Amplitude attenuation of time-variant properties of fluid streams

A method for attenuating the amplitude of a time-variant property of a fluid stream which comprises dividing an inlet fluid stream having a time-variant property into three or more individual fluid streams, introducing each of the individual fluid streams into a mixing zone at a different entrance location in the zone, and withdrawing from an outlet location of the mixing zone an outlet fluid stream having a time-variant property amplitude which is attenuated relative to the amplitude of the time-variant property of the inlet fluid stream, wherein (1) at least first, second, and third individual fluid streams are withdrawn successively from the inlet fluid stream and introduced into the mixing zone at first, second, and third entrance locations, respectively, wherein the distances from the outlet location to the first, second, and third entrance locations increase respectively, and wherein the distance between the second and third entrance locations is less than the distance between the first and second entrance locations, or (2) the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams, or (3) the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams and at least first, second, and third individual fluid streams are withdrawn successively from the inlet fluid stream and introduced into the mixing zone at first, second, and third entrance locations, respectively, wherein the distances from the outlet location to the first, second, and third entrance locations increase respectively, and wherein the distance between the second and third entrance locations is less than the distance between the first and second entrance locations.

A method for attenuating the amplitude of a time-variant property of a fluid stream which comprises

• (a) dividing an inlet fluid stream having a time-variant property into three or more individual fluid streams, introducing each of the individual fluid streams into a mixing zone at a different entrance location in the zone, and withdrawing from the mixing zone an outlet fluid stream having a time-variant property amplitude which is attenuated relative to the amplitude of the time-variant property of the inlet fluid stream, wherein (1) the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations, or (2) the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams, or (3) the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations and the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams;
• and
• (b) attenuating the amplitude of a time-variant property of the outlet fluid stream by dividing the outlet fluid stream into three or more additional individual fluid streams, introducing each of the additional individual fluid streams into an additional mixing zone at a different respective entrance location in the zone, and withdrawing from the additional mixing zone a second outlet fluid stream having a time-variant property of which the amplitude is further attenuated relative to the amplitude of the time-variant property of the outlet fluid stream, wherein in the additional mixing vessel (1) the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations, or (2) the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams, or (3) the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations and the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams.

A method for attenuating the amplitude of a time-variant property of a fluid stream which comprises

• (a) introducing an inlet fluid stream having a time-variant property into a mixing zone, withdrawing three or more individual fluid portions at different exit locations in the mixing zone, and combining the three or more individual fluid portions into a combined exit fluid stream having a time-variant property of which the amplitude is attenuated relative to the amplitude of the time-variant property of the inlet fluid stream, wherein (1) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations, or (2) the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions, or (3) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations and the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions;
• and
• (b) introducing the combined exit fluid stream into an additional mixing zone, withdrawing three or more individual fluid portions at different exit locations in the mixing zone, and combining the three or more individual fluid portions into another combined exit fluid stream having a time-variant property of which the amplitude is attenuated relative to the amplitude of a time-variant property of the combined exit fluid stream, wherein (1) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations, or (2) the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions, or (3) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations and the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions.

A method for attenuating the amplitude of a time-variant property of a fluid stream which comprises dividing an inlet fluid stream having a time-variant property into three or more individual fluid streams, introducing each of the individual fluid streams into a mixing zone at a different entrance location in the zone, and withdrawing from the mixing zone an outlet fluid stream having a time-variant property amplitude which is attenuated relative to the amplitude of the time-variant property of the inlet fluid stream, wherein

• (a) the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations;
• or the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams;
• or the distance between at least one pair of adjacent entrance locations is different than the distance between another pair of adjacent entrance locations and the flow rate of one of the individual fluid streams is different than the flow rate of another of the individual fluid streams;
• and
• (b) the residence time distribution of the outlet fluid stream is characterized by a flatness constraint Fθ equal to or less than about 0.11 and a symmetry constraint Sθ equal or less than about 0.075, wherein the flatness constraint Fθ is defined as F θ = ∫ 0 2 ⁢ [ 0.5 - E θ ⁢ ( θ ) ] 2 ⁢ ⁢ ⅆ θ + ∫ 2 ∞ ⁢ [ E θ ⁢ ( θ ) ] 2 ⁢ ⁢ ⅆ θ
• and the symmetry constraint Sθ is defined as S θ = ∫ 0 1 ⁢ [ E θ ⁢ ( θ ) - E θ ⁢ ( 2 - θ ) ] 2 ⁢ ⁢ ⅆ θ + ∫ 2 ∞ ⁢ [ E θ ⁢ ( θ ) ] 2 ⁢ ⁢ ⅆ θ
• where the function Eθ (θ) is the overall dimensionless residence time distribution of the outlet fluid stream and θ is the dimensionless time.

A method for attenuating the amplitude of a time-variant property of a fluid stream which comprises introducing an inlet fluid stream having a time-variant property into a mixing zone, withdrawing three or more individual fluid portions at different exit locations in the mixing zone, and combining the three or more individual fluid portions into a combined exit fluid stream having a time-variant property of which the amplitude is attenuated relative to the amplitude of the time-variant property of the inlet fluid stream, wherein

• (a) the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations;
• or the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions;
• or the distance between at least one pair of adjacent exit locations is different than the distance between another pair of adjacent exit locations and the flow rate of one of the individual fluid portions is different than the flow rate of another of the individual fluid portions;
• and
• (b) the residence time distribution of the outlet fluid stream is characterized by a flatness constraint Fθ equal to or less than about 0.11 and a symmetry constraint Sθ equal or less than about 0.075, wherein the flatness constraint Fθ is defined as F θ = ∫ 0 2 ⁢ [ 0.5 - E θ ⁢ ( θ ) ] 2 ⁢ ⁢ ⅆ θ + ∫ 2 ∞ ⁢ [ E θ ⁢ ( θ ) ] 2 ⁢ ⁢ ⅆ θ
• and the symmetry constraint Sθ is defined as S θ = ∫ 0 1 ⁢ [ E θ ⁢ ( θ ) - E θ ⁢ ( 2 - θ ) ] 2 ⁢ ⁢ ⅆ θ + ∫ 2 ∞ ⁢ [ E θ ⁢ ( θ ) ] 2 ⁢ ⁢ ⅆ θ
• where the function Eθ (θ) is the overall dimensionless residence time distribution of the outlet fluid stream and θ is the dimensionless time.