Rise in core wettability characterization method
View Patent ↗The various embodiments herein provide a method for determining core wettability characteristics of reservoir rock samples based on modified form of Washburn equation. The method involves saturating a core sample with a first reservoir fluid such as water and imbibing with a second reservoir fluid such as oil. The change in square of the core mass with respect to time is monitored during an imbibition process to acquire a data to calculate a contact angle to determine the wettability of the sample. The contact angle is calculated by using the modified form of Washburn equation. A single or twin core sample is used to calculate the wettability characteristics. The method measures wettability characteristics in terms of contact angle and not in terms of wettability index.
1. A method for determining Reservoir Rock wettability comprising steps of:
generating and utilizing core samples, wherein a core sample is generated by dividing a core plug into a plurality of core samples of a preset size and wherein the preset size of each core sample in the plurality of core samples is an average diameter of 3.8 cm and a length of 1.5 cm;
sealing a side of the core sample with an epoxy resin, wherein the side of the core sample is sealed to ensure a one-dimensional liquid penetration into the core sample;
mounting a hook on a top side of the core sample;
saturating the core sample with a first reservoir fluid;
connecting the saturated core sample to a high precision balance, wherein the saturated core sample is connected using a thin rope;
taking a second reservoir fluid in an imbibition beaker;
hanging the saturated core sample over the second reservoir fluid contained in the imbibition beaker, wherein the saturated core sample is hanged using a thread and wherein the saturated core sample is hanged in a way such that a bottom part of the saturated core sample barely touches the second reservoir fluid;
commencing an imbibition process for the hanged and saturated core sample;
monitoring a change in a mass of the hanged and saturated core sample over a period of time as imbibitions taking place to obtain a data and wherein the data is a square of the change in the mass of the hanged and saturated core sample over a period of time;
generating a curve using the obtained data by plotting a square of the change in the mass of the hanged and saturated core sample with respect to time;
calculating a slope of the generated curve;
computing a value of a rock constant for the core sample; and
applying the calculated slope of the generated curve and the computed value of a rock constant for the core sample in a modified form of Washburn equation to compute a value of a contact angle;
wherein the computed value of contact angle represents a wettability of the core sample and in turn represents the wettability of a reservoir rock from which the core plug is generated.
2. The method according to claim 1 , wherein the constant is a characteristic of a core sample.
3. The method according to claim 2 , wherein the step of determining the constant C comprises:
generating twin core samples;
saturating one of the generated twin core samples with air;
imbibing the saturated twin core sample with a reference fluid and wherein the reference fluid has low surface energy and wherein the reference fluid is Dodecane;
monitoring a change of a mass of the twin core sample with respect to time using a high precision balance;
plotting a curve using a square of the change of the mass of the twin core sample with respect to time;
determining a slope of a straight line part of the plotted curve;
determining a value of the constant C for the core sample by applying the determined value of the slope of the straight line part of the plotted curve and by applying a value of the contact angle in a modified Washburn equation, wherein the value of contact angle is assumed to be zero since the reference fluid completely wets the core sample in presence of air.
4. The method according to claim 1 , wherein the first reservoir fluid is water.
5. The method according to claim 1 , wherein the second reservoir fluid is oil.
6. The method according to claim 1 , wherein the reservoir rock sample is completely water wet at a contact angle of 0°, weakly water wet to weakly oil wet between the contact angles of 62° to 133°, completely oil wet at a contact angle of 180° and neutral at a contact angle of 90°.
7. The method according to claim 1 , wherein the method is used for Rock/liquid/liquid System.
8. A method for determining wettability characteristics of reservoir core samples comprising steps of:
starting with a preserved core plug;
generating a first twin core sample and a second twin core sample, and wherein the generated first twin core sample is used to determine a constant of a modified Washburn equation, and wherein the generated second twin core sample is used to determine wettability of a rock;
cleaning the generated first twin core sample;
drying the cleaned first twin core sample;
saturating the dried first twin core sample with air;
imbibing the air saturated first twin core sample with a low energy fluid, wherein the low energy fluid is Dodecane;
monitoring a change in a mass of the first twin core sample with respect to time as dodecane imbibes into the first twin core sample;
generating a curve by plotting a square of the change in the mass of the first twin core sample with respect to time;
determining a slope value of the generated curve;
calculating a value of a rock constant by applying the determined slope value of the generated curve and a contact angle of the first twin core sample for the reference fluid in a modified Washburn Equation, wherein the applied contact value of the first twin core sample for the reference fluid is equal to zero as the reference fluid is a dodecane and the dodecane wets the first twin core sample completely;
saturating the second twin core sample with a first reservoir fluid, wherein the second twin core sample is saturated in the first reservoir fluid completely;
imbibing the saturated second twin core sample with a second reservoir fluid;
monitoring a change in a core mass of the second twin core sample with respect to time as the second reservoir fluid is imbibed into the second twin core sample;
calculating a square of the change in the mass of the second twin core sample with respect to time;
generating a curve for the second twin core sample by plotting the calculated square of the change in the mass of the second twin core sample with respect to time;
calculating a slope of the generated curve for the second twin core sample;
calculating a value of contact angle by applying the calculated slope of the generated curve for the second twin core sample and the computed value of a rock constant for the first twin core sample in a modified form of Washburn equation; and
wherein the calculated value of contact angle represents a wettability of the second twin core sample and in turn corresponds to a wettability of a reservoir rock from which the core plug is extracted.
9. The method according to claim 8 , wherein the change in square of the mass of the core sample with respect to time is monitored using a high precision balance and a computer.
10. The method according to claim 8 , wherein the wettability characteristics is determined on the basis of the contact angle.
11. The method according to claim 8 , wherein the contact angle is determined using the modified Washburn equation.
12. The method according to claim 8 , wherein the reservoir rock sample is completely water wet at a contact angle of 0°, weakly water wet to weakly oil wet between contact angles of 62° to 133°, completely oil wet at a contact angle of 180° and neutral at a contact angle of 90°.
13. The method according to claim 8 , wherein the method is used for Rock/liquid/liquid System.
14. The method according to claim 11 , wherein the modified form a Washburn equation for a Rock/liquid/liquid System is derived from a Washburn equation provided for calculating a penetration rate for a liquid/air/rock system.
15. The method according to claim 14 , wherein the step of deriving the modified form of the Washburn equation for a Rock/liquid/liquid System comprises:
acquiring a Washburn equation for a rock/liquid/liquid system, and wherein Washburn equation for a rock/liquid/liquid system is represented by
t
=
μ
C
·
ρ
2
γ
cos
θ
·
m
2
,
(
1
)
wherein equation (1) is a Washburn equation for liquid/air/rock system, and wherein t is a penetration rate of a liquid into a porous sample, and wherein is a viscosity of the liquid, and wherein ρ is a density of the liquid, and wherein γ is a surface tension of the liquid, and wherein θ is a contact angle made by the liquid, and wherein m is a mass of the liquid penetrated into the porous sample and wherein C is a Constant of Characterization of the porous sample;
evaluating a value of γ os using a young's equation for a rock surface/oil/air system and a value of γ ws using a young's equation for a rock surface/water/air system and wherein the young's equation for a liquid/liquid/rock system is represented by equation (2)
γ ow cos θ=γ os −γ ws (2),
wherein γ ow is a surface tension between oil and water system, and wherein γ os is a surface tension between oil and solid system, and wherein γ ws is a surface tension between water and solid system;
substituting the evaluated value of γ os using a young's equation for a rock surface/oil/air system and value of γ ws using a young's equation for a rock surface/water/air system and substituting in equation (2) to obtain an equation (3), and wherein the equation (3) is
cos
θ
wo
=
(
γ
o
cos
θ
o
)
-
(
γ
w
cos
θ
w
)
γ
wo
;
(
3
)
rearranging equation (1) to factor out γ LV to obtain an equation (4), and wherein γ LV is a liquid-vapor surface tension, and
γ
LV
=
μ
C
·
ρ
2
·
cos
θ
·
m
2
t
;
(
4
)
realizing that γ LV (liquid-vapor surface tension) is equivalent to γ o (oil-air surface tension), or γ w (water-air surface tension), substitute equation 4 in equation 3 and cancelling out similar terms to obtain equation (5), and wherein equation (5) is
cos
θ
wo
=
(
m
2
·
μ
o
C
ρ
o
2
t
)
-
(
m
2
·
μ
w
C
ρ
w
2
t
)
γ
wo
;
(
5
)
wherein γ LV is liquid-vapor surface tension, and wherein γ o is oil-air surface tension and wherein γ w is water-air surface tension, and wherein μ o is viscosity of oil, and wherein μ w is viscosity of water, and wherein cos θ is contact angle between water and oil;
representing a relation ship between a mass of water imbibed into the core sample and a mass of oil imbibed in the core sample with a equation (6), wherein the equation (6) is ρ w g V w =ρ o g V o ;
wherein ρ w is density of water and V w is volume of water imbibed, wherein ρ o is density of oil and V o is volume of oil imbibed, wherein the amount of water imbibed and amount of oil imbibed under gravity are same; and wherein air behaves as a strong non-wetting phase in both of a oil/air/solid and a water/air/solid systems, thereby indicating that both oil and water behaves as a strong wetting phases, resulting in an equal air/oil and air/water capillary forces for a same porous media and for a given pore size distribution, and wherein a mass change of a core sample due to a water imbibition is equal to a mass change of a core sample as a due to an oil imbibition because water or oil penetration of the porous media at any time is a function of a balance between a gravity and a capillary forces, and wherein a mass of water imbibed into a core sample is approximately equal to a mass of oil imbibed in the core sample core samples of a same rock type and dimensions, and for equal capillary forces;
cancelling out g in equation (6) represented ρ w g V w =ρ o g V o to obtain an equation (7), wherein equation (7) is ρ w V w =ρ o V o to acquire an equation (8), and wherein
equation (8) is
m w =m o (8),
wherein m w is mass of water and wherein m o is mass of oil;
factoring out C·m 2 /t from equation (5) to obtain equation (9), wherein equation (9) is a modified Washburn equation, and wherein the modified Washburn equation is
cos
θ
12
=
(
μ
1
·
ρ
2
2
)
-
(
μ
2
·
ρ
1
2
)
ρ
1
2
ρ
2
2
·
C
·
γ
L
2
L
1
·
m
2
t
wherein θ 12 is the contact angle of liquid/liquid/rock system, and wherein μ 1 is a Viscosity of oil phase, and wherein ρ 2 is a Viscosity of water phase, and
wherein ρ 1 is a density of oil phase in g/cm 3 , and wherein ρ 2 is a density of water phase in g/cm 3 , and wherein m is a mass of fluid penetrated into a porous rock in g, and wherein t is a time in min, and wherein γ L2L1 is a surface tension between a oil and a water in dyne/cm, and C is a Characteristic Constant, of the porous rock.