

A. establishing a pore network model, and adding a pore filling type hydrate model into a pore throat space of the pore network model; the method comprises the following steps:

A1. the nodes in the established pore network model represent the central points of pores in the sediment; the conduit in the pore network model represents a communication part between the central points of two adjacent pores in the sediment; the catheter comprises: a left node half-pore, a throat between two nodes and a right node half-pore in two adjacent pore nodes;

A2. adding a pore filling type hydrate model in a pore throat space of the pore network model, namely adding geometric characteristic characterization array parameters of the pore hydrate into a geometric class of the model;

A21. the geometric characteristic characterization array parameters of the added pore hydrate comprise: diameter array h of hydrate generated in pore center_iThe thickness array h of the hydrate generated on the surface of the pore_pThickness array h of hydrate generated on surface of throat_t；

A22. Setting the pore diameter array in the pore network model as D, the throat length array as L and the throat diameter array as T, and when hydrate grows on the pore surface, setting the pore diameter array as D-h_p(ii) a When the hydrate grows on the surface of the throat, the diameter of the throat is recorded as an array T-h_t；

B. Establishing a permeability conduction equation, and calculating the permeability of a pore network model containing the natural gas hydrate by adopting a calculation method of the permeability between nodes under the condition that the pores contain the hydrate; the following operations are performed:

B1. for the hydrate generated in the center of the pore, dividing the conduit between the nodes into 5 sections, including a cylindrical shape and an annular column shape;

by permeability g_loopThe permeability of a ring-shaped section having a ring-column shape is represented and calculated by formula 1:

in the formula 1, D is the outer diameter of the annular section, namely the diameter of a pore; h is_iThe inner diameter of the annular section is the diameter of the hydrate, L is the length of the section, mu is the viscosity of the pore fluid;

by permeability g_cRepresents the cylindrical section permeability, calculated by equation 2:

the permeability g of the internodal catheter is expressed as formula 3:

wherein, g_zone1～g_zone55 segments into which the inter-node conduit is divided;

B2. for the hydrate generated on the surfaces of the pore and the throat, the diameter of the pore and the diameter of the throat are respectively taken as D-h_pAnd T-h_tThen calculating to obtain the permeability between the catheters;

assuming that the fluid flow state in the conduit between the nodes is laminar flow; the fluid seepage flow Qij in the throat is expressed by equation 4:

wherein p is the pressure of the fluid; rij and lij are the radius and length of the throat, respectively; μ is the viscosity coefficient of the fluid; gij is the throat inverse flow rate;

assuming that the fluid in the formation pores is incompressible, for a single pore, the sum of the flow rates of all throats communicating with it should be zero, expressed as equation 5:

∑Q_ijeither case 0 (formula 5)

Thereby obtaining a linear equation system with the pressure as an unknown number; solving to obtain the pressure distribution of the formation pores;

calculating the inlet flow and the outlet flow of the stratum, and solving the absolute permeability of the stratum by applying Darcy's law;

and obtaining the permeability of the sediments containing the natural gas hydrate through the steps.

2. The device for acquiring the permeability of the sediments containing the natural gas hydrate comprises a memory and a processor;

the memory for storing a computer program;

the processor, when executing the computer program, is configured to implement the method for obtaining permeability of a gas hydrate-containing deposit according to claim 1.

3. A computer-readable storage medium, characterized in that the storage medium has stored thereon a computer program which, when being executed by a processor, carries out the method for obtaining natural gas hydrate-containing deposit permeability according to claim 1.

4. The system is characterized in that the system is developed for the second time on the basis of a pore network model open source computing tool OpenPNM; the system comprises the following modules:

the pore network model establishing module is used for establishing a pore network model of the sediment;

the pore filling type hydrate model adding module is used for adding a pore filling type hydrate model in the pore throat space of the pore network model;

a permeability conduction equation establishing module, wherein the permeability comprises the permeability of an annular section of an annular column shape and the permeability of a cylindrical section;

and the permeability calculation module is used for calculating the permeability of the natural gas hydrate-containing pore network model by using a calculation method for the permeability between nodes under the condition that the pores contain hydrates.

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