CN109184644B - Early-stage polymer injection effect evaluation method considering non-Newtonian property and seepage additional resistance of polymer - Google Patents
Early-stage polymer injection effect evaluation method considering non-Newtonian property and seepage additional resistance of polymer Download PDFInfo
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Abstract
The invention discloses an early stage polymer injection effect evaluation method considering non-Newtonian property and seepage additional resistance of a polymer. The invention establishes an improved Hall curve suitable for evaluating the early polymer flooding effect on the basis of respectively considering the non-Newtonian property and the additional resistance effect of the polymer solution. According to the slope and intercept of the improved Hall curve, indexes such as flow index, average effective working viscosity in a swept range, fluidity, resistance coefficient, starting pressure gradient and the like of the underground polymer solution at any time of polymer injection can be solved, and the effectiveness of early polymer injection is more accurately evaluated.
Description
Technical Field
The invention relates to the field of petrochemical industry, in particular to an early stage polymer injection effect evaluation method considering non-Newtonian property and seepage additional resistance of a polymer.
Background
At present, the main method for judging the effectiveness of polymer injection is to draw a Hall curve according to field data and judge whether polymer injection is effective or not through the change of the slope of a polymer flooding stage and a water flooding stage[1,2]And calculating a drag coefficient and a residual drag coefficient from the slope[3,4]. However, the early polymer flooding of the offshore oil field is different from the middle and later polymer flooding of the onshore oil field, and has the main characteristics of early polymer injection time, short water flooding stage, even polymer injection in production and no water flooding stage[5-8]Therefore, the traditional Hall curve is not suitable for the evaluation of early polymer flooding of offshore oil fields. In addition, for early polymer flooding development in offshore fields, the main components of the subterranean fluid are oil and polymer solutions. The hydrophobic association polymer for offshore oil field belongs to non-Newtonian fluid[9-12]Whereas the conventional Hall curve is established on the basis of Newtonian fluids[13]Therefore, the offshore early polymer flooding puts higher requirements on the reliability of Hall curve evaluation and the applicability of application.
Liu Rui [14]An improved Hall curve method is established on the basis of considering non-Newtonian property, indexes such as flow state index, average effective working viscosity in a swept range, resistance coefficient and the like of the underground polymer solution can be obtained, and the indexes are used for evaluating the polymer drive effect of the offshore oilfield at early stage. The polymer flooding experiment of Zhang Shi Ying and the like shows that[15]And an additional resistance effect exists during polymer flooding, so that the dynamic prediction of polymer flooding development is greatly influenced. Therefore, further refinement of the hall curve is required.
Disclosure of Invention
The invention aims to provide an early stage injection effect evaluation method considering the non-Newtonian property and seepage additional resistance of a polymer.
The invention provides an early stage polymer injection effect evaluation method considering polymer non-Newtonian property and seepage additional resistance, which is based on the following mathematical model:
1.1 hypothesis Condition
In order to meet the requirement of offshore oilfield development and evaluation, the characteristics of offshore early polymer flooding development are combined, and the conventional Hall curve structure is used for reference[13]Deriving an improved Hall curve formula, and providing the following basic assumption conditions for improving the Hall curve construction:
the stratum is homogeneous, equal in thickness and isotropic;
the flow is in the plane radial direction, and the influences of capillary force, gravity, compressibility of rocks and fluid and temperature are ignored;
③ the injected fluid is non-Newtonian pseudoplastic fluid, the property of the fluid is the same as that of the fluid in the stratum, and the constitutive equation thereof[16]Following the Ostwald-dewaele power law model
(0<n<1)；
Fourthly, the calculation formula of the equivalent shear rate of the fluid in the porous medium is as follows[17]：
The fluid is oil-water two-phase, and the polymer only exists in the water phase;
sixthly, considering the non-Newtonian property of the polymer;
(vii) considering the additional drag effect of the injected polymer;
and allowing the injection mode of the oil field to be early stage injection, namely production and injection.
1.2 improved Hall Curve formulation considering Start pressure gradient
Considering the non-Newtonian behaviour of the polymer solutions respectively[16-19]And on the basis of starting the pressure gradient, an improved Hall curve formula suitable for evaluating the early polymer injection effect is constructed.
Power law fluid seepage flow basic differential equation
The basic differential equation or seepage equation of the known power-law fluid stable seepage is[18]：
If the additional drag effect is taken into account, the basic differential equation becomes:
the inner boundary determining conditions are as follows:
the conditions for determining the solution of the outer boundary are as follows:
p|r＝R＝pe 4
in the formula: r is the displacement radius; p is a radical ofeIs the original formation pressure.
Substituting equations (3) and (4) into equation (2) to determine the bottom hole pressure of the injection well as:
since the condition is assumed to be production-ready, i.e., injection-polymerization, the permeability k in the above formularIn effect the permeability k of the polymer solution as it flows in the formationp. To express the uniformity in form, equation (5) is modified to:
considering that adsorption retention of polymer solution after injection may cause a decrease in formation permeability, the permeability decrease factor R is usedkPermeability k in formula (6)pMake corrections[17]。
In the formula: k is the formation permeability; k is a radical ofpIs the permeability of the polymer solution as it flows in the formation.
Substituting the formula (7) into the formula (6) to simplify the formula:
the formula of the bottom hole pressure of the injection well of any small layer is obtained from the formula (8):
in the formula: q. q.siFlow of any ith sublayer, m3/s；hiIs the effective thickness of any ith sublayer, m; k is a radical ofiFormation permeability of any ith sublayer, m2。
It is known that:
in the formula: q is the total flow, m3S; h is the total effective thickness, m.
Therefore, substituting equation (10) into equation (9) simplifies the process:
the bottom hole pressure of the injection well for the entire reservoir is then:
wherein m is the number of small layers.
Considering the water flooding stage before early stage of injection, the above formula can be:
in the formula: r is the leading edge position of the polymer displacement, m; rwIs the position of the front edge of the water drive before the polymer injection. Equal to wellbore radius when no flooding early injection, Rw＝rwAnd m. In actual development, there is often a short water flooding stage, which can be calculated by equation (14):
in the formula: r is the radius of the leading edge location of the polymer displacement, m; rwThe radius of the front edge position of the water flooding before the water flooding is equal to the radius of a shaft when the water flooding early stage is not injected, namely Rw＝rw，m；RpIs the actual displacement distance of the polymer solution, m; wi1Cumulative injection volume, m, for early stage flooding3；Wi2Cumulative injection amount of polymer solution after water flooding, m3(ii) a h is the effective thickness of the polymer injection layer, m; phi is the porosity of the stratum and has no dimensional quantity; sorResidual oil saturation, dimensionless amount; swcTo constrain water saturation, there is no dimensional quantity.
Converting the formula (14) from international units to legal units and then simplifying the formula:
in the formula: p is a radical ofwfThe bottom hole pressure of an injection well is MPa; p is a radical ofeIs the formation pressure, MPa; n is a flow index, dimensionless quantity, 0<n<1; q is the flow rate, m3D; t is the cumulative injection time, d; mu.seIs the effective viscosity of the subterranean polymer solution, mPa · s; k is a radical ofiPermeability of the ith sublayer (i ═ 1, 2, … …, m), μm2；RkPermeability reduction factor; m is the number of oil reservoir small layers and has no dimension; h is the total effective thickness of the oil reservoir, m; r is the leading edge position of the polymer displacement, m; rwFor the front edge position of water flooding before water flooding, when water flooding is not performed at the early stage, the front edge position is equal to the radius of a shaft, namely Rw＝rwM; lambda is the starting pressure gradient, MPa/m.
Expression (15) can be expressed as:
pwf-pe＝Cqn+A 16
wherein:
taking the natural logarithm of the formula (16), and respectively carrying out time integration on two sides with equal sign to obtain the product after simplification:
pwfthe bottom hole pressure of an injection well is MPa;
peis the formation pressure, MPa;
n is a flow state index, a dimensionless quantity, 0< n < 1;
q is the daily injection, m3/d；
t is production time in units of d;
equation (19) is an expression a of an improved Hall curve under the legal unit system, and the non-Newtonian property of the injected polymer solution, the starting pressure gradient and the heterogeneity of the multilayer oil reservoir are considered.
Wherein:
if (16) is directly integrated, then:
∫(pwf-pe)dt＝C∫qndt+b 20
in the formula:
the equation (20) is an expression b of an improved Hall curve which is prepared by a legal unit and considers the non-Newtonian property of the injected polymer solution, the starting pressure gradient and the heterogeneity of the multilayer oil reservoir.
2 evaluation index
And establishing an evaluation index for evaluating the early polymer flooding effect by improving the Hall curves a and b.
(1) Index of flow state n
As can be seen from equation (17): the slope of the polymer flooding section in the Hall curve a is improved and is equal to the flow state index n in the sweep range of the underground polymer solution in value.
(2) Mean working effective viscosity mue
As can be seen from equations (20) and (17): mu.seIs an unknown term in improving the slope C of the curve in the Hall curve b, so that μ can be found from this slopeeComprises the following steps:
n is a flow state index, a dimensionless quantity, 0< n < 1;
m is the number of oil reservoir small layers and has no dimension;
h is the total effective thickness of the oil reservoir, m;
Rkpermeability reduction factor;
Rwfor the front edge position of water flooding before water flooding, when water flooding is not performed at the early stage, the front edge position is equal to the radius of a shaft, namely Rw＝rw，m；
kiPermeability of the ith sublayer (i ═ 1, 2, … …, m), μm2；
Mu solved by the above formulaeThe average effective viscosity of a polymer solution when working underground is described as a quantity that varies with the length of the injection time. In the formula, units are prepared by a method.
(3) Working flow lambda of underground polymer solutionp
Comparing the formulas (6) and (12), the average effective permeability of the polymer solution flowing in the formation under the multilayer conditions is:
pwf-pe＝Cqn+A 16
the coefficient term C in equation (16) can be converted into:
the working fluidity of the underground polymer solution is obtained according to the definition of the fluidity:
this gives:
n is a flow state index, a dimensionless quantity, 0< n < 1;
r is the leading edge position of the polymer displacement, m;
Rwfor the front edge position of water flooding before water flooding, when water flooding is not performed at the early stage, the front edge position is equal to the radius of a shaft, namely Rw＝rw，m；
h is the total effective thickness of the oil reservoir, m;
therefore, it is known that the work flow rate of the underground polymer solution can be solved by improving the slope and intercept of the Hall curve, and the unit of the method is adopted in the formula.
(4) Flow coefficient of underground polymer solution in operation
According to the definition of the flow coefficient, the flow coefficient of the underground polymer solution in work is obtained as follows:
working flow lambda of underground polymer solutionp；
h is the total effective thickness of the oil reservoir, m;
kiis the permeation of the ith sublayerTransmittance (i ═ 1, 2, … …, m), μm2；
Therefore, after the working fluidity of the underground polymer solution is obtained by the formula (23), the flow coefficient of the underground polymer solution in working can be solved by the formula (24), and the unit of a method is adopted in each unit.
(5) Resistance coefficient of early stage injection Rf
The drag coefficient, also known as the drag factor, refers to the ratio of the fluidity of water to the fluidity of the polymer solution during polymer flooding. The drag coefficient is a measure of the improvement in the mobility ratio of a polymer flooding and a significant increase in the value indicates an increased ability of the polymer solution to improve the oil-water mobility ratio.
The following results are obtained by defining the drag coefficient:
coefficient of resistance RfIs a dimensionless quantity, and the units in the formula all adopt legal units.
Working flow lambda of underground polymer solutionp；
RkPermeability reduction factor;
mean working effective viscosity mue；
(6) Initiation pressure gradient of injected polymer
As can be seen from equations (20) and (21): λ is an unknown term in the intercept b in the modified hall curve-b, so from this slope one can find λ as:
n is a flow state index, a dimensionless quantity, 0< n < 1;
r is the leading edge position of the polymer displacement, m;
Rwfor the front edge position of water flooding before water flooding, when water flooding is not performed at the early stage, the front edge position is equal to the radius of a shaft, namely Rw＝rw，m；
T is the cumulative injection time, d;
from the above, the present invention provides a method for evaluating early stage focusing effect by considering non-Newtonian property and seepage additional resistance of polymer, comprising:
1) and drawing an improved Hall curve a and an improved Hall curve b by using the following dynamic data in the polymer injection well: flow rate q, injection well bottom pressure pwfOriginal formation pressure peAnd a production time t;
wherein, the improved Hall curve a is represented by ^ ln (p)wf-pe) dt is the ordinate, and is obtained by drawing by taking the [ integral ] ln qdt as the abscissa;
the improved Hall curve a corresponds to the following equation:
in said formula 19, pwfThe bottom hole pressure of an injection well is MPa;
peoriginal formation pressure, MPa;
q is the daily injection, m3/d；
t is production time in units of d;
n is a flow state index, a dimensionless quantity, 0< n < 1;
in said formulas 17 and 18, RkPermeability reduction factor;
μeis the average working effective viscosity, mPa · s, of the subterranean polymer solution;
Rwis the radius, m, of the water-flooding front edge position before polymer injection;
m is the number of oil reservoir small layers and has no dimension;
h is the total effective thickness of the oil reservoir, m;
kipermeability of the ith sublayer (i ═ 1, 2, … …, m), μm2；
R is the radius of the leading edge location of the polymer displacement, m;
n is a flow state index, a dimensionless quantity, 0< n < 1;
lambda is starting pressure gradient, MPa/m;
the Hall curve b is modified to
Is a vertical coordinate, in ^ qnd is plotted on the abscissa;
the equation corresponding to the improved hall curve b is shown in equation 20:
∫(pwf-pe)dt＝C∫qndt+b 20
in the above-mentioned formula 20, the first,
c is the slope of the polymer flooding section of the improved Hall curve b;
b is the intercept of the improved Hall curve b;
pwfthe bottom hole pressure of an injection well is MPa;
peoriginal formation pressure, MPa;
q is the daily injection, m3/d；
t is production time in units of d;
n is a flow state index, a dimensionless quantity, 0< n < 1;
lambda is starting pressure gradient, MPa/m;
r is the radius of the leading edge location of the polymer displacement, m;
Rwis the radius, m, of the water-flooding front edge position before polymer injection;
t is the cumulative injection time, d;
Rkpermeability reduction factor;
μeis the average working effective viscosity, mPa · s, of the subterranean polymer solution;
m is the number of oil reservoir small layers and has no dimension;
h is the total effective thickness of the oil reservoir, m;
kipermeability of the ith sublayer (i ═ 1, 2, … …, m), μm2；
2) Calculating the slope of the injection stage in the improved Hall curve a obtained in the step 1), wherein the slope is equal to the value n;
3) substituting n obtained in the step 2) into a formula 22 to obtain the average working effective viscosity mue；
In the above-mentioned formula 22, the first,
n is a flow state index, a dimensionless quantity, 0< n < 1;
m is the number of oil reservoir small layers and has no dimension;
h is the total effective thickness of the oil reservoir, m;
c is the slope of the polymer flooding section of the improved Hall curve b;
r is the radius of the leading edge location of the polymer displacement, m;
Rkpermeability reduction factor;
Rwis the radius, m, of the water-flooding front edge position before polymer injection;
kipermeability of the ith sublayer (i ═ 1, 2, … …, m), μm2；
4) Calculating the slope C of the polymer flooding section in the improved Hall curve b obtained in the step 1), substituting the slope C and n obtained in the step 2) into a formula 23 to obtain the work fluidity lambda of the underground polymer solutionp；
n is a flow state index, a dimensionless quantity, 0< n < 1;
r is the radius of the leading edge location of the polymer displacement, m;
Rwis the radius, m, of the water-flooding front edge position before polymer injection;
c is the slope of the polymer flooding section of the improved Hall curve b;
h is the total effective thickness of the oil reservoir, m;
5) the working fluidity lambda of the underground polymer solution obtained in the step 4)pSubstituting into formula 24 to obtain the flow coefficient of underground polymer solution during operation
h is the total effective thickness of the oil reservoir, m;
6) the working fluidity lambda of the underground polymer solution obtained in the step 4)pSubstituting into formula 25 to obtain the resistance coefficient R of early stage polymer injectionf；
In said formula 25, RkPermeability reduction factor;
μeis the average working effective viscosity, mPa · s, of the subterranean polymer;
μwformation water viscosity, mPa · s;
λwis the formation water mobility, mum2/(mPa·s)；
λpWorking flow of underground polymer solution, mum2/(mPa·s)；
k is the permeability in μm2；
7) Calculating intercept b in the improved Hall curve b, and calculating to obtain a starting pressure gradient lambda of the injected polymer according to a formula 26;
b is the intercept of the improved Hall curve b;
n is a flow state index, a dimensionless quantity, 0< n < 1;
r is the radius of the leading edge location of the polymer displacement, m;
Rwis the radius, m, of the water-flooding front edge position before polymer injection;
t is the cumulative injection time, d;
n obtained in the step 2) and mu obtained in the step 3) can be obtainedeLambda obtained in step 4)pStep 5) obtaining
R obtained in step 6)fAnd the start pressure gradient lambda of the injected polymer.
The invention establishes an improved Hall curve suitable for evaluating the early polymer flooding effect on the basis of respectively considering the non-Newtonian property and the additional resistance effect of the polymer solution. According to the slope and intercept of the improved Hall curve, indexes such as flow index, average effective working viscosity in a swept range, fluidity, resistance coefficient, starting pressure gradient and the like of the underground polymer solution at any time of polymer injection can be solved, and the effectiveness of early polymer injection is more accurately evaluated.
Drawings
FIG. 1 is a traditional Hall curve of a Bohai sea typical oil reservoir well A;
FIG. 2 is a Bohai sea typical reservoir A well improved Hall curve, wherein a is the Bohai sea typical reservoir A well improved Hall curve-a; b is a Bohai sea typical oil reservoir A well improved Hall curve-b;
FIG. 3 is a schematic diagram of a capillary balance method device;
FIG. 4 is a diagram showing the capillary pressure method for measuring the starting pressure gradient at different permeabilities;
FIG. 5 is a graph of flow state index as a function of time of polymer injection;
FIG. 6 is a graph of mean working effective viscosity of subterranean polymers as a function of time of polymer injection;
FIG. 7 is a graph of subsurface polymer solution flow coefficient as a function of time of polymer injection;
FIG. 8 is a graph of resistivity of a subterranean polymer solution as a function of time of polymer injection.
Detailed Description
The present invention will be further illustrated with reference to the following specific examples, but the present invention is not limited to the following examples. The method is a conventional method unless otherwise specified. The starting materials are commercially available from the open literature unless otherwise specified.
Example 1 evaluation of early Polymer flooding Effect of actual injection well
Average permeability of Bohai sea typical oil reservoir A well oil layer is 5000 multiplied by 10-3μm2. And (3) beginning to inject polymer after 30 days of water injection, wherein the polymer product is AP-P4, the polymer injection concentration is 1750mg/l, and the wellhead injection viscosity is 24.6mPa & s. The average daily injection q was 355m3/d。
Static data for well a are shown in tables 1 and 2.
TABLE 1 static parameters of well A
| Parameter compliance | Parameter name | Unit of | Numerical value |
| Sor | Residual oil saturation | Dimensionless quantity | 0.2 |
| Swc | Irreducible water saturation | Dimensionless quantity | 0.37 |
| Rk | Coefficient of permeability decrease | Dimensionless quantity | 2.6 |
| μw | Viscosity of formation water | mPa·s | 0.5 |
TABLE 2 Small layer thickness and layered Permeability of A well
| Layer number of small | Small layer thickness (m) | Permeability of small layer (mum)2) |
| 1 | 2.9 | 5.7139 |
| 2 | 5.7 | 8.5521 |
| 3 | 3.7 | 4.6511 |
| 4 | 6.9 | 2.7001 |
| 5 | 11.4 | 6.6586 |
1) The conventional hall curves and the modified hall curves were plotted according to the production dynamics data shown in table 3 for 1530 days (about 4 years and 3 months) of a well development, see fig. 1 and 2.
Wherein, the improved Hall curve a is represented by ^ ln (p)wf-pe) dt is the ordinate and ^ ln qdt is the abscissa, and the corresponding equation is as follows:
in the formula 19, pwfThe bottom hole pressure of an injection well is MPa;
peoriginal formation pressure, MPa;
q is the daily injection, m3/d；
t is production time in units of d;
n is a flow state index, a dimensionless quantity, 0< n < 1;
in the equations 17 and 18, the data is shown,
Rkthe permeability reduction factor is 2.6 (see table 1 for details);
μeis the average working effective viscosity, mPa · s, of the subterranean polymer solution;
r is the radius of the polymer displaced leading edge position, calculated to a value of 196m according to table 1 and equation (14);
Rwcalculating to obtain a numerical value of 27m for the radius of the water flooding front edge position before polymer injection according to the table 1 and the formula (14);
(1) m is the number of oil reservoir small layers, the dimensionless quantity is zero, and the numerical value is 5;
h is the total effective thickness of the oil reservoir, and the value is calculated to be 30.6m according to the table 5;
kithe permeability of the ith sublayer (i ═ 1, 2, … …, m), and the values are given in table 2;
the Hall curve b is improved to
Is a vertical coordinate, in ^ qnd is plotted on the abscissa;
the equation corresponding to the modified hall curve b is shown in equation 20:
∫(pwf-pe)dt＝C∫qndt+b 20
in the formula 20, the first and second phases,
it can be seen that C is equal in value to the slope of the polymer drive segment of the modified hall curve b, for this well, the value is 1.0036; b is numerically equal to the intercept of the modified Hall curve b, for this well, the value is-77.557;
2) calculating the slope of the injection stage in the improved hall curve a obtained in step 1) to be 0.321, wherein the slope is equal to n in value and is 0.321 (see table 4 for details);
3) substituting C obtained in the step 1) and n obtained in the step 2) into a formula 22 to obtain the average working effective viscosity mu of the polymer solution in the swept rangee；
In the above-mentioned formula 22, the first,
n is a flow state index and a dimensionless quantity, wherein n is more than 0 and less than 1, and the numerical value is 0.321 through calculation according to the step (2);
c is equal in value to the slope of the polymer flooding segment of the modified Hall curve b, and the value obtained by calculation according to step (1) is 1.0036
m is the number of oil reservoir small layers, a dimensionless quantity, and is 5;
h is the total effective thickness of the oil reservoir, and the value is calculated to be 30.6m according to the table 5;
Rkthe permeability reduction factor is 2.6 (see table 1 for details);
r is the radius of the polymer displaced leading edge position, calculated to a value of 196m according to table 1 and equation (14);
Rwcalculating to obtain a numerical value of 27m for the radius of the water flooding front edge position before polymer injection according to the table 1 and the formula (14); (ii) a
kiThe permeability of the ith sublayer (i ═ 1, 2, … …, m), and the values are given in table 2;
calculating to obtain the average working effective viscosity mu of the underground polymer solution in the swept rangeeIs 6.74 mPas;
4) modifying the obtained in the step 1)Putting the slope C of the polymer flooding section in the Hall curve b and n obtained in the step 2) into a formula 23 to obtain the working fluidity lambda of the underground polymer solutionp；
n is a flow state index and a dimensionless quantity, wherein n is more than 0 and less than 1, and the numerical value is 0.321 through calculation according to the step (2);
c is equal in value to the slope of the polymer flooding section of the improved Hall curve b, and the value obtained by calculation according to the step (1) is 1.0036;
r is the radius of the polymer displaced leading edge position, calculated to a value of 196m according to table 1 and equation (14);
Rwcalculating to obtain a numerical value of 27m for the radius of the water flooding front edge position before polymer injection according to the table 1 and the formula (14);
h is the total effective thickness of the oil reservoir, and the value is calculated to be 30.6m according to the table 5;
after calculation, the working fluidity lambda of the underground polymer solution is obtainedpIs 0.28 μm2/(mPa·s)。
5) The working fluidity lambda of the underground polymer solution obtained in the step 4)pSubstituting into formula 24 to obtain the flow coefficient of underground polymer solution during operation
h is the total effective thickness of the oil reservoir, and the value is calculated to be 30.6m according to the table 5;
λpthe working fluidity of the underground polymer solution was calculated according to step 4) to be 0.28. mu.m2/(mPa·s)；
Calculating to obtain the flow coefficient of underground polymer solution during working
Is 8.5 (m.mu.m)2)/(mPa·s)；
6) The working fluidity lambda of the underground polymer solution obtained in the step 4)pSubstituting into formula 25 to obtain the resistance coefficient R of early stage polymer injectionf；
In said formula 25, RkThe permeability reduction factor is 2.6 (see table 1 for details);
μecalculating to obtain 6.74 mPas according to the step 3) for the average working effective viscosity of the underground polymer solution within the swept range;
μwformation water viscosity, 0.5mPa · s (see table 1 for details);
calculating to obtain the resistance coefficient R of early polymer injectionfIt was 35.05.
7) Calculating intercept b in the improved Hall curve b, and calculating to obtain a starting pressure gradient lambda of the injected polymer according to a formula 26;
b is the intercept of the improved Hall curve b, and the value obtained by calculation according to the step (1) is-77.557;
n is a flow state index and a dimensionless quantity, wherein n is more than 0 and less than 1, and the numerical value is 0.321 through calculation according to the step (2);
r is the radius of the polymer displaced leading edge position, calculated to a value of 196m according to table 1 and equation (14);
Rwcalculating to obtain a numerical value of 27m for the radius of the water flooding front edge position before polymer injection according to the table 1 and the formula (14);
t is the cumulative injection time, 1405.5 d.
The initial pressure gradient lambda of the early stage injection is calculated to be 1 multiplied by 10-4。
As can be seen from fig. 1, for the conventional hall curve method, the drag coefficient obtained by the slope ratio of the water flooding section and the polymer flooding section cannot be utilized because the water flooding time is too short. The calculation results of each parameter obtained by applying the slope and intercept of the improved Hall curve polymer flooding section are shown in Table 4.
TABLE 4 Bohai sea typical oil reservoir A well improved Hall curve calculation parameter table
As seen from table 4, the calculation results are larger after considering the starting pressure gradient than after not considering the starting pressure gradient. This is because the slope of the hall curve does not change, but the intercept increases, taking into account the starting pressure gradient at which the polymer flow requires a certain starting pressure. The underground working viscosity of the polymer is in direct proportion to the intercept, so that the flow index of the underground polymer is unchanged after the start pressure gradient is considered, the working viscosity is larger than the result obtained when the start pressure gradient is not considered, and the flow coefficient is smaller.
3.2 Experimental validation
The polymer onset pressure gradient was measured using the capillary equilibrium method and set up as shown in figure 3. The capillary tube balancing method is characterized in that a U-shaped tube balancing principle is utilized, two liquid columns are arranged at two ends of a rock core, liquid enters one end with low pressure through the rock core under the action of pressure difference through one end with high pressure until liquid levels at two ends are stable, and the liquid level height difference at two ends of the rock core is read to determine a starting pressure gradient. After entering the core, the liquid needs to overcome a certain resistance to start flowing. When the injection pressure is higher than the starting pressure, the fluid continuously flows out of the outlet end; when the injection pressure is less than the start pressure, the fluid stops flowing; when the injection pressure is exactly equal to the start pressure, the fluid will be in a critical state before flowing[20]。
The polymer was injected into the core at a certain viscosity until the pressure remained steady and polymer solution appeared at the exit end. Installing vertical long pipes at two ends of the core, fixing a container filled with polymer solution with the same viscosity at an inlet section, and keeping a certain height; the outlet end is connected with the atmosphere. After a sufficiently long time, the liquid levels on both sides stabilize at a certain height difference, which is recorded and converted to a pressure difference according to equation (27), which is the starting pressure and converted to a starting pressure gradient.
P＝ρgh 27
In the formula, rho-liquid density, kg/m3(ii) a h is the height difference of liquid columns at two ends of the rock core, m; p-pressure difference, Pa
Three permeability levels (1500X 10) were selected-3μm2、2000×10-3μm2And 2500X 10-3μm2) And (5) carrying out a capillary balance method injection experiment. Due to the shear viscosity reduction benefit of the polymer solution when the polymer solution flows in the shaft during on-site actual injection, the viscosity of the polymer solution reaching the bottom of the well is about 10-12 mPa & s. Therefore, the viscosity of the solution of the prepared polymer in the experiment is 10 mPas, and the apparent starting pressure gradient of the obtained rock cores with different permeabilities is shown in Table 5 and FIG. 4.
TABLE 5 capillary method for measuring the starting pressure gradient
As can be seen in fig. 4, the lower the permeability, the higher the start-up pressure gradient. Apparent starting pressure gradient p when the polymer injection viscosity is 10 mPasTThe following relationship exists with respect to permeability k: p is a radical ofT＝0.0078e-0.4581k. The formula is applied to a Bohai sea typical oil reservoir A well, and the average permeability weighted by the thickness of the small layer is calculated to be 5.786 mu m according to the table 22. The starting pressure gradient of the well A obtained in the substitution formula is 0.0003MPa/m, and is similar to the starting pressure gradient value obtained by applying an improved Hall curve.
3.3 variation of subsurface Polymer solution parameters with time
For the Bohai sea typical oil reservoir well A, the flow state index, the effective working viscosity, the flow coefficient and the resistance coefficient of the underground polymer solution at different polymer injection time are calculated by applying an improved Hall curve and are changed along with time, and the flow state index, the effective working viscosity, the flow coefficient and the resistance coefficient are shown in a figure 5-a figure 8.
As can be seen from FIGS. 5-8, the flow index increases slightly with increasing duration, but does not change much, the flow coefficient increases, the drag coefficient decreases, and the mean working effective viscosity of the underlying polymer decreases within the swept range. This is because the same polymer solution is injected, and the non-Newtonian behavior in the polymer sweep range is slightly reduced but does not vary much. The effective working viscosity of the polymer solution after polymer injection is affected by the actions of mechanical shearing, adsorption and the like, about 50 percent of loss is caused after 4 years of polymer injection, the resistance coefficient is reduced, the flow coefficient is increased, and the effect of improving the oil-water fluidity ratio is gradually reduced.
4 conclusion
1) For the conditions of early injection and short water flooding time, the conventional Hall curve cannot calculate the resistance coefficient. The improved Hall curve method directly utilizes the change of the production dynamics to obtain the average working effective viscosity mu of the polymer solution in the swept range on the basis of considering the additional resistanceeThis important criterion, the drag coefficient, is obtained by the ratio of the polymer viscosity to the water viscosity. The problem that the early polymer injection resistance coefficient cannot be solved or the solving is invalid is solved.
2) The improved Hall curve allows the calculation of the starting pressure gradient of the polymer flow in the ground by the mathematical change of the pressure difference and the flow rate. The starting pressure gradient obtained by the calculation method and the experimental result are verified, and the starting pressure gradient calculated by the method has certain reliability.
3) As the injection time was extended, it was seen that the non-newtonian properties of the underground polymer solution were slightly reduced, but not much changed. The average working effective viscosity of the lower polymer within the swept range is affected by the actions of mechanical shearing, adsorption and the like, and about 50% of the average working effective viscosity is lost after 4 years of polymer injection. The subsurface polymer solution flow coefficient increases and the drag coefficient decreases. The effect of improving the oil-water fluidity ratio gradually becomes worse.
TABLE 3 well development production dynamic data
Remarking: because there are too many table rows (total 1530 rows), data in the middle of development is omitted.
Claims (1)
1. A method for evaluating the effect of polymer injection comprises the following steps:
1) and drawing an improved Hall curve a and an improved Hall curve b by using the following dynamic data in the polymer injection well: daily injection quantity q and bottom hole pressure p of injection wellwfOriginal formation pressure peAnd a production time t;
wherein, the improved Hall curve a is represented by ^ ln (p)wf-pe) dt is the ordinate, and is obtained by drawing by taking the [ integral ] lnqdt as the abscissa;
the improved Hall curve a corresponds to the following equation:
in said formula 19, pwfThe bottom hole pressure of an injection well is MPa;
peoriginal formation pressure, MPa;
q is the daily injection, m3/d；
t is production time in units of d;
n is a flow state index, a dimensionless quantity, 0< n < 1;
in said formulas 17 and 18, RkPermeability reduction factor;
μeis the average working effective viscosity, mPa · s, of the subterranean polymer solution;
Rwis the radius, m, of the water-flooding front edge position before polymer injection;
m is the number of oil reservoir small layers and has no dimension;
h is the total effective thickness of the oil reservoir, m;
kipermeability of the i-th sublayer, μm2，i＝1，2，……，m；
R is the radius of the leading edge location of the polymer displacement, m;
n is a flow state index, a dimensionless quantity, 0< n < 1;
lambda is starting pressure gradient, MPa/m;
the improved Hall curve b is multiplied by ^ (p)wf-pe) dt is ordinate, in ^ qndt is plotted on the abscissa;
the equation corresponding to the improved hall curve b is shown in equation 20:
∫(pwf-pe)dt＝C∫qndt+b 20
in the above-mentioned formula 20, the first,
c is the slope of the polymer flooding section of the improved Hall curve b;
b is the intercept of the improved Hall curve b;
pwfthe bottom hole pressure of an injection well is MPa;
peoriginal formation pressure, MPa;
q is the daily injection, m3/d；
t is production time in units of d;
n is a flow state index, a dimensionless quantity, 0< n < 1;
lambda is starting pressure gradient, MPa/m;
r is the radius of the leading edge location of the polymer displacement, m;
Rwis the radius, m, of the water-flooding front edge position before polymer injection;
t is the cumulative injection time, d;
Rkpermeability reduction factor;
μeis the average working effective viscosity, mPa · s, of the subterranean polymer solution;
m is the number of oil reservoir small layers and has no dimension;
h is the total effective thickness of the oil reservoir, m;
kipermeability of the i-th sublayer, μm2，i＝1，2，……，m；
2) Calculating the slope of the injection stage in the improved Hall curve a obtained in the step 1), wherein the slope is equal to the value n;
3) substituting n obtained in the step 2) into a formula 22 to obtain the average working effective viscosity mue；
In the above-mentioned formula 22, the first,
n is a flow state index, a dimensionless quantity, 0< n < 1;
m is the number of oil reservoir small layers and has no dimension;
h is the total effective thickness of the oil reservoir, m;
c is the slope of the polymer flooding section of the improved Hall curve b;
r is the radius of the leading edge location of the polymer displacement, m;
Rkpermeability reduction factor;
Rwis the radius, m, of the water-flooding front edge position before polymer injection;
kipermeability of the i-th sublayer, μm2，i＝1，2，……，m；
4) Calculating the slope C of the polymer flooding section in the improved Hall curve b obtained in the step 1), substituting the slope C and n obtained in the step 2) into a formula 23 to obtain the work fluidity lambda of the underground polymer solutionp；
n is a flow state index, a dimensionless quantity, 0< n < 1;
r is the radius of the leading edge location of the polymer displacement, m;
Rwis the radius, m, of the water-flooding front edge position before polymer injection;
c is the slope of the polymer flooding section of the improved Hall curve b;
h is the total effective thickness of the oil reservoir, m;
5) the working fluidity lambda of the underground polymer solution obtained in the step 4)pSubstituting into formula 24 to obtain the flow coefficient of underground polymer solution during operation
h is the total effective thickness of the oil reservoir, m;
kpis the permeability of the polymer solution as it flows in the formation;
6) the working fluidity lambda of the underground polymer solution obtained in the step 4)pSubstituting into formula 25 to obtain the resistance coefficient R of early stage polymer injectionf；
In said formula 25, RkPermeability reduction factor;
μeis the average working effective viscosity, mPa · s, of the subterranean polymer;
μwformation water viscosity, mPa · s;
λwis the formation water mobility, mum2/(mPa·s)；
λpWorking flow of underground polymer solution, mum2/(mPa·s)；
k is the permeability in μm2；
kpIs the permeability of the polymer solution as it flows in the formation;
7) calculating intercept b in the improved Hall curve b, and calculating to obtain a starting pressure gradient lambda of the injected polymer according to a formula 26;
b is the intercept of the improved Hall curve b;
n is a flow state index, a dimensionless quantity, 0< n < 1;
r is the radius of the leading edge location of the polymer displacement, m;
Rwis the radius, m, of the water-flooding front edge position before polymer injection;
t is the cumulative injection time, d;
n obtained in the step 2) and mu obtained in the step 3) can be obtainedeLambda obtained in step 4)pStep 5) obtaining
R obtained in step 6)fAnd the start pressure gradient lambda of the injected polymer.
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