CN107165619B - A kind of method for numerical simulation considering dynamic capillary force - Google Patents
A kind of method for numerical simulation considering dynamic capillary force Download PDFInfo
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- CN107165619B CN107165619B CN201710554578.5A CN201710554578A CN107165619B CN 107165619 B CN107165619 B CN 107165619B CN 201710554578 A CN201710554578 A CN 201710554578A CN 107165619 B CN107165619 B CN 107165619B
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B47/00—Survey of boreholes or wells
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B47/00—Survey of boreholes or wells
- E21B47/06—Measuring temperature or pressure
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
Abstract
The invention discloses a kind of method for numerical simulation for considering dynamic capillary force, comprising: multiple measuring points are arranged to rock core, obtain the dynamic capillary pressure curve under each measuring point under different displacement velocities by dynamic hollow billet force test method；It is derived by the functional relation between dynamic capillary force and water saturation, flow velocity using permeation fluid mechanics method, is fitted using the dynamic capillary pressure curve that this functional relation obtains experiment test, obtains the undetermined coefficient in functional relation；Difference is carried out to basic oily phase equation and basic water phase equation according to functional relation, obtain the difference discrete equation of oily phase equation, and obtain the difference discrete equation relevant to dynamic capillary force of water phase equation, the difference discrete equation relevant to dynamic capillary force of difference discrete equation and water phase equation to oily phase equation carries out fully implicit solution iterative solution, the coefficient matrix linearized.The present invention solves the problems, such as that the coefficient matrix of linearisation can not be obtained in the prior art.
Description
Technical field
The present invention relates to Research Numerical Simulation Techique application field more particularly to a kind of Numerical-Modes for considering dynamic capillary force
Quasi- method.
Background technique
Capillary force is the abbreviation of capillary pressure, refer to two kinds of meniscus two sides fluid in capillary (non-wet phase fluid with
Wetting phase fluid) pressure difference.In developing of reservoirs, the Oil, Water, Gas in reservoir flows always, since fluid flows
It necessarily will cause dynamic wettability hysteresis (fluid-flow rate is greater than angle of wetting caused by three-phase circumference movement speed and changes), thus shadow
Ring the numerical value of capillary force in process fluid flow.The capillary force being related to during permeation fluid mechanics and reservoir numerical simulation, should
It is dynamic capillary force relevant to fluid-flow rate.But core holding unit applied by the test experiments of capillary force at present
It is all that one end enters high-pressure fluid, the other end is closed, the type of flow of fluid and the fluid stream under reservoir condition in test process
Flowing mode is completely different, and what the pressure change of whole experiment process embodied is the difference of pore throat radius, and its essence is " static hollow billets
Power ", the capillary force that not fluid flows under reservoir condition.
Research achievement in hydrodynamics field, dynamic capillary force is more, but is all the air water two-phase of test in back-up sand mould
Dynamic capillary force in type, the experimental result for the air water two-phase tested from Camps-Roach know static capillary force and move
State capillary force there are notable differences.Kalaydjian utilizes the test device by repacking, and test has obtained water-oil phase
The experimental result of dynamic capillary force still remains larger difference from test result analysis between static capillary force and dynamic capillary force
It is different.Dynamic capillary force numerical value has been calculated using material balance method in many scholars, and to the influence factor of dynamic capillary force
Analysis is carried out, it is believed that dynamic capillary force is not only controlled by the Static implicit methods such as pore structure, permeability, fluid properties, Er Qieshou
It controls in dynamic factors such as fluid-flow rates.
Hassanizadeh and Gray proposes that following number can be used in the difference between dynamic capillary force and static capillary force
Equation is learned to be described:
In formula (1), PdynIt is dynamic capillary force；PstatBe static capillary force (capillary force in equilibrium state, i.e.,τ is coefficient of dynamics, for describing saturation degree variation to the influence degree of capillary force.Have a large amount of scholar's researchs
The changing rule and obtaining value method of dynamic capillary force at different conditions.Hassanizadeh is using laboratory experiment as a result, mentioning
The value range of τ is 5 × 10 out4~6 × 104Pa·s.Stauffer summarizes to the result of a large amount of laboratory experiments, proposes
The specific formula for calculation of τ:
In formula, α is dimensionless coefficient, usually takes 0.1；φ is porosity, unit f；K is permeability, unit md；μ
It is wetting phase fluid viscosity, unit mPas；G is acceleration of gravity, unit N/kg；ρ is wetting phase fluid density, unit g/
m3；PdIt is that hole enters pressure, unit Mpa；λ is particle diameter distribution coefficient, unit f.
However, widely used numerical reservoir simulation method all thinks capillary force only when handling capillary force at present
It is only the function of water saturation, for capillary force used in numerical simulation in value, reference is mercury injection method, centrifugal process or half
The capillary force that permeable barrier method is tested, it is contemplated that capillary force is divided into the capillary force for the process of sucking by wetting hysteresis effect
With the capillary force of displacement process.In basic percolation equationk establishment process and basic percolation equationk difference solution procedure, do not account for
The influence of fluid-flow rate and saturation degree pace of change to capillary force.Sandoval-Torres etc. utilizes Finite Element Method, will
Dynamic capillary force, which is introduced into, to be calculated in the vacuum drying Numerical simulation equation of wood, and the calculated result of numerical simulation and experiment are tied
Fruit is compared, it is believed that the numerical simulator of foundation is accurate and reliable.Shu etc. is also with Finite Element Method, by dynamic hair
Guan Li is introduced into the Numerical simulation equation for calculating oil-water two-phase flow, and consideration dynamic capillary force under one-dimensional condition has been calculated
Numerical simulation result, analyze influence of the dynamic capillary force to grease migration rule under one-dimensional condition.But numerical reservoir mould
Quasi- device more selects finite difference method, and reservoir numerical simulation is directed to the grease migration rule of the three-dimensional space of macroscopic view
Rule.Above two model can not be used for the numerical simulation calculation under reservoir condition well.Tian etc. draws dynamic capillary force
Enter into the basic percolation equationk of reservoir numerical simulation, and is solved with finite difference method, but what method for solving was selected
It is IMPES (explicit saturation degree, implicit pressure) method, the stability and accuracy of calculating are not so good as fully implicit solution, also, calculate
As a result it is only compared with laboratory experiment result, is not compared with actual production data.
Do not consider that the mode of dynamic capillary force influences the accuracy of analog result in reservoir numerical simulation in the prior art.
Summary of the invention
In order to solve the above-mentioned technical problem, a kind of method for numerical simulation for considering dynamic capillary force of the present invention.
The method for numerical simulation provided by the invention for considering dynamic capillary force, comprising:
Step 1, multiple measuring points are arranged to rock core, different displacement speed under each measuring point is obtained by dynamic hollow billet force test method
Dynamic capillary pressure curve under degree；
Step 2, the function between dynamic capillary force and water saturation, flow velocity is derived by using permeation fluid mechanics method to close
System is fitted using the dynamic capillary pressure curve that this functional relation obtains experiment test, is obtained undetermined in functional relation
Coefficient；
Step 3, difference is carried out to basic oily phase equation and basic water phase equation according to the functional relation, obtains oily phase side
The difference discrete equation of journey, and the difference discrete equation relevant to dynamic capillary force of water phase equation is obtained, to the oily phase
The difference discrete equation relevant to dynamic capillary force of the difference discrete equation of equation and the water phase equation carries out fully implicit solution and changes
In generation, solves, the coefficient matrix linearized.
The method for numerical simulation of above-mentioned consideration dynamic capillary force also has the following characteristics that
The abscissa of dynamic capillary pressure curve is water saturation S in the step 1w, ordinate is dynamic capillary force number
ValuevwIndicate water phase displacement flow velocity；
In the step 2, the functional relation are as follows:
Undetermined coefficient in the functional relation is k1 and k2；
Wherein,
Refer to static capillary force, αsIt is experimental constant, μwIt is aqueous viscosity,It is porosity, CtIt is the compressed coefficient, K
It is absolute permeability, λ and peIt is the capillary pressure factor in Brook-Corey model, ρwIt is water density, g is acceleration of gravity.
The method for numerical simulation of above-mentioned consideration dynamic capillary force also has the following characteristics that
The difference discrete equation relevant to dynamic capillary force of water phase equation in the step 3 are as follows:
It is second order difference operator, the principle function of second order difference operator is Δ (xiΔyi)=x(i+1)/2
(yi+1-yi)-x(i-1)/2(yi-yi-1),It is the conductivity of (n+1)th time step,It is the gesture of (n+1)th time step,Refer to the water phase injection rate at the (n+1)th moment, VijkRefer to that coordinate is the pore volume of (i, j, k) grid, Δ tn+1(n+1)th
The time interval of a time step, φ are porositys.
The method for numerical simulation of above-mentioned consideration dynamic capillary force also has the following characteristics that
To the relevant to dynamic capillary force of the difference discrete equation of the oily phase equation and the water phase equation in step 3
Difference discrete equation carries out fully implicit solution iterative solution
Parameter gesture is setFor
Refer to the oily phase pressure at the n-th moment,Refer to the water phase pressure at the n-th moment,Refer to n-th of time step
Capillary force, x refer to the direction of coordinate x, and p is finger pressure, and t refers to time, γwRefer to the severe of water, D refers to vertical height；
According to the parameter gesture to the difference discrete equation of the oily phase equation and the water phase equation and dynamic hollow billet
The relevant difference discrete equation of power carries out fully implicit solution iterative solution, the coefficient matrix linearized.
The method for numerical simulation of above-mentioned consideration dynamic capillary force also has the following characteristics that
The dynamic hollow billet force test method includes:
Oily phase pressure sensor and water phase pressure sensor is arranged, in the oil of rock core in step 1 in rock core different measuring points
Input port connects oil vessel, water container is connected in the water input of rock core, in the defeated of experiment oil vessel and experimental water container
Enter end connection displacement pump；
Step 2 determines oil-water ratio, determines the displacement velocity of displacement pump；
Step 3 meets the experiment oil of the oil-water ratio in experiment oil vessel and the placement of experimental water container respectively
And experimental water；
The experimental water displacement of the experiment oil and the water container of the oil vessel is entered the rock core, In by step 4
After displacement is stablized, pass through the oily phase pressure sensor and the water phase pressure sensor real-time detection and record oily phase pressure and
Water phase pressure；
Step 5 changes oil-water ratio and displacement velocity, repeats step 2 and step 3, obtain different displacement velocities
Under the conditions of oily phase pressure, water phase pressure and saturation degree variation, to obtain under each measuring point the dynamic hair under different displacement velocities
Pipe force curve discrete parameter.
The present invention solves the problems, such as that the coefficient matrix of linearisation can not be obtained in the prior art.The present invention is by dynamic hollow billet
Power is introduced into the basic percolation equationk of reservoir numerical simulation, and the method for fully implicit solution is selected to carry out difference to saturation degree and pressure
It solves, improves the accuracy of analog result.Applicant produces calculated result with laboratory experiment result and practical oil field respectively
Data are compared, and the reliability and accuracy of this method are demonstrated.
Detailed description of the invention
Fig. 1 is the flow chart that the method for numerical simulation of dynamic capillary force is considered in the present invention.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.It needs
Illustrate, in the absence of conflict, the features in the embodiments and the embodiments of the present application can mutual any combination.
Fig. 1 is the flow chart that the method for numerical simulation of dynamic capillary force is considered in the present invention.This considers dynamic capillary force
Method for numerical simulation includes:
Step 1, multiple measuring points are arranged to rock core, different displacement speed under each measuring point is obtained by dynamic hollow billet force test method
Dynamic capillary pressure curve under degree；
Step 2, the function between dynamic capillary force and water saturation, flow velocity is derived by using permeation fluid mechanics method to close
System is fitted using the dynamic capillary pressure curve that this functional relation obtains experiment test, is obtained undetermined in functional relation
Coefficient；
Step 3, difference is carried out to basic oily phase equation and basic water phase equation according to the functional relation, obtains oily phase side
The difference discrete equation of journey, and the difference discrete equation relevant to dynamic capillary force of water phase equation is obtained, to the oily phase
The difference discrete equation relevant to dynamic capillary force of the difference discrete equation of equation and the water phase equation carries out fully implicit solution and changes
In generation, solves, the coefficient matrix linearized.
Wherein,
The abscissa of dynamic capillary pressure curve is water saturation S in step 1w, ordinate is dynamic capillary force numerical value
vwIndicate water phase displacement flow velocity.
In step 1, the dynamic hollow billet force test method includes:
Oily phase pressure sensor and water phase pressure sensor is arranged, in the oil of rock core in step 1 in rock core different measuring points
Input port connects oil vessel, water container is connected in the water input of rock core, in the defeated of experiment oil vessel and experimental water container
Enter end connection displacement pump；
Step 2 determines oil-water ratio, determines the displacement velocity of displacement pump；
Step 3 meets the experiment oil of the oil-water ratio in experiment oil vessel and the placement of experimental water container respectively
And experimental water；
The experimental water displacement of the experiment oil and the water container of the oil vessel is entered the rock core, In by step 4
After displacement is stablized, pass through the oily phase pressure sensor and the water phase pressure sensor real-time detection and record oily phase pressure and
Water phase pressure；
Step 5 changes oil-water ratio and displacement velocity, repeats step 2 and step 3, obtain different displacement velocities
Under the conditions of oily phase pressure, water phase pressure and saturation degree variation, to obtain under each measuring point the dynamic hair under different displacement velocities
Pipe force curve discrete parameter.
It can be seen that influence of the displacement velocity to dynamic capillary pressure curve from the dynamic capillary pressure curve of different displacement velocities
More sensitive, displacement velocity is bigger, and dynamic capillary pressure curve numerical value is bigger, near irreducible water saturation and residual oil saturation
Near, the dynamic capillary force difference under different displacement velocities is smaller, the interlude in two-phase permeation area, under different displacement velocities
Dynamic capillary force difference is larger.
This functional relation in step 2 are as follows:
Undetermined coefficient in the functional relation is k1 and k2；
Wherein,
Refer to static capillary force, αsIt is experimental constant, μwIt is aqueous viscosity,It is porosity, CtIt is the compressed coefficient, K
It is absolute permeability, λ and peIt is the capillary pressure factor in Brook-Corey model, ρwIt is water density, g is acceleration of gravity.
The difference discrete equation relevant to dynamic capillary force of water phase equation is in step 3
It is second order difference operator, the principle function of second order difference operator is Δ (xiΔyi)=x(i+1)/2
(yi+1-yi)-x(i-1)/2(yi-yi-1),It is the conductivity of (n+1)th time step,It is the gesture of (n+1)th time step,Refer to the water phase injection rate at the (n+1)th moment, VijkRefer to that coordinate is the pore volume of (i, j, k) grid, Δ tn+1(n+1)th
The time interval of a time step, φ are porositys.
Wherein,
To the relevant to dynamic capillary force of the difference discrete equation of the oily phase equation and the water phase equation in step 3
Difference discrete equation carries out fully implicit solution iterative solution
Parameter gesture is setFor
Refer to the oily phase pressure at the n-th moment,Refer to the water phase pressure at the n-th moment,Refer to n-th of time step
Capillary force, x refers to the direction of coordinate x, and p is finger pressure, and t refers to time, γwRefer to the severe of water, D refers to vertical height.
According to the parameter gesture to the difference discrete equation of the oily phase equation and the water phase equation and dynamic hollow billet
The relevant difference discrete equation of power carries out fully implicit solution iterative solution, the coefficient matrix linearized.
The present invention solves the problems, such as that the coefficient matrix of linearisation can not be obtained in the prior art.The present invention is by dynamic hollow billet
Power is introduced into the basic percolation equationk of reservoir numerical simulation, and the method for fully implicit solution is selected to carry out difference to saturation degree and pressure
It solves, improves the accuracy of analog result.Applicant produces calculated result with laboratory experiment result and practical oil field respectively
Data are compared, and the reliability and accuracy of this method are demonstrated.
Descriptions above can combine implementation individually or in various ways, and these variants all exist
Within protection scope of the present invention.
It should be noted that, in this document, the terms "include", "comprise" or its any other variant are intended to non-row
His property includes, so that including the article of a series of elements or equipment not only includes those elements, but also including not having
There is the other element being expressly recited, or further includes for this article or the intrinsic element of equipment.Do not limiting more
In the case where system, the element that is limited by sentence " including ... ", it is not excluded that in the article or equipment for including the element
There is also other identical elements.
The above examples are only used to illustrate the technical scheme of the present invention and are not limiting, reference only to preferred embodiment to this hair
It is bright to be described in detail.Those skilled in the art should understand that can modify to technical solution of the present invention
Or equivalent replacement should all cover in claim model of the invention without departing from the spirit and scope of the technical solution of the present invention
In enclosing.
Claims (4)
1. a kind of method for numerical simulation for considering dynamic capillary force characterized by comprising
Step 1, multiple measuring points are arranged to rock core, are obtained under each measuring point under different displacement velocities by dynamic hollow billet force test method
Dynamic capillary pressure curve；The abscissa of dynamic capillary pressure curve is water saturation S in the step 1w, ordinate is dynamic
Capillary force numerical valuevwIndicate water phase displacement flow velocity；
Step 2, it is derived by the functional relation between dynamic capillary force and water saturation, flow velocity using permeation fluid mechanics method,
It is fitted using the dynamic capillary pressure curve that this functional relation obtains experiment test, obtains the system undetermined in functional relation
Number；
In the step 2, the functional relation are as follows:
Undetermined coefficient in the functional relation is k1 and k2；
Wherein,
Refer to static capillary force, αsIt is experimental constant, μwIt is aqueous viscosity,It is porosity, CtIt is the compressed coefficient, K is exhausted
To permeability, λ and peIt is the capillary pressure factor in Brook-Corey model, ρwIt is water density, g is acceleration of gravity；
Step 3, difference is carried out to basic oily phase equation and basic water phase equation according to the functional relation, obtains oily phase equation
Difference discrete equation, and the difference discrete equation relevant to dynamic capillary force of water phase equation is obtained, to the oily phase equation
Difference discrete equation and the water phase equation difference discrete equation relevant to dynamic capillary force carry out fully implicit solution iteration ask
Solution, the coefficient matrix linearized.
2. considering the method for numerical simulation of dynamic capillary force as described in claim 1, which is characterized in that
The difference discrete equation relevant to dynamic capillary force of water phase equation in the step 3 are as follows:
It is second order difference operator, the principle function of second order difference operator is Δ (xiΔyi)=x(i+1)/2(yi+1-
yi)-x(i-1)/2(yi-yi-1),It is the conductivity of (n+1)th time step,It is the gesture of (n+1)th time step,Refer to
The water phase injection rate at the (n+1)th moment, VijkRefer to that coordinate is the pore volume of (i, j, k) grid, Δ tn+1(n+1)th time step
Time interval, φ is porosity.
3. considering the method for numerical simulation of dynamic capillary force as described in claim 1, which is characterized in that
To the difference discrete equation of the oily phase equation and the difference relevant to dynamic capillary force of the water phase equation in step 3
Discrete equation carries out fully implicit solution iterative solution
Parameter gesture is setFor
Refer to the oily phase pressure at the n-th moment,Refer to the water phase pressure at the n-th moment,Refer to the hollow billet of n-th of time step
Power, x refer to the direction of coordinate x, and p is finger pressure, and t refers to time, γwRefer to the severe of water, D refers to vertical height；
According to the parameter gesture to the difference discrete equation of the oily phase equation and the water phase equation and dynamic capillary force phase
The difference discrete equation of pass carries out fully implicit solution iterative solution, the coefficient matrix linearized.
4. the method for numerical simulation of the consideration dynamic capillary force as described in claims 1 or 2 or 3, which is characterized in that
The dynamic hollow billet force test method includes:
Oily phase pressure sensor and water phase pressure sensor is arranged in step 1 in rock core different measuring points, in the oil input of rock core
Mouth connection oil vessel connects water container in the water input of rock core, in the input terminal of experiment oil vessel and experimental water container
Connect displacement pump；
Step 2 determines oil-water ratio, determines the displacement velocity of displacement pump；
Step 3, it is oily and real in the experiment that experiment oil vessel and the placement of experimental water container meet the oil-water ratio respectively
It tests and uses water；
The experimental water displacement of the experiment oil and the water container of the oil vessel is entered the rock core, in displacement by step 4
After stabilization, by the oily phase pressure sensor and the water phase pressure sensor real-time detection and oily phase pressure and water phase are recorded
Pressure；
Step 5 changes oil-water ratio and displacement velocity, repeats step 2 and step 3, obtain different displacement velocity conditions
Under oily phase pressure, water phase pressure and saturation degree variation, to obtain under each measuring point the dynamic capillary force under different displacement velocities
Curve discrete parameter.
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