PLYVMH

Recognised by the OPM Flow parserPROPS

This keyword, PLYVMH, defines the constants used to calculate viscosity of the polymer solution as a function of the polymer molecular weight and the polymer concentration, for the simulator's Polymer Molecular Weight Transport option, that uses the polymer molecular weight in calculating the polymer viscosity. The keyword consists of a series of row vectors, which each vector having four elements, that define the constants used in calculating the polymer viscosity

This keyword should only be used if the POLYMER and POLYMW keywords in the RUNSPEC section are also activated.

Note

This is an OPM Flow specific keyword that employs an alternative polymer flood model based on a Polymer Molecular Weight Transport equation, that is not available in the commercial simulator.

The model has been tested using metric units; however, using either field or laboratory units with the option should be considered experimental.

Notes:

The keyword is followed by NPLYVHM records as declared on the PINTDIMS keyword in the RUNSPEC section, with each record terminated by a “/” and the keyword itself should be terminated by a “/”.

The high molecular weight of polymers greatly increase the viscosity of the injected water in which they are dissolved, thus adjusting the mobility ration of the displacing phase. The increase in viscosity is caused by strong internal friction between the randomly coiled and swollen macro molecules and the surrounding water molecules. And is dependent on both the nature of the polymer and the injected water acting as the solvent. There are several formulations of viscosity associated with polymer rheology, namely:

Relative viscosity is defined as:

[%eta_rel~=~ %eta over %eta_s]

(8.73)

where:

[%eta_rel]=is the relative viscosity,

[%eta]= is the viscosity of the solution, and

[%eta_s]=is the viscosity of the solvent (injected water).

Specific viscosity is defined as:

[%eta_{"sp"} ~=~ left( %eta - %eta_s right) over %eta_s newline ~~~`" " = ~ %eta over %eta_s ``-`` 1 newline ~~~````" " = ~ %eta_rel ``-`` 1]

(8.74)

where:

[%eta_"sp"]=is the specific water-polymer viscosity, and

[%eta_s]= is the viscosity of the solvent (injected water).

Reduced Specific Viscosity is given by:

[%eta_{"red"} ~=~ %eta_"sp" over C_p newline ~~~~~~~~~~````" " = ~left( %eta_rel ``-`` 1 right) over C_p]

(8.75)

where:

[%eta_"red"]=is the reduced specific water-polymer viscosity, and

[C_p]= is the polymer concentration.

Finally, the Intrinsic Velocity, which is defined as a measure for the internal friction in polymer solutions at the limit of zero polymer concentration. Thus, this quantity describes the effect of completely separated polymer chains on the solution viscosity, and is defined as:

[left [%eta right ] ~=~ lim from{ C_p toward 0 } {%eta_"sp" over C_p} newline ~~~~~``" " = ~lim from{ C_p toward 0 } {{%eta - %eta_0} over {%eta_0 C_p}}]

(8.76)

where:

[left[ %eta right]"]=is the intrinsic water-polymer viscosity and describes the increase in

viscosity arising from an individual polymer chain and is a measure of the polymers' thickening power, and

[%eta_o]= zero-shear viscosity.

For any given solvent pair, the intrinsic viscosity increases as the molecular weight of the polymer increases; here, the Mark-Houwink equation, also known as the Mark-Houwink-Staudinger equation211 H. Mark, in R. Saenger, Der feste Koerper, Hirzel, Leipzig, 1938., 212 R. Houwink , J. Prakt. Chem., Vol. 157, Issue 1-3, p. 15 (1940)., and 213 H. Staudinger, Die Hochmolekulare Organischen Verbindungen, Julius Springer, Berlin 1932.is used to calculate [η], that is:

H. Mark, in R. Saenger, Der feste Koerper, Hirzel, Leipzig, 1938.

R. Houwink , J. Prakt. Chem., Vol. 157, Issue 1-3, p. 15 (1940).

H. Staudinger, Die Hochmolekulare Organischen Verbindungen, Julius Springer, Berlin 1932.

[left [%eta right ] ~=~ K` cdot `{M_w}^a]

(8.77)

where:

[K]=is the polymer specific constant in the Mark-Houwink equation, the MHK

parameter in Table 8.109,

[M_w]= is the polymer molecular weight, and

[a]=the exponent constant in the Mark-Houwink equation, the MHA parameter

in Table 8.109.

The Mark-Houwink parameters can be determined from a double logarithmic plot of intrinsic viscosity versus molecular weight which yields straight lines, that is:

[ln left( [%eta] right) ~=~ ln(K) ~+~ a `times `ln (M_w)]

(8.78)

OPM Flow uses a form of the Huggins214 Huggins, M. L. 1942. The viscosity of dilute solutions of long-chain molecules. IV. Dependence on concentration.» Journal of the American Chemical Society 64 (11): 2716-2718. equation to calculate the polymer apparent viscosity, as shown below:

Huggins, M. L. 1942. The viscosity of dilute solutions of long-chain molecules. IV. Dependence on concentration.» Journal of the American Chemical Society 64 (11): 2716-2718.

[~~~~~~~~~~~%eta_0 over %eta_s ~=~ 1``+`` %gamma left(X``+`` %kappa X^2 right) newline "where"~~~~~ X~=~ left[%eta right] C_p]

(8.79)

where:

[%gamma]=a user defined constant, GAMMA in Table 8.109, and

[%kappa]= a user defined constant, KAPPA in Table 8.109.

Which can be used to calculate the zero-shear viscosity, η0, based on the quadratic function in equation (8.79)time polymer concentration (Cp) and polymer intrinsic viscosity described in equation (8.77).

In terms of the keyword units, given the intrinsic viscosity in ml/g, polymer concentration in kg/m3, and the molecular weight as kg/kg-M, then equation (8.77)becomes:

[left[ %eta right]~ = ~ K left(M_w ` cdot `1.0 times 10^-3 right)^a dot " " 1.0 times 10^-3]

(8.80)

and equation (8.79)becomes:

[~~~~~~~~~~~%eta_0 over %eta_s ~=~ 1``+`` %gamma left(X``+`` %kappa X^2 right) newline "where"~~~~~ X~=~ 1.0 times 10^-6left[%eta right] C_p]

(8.81)

Note that the model does not account for non-Newtonian flow; the apparent viscosity is simply set equal to the zero-shear viscosity, and that the model only considers the full mixing between the polymer and water.

See also the PLYMWINJ keyword in the PROPS section, that describes the relationship of the injected polymer molecular weight as a function of polymer throughput and polymer velocity. Note that the standard polymer property data keywords: PLYROCK, PLYADS, PLYMAX, etc., are still required to fully describe the polymer fluid.

Records

Fixed number of records

Items per record

4

Parameters

Example

Given NPLYVMH equals two on the PINTDIMS keyword in the RUNSPEC section, then:
--
-- POLYMER MOLECULAR WEIGHT MODEL POLYMER VISCOSITY CONSTANTS
-- (OPM FLOW PROPS KEYWORD)
--
-- MHK MHA VISC VISC
-- CONST EXPON GAMMA KAPPA
PLYVMH
0.02 0.50 0.40 0.60 /
0.03 0.51 0.42 0.63 /
/
Two sets of data should be entered with the PLYVMH keyword, as shown above.
| Note This is an OPM Flow specific keyword that employs an alternative polymer flood model based on a Polymer Molecular Weight Transport equation, that is not available in the commercial simulator. The model has been tested using metric units; however, using either field or laboratory units with the option should be considered experimental. |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| [%eta_rel~=~ %eta over %eta_s] | (8.73) |
|--------------------------------|--------|
| [%eta_{"sp"} ~=~ left( %eta - %eta_s right) over %eta_s newline
~~~`" " = ~ %eta over %eta_s ``-`` 1 newline
~~~````" " = ~ %eta_rel ``-`` 1] | (8.74) |
|-----------------------------------------------------------------------------------------------------------------------------------------------|--------|
| [%eta_{"red"} ~=~ %eta_"sp" over C_p  newline
~~~~~~~~~~````" " = ~left( %eta_rel ``-`` 1 right) over C_p] | (8.75) |
|------------------------------------------------------------------------------------------------------------|--------|
| [left [%eta right ] ~=~ lim from{ C_p toward 0 }  {%eta_"sp" over C_p}  newline
~~~~~``" "   = ~lim from{ C_p toward 0 }  {{%eta - %eta_0} over {%eta_0 C_p}}] | (8.76) |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------|--------|
| [left [%eta right ] ~=~ K` cdot `{M_w}^a] | (8.77) |
|-------------------------------------------|--------|
| [ln left( [%eta] right) ~=~ ln(K) ~+~ a `times `ln (M_w)] | (8.78) |
|-----------------------------------------------------------|--------|
| [~~~~~~~~~~~%eta_0 over %eta_s ~=~ 1``+`` %gamma left(X``+`` %kappa X^2 right) newline 
"where"~~~~~ 
X~=~ left[%eta right] C_p] | (8.79) |
|----------------------------------------------------------------------------------------------------------------------------------|--------|
| [left[ %eta right]~ = ~ K left(M_w ` cdot `1.0 times 10^-3 right)^a  dot " " 1.0 times 10^-3] | (8.80) |
|-----------------------------------------------------------------------------------------------|--------|
| [~~~~~~~~~~~%eta_0 over %eta_s ~=~ 1``+`` %gamma left(X``+`` %kappa X^2 right) newline 
"where"~~~~~ 
X~=~ 1.0 times 10^-6left[%eta right] C_p] | (8.81) |
|-------------------------------------------------------------------------------------------------------------------------------------------------|--------|

Manual source: parts/chapters/subsections/8.3/PLYVMH.fodt