CN109611067A - The numerical computation method of deep layer limestone reservoir acid fracturing effective distance of live acid - Google Patents
The numerical computation method of deep layer limestone reservoir acid fracturing effective distance of live acid Download PDFInfo
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- 239000002253 acid Substances 0.000 title claims abstract description 178
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- 238000013461 design Methods 0.000 abstract description 9
- 239000000446 fuel Substances 0.000 abstract description 4
- 239000003208 petroleum Substances 0.000 description 9
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- BVKZGUZCCUSVTD-UHFFFAOYSA-L Carbonate Chemical compound [O-]C([O-])=O BVKZGUZCCUSVTD-UHFFFAOYSA-L 0.000 description 2
- 230000008878 coupling Effects 0.000 description 2
- 238000010168 coupling process Methods 0.000 description 2
- 238000005859 coupling reaction Methods 0.000 description 2
- 238000005530 etching Methods 0.000 description 2
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- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 239000004215 Carbon black (E152) Substances 0.000 description 1
- 235000008733 Citrus aurantifolia Nutrition 0.000 description 1
- 235000011941 Tilia x europaea Nutrition 0.000 description 1
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- 239000010459 dolomite Substances 0.000 description 1
- 229910000514 dolomite Inorganic materials 0.000 description 1
- 235000013399 edible fruits Nutrition 0.000 description 1
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- 238000005516 engineering process Methods 0.000 description 1
- 229930195733 hydrocarbon Natural products 0.000 description 1
- 150000002430 hydrocarbons Chemical class 0.000 description 1
- 239000004571 lime Substances 0.000 description 1
- 239000011159 matrix material Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 230000000638 stimulation Effects 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
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- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
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Abstract
The invention discloses the numerical computation methods of deep layer limestone reservoir acid fracturing effective distance of live acid, comprising: (1) calculates the bottom hole temperature (BHT) at the end of construction；(2) it calculates the crack at the end of construction and stitches length, in seam length direction grid division unit and calculate the average slit width of each unit, obtain each unit acid solution flow velocity；(3) using bottom hole temperature (BHT) as primary condition, acid liquor temperature and acid strength that each unit does not consider acid-rock reaction heat are calculated；(4) the sour rock molar reaction heat of each unit is calculated；(5) each unit acid liquor temperature and acid strength for calculating consideration acid-rock reaction heat, establish acid strength distribution curve, define the 10% of the initial implantation concentration of acid solution and are used as residual sour limting concentration, stitch a length of effective distance of live acid so that residual sour limting concentration is corresponding.The present invention considers the fuel factor that acid solution during acid fracturing is subject to, and improves the accuracy of effective distance of live acid calculating, has directive significance to deep layer limestone reservoir acid fracturing design.
Description
Technical field
The present invention relates to effective distance of live acid during petroleum works field, especially deep layer limestone reservoir acid fracturing
Numerical computation method.Effective distance of live acid under hot conditions is calculated using numerical computation method, improves deep layer lime
The accuracy of rock reservoir acid fracturing design realizes the efficient acidfracturing treatment of deep layer limestone reservoir.
Background technique
The folded system deep carbonate reservoirs of western sichuan region two show good Exploration Potential, it has also become the Sichuan Basin shows rank
Section is most real to take over one of series of strata.Reservoir has based on limestone, dolomite and buries deep (> 5000m), temperature height (> 145
DEG C) etc. features.This area's exploitation is difficult to nature and obtains commercial hydrocarbon flow, and matrix acidizing technology is the main storey increase design of block reservoir
(the application logging reservoir quality comprehensive evaluation index such as Qi Baoquan, Zhao Zuoan, He Hongju carrys out the effective of discrimination of reservoir to one of means
Property --- [J] gas industry by taking the Permian Chihsia group of West of Sichuan Basin as an example, 2018,38 (02): 25-32).
Acid fracturing (abbreviation acid fracturing) refers in the case where being higher than the clossing pressure of reservoir fracture pressure or intrinsic fracture, by acid solution
Reservoir is squeezed into, forms crack in reservoir, while acid solution is chemically reacted with crack wall surface rock, non-homogeneous etching fracture wall
Rock forms channel form or rough etching fracture, and crack is not completely closed after construction, and ultimately forming has centainly
The acid-etched fracture of geometric dimension and flow conductivity realizes well production increment.Effective distance of live acid is evaluation acid fracturing effect
One of important indicator, it is mainly influenced by factors such as temperature, acid strengths.Wherein, temperature is to influence limestone reservoir acid fracturing effect
An important factor for fruit (Li Yingchuan petroleum production engineering [M] petroleum industry publishing house, 2009).
Currently used effective distance of live acid calculation method be primarily upon residual sour limting concentration calculating (Li Jianhui,
Mu Lijun, Zhao Zhenfeng, the wait a kind of method based on residual sour limit evaluation effective distance of live acid, CN105044288A [P]
.2015), seldom comprehensively consider influence of the temperature change of acid solution in fracturing process for acidfracturing treatment effect.Therefore, for river
The high feature of western area reservoir temperature, studies acid fracturing process acid liquor temperature changing rule, specifies temperature for acid fracturing effect (acid solution
EFFECTIVE RANGE) influence, for western sichuan region reservoir acidfracturing treatment design it is most important.
Summary of the invention
The purpose of the present invention is to provide the numerical computation method of deep layer limestone reservoir acid fracturing effective distance of live acid,
The fuel factor (wellbore heat, acid solution fluid interchange, acid-rock reaction heat release) that acid solution is subject to during this method primary study acid fracturing,
The acid liquor temperature and concentration that the above fuel factor is considered using numerical calculations are based ultimately upon acid strength and determine that acid solution is effectively made
With distance.This method principle is reliable, is conducive to the acid liquor temperature and concentration that calculate high-temperature stratum, improves effective distance of live acid
The accuracy of calculating has directive significance to deep layer limestone reservoir acid fracturing design.
To reach the above technical purpose, the present invention provides following technical scheme.
Firstly, establishing Wellbore Temperature Field modeling wellbore heat and calculating bottom hole temperature (BHT)；Secondly, using PKN formula meter
The seam length and slit width for calculating acid fracturing crack, according to crack slit width distributed problem solving acid solution flow velocity；Furthermore using bottom hole temperature (BHT) as initial strip
Part solves acid liquor temperature and concentration according to flow velocity；Then, pass through acid liquor temperature and concentration calculation acid-rock reaction heat；Finally, calculating
Acid liquor temperature and concentration after considering acid-rock reaction heat, establish the relation curve of acid strength and fracture length, determine that acid solution has
Imitate operating distance.
The numerical computation method of deep layer limestone reservoir acid fracturing effective distance of live acid, successively the following steps are included:
(1) it uses Eickmeier Wellbore Temperature Field modeling Wellbore Temperature Field and calculates the shaft bottom temperature at the end of construction
Degree (Beijing Wang Hongxun, Zhang Shicheng hydraulic fracturing design value calculation method [M]: petroleum industry publishing house, 1998)；
(2) crack at the end of construction is calculated using PKN formula and stitches long (Beijing Li Yingchuan petroleum production engineering [M]: petroleum work
Industry publishing house, 2001), in seam length direction grid division unit and the average slit width of each unit is calculated, then calculates each unit acid solution
Flow velocity；
(3) for the bottom hole temperature (BHT) calculated using step (1) as primary condition, the acid solution flow relocity calculation calculated by step (2) is each
Unit does not consider the acid liquor temperature and acid strength of acid-rock reaction heat；
(4) pass through the sour rock molar reaction heat of the acid liquor temperature and concentration calculation each unit that calculate in step (3)；
(5) the sour rock molar reaction heat for calculating step (4) substitutes into step (3), calculates and considers each of acid-rock reaction heat
Unit acid liquor temperature and acid strength establish acid strength distribution curve.Define 10% conduct of the initial implantation concentration of acid solution
Residual acid limting concentration stitches a length of effective distance of live acid according to distribution curve with residual sour limting concentration is corresponding.
In the present invention, in the step (1), simultaneously using Eickmeier Wellbore Temperature Field modeling Wellbore Temperature Field
The bottom hole temperature (BHT) at the end of construction is calculated, process is as follows:
Target well shaft models for temperature field and grid division are established using Eickmeier Wellbore Temperature Field model modelling approach
Unit.Using oil pipe center as axis: radially, defining riFor grid cell radius, divide N number of grid cell (i=0,1,2 ...,
N).Wherein model boundary point rNThe selection of point should meet temperature at the point and be consistently equal to formation temperature；On longitudinal direction, if purpose layer depth
Degree is H, and unit depth is Δ H, then can be divided into M unit (j=0,1,2 ..., M) on longitudinal direction, and boundary point M is that (H/ Δ H) takes
It is whole.Definition construction total time is tT, time step is Δ t, and time step is n (n=0,1,2 ..., tT).Combining target well geology work
Journey parameter calculates the temperature of n moment unit (i, j) using following formulaFinally obtain the bottom hole temperature (BHT) at the end of construction
In formula: Q --- acid filling discharge capacity, m3/min；
ρi--- the density of grid cell i, kg/m3；
Ci--- the specific heat capacity of grid cell i, J/ (kg DEG C)；
ΔHj--- the height of grid cell j, m；
ri--- model radial grid radius, m；
λi--- the coefficient of heat conduction of grid cell i, W/ (m DEG C)；
Δ t --- time step, min；
tT--- construction total time, min；
N --- time step, min；
--- n moment grid cell (i, j) temperature (For the bottom hole temperature (BHT) at the end of construction), DEG C.
In the present invention, in the step (2), the crack at the end of construction is calculated using PKN formula and stitches length, it is rectangular stitching
To grid division unit and the average slit width of each unit is calculated, then calculates each unit acid solution flow velocity, process is as follows:
1) terminate to be n=t by calculating constructionTWhen crack stitch length, defining x is seam length direction and grid division unit,
Calculate the corresponding average slit width w of each unit:
In formula: L --- the seam at the end of construction is long, m；
C --- acid liquid loss coefficient, m/min0.5；
μf--- acid liquid viscosity, Pamin；
H --- fracture height, m；
E --- reservoir rock Young's modulus, Pa
ε --- reservoir rock Poisson's ratio, zero dimension；
X --- unit coordinate on seam length direction, m；
W --- the average slit width of each unit, m at the end of construction.
2) each unit acid solution flow velocity v is obtained by following formulax:
In formula: vl--- each unit filtration rate, m/s；
vx--- the direction each unit x flow velocity, m/s.
The derivation process of formula (3) is as follows:
Acid solution continuity equation are as follows:
Assuming that acid solution flow velocity is thought of as mean flow rate in crack, stitches interior pressure and be uniformly distributed, in crack near axis (i.e. y
At=0) barometric gradient be 0, so there is vy|Y=0=0.In addition, acid solution flow velocity is equal to fluid loss rate on the wall surface of crack, i.e.,Therefore formula (4) is integrated by crack axis (y=0) to crack wall surface (y=w/2), it can derivation formula (3).
In the present invention, in the step (3), the bottom hole temperature (BHT) calculated using step (1) passes through step as primary condition
(2) the acid solution flow relocity calculation each unit calculated does not consider the acid liquor temperature and acid strength of acid-rock reaction heat, and process is as follows:
1) assume that crack inlet temperature is equal to the bottom hole temperature (BHT) that step (1) calculates, seam length direction each unit temperature is thought of as
Mean temperature, the acid solution flow velocity that step (2) are solved substitute into following formula and solve each unit acid liquor temperature and crack wall surface temperature:
Wherein, convection transfer rate can be solved by Nu Xieerte criterion:
hT=NNuKhf/w (7)
In formula: T --- each unit acid solution mean temperature, DEG C；
Tw--- each unit crack wall surface temperature, DEG C；
hT--- convection transfer rate, J/ (m2·min·℃)；
NNu--- nusselt number, zero dimension；
Khf--- the thermal coefficient of acid solution, J/ (mmin DEG C)；
ρf--- reservoir rock density, kg/m3；
Cf--- reservoir rock specific heat capacity, J/ (kg DEG C).
2) assume acid solution heat convection heat hT(Tw- T) mainly mentioned by stratum heat transfer and acid-rock reaction heat
For:
hT(Tw- T)=q (tT)-kRCmΔrQm(Tw,p) (8)
In formula: kR--- acid-rock reaction rate constant, (kg/m3)-m·mol/(m2·s)；
C --- each unit acid strength, kg/m3；
ΔrQm(Tw, p) --- sour rock molar reaction heat, kJ/mol；
M --- the order of reaction, zero dimension；
q(tT) --- construction terminates stratum heat transfer, kJ.
Wherein, hot-fluid function formula is (Whitsitt, Dysart.The effect of temperature on
Stimulation design [J] .SPE 2497,1970):
In formula: Mma--- formation rock volumetric heat capacity, J/m3·℃；
Khr--- formation rock thermal coefficient, W/ (m DEG C)；
--- porosity, %.
Since acid-rock reaction heat is the function about acid liquor temperature and concentration, sour rock is not considered first in step (3)
Reaction heat (sets its value as 0), and formula (9), formula (8) substitution formula (6) can be found out the acid solution that each unit does not consider acid-rock reaction heat
Temperature.
The derivation process of formula (6) is as follows:
Assuming that acid liquor temperature field is stable state.Each unit can establish energy conservation equation:
The processing method of same formula (5) is integrated formula (10) by crack axis (y=0) to crack wall surface (y=w/2):
Since axis (y=0) velocity gradient in crack is 0, temperature gradient is also 0.Each unit temperature is thought of as average
Temperature handles formula (11) for ODE:
Convection transfer rate is the parameter for characterizing exchange capability of heat between fluid and the surface of solids, is defined as unit area exchange
The ratio (Beijing He Chaohong, Feng Xiao Principles of Chemical Engineering [M]: Science Press, 2001:190) of heat and fluid-solid temperature difference.
Therefore, h is definedTFor convection transfer rate:
It should be noted that formula (7) is the solution formula that derivation is defined based on Nu-number, it is hTAnother kind performance shape
Formula.Formula (3), formula (13) are substituted into formula (12), formula (6) can be derived.
3) assume that each unit acid strength is mean concentration, the acid solution flow velocity that step (2) solve is substituted into following formula and is obtained respectively
Unit acid strength and crack wall surface concentration:
In formula: kg--- convective transfer coefficient, m/min；
Cw--- each unit crack wall surface acid strength, kg/m3；
Assuming that the acid solution of crack wall surface is reacted completely with crack wall surface rock, so that
kg(C-Cw)=kRCw m (15)
It in formula, is defined by sherwood number, convective transfer coefficient can indicate are as follows:
kg=DeNSh/w (16)
Acid-rock reaction rate constant KR(Beijing Li Yingchuan petroleum production engineering [M]: petroleum work is solved by Arrhenius formula
Industry publishing house, 2001):
In formula: De--- acid solution hydrogen ion efficient coefficient, m2/s；
Nsh--- sherwood number, zero dimension；
k0--- frequency factor, (kg/m3)-m·mol/(m2·s)；
Ea--- reaction activity, J/mol；
R --- gas constant, 8.314J/ (mol DEG C).
Therefore, each unit acid liquor temperature that step 2) solves is substituted into formula (17) solution and obtains KR, then simultaneous solution formula
(14), formula (15) can acquire each unit acid strength.
The derivation process of formula (14) is as follows:
Each unit establishes acid strength matter balance equation:
The processing method of same formula (5) is integrated formula (18) by crack axis (y=0) to crack wall surface (y=w/2):
Since axis (y=0) velocity gradient in crack is 0, concentration gradient is also 0.Each unit concentration is thought of as average
Concentration handles formula (19) for ODE:
(Liu Jin, Wang Hao, Wang Zhihong heat and mass transfer [M] Southwest Petrol University, 2007) is defined by convective transfer coefficient:
It should be noted that formula (16) is the solution formula that derivation is defined based on sherwood number, it is kgAnother kind performance shape
Formula.Formula (3), formula (21) are substituted into formula (20), formula (14) can be derived.To sum up, each unit can be acquired by step (3) and does not consider acid
The acid liquor temperature and concentration of rock reaction heat.
In the present invention, in the step (4), in conjunction with the acid liquor temperature and concentration calculation each unit calculated in step (3)
Sour rock molar reaction heat, process is as follows:
1) consider that target work area reservoir lithology is limestone, by consulting physical chemistry handbook (Sun Yanhui, He Guangping, horse
Just equal Beijing physical chemistry application manual [M] of state: Chemical Industry Press .2016) obtain the mark of each component in reaction system
Quasi- molar reaction heat, and calculate the molar reaction heat of reaction system
In formula: υi--- the stoichiometric coefficient of i component, zero dimension in reaction system；
--- the normalized molar reaction heat of i component, kJ/mol；
--- reaction system normalized molar reaction heat, kJ/mol.
2) calculated result for combining step 1), calculates high-temperature and high-pressure conditions acid rock molar reaction heat ΔrHm(Tw,p)(Guo
J,Liu H,Zhu Y,et al.Effects of acid–rock reaction heat on fluid temperature
profile in fracture during acid fracturing in carbonate reservoirs[J].Journal
Of petroleum science&engineering, 2014,122:31-37):
Wherein, fgFor free state CO2Molar fraction:
In formula: ΔrHm(Tw) --- temperature TwUnder molar reaction heat, kJ/mol；
P --- strata pressure, MPa；
Cp,mNormal pressure molar heat capacity of (i, T) --- the component i at temperature T, J/ (DEG C mol)；
fg——CO2Molar fraction, zero dimension；
Vco2——CO2Molal volume, m3/mol；
Vacid--- residual acid volume, m3；
Sco2--- CO in residual acid2Solubility, m3/m3。
ΔrHm(Tw, p) --- temperature TwMolar reaction heat under pressure p, kJ/mol.
3) during acid-rock reaction, reaction system is to CO2Do volumetric work.Therefore, comprehensively consider temperature, pressure and CO2Body
The influence of product function obtains sour rock molar reaction heat Δ under formation conditionrQm(Tw, p):
In the present invention, in the step (5), the sour rock molar reaction heat that step (4) are calculated is substituted into step (3),
The each unit acid liquor temperature and acid strength for considering acid-rock reaction heat are calculated, acid strength distribution curve is established.Define acid solution
The 10% of initial implantation concentration stitches a length of acid solution as residual sour limting concentration, according to distribution curve with residual sour limting concentration is corresponding
EFFECTIVE RANGE, process are as follows:
1) the sour rock molar reaction heat for calculating step (4), which substitutes into formula (8), calculates each unit acid-rock reaction heat, then
The each unit acid liquor temperature and acid strength for considering acid-rock reaction heat are calculated by step (3), and make to stitch length direction each unit acid
Liquid concentration profile；
2) define the initial implantation concentration of acid solution 10% takes as residual sour limting concentration with reference to acid strength distribution curve
The a length of effective distance of live acid of the residual corresponding crack seam of acid limting concentration.
Compared with prior art, the present invention provides a kind of effective distance of live acid for deep layer limestone reservoir
Numerical computation method.This method has coupled the hot three kinds of thermal effects of wellbore heat, acid solution heat convection, acid-rock reaction in calculating process
Answer: 1. calculating construction by temperature in wellbore field model first terminates bottom hole temperature (BHT)；2. solving seam using the slit width that PKN formula calculates
Length direction each unit acid solution flow velocity, using bottom hole temperature (BHT) as primary condition, by acid solution flow velocity solve each unit acid liquor temperature and
Concentration, and realize the coupling of wellbore heat and heat convection；3. acid-rock reaction heat is solved by each unit acid liquor temperature, concentration,
Each unit acid strength is calculated after coupling acid-rock reaction heat and obtains acid strength distribution curve, determines effective distance of live acid.
This method overcomes existing method and fails to comprehensively consider in fracturing process a variety of fuel factors for the office of acidfracturing treatment influential effect
Limit.
Detailed description of the invention
Fig. 1 is that Wellbore Temperature Field model meshes divide schematic diagram in the present invention.
Fig. 2 is bottom hole temperature (BHT) change modeling result figure in the present invention.
Fig. 3 is the hot calculated result of acid-rock reaction in the present invention.
Fig. 4 is effective distance of live acid calculated result figure in the present invention.
Specific embodiment
The present invention is further illustrated with application example with reference to the accompanying drawing, it is intended to which reconciliation is schematically illustrated to the present invention
It releases, not delimit the scope of the invention.It is specific as follows:
1. being based on target work area prospect pit X well acid fracturing design underlying parameter (table 1), X well shaft temperature field physics mould is established
Type and grid division (see Fig. 1) calculate dynamic shaft bottom during the well construction using the temperature in wellbore field model that step (1) is established
Temperature, the bottom hole temperature (BHT) at the end of being constructed.Comparison actual measurement bottom hole temperature (BHT) curve, can prove that the model is reliable (see Fig. 2).
1 X well acid fracturing design part basis parameter of table
2. the bottom hole temperature (BHT) at the end of to construct is primary condition, using in numerical calculations step (2) and step (3)
Crack acid liquor temperature and concentration equation, each unit acid liquor temperature and concentration at the end of being constructed.
3. acid liquor temperature and concentration calculation each unit based on each unit that the step 2 in specific embodiment is calculated
Acid-rock reaction heat, as shown in Figure 3.
4. each unit acid-rock reaction heat that the step 3 in specific embodiment is calculated substitutes into step 2, calculates and consider acid
The acid liquor temperature and acid strength of rock reaction heat obtain seam length direction each unit acid strength distribution curve, take the residual sour limit
A length of effective distance of live acid is stitched in the corresponding crack of concentration, as shown in Figure 4.
Claims (6)
1. the numerical computation method of deep layer limestone reservoir acid fracturing effective distance of live acid, successively the following steps are included:
(1) it uses Eickmeier Wellbore Temperature Field modeling Wellbore Temperature Field and calculates the bottom hole temperature (BHT) at the end of construction；
(2) crack at the end of construction is calculated using PKN formula and stitches length, in seam length direction grid division unit and calculate each unit
Average slit width, then calculate each unit acid solution flow velocity；
(3) bottom hole temperature (BHT) calculated using step (1) passes through the acid solution flow relocity calculation each unit of step (2) calculating as primary condition
The acid liquor temperature and acid strength of acid-rock reaction heat are not considered；
(4) pass through the sour rock molar reaction heat of the acid liquor temperature and concentration calculation each unit that calculate in step (3)；
(5) the sour rock molar reaction heat for calculating step (4) substitutes into step (3), calculates each unit for considering acid-rock reaction heat
Acid liquor temperature and acid strength establish acid strength distribution curve, and define the initial implantation concentration of acid solution 10% is used as residual acid
Limting concentration stitches a length of effective distance of live acid according to distribution curve with residual sour limting concentration is corresponding.
2. the numerical computation method of deep layer limestone reservoir acid fracturing effective distance of live acid as described in claim 1, special
Sign is that step (1) process is as follows:
Target well shaft models for temperature field and grid division unit are established, using oil pipe center as axis: radially, defining riFor grid
Cell radius divides N number of grid cell (i=0,1,2 ..., N), wherein model boundary point rNThe selection of point should meet at the point
Temperature is consistently equal to formation temperature；On longitudinal direction, if purpose layer depth is H, unit depth is Δ H, then M can be divided on longitudinal direction
Unit (j=0,1,2 ..., M), boundary point M are (H/ Δ H) rounding；Definition construction total time is tT, time step is Δ t, time
Step is n (n=0,1,2 ..., tT), the temperature of n moment unit (i, j) is calculated using following formulaAt the end of finally obtaining construction
Bottom hole temperature (BHT)
In formula: Q --- acid filling discharge capacity, m3/min；
ρi--- the density of grid cell i, kg/m3；
Ci--- the specific heat capacity of grid cell i, J/ (kg DEG C)；
ΔHj--- the height of grid cell j, m；
ri--- model radial grid radius, m；
λi--- the coefficient of heat conduction of grid cell i, W/ (m DEG C)；
Δ t --- time step, min；
tT--- construction total time, min；
N --- time step, min；
--- the temperature of n moment grid cell (i, j), DEG C.
3. the numerical computation method of deep layer limestone reservoir acid fracturing effective distance of live acid as described in claim 1, special
Sign is that step (2) process is as follows:
Calculating construction terminates to be n=tTWhen crack stitch length, defining x is seam length direction and grid division unit, calculates each unit pair
The average slit width w answered:
In formula: L --- the seam at the end of construction is long, m；
C --- acid liquid loss coefficient, m/min0.5；
μf--- acid liquid viscosity, Pamin；
H --- fracture height, m；
E --- reservoir rock Young's modulus, Pa
ε --- reservoir rock Poisson's ratio, zero dimension；
X --- unit coordinate on seam length direction, m；
W --- the average slit width of each unit, m at the end of construction；
To obtain each unit acid solution flow velocity vx:
In formula: vl--- each unit filtration rate, m/s；
vx--- the direction each unit x flow velocity, m/s.
4. the numerical computation method of deep layer limestone reservoir acid fracturing effective distance of live acid as described in claim 1, special
Sign is that step (3) process is as follows:
Assuming that crack inlet temperature is equal to bottom hole temperature (BHT), if ΔrQm(Tw, p) and it is 0, it finds out each unit and does not consider acid-rock reaction heat
Acid liquor temperature and crack wall surface temperature:
hT=NNuKhf/w
hT(Tw- T)=q (tT)-kRCmΔrQm(Tw,p)
In formula: T --- each unit acid solution mean temperature, DEG C；
Tw--- each unit crack wall surface temperature, DEG C；
hT--- convection transfer rate, J/ (m2·min·℃)；
NNu--- nusselt number, zero dimension；
Khf--- the thermal coefficient of acid solution, J/ (mmin DEG C)；
ρf--- reservoir rock density, kg/m3；
Cf--- reservoir rock specific heat capacity, J/ (kg DEG C)；
kR--- acid-rock reaction rate constant, (kg/m3)-m·mol/(m2·s)；
C --- each unit acid strength, kg/m3；
ΔrQm(Tw, p) --- sour rock molar reaction heat, kJ/mol；
M --- the order of reaction, zero dimension；
q(tT) --- construction terminates stratum heat transfer, kJ；
Mma--- formation rock volumetric heat capacity, J/m3·℃；
Khr--- formation rock thermal coefficient, W/ (m DEG C)；
--- porosity, %；
Each unit acid strength and crack wall surface concentration are obtained by following formula:
kg(C-Cw)=kRCw m
kg=DeNSh/w
In formula: kg--- convective transfer coefficient, m/min；
Cw--- each unit crack wall surface acid strength, kg/m3；
De--- acid solution hydrogen ion efficient coefficient, m2/s；
Nsh--- sherwood number, zero dimension；
k0--- frequency factor, (kg/m3)-m·mol/(m2·s)；
Ea--- reaction activity, J/mol；
R --- gas constant, 8.314J/ (mol DEG C).
5. the numerical computation method of deep layer limestone reservoir acid fracturing effective distance of live acid as described in claim 1, special
Sign is that step (4) process is as follows:
High-temperature and high-pressure conditions acid rock molar reaction heat Δ is calculated firstrHm(Tw, p):
In formula: ΔrHm(Tw) --- temperature TwUnder molar reaction heat, kJ/mol；
P --- strata pressure, MPa；
Cp,mNormal pressure molar heat capacity of (i, T) --- the component i at temperature T, J/ (DEG C mol)；
fg——CO2Molar fraction, zero dimension；
Vco2——CO2Molal volume, m3/mol；
Vacid--- residual acid volume, m3；
Sco2--- CO in residual acid2Solubility, m3/m3；
ΔrHm(Tw, p) --- temperature TwMolar reaction heat under pressure p, kJ/mol；
To obtain sour rock molar reaction heat Δ under formation conditionrQm(Tw, p):
6. the numerical computation method of deep layer limestone reservoir acid fracturing effective distance of live acid as described in claim 1, special
Sign is that step (5) process is as follows:
1) the sour rock molar reaction heat calculated by step (4) is calculated each unit acid solution for considering acid-rock reaction heat by step (3)
Temperature and acid strength, and make to stitch length direction each unit acid strength distribution curve；
2) it defines the 10% of the initial implantation concentration of acid solution and is used as residual sour limting concentration, take the corresponding crack seam length of residual sour limting concentration
For effective distance of live acid.
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| CN112345436B (en) * | 2020-09-22 | 2023-07-25 | 中国石油天然气股份有限公司 | Method for testing distribution of diversion capability of acid etching crack |
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