CN102809526B - Method for measuring diffusion coefficient of carbon dioxide in saturated oil core - Google Patents

Abstract

The invention relates to a method for measuring a diffusion coefficient of carbon dioxide in a saturated oil core. The method comprises the following steps of: performing nondimensionalization by using a convection-diffusion mathematical model, and performing numerical solution, wherein the diffusion coefficient Deff of the carbon dioxide in the saturated oil core is finally obtained by using the method and required to be used in the numerical solution process; and continuously correcting the value of D'eff, and repeatedly executing the step (13), so a curve c of delta Co and t<1/2> is completely coincided with a curve b of delta PTh and the t<1/2>, wherein the D'eff is the Deff and represents the diffusion coefficient of the carbon dioxide in the saturated oil core. The method has the advantages that the influence of the volumetric expansion of crude oil caused by dissolution of the carbon dioxide in the crude oil on the diffusion process and the influence of a porous medium on the diffusion process are taken into consideration, and the obtained effective diffusion coefficient of the carbon dioxide in the saturated oil core can accurately reflect the true diffusion process.

Description

A kind of method of measuring carbon dioxide coefficient of diffusion in saturated oil rock core

Technical field

The present invention relates to a kind of method of measuring carbon dioxide coefficient of diffusion in saturated oil rock core, belong to the technical field of petrochemical complex.

Background technology

The global warming problem causing due to a large amount of discharges of carbon dioxide is increasingly severe.And collecting carbonic anhydride with bury (CO ₂capture and Storage) technology thought a kind of potential, alternative carbon dioxide discharge-reduction scheme widely, can reduce the carbon dioxide content in atmosphere, alleviates climate warming problem.At carbon dioxide geological, bury in scheme, improve oil recovery factor (CO with carbon dioxide ₂-EOR), not only can reach the effect of burying of carbon dioxide, and can improve the recovery ratio of Reservoir Crude Oil, therefore carbon dioxide raising oil recovery factor technology is widely used in oil field.In the process of employing carbon-dioxide flooding, the quality transfer law of carbon dioxide in saturated crude oil rock core seems particularly important for the prediction of the migration characteristics of injecting carbon dioxide.Therefore the mensuration of the coefficient of diffusion of carbon dioxide in saturated crude oil rock core has great importance for the development of carbon dioxide flooding oil tech.

Measure at present carbon dioxide method of coefficient of diffusion in porous medium and be mainly the PVT method that non-expansion type spreads, the method has only been considered the diffusion of carbon dioxide in porous medium, do not have to consider, because the dissolving of carbon dioxide causes the impact of crude oil volumetric expansion on diffusion, can not well simulate the true diffusion process of carbon dioxide in saturated crude oil rock core.Meanwhile, the PVT of employing methods are measured the coefficient of diffusion of carbon dioxide in crude oil more at present, and the measurement of this coefficient of diffusion does not reflect the impact of porous medium on diffusion process, thereby can not be used for measuring the coefficient of diffusion of carbon dioxide at saturated crude oil rock core.

Summary of the invention

Summary of the invention

For above technical deficiency, the invention provides a kind of method of measuring carbon dioxide coefficient of diffusion in saturated oil rock core.The present invention, under the combined influence effect that considers crude oil volumetric expansion and porous medium, calculates the mathematical model of carbon dioxide coefficient of diffusion in saturated crude oil rock core by having derived in conjunction with one dimension advection diffusion equation and real gas state equation.By measure the Pressure Drop of carbon dioxide in conjunction with its corresponding calculated with mathematical model the coefficient of diffusion of carbon dioxide in saturated crude oil rock core.

The diffusion model of carbon dioxide in the rock core of saturation water and the difference of the diffusion model of carbon dioxide of the present invention in the rock core of saturated oil are: carbon dioxide solubility in water after, water expands hardly, be that the expansion of water is on not impact of diffusion, and the dissolving of carbon dioxide in oil can cause significantly expansion of oil in the present invention, in rock core, the expansion of oil has obvious influence to diffusion, so it is convection current-diffusion mathematical model that the present invention will be spread mathematics model modification, but because the Analytical Solution of convection current diffusion mathematical model is more difficult, so the present invention is directed to convection current-diffusion mathematical model, first carry out nondimensionalization, then carry out numerical solution, and in numerical solution process, need to use the diffusion coefficient D of the carbon dioxide of finally trying to achieve in saturated oil rock core _eff, described D _effthat the method for the invention solves and obtains.

Terminological interpretation:

Saturated fluid processing: refer to by vacuumizing the whole sucking-offs of air of loading in diffusion barrel in sample rock core interior detail fine porosity, then utilize constant-flux pump that Experimental Flowing Object displacement is entered in diffusion barrel, injection experiments fluid generation build the pressure, it is logical when pressure is suppressed 10MPa, Experimental Flowing Object in diffusion barrel is under high pressure pressed in the hole of filling sample rock core, has realized whole saturated upper Experimental Flowing Objects in the hole that loads sample rock core.

Detailed Description Of The Invention

Technical scheme of the present invention is as follows:

A kind of carbon dioxide diffusion coefficient D in saturated oil rock core of measuring _effmethod, comprise that step is as follows:

(1) diffusion barrel is dried;

(2) will sample cylinder rock core or artificial cylinder rock core as filling sample rock core, described filling sample rock core will be dried, after will upper and lower filling sample rock core both ends of the surface sealing with fluid sealant, pack in diffusion barrel;

(3) diffusion barrel is vacuumized;

(4) utilize well heater to heat diffusion barrel, constant temperature is to wanting simulated formation temperature, stand-by;

(5) in diffusion barrel, pump into Experimental Flowing Object, and be forced into 10MPa, to loading core sample, carry out saturated fluid processing; Described Experimental Flowing Object is simulated formation crude oil, and described simulated formation crude oil is the Simulation of Crude Oil identical with formation pore oil property;

(6) continue diffusion barrel inside Experimental Flowing Object to carry out pressurized operation, be forced into and want simulated formation pressure;

(7) in the bottom of described diffusion barrel, be provided with check valve, adjust the set pressure of check valve, described set pressure is compared with the little 0.1MPa of diffusion barrel internal pressure;

(8) to diffusion barrel, pump into carbon dioxide, the pressure of described carbon dioxide with want simulated formation pressure identical, due to the effect of check valve, the Experimental Flowing Object in emptying diffusion barrel;

(9) sealing diffusion barrel, utilizes pressure transducer to gather the original pressure P in diffusion barrel ₀, gather n time point t ₁～t _npressure P ₁～P _n, n is more than or equal to 2;

(10) Δ P _{ex, i}for testing the pressure P of n the time point recording ₁-P _nrespectively with original pressure P ₀pressure differential, as, Δ P _{ex, 1}=P ₁-P ₀, Δ P _{ex, 2}=P ₂-P ₀..., Δ P _{ex, n}=P _n-P ₀; By the pressure drop Δ P calculating _{ex, 1}~ Δ P _{ex, n}respectively with time point t ₁~ t _nthe corresponding mapping of 1/2 power, obtain the Pressure Drop Δ P that experiment records _exwith t ^1/2curve a, calculate the slope k of described curve a cathetus section part;

(11) to Δ P _exwith t ^1/2curve a revise: because carbon dioxide and the saturated crude oil at filling sample core surface place rigidly connect while touching, need to set up a stable liquid-gas interface boundary condition, thereby the pressure drop of experiment incipient stage is very fast, the Pressure Drop of experiment starting stage belongs to the pressure drop Δ P that the unstable stage of diffusion causes measurement _exwith t ^1/2curve map be upwards offset a segment distance, for the ease of calculating pressure fall-off curve b with theory below, contrast, need to be to Δ P _exwith t ^1/2curve a revise.Modification method is as follows: first find the flex point of described curve a, i.e. the corresponding time point t of curve a cathetus section part starting point _s; Then by formula, 1. obtain average error

$\stackrel{\&OverBar;}{\mathrm{\&delta;}}=\frac{\underset{i=s+1}{\overset{n}{\mathrm{\&Sigma;}}}(\mathrm{\&Delta;}{P}_{\mathrm{Ex},i}-k\sqrt{t_i})(t_i-t_{i-1})}{t_n-t_s}$ ①

Formula 1. in, Δ P _{ex, i}-for testing the pressure P of n the time point recording ₁～P _nrespectively with original pressure P ₀pressure differential, as, Δ P _{ex, 1}=P ₁-P ₀, Δ P _{ex, 2}=P ₂-P ₀..., Δ P _{ex, n}=P _n-P ₀, kPa; K-be the slope of the curve a cathetus section part of trying to achieve in step (10), t _i-for testing i the time point recording, min; t _s-be the corresponding time point of curve a cathetus section part starting point of trying to achieve in step (10), min;

According to 2. formula to experimental pressure drop Δ P _{ex, i}revise, obtain revising pressure drop values Δ P _{co, i}:

$\mathrm{\&Delta;}{P}_{\mathrm{Co},i}=\mathrm{\&Delta;}{P}_{\mathrm{Ex},i}-\stackrel{\&OverBar;}{\mathrm{\&delta;}}(i=s+1,s+2,\mathrm{\&Lambda;},n)$ ②

Make Δ P _cowith t ^1/2curve c;

(12) bring the slope k in step (10) into formula 3.,

$\mathrm{\&Delta;}{P}_{\mathrm{Ex}}=\frac{{4M}_{\&infin;}\mathrm{ZRT}\sqrt{D_{\mathrm{eff}}^{\&prime;}}}{r_{0}V\sqrt{\mathrm{\&pi;}}}\sqrt{t}=k\sqrt{t}$ ③

Formula 3. in, M _∞-the time levels off to carbon dioxide when infinite and diffuses into the amount in filling sample rock core, mol; Z-compressibility factor is determined by the pressure and temperature of testing; R-universal gas constant, 8.314Pam ³k ^-1mol ^-1; T-experimental temperature, K; D ' _effcarbon dioxide effective diffusion cofficient in-unexpansive system, m ²/ s; r ₀the xsect radius of-filling sample rock core, m; Annular volume between V-filling sample rock core and diffusion barrel, m ³; T-time point, comprises t ₁~ t _n; K-Δ P _exwith t ^1/2the slope of the straight-line segment part that forms;

By formula, 3. obtained, obtain the effective diffusion cofficient D ' of carbon dioxide in unexpansive system _eff;

(13) by D ' _effbring in convection current-diffusion mathematical model of nondimensionalization and carry out numerical solution, obtain nondimensional gas concentration lwevel and distribute

with crude oil volumetric expansion velocity distribution

(14) gas concentration lwevel is distributed

with crude oil volumetric expansion velocity distribution

there is bonding state equation after dimension, obtain corresponding theory and calculate pressure drop Δ P _th, utilize described theory to calculate pressure drop Δ P _thwith t ^1/2curve plotting b, curve b and the Δ P that has just started experiment and record _cowith t ^1/2curve a have error, the source of error is exactly D ' _eff;

(15) constantly revise D ' _effvalue, repeating step (13), makes Δ P _cowith t ^1/2curve c and Δ P _thwith t ^1/2curve b overlap completely, D ' now _effbe D _eff, wherein said D _efffor the coefficient of diffusion of carbon dioxide in saturated oil rock core.

The invention has the advantages that:

Present invention is directed at the diffusion process of carbon dioxide in saturated crude oil rock core, considered the crude oil volumetric expansion that causes due to the dissolving of carbon dioxide in the crude oil impact on diffusion process, considered again the impact of porous medium on diffusion process, the effective diffusion cofficient of the carbon dioxide of trying to achieve in saturated crude oil rock core can reflect real diffusion process comparatively accurately simultaneously.

Accompanying drawing explanation

Fig. 1 is that embodiment passes through the P in his-and-hers watches 1 ₁-P _ncorresponding time t ₁~ t _nmapping, i.e. pressure temporal evolution figure;

Fig. 2 is that embodiment passes through the pressure differential deltap P in his-and-hers watches 1 ₁-Δ P _nto time t ^1/2mapping, tests pressure differential deltap P _exwith t ^1/2variation a, and through revised Pressure Drop Δ P _cowith t ^1/2curve c, by Convection-diffusion model iterative computation Δ P out _thwith t ^1/2curve b.

Embodiment

According to embodiment and Figure of description, the present invention is described in detail below, but is not limited to this.

Embodiment,

As shown in Figure 1-2.

A kind of carbon dioxide diffusion coefficient D in saturated oil rock core of measuring _effmethod, comprise that step is as follows:

(1) diffusion barrel is dried;

(2) will sample cylinder rock core or artificial cylinder rock core as filling sample rock core, described filling sample rock core will be dried, after will upper and lower filling sample rock core both ends of the surface sealing with fluid sealant, pack in diffusion barrel;

(3) diffusion barrel is vacuumized;

(4) utilize well heater to heat diffusion barrel, constant temperature is to wanting simulated formation temperature, stand-by;

(5) in diffusion barrel, pump into Experimental Flowing Object, and be forced into 10MPa, to loading core sample, carry out saturated fluid processing; Described Experimental Flowing Object is simulated formation crude oil, and described simulated formation crude oil is the Simulation of Crude Oil identical with formation pore oil property;

(6) continue diffusion barrel inside Experimental Flowing Object to carry out pressurized operation, be forced into and want simulated formation pressure;

(7) in the bottom of described diffusion barrel, be provided with check valve, adjust the set pressure of check valve, described set pressure is compared with the little 0.1MPa of diffusion barrel internal pressure;

(8) to diffusion barrel, pump into carbon dioxide, the pressure of described carbon dioxide with want simulated formation pressure identical, due to the effect of check valve, the Experimental Flowing Object in emptying diffusion barrel;

(9) sealing diffusion barrel, utilizes pressure transducer to gather the original pressure P in diffusion barrel ₀, gather n time point t ₁~ t _npressure P ₁～P _n, (n is more than or equal to 2);

(10) Δ P _{ex, i}for testing the pressure P of n the time point recording ₁-P _nrespectively with original pressure P ₀pressure differential, as, Δ P _{ex, 1}=P ₁-P ₀, Δ P _{ex, 2}=P ₂-P ₀..., Δ P _{ex, n}=P _n-P ₀; By the pressure drop Δ P calculating _{ex, 1}~ Δ P _{ex, n}respectively with time point t ₁~ t _nthe corresponding mapping of 1/2 power, obtain the Pressure Drop Δ P that experiment records _exwith t ^1/2curve a, calculate the slope of described curve a cathetus section part

(11) to Δ P _exwith t ^1/2curve a revise: because carbon dioxide and the saturated crude oil at filling sample core surface place rigidly connect while touching, need to set up a stable liquid-gas interface boundary condition, thereby the pressure drop of experiment incipient stage is very fast, the Pressure Drop of experiment starting stage belongs to the pressure drop Δ P that the unstable stage of diffusion causes measurement _exwith t ^1/2curve map be upwards offset a segment distance, for the ease of calculating pressure fall-off curve b with theory below, contrast, need to be to Δ P _exwith t ^1/2curve a revise.Modification method is as follows: first find the flex point of described curve a, i.e. the corresponding time point t of curve a cathetus section part starting point _s=19.27min; Then by formula, 1. obtain average error

$\stackrel{\&OverBar;}{\mathrm{\&delta;}}=\frac{\underset{i=s+1}{\overset{n}{\mathrm{\&Sigma;}}}(\mathrm{\&Delta;}{P}_{\mathrm{Ex},i}-k\sqrt{t_i})(t_i-t_{i-1})}{t_n-t_s}$ ①

, $\stackrel{\&OverBar;}{\mathrm{\&delta;}}=245.31\left(\mathrm{kPa}\right)$

Formula 1. in, Δ P _{ex, i}-for testing the pressure P of n the time point recording ₁～P _nrespectively with original pressure P ₀pressure differential, as, Δ P _{ex, 1}=P ₁-P ₀, Δ P _{ex, 2}=P ₂-P ₀..., Δ P _{ex, n}=P _n-P ₀, kPa; K-is the slope of the curve a cathetus section part of trying to achieve in step (10),

t _i-for testing i the time point recording, min; t _s-be the corresponding time point of curve a cathetus section part starting point of trying to achieve in step (10), min;

According to 2. formula to experimental pressure drop Δ P _{ex, i}revise, obtain revising pressure drop values Δ P _{co, i}:

$\mathrm{\&Delta;}{P}_{\mathrm{Co},i}=\mathrm{\&Delta;}{P}_{\mathrm{Ex},i}-\stackrel{\&OverBar;}{\mathrm{\&delta;}}(i=s+1,s+2,\mathrm{\&Lambda;},n)$ ②

Make Δ P _cowith t ^1/2curve c;

Table 1: utilize pressure transducer to gather the pressure P of each time point ₁～P _nwith the pressure differential deltap P calculating _exwith correction pressure differential deltap P _co

By the pressure in his-and-hers watches 1, the time is mapped, obtain pressure temporal evolution figure, as shown in Figure 1.

(12) bring the slope k in step (10) into formula 3.,

$\mathrm{\&Delta;}{P}_{\mathrm{Ex}}=\frac{{4M}_{\&infin;}\mathrm{ZRT}\sqrt{D_{\mathrm{eff}}^{\&prime;}}}{r_{0}V\sqrt{\mathrm{\&pi;}}}\sqrt{t}=k\sqrt{t}$ ③

Formula 3. in, M _∞-the time levels off to carbon dioxide when infinite and diffuses into the amount in filling sample rock core, mol; Z-compressibility factor is determined by the pressure and temperature of testing; R-universal gas constant, 8.314Pam ³k ^-1mol ^-1; T-experimental temperature, K; D ' _effcarbon dioxide effective diffusion cofficient in-unexpansive system, m ²/ s; r ₀the xsect radius of-filling sample rock core, m; Annular volume between V-filling sample rock core and diffusion barrel, m ³; T-time point, comprises t ₁~ t _n; K-Δ P _exwith t ^1/2the slope of the straight-line segment part that forms;

By formula, 3. obtained, $k=\frac{4M_{\&infin;}\mathrm{ZRT}\sqrt{D_{\mathrm{eff}}^{\&prime;}}}{r_{0}V\sqrt{\mathrm{\&pi;}}}=24.3033\mathrm{kPa}/\sqrt{\min },$ Obtain the effective diffusion cofficient D ' of carbon dioxide in unexpansive system _eff=2.95 × 10 ^-10m ²/ s;

(13) by D ' _effbring in convection current-diffusion mathematical model of nondimensionalization and carry out numerical solution, obtain nondimensional gas concentration lwevel and distribute

with crude oil volumetric expansion velocity distribution

$\left\{\begin{array}{c}\frac{\&PartialD;\stackrel{\&OverBar;}{c}}{\&PartialD;\mathrm{\&tau;}}+\stackrel{\&OverBar;}{c}\frac{\&PartialD;\stackrel{\&OverBar;}{u}}{\&PartialD;\stackrel{\&OverBar;}{r}}+\frac{\stackrel{\&OverBar;}{c}\stackrel{\&OverBar;}{u}}{\stackrel{\&OverBar;}{r}}+\mathrm{\&lambda;}\frac{\&PartialD;\stackrel{\&OverBar;}{c}}{\&PartialD;\stackrel{\&OverBar;}{r}}=\frac{{\&PartialD;}^2\stackrel{\&OverBar;}{c}}{\&PartialD;{\stackrel{\&OverBar;}{r}}^2}\\ \begin{array}{cc}\stackrel{\&OverBar;}{c}=1& (\stackrel{\&OverBar;}{r}=1,\mathrm{\&tau;}>0)\\ \stackrel{\&OverBar;}{u}=0,\frac{\&PartialD;\stackrel{\&OverBar;}{c}}{\&PartialD;\stackrel{\&OverBar;}{r}}=0& (\stackrel{\&OverBar;}{r}=0,\mathrm{\&tau;}>0)\\ \stackrel{\&OverBar;}{u}=0,\stackrel{\&OverBar;}{c}=0& (\mathrm{\&tau;}=0,\stackrel{\&OverBar;}{r}<1)\\ \stackrel{\&OverBar;}{u}=0,\stackrel{\&OverBar;}{c}=1& (\mathrm{\&tau;}=0,\stackrel{\&OverBar;}{r}=1)\end{array}\end{array}\right.$ ④

Formula 4. in, dimensionless time: dimensionless radius:

nondimensional velocity:

dimensionless concentration: $\stackrel{\&OverBar;}{c}=\frac{\mathrm{<figure-callout\; id="0"\; label="c\; c"\; filenames="HDA00002061470000012.png"\; state="\{\{state\}\}">c</figure-callout>}}{c_{}};$ $\mathrm{\&lambda;}=\stackrel{\&OverBar;}{u}-\frac{1}{\stackrel{\&OverBar;}{r}};$

Consider that dimensionless diffusion-convection equation fully implicit solution finite difference method that crude oil expands carries out solution procedure as follows, in departure process, the single order of speed single order differential and concentration and second-order differential central difference schemes, the single order differential of time adopts forward difference form.Above-mentioned equation is carried out to discretize, discretize form:

$\frac{\&PartialD;\stackrel{\&OverBar;}{c}}{\&PartialD;\mathrm{\&tau;}}=\frac{1}{\mathrm{\&Delta;\&tau;}}({\stackrel{\&OverBar;}{c}}_i^{n+1}-{\stackrel{\&OverBar;}{c}}_i^n)+O\left(\mathrm{\&Delta;\&tau;}\right)$

$\frac{\&PartialD;\stackrel{\&OverBar;}{c}}{\&PartialD;\stackrel{\&OverBar;}{r}}=\frac{1}{2\mathrm{\&Delta;}\stackrel{\&OverBar;}{r}}({\stackrel{\&OverBar;}{c}}_{i+1}^{n+1}-{\stackrel{\&OverBar;}{c}}_{i-1}^{n+1})+O\left(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{r}}^2\right)$

$\frac{{\&PartialD;}^2\stackrel{\&OverBar;}{c}}{\&PartialD;{\stackrel{\&OverBar;}{r}}^2}=\frac{1}{\mathrm{\&Delta;}{\stackrel{\&OverBar;}{r}}^2}({\stackrel{\&OverBar;}{c}}_{i+1}^{n+1}-2{\stackrel{\&OverBar;}{c}}_i^{n+1}+{\stackrel{\&OverBar;}{c}}_{i-1}^{n+1})+O\left(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{r}}^2\right)$

$\frac{\&PartialD;\stackrel{\&OverBar;}{u}}{\&PartialD;\stackrel{\&OverBar;}{r}}=\frac{1}{2\mathrm{\&Delta;}\stackrel{\&OverBar;}{r}}({\stackrel{\&OverBar;}{u}}_{i+1}^{n+1}-{\stackrel{\&OverBar;}{u}}_{i-1}^{n+1})+O\left(\mathrm{\&Delta;}{\stackrel{\&OverBar;}{r}}^2\right)$

Applying finite difference scheme partial differential equation is above write as:

$a_i{\stackrel{\&OverBar;}{c}}_{i-1}^{n+1}+b_i{\stackrel{\&OverBar;}{c}}_i^{n+1}+e_i{\stackrel{\&OverBar;}{c}}_{i+1}^{n+1}=f_i,i=\mathrm{0,1,2}\mathrm{\&Lambda;},I$

Wherein: $a_i=-\frac{\mathrm{\&Delta;\&tau;}}{\mathrm{\&Delta;}{\stackrel{\&OverBar;}{r}}^2}-\frac{\mathrm{\&lambda;\&Delta;\&tau;}}{2\mathrm{\&Delta;}\stackrel{\&OverBar;}{r}},$ $b_i=1+\frac{\mathrm{\&Delta;\&tau;}}{2\mathrm{\&Delta;}\stackrel{\&OverBar;}{r}}({\stackrel{\&OverBar;}{u}}_{i+1}^{n+1}-{\stackrel{\&OverBar;}{u}}_{i-1}^{n+1})+\frac{\mathrm{\&Delta;\&tau;}}{{\stackrel{\&OverBar;}{r}}_i}{\stackrel{\&OverBar;}{u}}_i^{n+1}+\frac{2\mathrm{\&Delta;\&tau;}}{\mathrm{\&Delta;}{\stackrel{\&OverBar;}{r}}^2},$ $e_i=\frac{\mathrm{\&lambda;\&Delta;\&tau;}}{2\mathrm{\&Delta;}\stackrel{\&OverBar;}{r}}-\frac{\mathrm{\&Delta;\&tau;}}{\mathrm{\&Delta;}{\stackrel{\&OverBar;}{r}}^2},$

$f_i=c_i^n.$

Boundary condition discretize can obtain:

${\stackrel{\&OverBar;}{c}}_{-1}^{n+1}={\stackrel{\&OverBar;}{c}}_1^{n+1},$ ${\stackrel{\&OverBar;}{c}}_I^{n+1}=1.$

The system of equations of substitution boundary condition discretize can be write as:

$\left[\begin{array}{ccccccc}{b}_0& a_0+e_0& & & & & \\ a_1& b_1& e_1& & & & \\ & a_2& b_2& e_2& & & \\ & & \&CenterDot;& \&CenterDot;& \&CenterDot;& & \\ & & & \&CenterDot;& \&CenterDot;& \&CenterDot;& \\ & & & & \&CenterDot;& \&CenterDot;& \&CenterDot;\\ & & & & & a_{I-1}& b_{I=1}\end{array}\right]\left[\begin{array}{c}{\stackrel{\&OverBar;}{c}}_0^{n+1}\\ {\stackrel{\&OverBar;}{c}}_1^{n+1}\\ {\stackrel{\&OverBar;}{c}}_2^{n+1}\\ \&CenterDot;\\ \&CenterDot;\\ {\stackrel{\&OverBar;}{c}}_{I-1}^{n+1}\end{array}\right]=\left[\begin{array}{c}{f}_0\\ f_1\\ f_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ f_{I-1}-e_{I-1}\end{array}\right]$

Your alternative manner of application Gauss-Saden calculates concentration and the velocity distribution of each time step.To each time step, by the concentration of previous time step as the velocity distribution in this time step of calculation of initial value.Adopt velocity distribution in this time step to calculate the CONCENTRATION DISTRIBUTION of next time step.Then by new CONCENTRATION DISTRIBUTION, calculate the velocity distribution in next time step.The condition that above-mentioned iterative process finishes is that the concentration maximum relative error of each radial direction Nodes is less than limits of error e (e=10 in the present invention ^-4).

(14) gas concentration lwevel is distributed with crude oil volumetric expansion velocity distribution

there is bonding state equation after dimension, obtain corresponding theory and calculate pressure drop Δ P _th, utilize described theory to calculate pressure drop Δ P _thwith t ^1/2curve plotting b, curve b and the Δ P that has just started experiment and record _cowith t ^1/2curve a have error, the source of error is exactly D ' _eff:

The dimensionless gas concentration lwevel of trying to achieve in step (13) is distributed and crude oil volumetric expansion velocity distribution

Δ P falls in the pressure carbon dioxide that has dimension and obtain intumescent system _tht in time ^1/2variation relation

${\mathrm{\&Delta;P}}_{\mathrm{Th}}=\frac{\mathrm{qZRT}-{\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="HDA00002061470000012.png"\; state="\{\{state\}\}">P</figure-callout>}}_0\mathrm{\&Delta;V}}{V-\mathrm{\&Delta;<figure-callout\; id="5"\; label="V"\; filenames="HDA00002061470000012.png"\; state="\{\{state\}\}">V</figure-callout>}}$ ⑤

Formula 5. in, Z-compressibility factor by the pressure and temperature of testing determine; R-universal gas constant, 8.314Pam ³k ^-1mol ^-1; T-experimental temperature, K; P ₀carbon dioxide original pressure in-diffusion barrel, MPa; Annular volume between V-rock sample and diffusion barrel, m ³; Δ V-obtained by 6. formula, crude oil volumetric expansion does not cause the reduction of diffusion barrel inner volume, m in the same time ³; Q-do not diffuse into the in the same time CO in saturated oil rock core ₂be dissolved in the CO that expands in crude oil ₂amount of substance sum, mol.

$\mathrm{\&Delta;V}=2\mathrm{\&pi;}{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002061470000012.png"\; state="\{\{state\}\}">r</figure-callout>}}_0^2\mathrm{h\&phi;}\underset{\mathrm{\&tau;}=0}{\overset{\mathrm{\&tau;}}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{u}}_{\stackrel{\&OverBar;}{r}=1,\mathrm{\&tau;}}\mathrm{\&Delta;\&tau;}$ ⑥

Formula 6. in, r ₀the xsect radius of-filling sample rock core, m; The length of h-filling sample rock core, m;

-nondimensional velocity; τ-dimensionless time.

The Pressure Drop Δ P of the Convection-diffusion model of trying to achieve _thwith time relationship as following table 2,

Table 2: Δ P falls in Convection-diffusion model calculating pressure _thwith time relationship table

(15) constantly revise D ' _effvalue, repeating step (13), makes Δ P _cowith t ^1/2curve a and Δ P _thwith t ^1/2curve b overlap completely, D ' now _effbe D _eff, wherein said D _efffor the coefficient of diffusion of carbon dioxide in saturated oil rock core:

By the Δ P doing in step (10) _cowith t ^1/2curve c and step (14) in do Δ P _thwith t ^1/2curve b contrast, as Fig. 2.If two curve differs larger, revise effective diffusion cofficient D ' _effand get back in step (13).If two curve relative error is less than limits of error e (e=10 in this method ^-4), stop iterative process, effective diffusion cofficient D now _eff==3.19 × 10 ^-10m ²/ s is the effective diffusion cofficient of carbon dioxide in saturated crude oil rock core.

Claims (1)

1. measure carbon dioxide diffusion coefficient D in saturated oil rock core for one kind _effmethod, it is characterized in that, it is as follows that the method comprising the steps of:

(1) diffusion barrel is dried;

(2) will sample cylinder rock core or artificial cylinder rock core as loading core sample, described filling core sample will be dried, after will upper and lower fillings core sample both ends of the surface sealing with fluid sealant, pack in diffusion barrel;

(3) diffusion barrel is vacuumized;

(4) utilize well heater to heat diffusion barrel, constant temperature is to wanting simulated formation temperature, stand-by;

(5) in diffusion barrel, pump into Experimental Flowing Object, and be forced into 10MPa, to loading core sample, carry out saturated fluid processing; Described Experimental Flowing Object is simulated formation crude oil, and described simulated formation crude oil is the Simulation of Crude Oil identical with formation pore oil property;

(6) continue diffusion barrel inside Experimental Flowing Object to carry out pressurized operation, be forced into and want simulated formation pressure;

(7) in the bottom of described diffusion barrel, be provided with check valve, adjust the set pressure of check valve, described set pressure is compared with the little 0.1MPa of diffusion barrel internal pressure;

(8) to diffusion barrel, pump into carbon dioxide, the pressure of described carbon dioxide with want simulated formation pressure identical, due to the effect of check valve, the Experimental Flowing Object in emptying diffusion barrel;

(9) sealing diffusion barrel, utilizes pressure transducer to gather the original pressure P in diffusion barrel ₀, gather n time point t ₁～t _npressure P ₁～P _n, n is more than or equal to 2;

(10) Δ P _{ex, i}for testing the pressure P of n the time point recording ₁-P _nrespectively with original pressure P ₀pressure differential, as, Δ P _{ex, 1}=P ₁-P ₀, Δ P _{ex, 2}=P ₂-P ₀..., Δ P _{ex, n}=P _n-P ₀; By the pressure drop Δ P calculating _{ex, 1}～Δ P _{ex, n}respectively with time point t ₁～t _nthe corresponding mapping of 1/2 power, obtain the Pressure Drop Δ P that experiment records _exwith t ^1/2curve a, calculate the slope k of described curve a cathetus section part;

(11) to Δ P _exwith t ^1/2curve a revise, method is as follows: first find the flex point of described curve a, i.e. the corresponding time point t of curve a cathetus section part starting point _s; Then by formula, 1. obtain average error

:

$\stackrel{\&OverBar;}{\mathrm{\&delta;}}=\frac{\underset{i=s+1}{\overset{n}{\mathrm{\&Sigma;}}}({\mathrm{\&Delta;P}}_{\mathrm{Ex},i}-k\sqrt{t_i})(t_i-t_{i-1})}{t_n-t_s}$ ①

Formula 1. in, Δ P _{ex, i}-for testing the pressure P of n the time point recording ₁～P _nrespectively with original pressure P ₀pressure differential, as, Δ P _{ex, 1}=P ₁-P ₀, Δ P _{ex, 2}=P ₂-P ₀..., Δ P _{ex, n}=P _n-P ₀, kPa; K-be the slope of the curve a cathetus section part of trying to achieve in step (10),

t _i-for testing i the time point recording, min; t _s-be the corresponding time point of curve a cathetus section part starting point of trying to achieve in step (10), min;

According to 2. formula to experimental pressure drop Δ P _{ex, i}revise, obtain revising pressure drop values Δ P _{co, i}:

$\mathrm{\&Delta;}{P}_{\mathrm{Co},i}={\mathrm{\&Delta;P}}_{\mathrm{Ex},i}-\stackrel{\&OverBar;}{\mathrm{\&delta;}},(i=s+1,s+2,...,n)$ ②

Make Δ P _cowith t ^1/2curve c;

(12) bring the slope k in step (10) into formula 3.,

${\mathrm{\&Delta;P}}_{\mathrm{Ex}}=\frac{4M_{\&infin;}\mathrm{ZRT}\sqrt{D_{\mathrm{eff}}^{\&prime;}}}{r_{0}V\sqrt{\mathrm{\&pi;}}}\sqrt{t}=k\sqrt{t}$ ③

Formula 3. in, M _∞-the time levels off to carbon dioxide when infinite and diffuses into the amount of loading in core sample, mol; Z-compressibility factor, is determined by the pressure and temperature of testing; R-universal gas constant, 8.314Pam ³k ^-1mol ^-1; T-experimental temperature, K; D ' _effcarbon dioxide effective diffusion cofficient in-unexpansive system, m ²/ s; r ₀the xsect radius of-filling core sample, m; Annular volume between V-filling core sample and diffusion barrel, m ³; T-time point, comprises t ₁～t _n; K-Δ P _exwith t ^1/2the slope of the straight-line segment part that forms;

By formula, 3. obtained,

obtain the effective diffusion cofficient D ' of carbon dioxide in unexpansive system _eff;

(13) by D ' _effbring in convection current-diffusion mathematical model of nondimensionalization and carry out numerical solution, obtain nondimensional gas concentration lwevel and distribute

with crude oil volumetric expansion velocity distribution

;

(14) gas concentration lwevel is distributed

with crude oil volumetric expansion velocity distribution

have after dimension in conjunction with real gas state equation, obtain corresponding theory and calculate pressure drop Δ P _th, utilize described theory to calculate pressure drop Δ P _thwith t ^1/2curve plotting b, curve b and the Δ P that has just started experiment and record _cowith t ^1/2curve a have error, the source of error is exactly D ' _eff;

(15) constantly revise D ' _effvalue, repeating step (13), makes Δ P _cowith t ^1/2curve c and Δ P _thwith t ^1/2curve b overlap completely, D ' now _effbe D _eff, wherein said D _efffor the coefficient of diffusion of carbon dioxide in saturated oil rock core.

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