1. A method for generating a calibrated parallel magnetic resonance image, comprising:
a) applying a magnetic resonance imaging excitation;
b) acquiring a plurality of echoes at different echo times (TE); and
c) using the acquired plurality of echoes from different echo times to create a chemical shift corrected calibration map.
2. The method as recited in claim 1, wherein the chemical shift corrected calibration map provides a spatial distribution of sensitivity of an array of RF receive coils.
3. The method, as recited in claim 2, wherein the using the acquired plurality of echoes comprises:
forming low resolution images for each RF receive coil of the array of RF receive coils; and
processing the low resolution images to remove spin and density information, leaving only a map of sensitivity of each coil.
4. The method, as recited in claim 3, wherein the using the acquired plurality of echoes further comprises using low bandwidth imaging.
5. The method, as recited in claim 4, wherein the using the acquired plurality of echoes further comprises using an iterative least-squared decomposition with echo asymmetry and least squares estimation.
6. The method, as recited in claim 5, wherein the iterative least-squared decomposition with echo asymmetry and least squares estimation provides a first species signal and a second species signal, and further comprising combining the first species signal and the second species signal with chemical shift correction to obtain chemical shift corrected images.
7. The method, as recited in claim 6, wherein the using the acquired plurality of echoes from different echo times to create a chemical shift corrected calibration map further comprises using the chemical shift corrected images to generate sensitivity maps.
8. The method, as recited in claim 1, wherein the acquiring the plurality of echoes acquires undersampled data in a manner that allows fully sampled images to be generated at each echo time that are lower resolution than the undersampled data.
9. The method, as recited in claim 8, wherein the chemical shift corrected calibration map is used to generate fully sampled high resolution images from the undersampled data acquired at each echo time.
10. The method, as recited in claim 9, wherein the fully sampled high resolution images are processed with IDEAL to produce high resolution water-fat separated images.
11. The method, as recited in claim 1, wherein the using the acquired plurality of echoes comprises:
forming low resolution images for each RF receive coil of the array of RF receive coils; and
processing the low resolution images to remove spin and density information, leaving only a map of sensitivity of each coil.
12. The method, as recited in claim 1, wherein the using the acquired plurality of echoes comprises using low bandwidth imaging.
13. The method, as recited in claim 1, wherein the using the acquired plurality of echoes comprises using an iterative least-squared decomposition with echo asymmetry and least squares estimation.
14. The method, as recited in claim 13, wherein the iterative least-squared decomposition with echo asymmetry and least squares estimation provides a first species signal and a second species signal, and further comprising combining the first species signal and the second species signal with chemical shift correction to obtain chemical shift corrected images.
15. The method, as recited in claim 1, wherein the using the acquired plurality of echoes from different echo times to create a chemical shift corrected calibration map further comprises using the chemical shift corrected images to generate sensitivity maps.
16. The method, as recited in claim 1, wherein the using the acquired plurality of echoes from different echo times to create a chemical shift corrected calibration map, comprises:
using the acquired plurality of echoes to provide a first species signal;
using the acquired plurality of echoes to provide a second species signal; and
combining the first species signal and the second species signal with chemical shift correction to obtain chemical shift corrected images.
17. A method for generating a calibrated parallel multiecho magnetic resonance image, comprising:
a) applying a magnetic resonance imaging excitation;
b) acquiring a plurality of echoes at different echo times (TE);
c) using the acquired plurality of echoes to provide a first species signal;
d) using the acquired plurality of echoes to provide a second species signal; and
e) combining the first species signal and the second species signal with chemical shift correction to obtain a chemical shift corrected calibration map.
18. The method as recited in claim 17, wherein the chemical shift corrected calibration map provides a spatial distribution of sensitivity of an array of RF receive coils.
19. An apparatus for providing a calibrated parallel multiecho magnetic resonance image, comprising:
a magnet system;
a controller electrically connected to the magnet system, comprising:
a display;
at least one processor; and
computer readable media, comprising:
computer readable code for signaling the magnetic system to apply a magnetic resonance imaging excitation;
computer readable code for signaling the magnetic system to acquire a plurality of magnetic resonance image echo signals at different echo times; and
computer readable codes for using the acquired plurality of echoes from different echo times to create a chemical shift corrected calibration map.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method of optimizing a product output rate from a distillation column having a top and a bottom, comprising:
(a) setting a desired product output rate from the distillation column having a packing;
(b) calculating a fraction of flood point of the distillation column at a reflux ratio;
(c) determining a two-phase pressure drop value within the distillation column at the fraction of flood point;
(d) calculating a pressure at the bottom of the distillation column for a pressure at the top of the distillation column, and calculating the two-phase pressure drop value within the distillation column of a given length;
(e) calculating a temperature corresponding to the calculated pressure at the bottom of the distillation column; and
(f) adjusting the desired product output rate or the reflux ratio or the pressure at the top of the distillation column.
2. The method of claim 1, wherein the distillation column is a subject packed column.
3. The method of claim 2, wherein the subject packed column is operated with gas as vapor continuous phase and liquid as dispersed phase.
4. The method of claim 1, wherein determining a two-phase pressure drop value within the distillation column at the fraction of flood point includes using a plot of two-phase pressure drop value as a function of fraction of flood point, the plot obtained by the computer-implemented steps of:
(aa) providing a reference data set of two-phase pressure drop values as a function of gas and liquid flow rates for a reference liquid and a reference gas at several liquid flow rates through a reference packed column containing the same packing being used in the distillation column;
(bb) converting the reference data set to dimensionless two-phase pressure drop values as a function of the density of the liquid phase of a subject packed column thereby making the two-phase pressure drop values at flood inversely proportional to the density of the liquid phase;
(cc) providing a known flood point value for one liquid flow rate in the reference data set;
(dd) setting working flood point values for higher liquid flow rates at values lower than the known flood point value;
(ee) setting working flood point values for lower liquid flow rates at values higher than the known flood point value;
(ff) expressing gas flow rates for liquid flow rates as fractions of the working flood point value for each respective liquid flow rate in the reference data set; and
(gg) at a constant two-phase pressure drop value:
i) from the fractions of the working flood point value calculating an average fractional flood point value for the liquid flow rates; and
ii) minimizing the standard deviation between the fractional flood point value at different liquid flow rates and the calculated average fractional flood point value by repeating steps (cc)-(gg) over reference two-phase pressure drop and liquid flow rate data.
5. The method of claim 4, wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about one and a half inches of water per foot of column for the gas being air and the liquid being water.
6. The method of claim 4, wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about two inches of water per foot of column for the gas being air and the liquid being water.
7. The method of claim 4, wherein the known flood point value for one liquid flow rate equals a gas flow rate at which a slope of dimensionless two-phase pressure drop values as a function of gas flow rate is equal to or greater than about two.
8. The method of claim 4, wherein the known flood point value for one liquid flow rate includes a user observation of an accumulation of liquid at the top of the packing.
9. The method of claim 1, wherein determining a pressure drop within the distillation column at the fraction of flood point includes using a mathematical expression of two-phase pressure drop as a function of fraction of flood point, the expression obtained by the computer-implemented steps of:
(aa) providing a reference data set of two-phase pressure drop values as a function of gas and liquid flow rates at several liquid flow rates through a packed column;
(bb) converting the reference data set to dimensionless two-phase pressure drop values as a function of the density of the liquid phase of a subject packed column thereby making the two-phase pressure drop values at flood inversely proportional to the density of the liquid phase;
(cc) providing a known flood point value for one liquid flow rate in the reference data set;
(dd) setting working flood point values for higher liquid flow rates at values lower than the known flood point value;
(ee) setting working flood point values for lower liquid flow rates at values higher than the known flood point value;
(ff) expressing gas flow rates for liquid flow rates as fractions of the working flood point value for each respective liquid flow rate in the reference data set; and
(gg) at a constant two-phase pressure drop value:
i) from the fractions of the working flood point value calculating an average fractional flood point value for the liquid flow rates; and
ii) minimizing the standard deviation between the fractional flood point value at different liquid flow rates and the calculated average fractional flood point value by repeating steps (cc)-(gg) over reference two-phase pressure drop and liquid flow rate data.
10. The method of claim 9, wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about one and a half inches of water per foot of column for the gas being air and the liquid being water.
11. The method of claim 9, wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about two inches of water per foot of column for the gas being air and the liquid being water.
12. The method of claim 9, wherein the known flood point value for one liquid flow rate equals a gas flow rate at which a slope of dimensionless two-phase pressure drop values as a function of gas flow rate is equal to or greater than about two.
13. The method of claim 9, wherein the known flood point value for one liquid flow rate includes a user observation of an accumulation of liquid at the top of the column.
14. A method of optimizing a product output rate from a distillation column having a top and a bottom, comprising:
(a) setting a desired product output rate from the distillation column having a packing;
(b) calculating a fraction of flood point of the distillation column at a reflux ratio;
(c) determining a two-phase pressure drop value within the distillation column at the fraction of flood point;
(d) calculating a pressure at the top of the distillation column for a pressure at the bottom of the distillation column, and calculating the two-phase pressure drop value within the distillation column of a given length;
(e) calculating a temperature corresponding to the calculated pressure at the top of the distillation column; and
(f) adjusting the desired product output rate or the reflux ratio or the pressure at the top of the distillation column.
15. The method of claim 14, wherein the distillation column is a subject packed column.
16. The method of claim 15, wherein the subject packed column is operated with gas as vapor continuous phase and liquid as dispersed phase.
17. The method of claim 14, wherein determining a two-phase pressure drop value within the distillation column at the fraction of flood point includes using a plot of two-phase pressure drop value as a function of fraction of flood point, the plot obtained by the computer-implemented steps of:
(aa) providing a reference data set of two-phase pressure drop values as a function of gas and liquid flow rates for a reference liquid and a reference gas at several liquid flow rates through a reference packed column containing the same packing being used in the distillation column;
(bb) converting the reference data set to dimensionless two-phase pressure drop values as a function of the density of the liquid phase of a subject packed column thereby making the two-phase pressure drop values at flood inversely proportional to the density of the liquid phase;
(cc) providing a known flood point value for one liquid flow rate in the reference data set;
(dd) setting working flood point values for higher liquid flow rates at values lower than the known flood point value;
(ee) setting working flood point values for lower liquid flow rates at values higher than the known flood point value;
(ff) expressing gas flow rates for liquid flow rates as fractions of the working flood point value for each respective liquid flow rate in the reference data set; and
(gg) at a constant two-phase pressure drop value:
i) from the fractions of the working flood point value calculating an average fractional flood point value for the liquid flow rates; and
ii) minimizing the standard deviation between the fractional flood point value at different liquid flow rates and the calculated average fractional flood point value by repeating steps (cc)-(gg) over reference two-phase pressure drop and liquid flow rate data.
18. The method of claim 17, wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about one and a half inches of water per foot of column for the gas being air and the liquid being water.
19. The method of claim 17, wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about two inches of water per foot of column for the gas being air and the liquid being water.
20. The method of claim 17, wherein the known flood point value for one liquid flow rate equals a gas flow rate at which a slope of dimensionless two-phase pressure drop values as a function of gas flow rate is equal to or greater than about two.
21. The method of claim 17, wherein the known flood point value for one liquid flow rate includes a user observation of an accumulation of liquid at the top of the packing.
22. The method of claim 14, wherein determining a pressure drop within the distillation column at the fraction of flood point includes using a mathematical expression of two-phase pressure drop as a function of fraction of flood point, the expression obtained by the computer-implemented steps of:
(aa) providing a reference data set of two-phase pressure drop values as a function of gas and liquid flow rates at several liquid flow rates through a packed column;
(bb) converting the reference data set to dimensionless two-phase pressure drop values as a function of the density of the liquid phase of a subject packed column thereby making the two-phase pressure drop values at flood inversely proportional to the density of the liquid phase;
(cc) providing a known flood point value for one liquid flow rate in the reference data set;
(dd) setting working flood point values for higher liquid flow rates at values lower than the known flood point value;
(ee) setting working flood point values for lower liquid flow rates at values higher than the known flood point value;
(ff) expressing gas flow rates for liquid flow rates as fractions of the working flood point value for each respective liquid flow rate in the reference data set; and
(gg) at a constant two-phase pressure drop value:
i) from the fractions of the working flood point value calculating an average fractional flood point value for the liquid flow rates; and
ii) minimizing the standard deviation between the fractional flood point value at different liquid flow rates and the calculated average fractional flood point value by repeating steps (cc)-(gg) over reference two-phase pressure drop and liquid flow rate data.
23. The method of claim 22, wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about one and a half inches of water per foot of column for the gas being air and the liquid being water.
24. The method of claim 22, wherein the known flood point value for one liquid flow rate equals a two-phase pressure drop of about two inches of water per foot of column for the gas being air and the liquid being water.
25. The method of claim 22, wherein the known flood point value for one liquid flow rate equals a gas flow rate at which a slope of dimensionless two-phase pressure drop values as a function of gas flow rate is equal to or greater than about two.
26. The method of claim 22, wherein the known flood point value for one liquid flow rate includes a user observation of an accumulation of liquid at the top of the column.