CN107577895A - A kind of full three-dimensional visual simulation method for being acidified flowing experiment - Google Patents

A kind of full three-dimensional visual simulation method for being acidified flowing experiment Download PDF

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CN107577895A
CN107577895A CN201710860364.0A CN201710860364A CN107577895A CN 107577895 A CN107577895 A CN 107577895A CN 201710860364 A CN201710860364 A CN 201710860364A CN 107577895 A CN107577895 A CN 107577895A
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CN107577895B (en
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薛衡
黄祖熹
卢立泽
李鑫
刘榧
成
成一
周长江
岑玉达
曹丽娜
田雨
张博
臧克
臧克一
孙照磊
万丽娟
程洋
黄海平
黄凯
黄进腊
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Chengdu North Petroleum Exploration & Development Technology Ltd
China ZhenHua Oil Co Ltd
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Chengdu North Petroleum Exploration & Development Technology Ltd
China ZhenHua Oil Co Ltd
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Abstract

The invention discloses a kind of full three-dimensional visual simulation method for being acidified flowing experiment, using calculus of finite differences discrete fluid seepage flow continuity equation, acid solution mass transfer diffusion reaction equation, while establish H+ local equilibriums equation, porosity equation of change, permeability variation equation, pore throat radius equation of change；(4) simulation equation primary condition, boundary condition, described primary condition are substituted into；(5) using the equation described in (3), (4) step, primary condition, boundary condition, simulation program is worked out；(6) reservoir core is scanned, obtains porosity three-dimensional spatial distribution parameter；(7) porosity three-dimensional spatial distribution model is established, on the basis of the porosity three-dimensional spatial distribution model of foundation, the program worked out using (5) step be acidified the full Three-dimensional simulation of flowing experiment.Present invention employs complete three-dimensional numerical computations, computational accuracy is effectively increased, while helps quick and precisely to study the affecting laws that each parameter develops earthworm hole.

Description

A kind of full three-dimensional visual simulation method for being acidified flowing experiment
Technical field
The present invention relates to a kind of full three-dimensional visual simulation method for being acidified flowing experiment, belongs to oil-gas field development technology neck Domain.
Background technology
The key of Carbonate Oil gas well matrix acidifying is to form the effective earthworm hole for penetrating injury band, successful matrix Acidifying can form negative epidermis, reach volume increase purpose.Therefore fracture Oil/gas Well matrix acidifying research essentially consists in earthworm hole Research.The forming process of carbonate rock acidizing wormhole is：Corrosion can be produced when the hole that acid enters in carbonate rock, due to storage The anisotropism of layer blowhole, the acid being injected into porous carbonate formation are intended to flow in pore channels net, and And larger hole is preferentially entered, the mineral of acid and pore throat wall react, and dissolution of minerals, and pore throat expands, and acid flows through hole more Easily, when big hole is with than small hole and gap people growth rate much, it is big that considerable acid solution just flows into these Hole, due to the circulation of flowing-dissolving-flowing, earthworm hole will soon be formed along acid solution path.
At present, carrying out rock core acid solution flowing experiment needs installation and debugging experimental rig, prepares acid formula system, carries out acid The process of the very complicated such as liquid flowing experiment, manual record experimental data.And due to being chemically reacted between acid solution and rock, Its process has irreversible destruction to rock core, therefore can not be directed to same rock core and carry out repeated experiment research.However, Many limitation and imperfection be present in existing analogy method.Carry out the full three-dimensional visual simulation of acidifying flowing experiment, Neng Gou great Amplitude reduction experimental work intensity, experimental cost is saved, improve the matching of result of calculation and experimental result.Secondly, mould is carried out Intend research to rock core without destructiveness, can effectively carry out the acidizing effect analysis of same rock core under the conditions of variable element.
The content of the invention
It is an object of the invention to provide a kind of full three-dimensional visual simulation method for being acidified flowing experiment, solves prior art The problem of inaccurate caused by middle acidizing wormhole, reach the mesh for all processes that flowing experiment is acidified in real-playback three dimensions , and this method may be implemented in and repeat to study each parameter in the case of not destroying rock core internal structure to earthworm hole in three dimensions The affecting laws of growth.
The present invention is achieved through the following technical solutions：
A kind of full three-dimensional visual simulation method for being acidified flowing experiment, comprises the following steps：
Step (1) measures acid fluid system and rock forming mineral, the chemical reaction velocity in the range of certain acid strength, obtains Concentration-reaction speed curve；
Step (2) measures acid fluid system and rock forming mineral, the chemical reaction velocity in certain temperature range, obtains temperature Degree-reaction speed curve；
Step (3) is established simultaneously using calculus of finite differences discrete fluid seepage flow continuity equation, acid solution mass transfer diffusion reaction equation H+ local equilibriums equation, porosity equation of change, permeability variation equation, pore throat radius equation of change；
Step (4) substitutes into simulation equation primary condition, boundary condition, described primary condition；
Step (5) works out simulation program using the equation described in step (3), step (4), primary condition, boundary condition；
Step (6) scans reservoir core, obtains porosity three-dimensional spatial distribution parameter；
Step (7) establishes porosity three-dimensional spatial distribution model, in the base of the porosity three-dimensional spatial distribution model of foundation On plinth, the program worked out using step (5) be acidified the full Three-dimensional simulation of flowing experiment.
The method of the present invention carries out numerical simulation to acidizing wormhole dynamic extension process in three dimensions, being capable of real-playback The all processes of flowing experiment are acidified in three dimensions, and this method may be implemented in the case of not destroying rock core internal structure The affecting laws that each parameter grows to earthworm hole in three dimensions are studied in repetition, and method of the invention overcomes existing analogy method and deposited The many limitations and imperfection the problem of, it can be used for the full three-dimensional visual simulation for carrying out acidifying flowing experiment, Neng Gou great Amplitude reduction experimental work intensity, experimental cost is saved, improve the matching of result of calculation and experimental result, meanwhile, carry out mould Intend research to rock core without destructiveness, can effectively carry out the acidizing effect analysis of same rock core under the conditions of variable element.
Calculus of finite differences specifically includes as follows in the step (3)：
(31) difference discrete processing, fluid neuron network continuity equation, the diffusion of acid solution mass transfer are carried out to institute's survey region space Reactional equation, H+ local equilibriums equation, porosity equation of change, permeability variation equation, pore throat radius equation of change are：
In formula, CfLiquid phase mass concentration (kmol/m is reacted for pore interior3)；CsFor hole wall acid solution mass concentration (kmol/m3)；R(Cs) it is surface reaction rate, the logistics capacity (kmol/ (s that the expression unit interval is flowed on unit rock area m2))；ksFor reaction speed (m/s)；α is solution ration number (kg/kmol)；avFor hole specific surface area (m2/m3)；ρsFor rock Density (kg/m3)；DexFor effective diffusion cofficient of the acid solution in x directions, m2/s；DeyFor effective diffusion cofficient of the acid solution in y directions, m2/s；DezFor effective diffusion cofficient of the acid solution in z directions, m2/s；vxThe flow velocity (m/s) through y-z interfaces that is fluid；vyFor fluid Flow velocity (m/s) through x-z interfaces；vzThe flow velocity (m/s) through x-y interfaces that is fluid；Φ0For initial porosity (zero dimension)；Φ is Porosity (zero dimension) after corrosion；K0For original permeability (mD)；K is the permeability (mD) after corrosion；β is to be measured by experiment Numerical value (zero dimension)；rp0Radius (m) is shouted for initial beginning hole；rpRadius (m) is shouted for the hole after corrosion；a0For initially than hole table Area (m2/m3)；
(32) difference method is used, the fluid neuron network continuity equation in (1) formula, acid solution mass transfer diffusion reaction equation are entered Row is discrete, obtains：
Wherein,
The step (4) substitutes into simulation equation primary condition, boundary condition, wherein described primary condition, boundary condition For：
Primary condition,
P|x,y,z=Pa；Cf|x,y,z=0 (4)
Boundary condition：
The method of the step (6) is specifically：Reservoir core is taken out in the target reservoir block of simulation, is swept by X ray Rock core is retouched, obtains the distributed constant of the porosity of the rock core in three dimensions.
The specific method of the step (7) is：The core porosity distributed constant obtained according to (6) step, establish corresponding Porosity three-dimensional spatial distribution model, on the basis of the porosity three-dimensional spatial distribution model of foundation, utilize (5) step compile The program of system carries out earthworm hole extension numerical simulation.
The present invention compared with prior art, has the following advantages and advantages：
A kind of full three-dimensional visual simulation method for being acidified flowing experiment of the present invention, should compared with existing acid solution flowing experiment Technical method can reduce experimental work intensity, save experimental cost；And rock core is advantageous to carry out change without destructiveness Acidizing effect comparative analysis under Parameter Conditions.Compared with existing analogy method, the technical method is with true core pore structure Based on, analog result is more accurately and reliably；Secondly, the process employs complete three-dimensional numerical computations, calculating is effectively increased Precision, while help quick and precisely to study the affecting laws that each parameter develops earthworm hole.
Brief description of the drawings
Accompanying drawing described herein is used for providing further understanding the embodiment of the present invention, forms one of the application Point, do not form the restriction to the embodiment of the present invention.In the accompanying drawings：
Fig. 1 is " concentration-reaction speed " curve map；
Fig. 2 is " temperature-reaction speed " curve map；
Fig. 3 is porosity three-dimensional spatial distribution model；
Fig. 4 is rock core inside corrosion structural simulation result figure in the case of different acid solution dosages；
Fig. 5 is rock core inside corrosion structural simulation result figure in the case of different injection rates.
Embodiment
For the object, technical solutions and advantages of the present invention are more clearly understood, the present invention is made with reference to embodiment Further to describe in detail, exemplary embodiment of the invention and its explanation are only used for explaining the present invention, are not intended as to this The restriction of invention.
Embodiment
A kind of full three-dimensional visual simulation method for being acidified flowing experiment of the present invention, in whole mistakes of research acid solution injection rock core Cheng Shi, acid solution dosage, injection rate are investigated to the affecting laws of rock core interior three-dimensional space corrosion structure, is studied in different parameters Under the conditions of sour corrosion structural form, carry out in accordance with the following steps：
Step (1) measures acid fluid system and rock forming mineral, the chemical reaction velocity in the range of certain acid strength, such as schemes Shown in 1, concentration-reaction speed curve is obtained, as shown in Figure 2；
Step (2) measures acid fluid system and rock forming mineral, the chemical reaction velocity in certain temperature range, obtains temperature Degree-reaction speed curve；
Step (3) is established simultaneously using calculus of finite differences discrete fluid seepage flow continuity equation, acid solution mass transfer diffusion reaction equation H+ local equilibriums equation, porosity equation of change, permeability variation equation, pore throat radius equation of change, specific method are：
(31) difference discrete processing, fluid neuron network continuity equation, the diffusion of acid solution mass transfer are carried out to institute's survey region space Reactional equation, H+ local equilibriums equation, porosity equation of change, permeability variation equation, pore throat radius equation of change are：
In formula, CfLiquid phase mass concentration (kmol/m is reacted for pore interior3)；CsFor hole wall acid solution mass concentration (kmol/m3)；R(Cs) it is surface reaction rate, the logistics capacity (kmol/ (s that the expression unit interval is flowed on unit rock area m2))；ksFor reaction speed (m/s)；α is solution ration number (kg/kmol)；avFor hole specific surface area (m2/m3)；ρsFor rock Density (kg/m3)；DexFor effective diffusion cofficient of the acid solution in x directions, m2/s；DeyFor effective diffusion cofficient of the acid solution in y directions, m2/s；DezFor effective diffusion cofficient of the acid solution in z directions, m2/s；vxThe flow velocity (m/s) through y-z interfaces that is fluid；vyFor fluid Flow velocity (m/s) through x-z interfaces；vzThe flow velocity (m/s) through x-y interfaces that is fluid；Φ0For initial porosity (zero dimension)；Φ is Porosity (zero dimension) after corrosion；K0For original permeability (mD)；K is the permeability (mD) after corrosion；β is to be measured by experiment Numerical value (zero dimension)；rp0Radius (m) is shouted for initial beginning hole；rpRadius (m) is shouted for the hole after corrosion；a0For initially than hole table Area (m2/m3)；
(32) difference method is used, the fluid neuron network continuity equation in (1) formula, acid solution mass transfer diffusion reaction equation are entered Row is discrete, obtains：
Wherein,
Step (4) substitutes into simulation equation primary condition, boundary condition, described primary condition, wherein described initial strip Part, boundary condition are：
Primary condition,
P|x,y,z=Pa；Cf|x,y,z=0 (4)
Boundary condition：
Step (5) works out simulation program using the equation described in step (3), step (4), primary condition, boundary condition；
Step (6) scans reservoir core, obtains porosity three-dimensional spatial distribution parameter；
The core porosity distributed constant that step (7) obtains according to (6) step, porosity three dimensions corresponding to foundation point Cloth model, on the basis of the porosity three-dimensional spatial distribution model of foundation, carry out earthworm hole using the program of (5) step establishment and prolong Stretch numerical simulation.
Using described equation, primary condition, boundary condition, simulation program is worked out.
Reservoir core is taken out in simulation reservoir region block, by X-ray scanning rock core, obtains core porosity distribution situation, The porosity distribution situation obtained according to scanning, establishes porosity three-dimensional spatial distribution model, in the porosity three-dimensional space of foundation Between on the basis of distributed model, using the program of establishment be acidified the full three-dimensional visual simulation numerical simulation of flowing experiment.
For the present invention when be acidified the simulation of flowing experiment full three-dimensional visual simulation, the porosity distributed in three dimensions used is as schemed Shown in 3, the underlying parameter used is as shown in the table：
The analog basis parameter of table 1, when research Parameters variation extends affecting laws to earthworm hole, studied parameter is separately dealt with
The present invention studies sour corrosion structure constant in other specification, to be formed when only changing acid solution dosage first, uses Acid solution dosage be respectively：0.1PV、0.25PV、0.75PV、1PV.
Analog result, can be with from analog result as shown in figure 4, dark parts represent that sour corrosion structure is referred to as earthworm hole in figure Find out：Under displacement effect, acid solution can preferentially enter high porosity regions, therefore first shape near rock core end face at acid filling initial stage Into the earthworm hole of competition development, with the increase of acid solution dosage, most of acid solution, which enters in predominant pathway, makes the sustainable growth of earthworm hole, most End form is into the main earthworm hole path for penetrating whole rock core.
Secondly research is constant in other specification by the present invention, the sour corrosion structure formed when only changing injection rate, uses Injection rate be respectively：0.02ml/min、0.07ml/min、0.2ml/min、5ml/min.
Analog result as shown in figure 5, dark parts represent earthworm hole in figure, from analog result it can be seen that：In low injection row Under amount, because convection velocity is slower, diffusion velocity rises in whole course of reaction and dominated, now can forming face corrosion structure；Suitably Injection discharge capacity is improved, now diffusion velocity slightly accounts for leading, then can form taper corrosion structure；When diffusion velocity and convection velocity Between when reaching suitable, then can form main earthworm hole path, acidifying efficiency highest this moment；And under huge discharge, due to flow velocity Relatively faster, multiple-branching construction or uniform corrosion structure is more readily formed in rock core to degree.
Above-described embodiment, the purpose of the present invention, technical scheme and beneficial effect are carried out further Describe in detail, should be understood that the embodiment that the foregoing is only the present invention, be not intended to limit the present invention Protection domain, within the spirit and principles of the invention, any modification, equivalent substitution and improvements done etc., all should include Within protection scope of the present invention.

Claims (5)

  1. A kind of 1. full three-dimensional visual simulation method for being acidified flowing experiment, it is characterised in that comprise the following steps：
    Step (1) measures acid fluid system and rock forming mineral, the chemical reaction velocity in the range of certain acid strength, obtains dense Degree-reaction speed curve；
    Step (2) measures acid fluid system and rock forming mineral, the chemical reaction velocity in certain temperature range, obtains temperature-anti- Answer rate curve；
    Step (3) establishes H+ offices using calculus of finite differences discrete fluid seepage flow continuity equation, acid solution mass transfer diffusion reaction equation Portion's equilibrium equation, porosity equation of change, permeability variation equation, pore throat radius equation of change；
    Step (4) substitutes into simulation equation primary condition, boundary condition, described primary condition；
    Step (5) works out simulation program using the equation described in step (3), step (4), primary condition, boundary condition；
    Step (6) scans reservoir core, obtains porosity three-dimensional spatial distribution parameter；
    Step (7) establishes porosity three-dimensional spatial distribution model, on the basis of the porosity three-dimensional spatial distribution model of foundation, The program worked out using step (5) be acidified the full Three-dimensional simulation of flowing experiment.
  2. 2. a kind of full three-dimensional visual simulation method for being acidified flowing experiment according to claim 1, it is characterised in that described Calculus of finite differences specifically includes as follows in step (3)：
    (31) difference discrete processing, fluid neuron network continuity equation, acid solution mass transfer diffusion reaction are carried out to institute's survey region space Equation, H+ local equilibriums equation, porosity equation of change, permeability variation equation, pore throat radius equation of change are：
    In formula, CfLiquid phase mass concentration (kmol/m is reacted for pore interior3)；CsFor hole wall acid solution mass concentration (kmol/ m3)；R(Cs) it is surface reaction rate, the logistics capacity (kmol/ (sm that the expression unit interval is flowed on unit rock area2))； ksFor reaction speed (m/s)；α is solution ration number (kg/kmol)；avFor hole specific surface area (m2/m3)；ρsFor rock density (kg/m3)；DexFor effective diffusion cofficient of the acid solution in x directions, m2/s；DeyFor effective diffusion cofficient of the acid solution in y directions, m2/ s；DezFor effective diffusion cofficient of the acid solution in z directions, m2/s；vxThe flow velocity (m/s) through y-z interfaces that is fluid；vyIt is fluid through x- The flow velocity (m/s) at z interfaces；vzThe flow velocity (m/s) through x-y interfaces that is fluid；Φ0For initial porosity (zero dimension)；Φ is corrosion Porosity (zero dimension) afterwards；K0For original permeability (mD)；K is the permeability (mD) after corrosion；β is the number measured by experiment It is worth (zero dimension)；rp0Radius (m) is shouted for initial beginning hole；rpRadius (m) is shouted for the hole after corrosion；a0Initially to compare pore surface area (m2/m3)；
    (32) use difference method, the fluid neuron network continuity equation in (1) formula, acid solution mass transfer diffusion reaction equation are carried out from Dissipate, obtain：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>SP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>AP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>BP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>CP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>DP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>EP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>WP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>FP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>SC</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>AC</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>BC</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>CC</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>DC</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>EC</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>WC</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msubsup> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>FC</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <msub> <mi>SP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mrow> <msub> <mi>&amp;mu;&amp;Delta;z</mi> <mi>k</mi> </msub> <msub> <mi>&amp;Delta;z</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>AP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <msub> <mi>&amp;mu;&amp;Delta;y</mi> <mi>j</mi> </msub> <msub> <mi>&amp;Delta;y</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <msub> <mi>BP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <msub> <mi>&amp;mu;&amp;Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&amp;Delta;x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>DP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <msub> <mi>&amp;mu;&amp;Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&amp;Delta;x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <msub> <mi>EP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <msub> <mi>&amp;mu;&amp;Delta;y</mi> <mi>j</mi> </msub> <msub> <mi>&amp;Delta;y</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>WP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>K</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mrow> <msub> <mi>&amp;mu;&amp;Delta;z</mi> <mi>k</mi> </msub> <msub> <mi>&amp;Delta;z</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> <mi>a</mi> <mi>n</mi> <mi>d</mi> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>CP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>BP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>SP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>WP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>EP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>NP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>AP</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>FF</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <msub> <mi>SS</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;z</mi> <mi>k</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>x</mi> </mrow> </msub> <msubsup> <mo>|</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <msub> <mi>&amp;Delta;z</mi> <mi>k</mi> </msub> <msub> <mi>&amp;Delta;z</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>AA</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;y</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>y</mi> </mrow> </msub> <msubsup> <mo>|</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <msub> <mi>&amp;Delta;y</mi> <mi>j</mi> </msub> <msub> <mi>&amp;Delta;y</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <msub> <mi>BB</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;x</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>x</mi> </mrow> </msub> <msubsup> <mo>|</mo> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <msub> <mi>&amp;Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&amp;Delta;x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>DD</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;x</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>x</mi> </mrow> </msub> <msubsup> <mo>|</mo> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <msub> <mi>&amp;Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&amp;Delta;x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <msub> <mi>EE</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>v</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;y</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>y</mi> </mrow> </msub> <msubsup> <mo>|</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <msub> <mi>&amp;Delta;y</mi> <mi>j</mi> </msub> <msub> <mi>&amp;Delta;y</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>WW</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;z</mi> <mi>k</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>z</mi> </mrow> </msub> <msubsup> <mo>|</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <msub> <mi>&amp;Delta;z</mi> <mi>k</mi> </msub> <msub> <mi>&amp;Delta;z</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>CC</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;z</mi> <mi>k</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;z</mi> <mi>k</mi> </msub> </mrow> </mfrac> <mo>)</mo> <mo>+</mo> <mo>(</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;y</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;y</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>)</mo> <mo>+</mo> <mo>(</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;x</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <mn>2</mn> <msub> <mi>&amp;Delta;x</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>)</mo> <mo>+</mo> <mfrac> <msubsup> <mi>&amp;phi;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mi>&amp;Delta;</mi> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <msubsup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>k</mi> <mi>c</mi> </msub> <msub> <mi>k</mi> <mi>s</mi> </msub> <msub> <mi>&amp;gamma;</mi> <mrow> <msup> <mi>H</mi> <mo>+</mo> </msup> <mo>,</mo> <mi>s</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mi>s</mi> </msub> <msub> <mi>&amp;gamma;</mi> <mrow> <msup> <mi>H</mi> <mo>+</mo> </msup> <mo>,</mo> <mi>s</mi> </mrow> </msub> </mrow> </mfrac> <msub> <mi>a</mi> <mi>v</mi> </msub> <mo>)</mo> </mrow> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>z</mi> </mrow> </msub> <msub> <mo>|</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>&amp;Delta;z</mi> <mi>k</mi> </msub> <msub> <mi>&amp;Delta;z</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>y</mi> </mrow> </msub> <msub> <mo>|</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>&amp;Delta;y</mi> <mi>j</mi> </msub> <msub> <mi>&amp;Delta;y</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>x</mi> </mrow> </msub> <msub> <mo>|</mo> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>&amp;Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&amp;Delta;x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>x</mi> </mrow> </msub> <msub> <mo>|</mo> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>&amp;Delta;x</mi> <mi>i</mi> </msub> <msub> <mi>&amp;Delta;x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>y</mi> </mrow> </msub> <msub> <mo>|</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>&amp;Delta;y</mi> <mi>j</mi> </msub> <msub> <mi>&amp;Delta;y</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&amp;phi;D</mi> <mrow> <mi>e</mi> <mi>z</mi> </mrow> </msub> <msub> <mo>|</mo> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>&amp;Delta;z</mi> <mi>k</mi> </msub> <msub> <mi>&amp;Delta;z</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>FF</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>&amp;phi;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mi>n</mi> </msubsup> <mrow> <mi>&amp;Delta;</mi> <mi>t</mi> </mrow> </mfrac> <msubsup> <mi>C</mi> <mrow> <mi>f</mi> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> <mi>n</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  3. 3. a kind of full three-dimensional visual simulation method for being acidified flowing experiment according to claim 1, it is characterised in that described Step (4) substitutes into simulation equation primary condition, boundary condition, wherein described primary condition, boundary condition are：
    Primary condition,
    P|x,y,z=Pa；Cf|x,y,z=0 (4)
    Boundary condition：
    <mrow> <mtable> <mtr> <mtd> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>Q</mi> <mi>i</mi> </msub> <mo>;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>P</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>x</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>x</mi> <mo>=</mo> <mi>M</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>P</mi> <msub> <mo>|</mo> <mrow> <mi>y</mi> <mo>=</mo> <mi>N</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mi>a</mi> </msub> <mo>;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>P</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>z</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>z</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>z</mi> <mo>=</mo> <mi>K</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> <mtr> <mtd> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mi>f</mi> </msub> <msub> <mo>|</mo> <mrow> <mi>y</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msubsup> <mi>C</mi> <mi>f</mi> <mn>0</mn> </msubsup> <mo>;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>C</mi> <mi>f</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>y</mi> <mo>=</mo> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>C</mi> <mi>f</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>x</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>x</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>x</mi> <mo>=</mo> <mi>M</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>C</mi> <mi>f</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>z</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <mi>z</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>z</mi> <mo>=</mo> <mi>K</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  4. 4. a kind of full three-dimensional visual simulation method for being acidified flowing experiment according to claim 3, it is characterised in that described The method of step (6) is specifically：Reservoir core is taken out in the target reservoir block of simulation, by X-ray scanning rock core, is somebody's turn to do The distributed constant of the porosity of rock core in three dimensions.
  5. 5. a kind of full three-dimensional visual simulation method for being acidified flowing experiment according to claim 4, it is characterised in that described The specific method of step (7) is：The core porosity distributed constant obtained according to (6) step, porosity corresponding to foundation are three-dimensional Spatial distribution model, on the basis of the porosity three-dimensional spatial distribution model of foundation, carried out using the program of (5) step establishment Earthworm hole extends numerical simulation.
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