CN110837132B - Carbonate rock logging permeability prediction method - Google Patents

Carbonate rock logging permeability prediction method Download PDF

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CN110837132B
CN110837132B CN201810925944.8A CN201810925944A CN110837132B CN 110837132 B CN110837132 B CN 110837132B CN 201810925944 A CN201810925944 A CN 201810925944A CN 110837132 B CN110837132 B CN 110837132B
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李博南
沈珲
李呈呈
马中高
杨丽
司文朋
王欢
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China Petroleum and Chemical Corp
Sinopec Geophysical Research Institute
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Abstract

The invention relates to a carbonate rock logging permeability prediction method, relates to the technical field of rock physics research, and is used for solving the technical problem that the logging permeability in the prior art is difficult to calculate. The method fully considers the rock physical characteristics of the multiple pore types of the carbonate rock in the permeability prediction process, completes component type permeability prediction on the basis of pore type division, can be applied to well logging permeability prediction due to the consideration of the permeability heterogeneity characteristic caused by the geometric morphology of pores in the carbonate rock, has higher precision than the traditional method of porosity-permeability linear fitting or empirical relationship prediction, and more accurately describes the permeability heterogeneity characteristic of the carbonate rock.

Description

Carbonate rock logging permeability prediction method
Technical Field
The invention relates to the technical field of petrophysical research, in particular to a carbonate logging permeability prediction method.
Background
The permeability is an important index for evaluating the economic value of a reservoir, and a logging permeability prediction technology is one of key technologies in exploration of the earth physics. Because carbonate rock is more single in composition compared with sandstone and the diagenesis process of carbonate rock causes more complex pore types, and the strict general mathematical relationship between the porosity and the permeability of a reservoir does not exist, the calculation of the logging permeability is very difficult.
The well logging permeability prediction method widely applied in industry cannot achieve a good effect on carbonate rocks, for example, the electrical property factor is considered in the calculation of the permeability by a resistivity method, and the universality is not achieved; the flow unit method and the lithology classification method are complex to implement and lack uniform division basis; the statistical method of the rock core pore-permeability relation is simple and easy to implement, and obtains a good effect in the permeability of the sandstone reservoir, but the permeability of the carbonate has the characteristic of strong heterogeneity, so the pore-permeability fitting relation of the total data may not meet the permeability prediction requirement of the multi-element pore type.
Disclosure of Invention
The invention provides a carbonate logging permeability prediction method, which is used for solving the technical problem that the logging permeability in the prior art is difficult to calculate.
The invention provides a carbonate logging permeability prediction method, which comprises the steps of
Step S10: classifying the pore types of the carbonate rocks according to the pore occurrence to obtain n pore types;
step S20: determining the value range of the critical porosity of each pore type based on experimental statistical data;
step S30: calculating the critical porosity of each core in the research area according to the logging speed
Figure GDA0003361074210000011
The value range of the critical porosity according to each pore type and the critical porosity of each core
Figure GDA0003361074210000012
Respectively determining the pore type of each core;
step S40: performing binomial fitting on the distribution of the porosity and the permeability of each core to obtain the critical porosity of the ith porosity type core
Figure GDA0003361074210000021
Permeability of (2)
Figure GDA0003361074210000022
Wherein the content of the first and second substances,
Figure GDA0003361074210000023
satisfies the following defined formula:
Figure GDA0003361074210000024
wherein, PiAn intercept for a binomial fit of the core of the ith pore type;
Qia gradient value for binomial fitting of the ith pore type core;
Figure GDA0003361074210000025
porosity of the core being of the ith porosity type.
In one embodiment, P is a member of the groupiTo and QiLinear interpolation is carried out to obtain the intercept of binomial fitting of the rock core with any pore type
Figure GDA0003361074210000026
And
Figure GDA0003361074210000027
the core of any pore type is at the critical porosity
Figure GDA0003361074210000028
Permeability of (2)
Figure GDA0003361074210000029
Satisfies the following defined formula:
Figure GDA00033610742100000210
in one embodiment, the critical porosity of the ith pore type core
Figure GDA00033610742100000211
Satisfies the following defined formula:
Figure GDA00033610742100000212
wherein, KmBulk modulus of a solid phase mineral mixture;
KPadditional modulus induced for the fluid;
Figure GDA00033610742100000213
the longitudinal wave velocity of the i-th pore type saturated rock;
Figure GDA00033610742100000214
the transverse wave velocity of the i-th pore type saturated rock;
Figure GDA00033610742100000215
the density of the i-th pore type saturated rock.
In one embodiment, the additional modulus K induced by the fluidPSatisfies the following defined formula:
Figure GDA00033610742100000216
wherein β satisfies the following defined formula:
Figure GDA00033610742100000217
wherein, KflBulk modulus of a fluid phase mineral mixture;
Kdryis the bulk modulus of dry rock.
In one embodiment, the bulk modulus K of the mixed mineralsmSatisfies the following defined formula:
Figure GDA0003361074210000031
wherein, KVVoigt limit for bulk modulus of solid phase mineral mixture;
KRthe reus limit for bulk modulus of solid phase mineral mixtures.
In one embodiment, the bulk modulus of the fluid phase mineral mixture is KflSatisfies the following defined formula:
Figure GDA0003361074210000032
wherein v isjVolume content of j-th fluid;
Kjis the bulk modulus of the jth fluid;
n is the amount of fluid.
In one embodiment, the density of the i-th pore type saturated rock
Figure GDA0003361074210000033
Satisfies the following defined formula:
Figure GDA0003361074210000034
wherein v iscalIs the volume content of calcite;
vdolis the volume content of dolomite;
vclayis a body of clayVolume content;
ρcaldensity of calcite;
ρdolis the density of dolomite;
ρclayis the density of the clay.
In one embodiment, the Voigt limit K of the bulk modulus of the solid phase mineral mixtureVSatisfies the following defined formula:
KV＝vcalKcal+vdolKdol+vclayKclay
reus limit K of bulk modulus of solid phase mineral mixtureRSatisfies the following defined formula:
Figure GDA0003361074210000035
wherein, KcalIs the bulk modulus of calcite;
Kdolis the bulk modulus of dolomite;
Kclayis the bulk modulus of clay.
In one embodiment, the Voigt limit Uv for the shear modulus of the solid phase mineral mixture satisfies the following defined formula:
UV＝vcalUcal+vdolUdol+vclayUclay
reus limit U of shear modulus of solid phase mineral mixtureRSatisfies the following defined formula:
Figure GDA0003361074210000041
wherein, UcalIs the shear modulus of calcite;
Udolis the shear modulus of dolomite;
Uclayis the shear modulus of clay.
Compared with the prior art, the invention has the advantages that: the rock physical characteristics of the multiple pore types of the carbonate rock are fully considered in the permeability prediction process, the component type permeability prediction is completed on the basis of pore type division, and the permeability heterogeneity characteristic caused by the geometric form of pores in the carbonate rock is considered, so that the method can be applied to well logging permeability prediction, has higher precision than the traditional method of porosity-permeability linear fitting or empirical relation prediction, and more accurately describes the permeability heterogeneity characteristic of the carbonate rock.
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The invention will be described in more detail hereinafter on the basis of embodiments and with reference to the accompanying drawings.
FIG. 1 is a flow chart of shale gas petrophysical model construction in an embodiment of the present invention;
FIG. 2 is a cross plot of porosity-permeability logs containing three carbonate horizons in an embodiment of the present invention;
FIG. 3 is a graph of well permeability predictions based on petrophysical models in an embodiment of the present invention.
Detailed Description
The invention will be further explained with reference to the drawings.
As shown in FIG. 1, the invention provides a carbonate logging permeability prediction method, which comprises the steps of firstly classifying the porosity types of the carbonate according to logging data, obtaining a critical porosity curve of rocks of each porosity type, secondly obtaining the permeability curve of rocks of each porosity type according to the porosity curve of the logging data, and finally performing linear fitting on the permeability curve to establish a porosity permeability prediction model under any porosity type.
The well log data of the present invention includes porosity, velocity, density and mineral composition.
Specifically, in the first step, the pore types of the carbonate rock are classified according to the pore occurrence, and a plurality of pore types are obtained.
The porosity of the carbonate rock ranges from 0.01 to 0.4. Generally, the porosity of carbonate rock is classified into four types of intergranular porosity, intragranular porosity (i.e., lysopore), microporosity, and fissured porosity according to the porosity occurrence.
Secondly, determining the value range [ a ] of the critical porosity of each pore type based on experimental statistical datan， an+1]. For example, the porosity of the intergranular pores is in the range of [ a ]1，a2) The porosity of the intra-granular pores has a value range of [ a2， a3) The value of the porosity of the micropores is in the range of [ a ]3，a4) The porosity of the crack pores has a value range of [ a4，a5]。
Wherein, a1＝0.01nm；a5＝0.4nm。
Thirdly, calculating the critical porosity of each core in the research area according to the logging speed
Figure GDA0003361074210000051
The value range of the porosity according to each pore type and the critical porosity of each core
Figure GDA0003361074210000052
The type of porosity of each core was determined separately. The type of porosity of the core can be obtained by visual observation or by CT scanning.
Critical porosity
Figure GDA0003361074210000053
The calculation of (c) will be described in detail below.
Critical porosity obtained by calculation
Figure GDA0003361074210000054
And comparing with the four value ranges, and determining that the core is of the porosity type if the core falls within the numerical range of the porosity of the type.
Fourthly, performing binomial fitting on the distribution of the porosity and permeability of each core to obtain the critical porosity of the ith porosity type core
Figure GDA0003361074210000055
Permeability of (2)
Figure GDA0003361074210000056
Wherein the content of the first and second substances,
Figure GDA0003361074210000057
satisfies the following defined formula:
Figure GDA0003361074210000058
wherein, PiAn intercept for a binomial fit of the core of the ith pore type;
Qia gradient value for binomial fitting of the ith pore type core;
Figure GDA0003361074210000059
porosity of the core being of the ith porosity type.
Binomial fitting of the porosity and permeability of the core is an existing conventional means and is not described in detail herein.
Further, due to the permeability calculated according to equation (1)
Figure GDA00033610742100000510
Is a discrete variable, so the above formula is linearly transformed to obtain the permeability
Figure GDA00033610742100000511
Is a continuous variable.
In particular, each PiTo and QiLinear interpolation is carried out to obtain the intercept of binomial fitting of the rock core with any pore type
Figure GDA00033610742100000512
And
Figure GDA00033610742100000513
the core of any pore type is at the critical porosity
Figure GDA00033610742100000514
Permeability of (2)
Figure GDA00033610742100000515
Satisfies the following defined formula:
Figure GDA0003361074210000061
the relation of the change of the permeability with the depth under any pore type can be calculated and obtained according to the formula (2).
Preferably, the value range [ a ] of the critical porosity of each pore type is obtained according to the experimental statistical data in the second stepn，an+1]Obtaining an average of the critical porosity for each pore type
Figure GDA0003361074210000062
Wherein the content of the first and second substances,
Figure GDA0003361074210000063
satisfies the following defined formula:
Figure GDA0003361074210000064
by using
Figure GDA0003361074210000065
Each PiTo and QiLinear interpolation is carried out to obtain the intercept of binomial fitting of the rock core with any pore type
Figure GDA0003361074210000066
And
Figure GDA0003361074210000067
wherein
Figure GDA0003361074210000068
And
Figure GDA0003361074210000069
are all about
Figure GDA00033610742100000610
As a function of (c).
The linear interpolation is a conventional means in the prior art, and is not described herein again.
The critical porosity of the core will be described below in the ith porosity type
Figure GDA00033610742100000611
For example, the calculation method will be described in detail.
First, the bulk modulus K of the mixed minerals according to Voigt-reus-Hill mean theory (1952)mSatisfies the following defined formula:
Figure GDA00033610742100000612
shear modulus of mixed minerals UmSatisfies the following defined formula:
Figure GDA00033610742100000613
wherein, KVVoigt limit for bulk modulus of solid phase mineral mixture;
KRreus limit, which is the bulk modulus of a solid phase mineral mixture;
UVvoigt limit for shear modulus of solid phase mineral mixture;
URthe reus limit for shear modulus of solid phase mineral mixtures.
Further, since carbonate rock generally has the characteristic of single rock-making mineral, it generally contains only three minerals, calcite, dolomite and clay. Thus, V of bulk modulus of solid phase mineral mixtureoil boundary KVSatisfies the following defined formula:
KV＝vcalKcal+vdolKdol+vclayKclay
reus limit K of bulk modulus of solid phase mineral mixtureRSatisfies the following defined formula:
Figure GDA00033610742100000614
wherein, KcalIs the bulk modulus of calcite;
Kdolis the bulk modulus of dolomite;
Kclayis the bulk modulus of clay;
vcalis the volume content of calcite;
vdolis the volume content of dolomite;
vclayis the volume content of clay.
In addition, the Voigt limit U of the shear modulus of the solid-phase mineral mixtureVSatisfies the following defined formula:
UV＝vcalUcal+vdolUdol+vclayUclay
reus limit U of shear modulus of solid phase mineral mixtureRSatisfies the following defined formula:
Figure GDA0003361074210000071
wherein, UcalIs the shear modulus of calcite;
Udolis the shear modulus of dolomite;
Uclayis the shear modulus of clay.
Second, according to Wood's mean theory, K is the bulk modulus of the fluid phase mineral mixture (or fluid phase suspension)flSatisfies the following defined formula:
Figure GDA0003361074210000072
wherein v isjVolume content of j-th fluid;
Kjis the bulk modulus of the jth fluid;
n is the amount of fluid.
Finally, the critical porosity is calculated
Figure GDA0003361074210000073
Bulk modulus K of saturated rock according to Gassmann equation velocity form rewritten by Murphy (1991)satBulk modulus K to dry rockdrySatisfies the following definitional formula:
Ksat＝Kdry+KP
wherein, KPAdditional modulus, K, induced for fluidsPSatisfies the following defined formula:
Figure GDA0003361074210000074
wherein β satisfies the following defined formula:
Figure GDA0003361074210000081
according to Nur (1995) Critical porosity model, KdrySatisfies the following defined formula:
Figure GDA0003361074210000082
Ksatsatisfies the following defined formula:
Figure GDA0003361074210000083
wherein，
Figure GDA0003361074210000084
The longitudinal wave velocity of the i-th pore type saturated rock;
Figure GDA0003361074210000085
the transverse wave velocity of the i-th pore type saturated rock;
Figure GDA0003361074210000086
the density of the i-th pore type saturated rock.
Thus, a critical porosity is obtained
Figure GDA0003361074210000087
Porosity of
Figure GDA0003361074210000088
And the relation between the logging speeds
Figure GDA0003361074210000089
Thereby critical porosity
Figure GDA00033610742100000810
Satisfies the following defined formula:
Figure GDA00033610742100000811
the prediction method of the present invention will be described below by taking a carbonate formation as an example.
As shown in fig. 2, the cross plot of porosity-permeability of the log of three carbonate layers is shown, the abscissa of the cross plot is porosity, the ordinate of the cross plot is predicted well-logging permeability (mD), and different gray scales represent different types of pores obtained by dividing the critical porosity. It can be seen that the prediction results of the method are not a single linear relationship of the full data fit, and have pore-permeability characteristics dependent on pore type.
As shown in fig. 3, the results of well permeability predictions based on petrophysical models are shown. Wherein the dotted line represents a permeability prediction result estimated based on a pore-permeability fitting relationship of the total data, the solid line represents a permeability prediction result obtained based on a pore-permeability fitting relationship of the porosity type, and the round dots represent actually measured permeability of the rock core and serve as detection points of the permeability prediction result.
Through calculation, the correlation coefficient of the dotted line fitting is 0.322, the correlation coefficient of the solid line is 0.703, and the correlation coefficient of the solid line is greatly improved, so that the effectiveness of the method is proved.
While the invention has been described with reference to a preferred embodiment, various modifications may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In particular, the technical features mentioned in the embodiments can be combined in any way as long as there is no structural conflict. It is intended that the invention not be limited to the particular embodiments disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (9)

1. A carbonate logging permeability prediction method is characterized by comprising the following steps:
step S10: classifying the pore types of the carbonate rocks according to the pore occurrence to obtain various pore types;
step S20: determining the value range of the critical porosity of each pore type based on experimental statistical data;
step S30: calculating the critical porosity of each core in the research area according to the logging speed
Figure FDA0003361074200000011
The value range of the critical porosity according to each pore type and the critical porosity of each core
Figure FDA0003361074200000012
Respectively determining the pore type of each core;
step S40: performing binomial fitting on the distribution of the porosity and the permeability of each core to obtain the critical porosity of the ith porosity type core
Figure FDA0003361074200000013
Permeability of (2)
Figure FDA0003361074200000014
Wherein the content of the first and second substances,
Figure FDA0003361074200000015
satisfies the following defined formula:
Figure FDA0003361074200000016
wherein, PiAn intercept for a binomial fit of the core of the ith pore type;
Qia gradient value for binomial fitting of the ith pore type core;
Figure FDA0003361074200000017
porosity of the core being of the ith porosity type.
2. The carbonate logging permeability prediction method of claim 1, wherein each P is PiTo and QiLinear interpolation is carried out to obtain the intercept of binomial fitting of the rock core with any pore type
Figure FDA0003361074200000018
And
Figure FDA0003361074200000019
the core of any pore type is at the critical porosity
Figure FDA00033610742000000110
Permeability of (2)
Figure FDA00033610742000000111
Satisfies the following defined formula:
Figure FDA00033610742000000112
3. the carbonate logging permeability prediction method of claim 2, wherein the critical porosity of the core of the ith pore type
Figure FDA00033610742000000113
Satisfies the following defined formula:
Figure FDA00033610742000000114
wherein, KmBulk modulus of a solid phase mineral mixture;
KPadditional modulus induced for the fluid;
Figure FDA00033610742000000115
the longitudinal wave velocity of the i-th pore type saturated rock;
Figure FDA0003361074200000021
the transverse wave velocity of the i-th pore type saturated rock;
Figure FDA0003361074200000022
the density of the i-th pore type saturated rock.
4. The carbonate log permeability prediction method of claim 3, wherein the additional modulus K induced by the fluidPSatisfies the following defined formula:
Figure FDA0003361074200000023
wherein β satisfies the following defined formula:
Figure FDA0003361074200000024
wherein, KflBulk modulus of a fluid phase mineral mixture;
Kdryis the bulk modulus of dry rock.
5. Carbonate logging permeability prediction method according to claim 3 or 4, characterized in that bulk modulus K of the mixed mineralsmSatisfies the following defined formula:
Figure FDA0003361074200000025
wherein, KVVoigt limit for bulk modulus of solid phase mineral mixture;
KRthe reus limit for bulk modulus of solid phase mineral mixtures.
6. The carbonate logging permeability prediction method of claim 4, wherein K is the bulk modulus of the fluid phase mineral mixtureflSatisfies the following defined formula:
Figure FDA0003361074200000026
wherein v isjIs jthThe volume content of the seed fluid;
Kjis the bulk modulus of the jth fluid;
n is the amount of fluid.
7. The carbonate logging permeability prediction method of claim 4, wherein the density of the i-th pore type saturated rock
Figure FDA0003361074200000027
Satisfies the following defined formula:
Figure FDA0003361074200000028
wherein v iscalIs the volume content of calcite;
vdolis the volume content of dolomite;
vclayis the volume content of clay;
ρcaldensity of calcite;
ρdolis the density of dolomite;
ρclayis the density of the clay.
8. Carbonate logging permeability prediction method according to claim 7, characterized by the Voigt limit K of the bulk modulus of the solid phase mineral mixtureVSatisfies the following defined formula:
KV＝vcalKcal+vdolKdol+vclayKclay
reus limit K of bulk modulus of solid phase mineral mixtureRSatisfies the following defined formula:
Figure FDA0003361074200000031
wherein, KcalIs the bulk modulus of calcite;
Kdolis the bulk modulus of dolomite;
Kclayis the bulk modulus of clay.
9. The carbonate logging permeability prediction method of claim 7, wherein the Voigt limit Uv for the shear modulus of the solid phase mineral mixture satisfies the following defined formula:
UV＝vcalUcal=vdolUdol+vclayUclay
reus limit U of shear modulus of solid phase mineral mixtureRSatisfies the following defined formula:
Figure FDA0003361074200000032
wherein, UcalIs the shear modulus of calcite;
Udolis the shear modulus of dolomite;
Uclayis the shear modulus of clay.
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