Distillation Curve Optimization Using Monotonic Interpolation
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The document discusses optimization of distillation curves for blending multiple distillation streams. It presents a methodology to interconvert temperatures between ASTM D86 and true boiling point (TBP) scales, interpolate the points to generate evaporation curves using monotonic interpolation, and blend the components using an ideal blending law. The methodology allows manipulating cutpoints of one or more streams' distillation curves to shift the front and back-ends and optimize the final blended product properties and flows while satisfying demands and specifications. An example optimization problem is presented to maximize the flow of two distillation streams in a blend subject to property and flow constraints.
![Distillation Curve Optimization Using Monotonic Interpolation
Brenno C. Menezes,1 Jeffrey D. Kelly,2 Ignacio E. Grossmann3
1Refining Optimization, PETROBRAS, Rio de Janeiro, Brazil. 2IndustrIALgorithms, Toronto, Canada. 3Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, United States.
Relative Yields Nonmalization: adjust the new yields given the old
yields 1%, 10%, 30%, etc., and the differences in 1% and 99%. New
flow (NF) is given by the old flow (OF) and these differences.
NY01 = 0.01 1 + DYNT99
NY10 = (0.10 + DYNT01) 1 + DYNT01 + DYNT99
NY30 = (0.30 + DYNT01) 1 + DYNT01 + DYNT99
NY50 = (0.50 + DYNT01) 1 + DYNT01 + DYNT99
NY70 = (0.70 + DYNT01) 1 + DYNT01 + DYNT99
NY90 = (0.90 + DYNT01) 1 + DYNT01 + DYNT99
NY99 = (0.99 + DYNT01) 1 + DYNT01 + DYNT99
Table. Inter-Converted TBP (ASTM D86) Temperatures in Degrees F.
DC1 DC2 DC3 DC4
1% 305.2 (353) 322.2 (367) 327.0 (385) 302.4 (368)
10% 432.9 (466) 447.1 (476) 405.2 (435) 369.7 (407)
30% 521.6 (523) 507.1 (509) 457.1 (462) 441.0 (449)
50% 565.3 (551) 549.5 (536) 503.3 (492) 513.8 (502)
70% 606.4 (581) 598.4 (573) 551.1 (528) 574.3 (550)
90% 668.3 (635) 666.1 (634) 605.8 (574) 625.4 (592)
99% 715.7 (672) 757.7 (689) 647.0 (608) 655.2 (620)
Conclusion: By shifting or adjusting the front- and back-ends of the
TBP curve for one or more distillate blending streams, it allows for
improved control and optimization of the final product demand quantity
and quality, affording better maneuvering closer and around
downstream bottlenecks such as tight property specifications and
volatile demand flow and timing constraints (Kelly, Menezes, &
Grossmann, 2014).
Goal: integrate blending of several streams’ distillation curves together
with also shifting or adjusting the cutpoints of one or more of the
distilled stream’s initial and/or final boiling-points (IBP and FBP) in order
to manipulate its TBP curve in an either off- or on-line environment.
Kerosene
Light Diesel
Methodology: inter-convert from ASTM D86 to TBP temperatures
where the blending component are mixed using the ideal blending law
and then interpolate the points into evaporation curves using
monotonic interpolation (Linear, PCHP, or Kruger).
ASTM D86
TBP
Inter-conversion
Interpolation
Evaporation
Curves
Ideal Blending
Evaporation
Curve
Multiple
Components
Final
Product
Interpolation
Inter-conversion
TBP
ASTM D86
From Other
Units
From CDU
N
ATR
C1C2
C3C4
N
K
LD
HD
Naphtha
Heavy Diesel
Crude
CDU
Cutpoint Temperature Optimization: a typical distillation curve can be
reasonably decomposed or partitioned into three distinct regions or
parts i.e., a front-end, middle and back-end.
YNT99 = 0.90 +
0.99 − 0.90
OT99 − OT90
NT99 − OT90
NF = OF 1 + DYNT01 + DYNT99
YNT01 = 0.10 −
0.10 − 0.01
OT10 − OT01
OT10 − NT01 DYNT01 = 0.01 − YNT01
DYNT99 = YNT99 − 0.99
Example: maximize the flow of DC1 and DC2 subject to their relative
and arbitrary pricing of 0.9 for DC1 and 1.0 DC2 with lower and upper
bounds of 0.0 and 100.0 each. For simplicity, the flows for DC3 and
DC4 are fixed to a marginal and arbitrary value of 1.0 and the total
blend flow cannot exceed 100.0 and its ASTM D86 specifications are
D10 ≤ 470, 540 ≤ D90 ≤ 630 and D99 ≤ 680.
Old Temperature: OT
New Temperature: NT
New Yield: YNT
Difference in Yield: DYNT
In the example is not possible to satisfy the blend with the most
valuable DC2 component as its D10, D90 and D99 are all greater than
the final blend distillation temperature specification. Furthermore, it is
also not possible to fill the blend with all DC1 as its D90 does not
comply with the specification. As such, this forces a mixture of DC1 and
DC2 and this also requires an adjustment or shifting to the distillation
curve for DC1 where only the DC1 material is allowed to have
manipulated cutpoint temperature.
Figure. ASTM D86 distillation curves, including the final blend, which is determined
by the blended TBP interconvertion to ASTM D86.
The new and optimized TBP curve for DC1 given its front and back-end
shifts is now [(1.053%,312.8), (10.015%,432.9), (31.188%,521.6),
(52.361%,565.3), (73.534%,606.4), (94.707%,668.3), (98.995%,689.3)]](https://image.slidesharecdn.com/dbctoaicheposter2014-141118074716-conversion-gate01/85/Distillation-Curve-Optimization-Using-Monotonic-Interpolation-1-320.jpg)
Distillation Curve Optimization Using Monotonic Interpolation
- 1. Distillation Curve Optimization Using Monotonic Interpolation Brenno C. Menezes,1 Jeffrey D. Kelly,2 Ignacio E. Grossmann3 1Refining Optimization, PETROBRAS, Rio de Janeiro, Brazil. 2IndustrIALgorithms, Toronto, Canada. 3Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, United States. Relative Yields Nonmalization: adjust the new yields given the old yields 1%, 10%, 30%, etc., and the differences in 1% and 99%. New flow (NF) is given by the old flow (OF) and these differences. NY01 = 0.01 1 + DYNT99 NY10 = (0.10 + DYNT01) 1 + DYNT01 + DYNT99 NY30 = (0.30 + DYNT01) 1 + DYNT01 + DYNT99 NY50 = (0.50 + DYNT01) 1 + DYNT01 + DYNT99 NY70 = (0.70 + DYNT01) 1 + DYNT01 + DYNT99 NY90 = (0.90 + DYNT01) 1 + DYNT01 + DYNT99 NY99 = (0.99 + DYNT01) 1 + DYNT01 + DYNT99 Table. Inter-Converted TBP (ASTM D86) Temperatures in Degrees F. DC1 DC2 DC3 DC4 1% 305.2 (353) 322.2 (367) 327.0 (385) 302.4 (368) 10% 432.9 (466) 447.1 (476) 405.2 (435) 369.7 (407) 30% 521.6 (523) 507.1 (509) 457.1 (462) 441.0 (449) 50% 565.3 (551) 549.5 (536) 503.3 (492) 513.8 (502) 70% 606.4 (581) 598.4 (573) 551.1 (528) 574.3 (550) 90% 668.3 (635) 666.1 (634) 605.8 (574) 625.4 (592) 99% 715.7 (672) 757.7 (689) 647.0 (608) 655.2 (620) Conclusion: By shifting or adjusting the front- and back-ends of the TBP curve for one or more distillate blending streams, it allows for improved control and optimization of the final product demand quantity and quality, affording better maneuvering closer and around downstream bottlenecks such as tight property specifications and volatile demand flow and timing constraints (Kelly, Menezes, & Grossmann, 2014). Goal: integrate blending of several streams’ distillation curves together with also shifting or adjusting the cutpoints of one or more of the distilled stream’s initial and/or final boiling-points (IBP and FBP) in order to manipulate its TBP curve in an either off- or on-line environment. Kerosene Light Diesel Methodology: inter-convert from ASTM D86 to TBP temperatures where the blending component are mixed using the ideal blending law and then interpolate the points into evaporation curves using monotonic interpolation (Linear, PCHP, or Kruger). ASTM D86 TBP Inter-conversion Interpolation Evaporation Curves Ideal Blending Evaporation Curve Multiple Components Final Product Interpolation Inter-conversion TBP ASTM D86 From Other Units From CDU N ATR C1C2 C3C4 N K LD HD Naphtha Heavy Diesel Crude CDU Cutpoint Temperature Optimization: a typical distillation curve can be reasonably decomposed or partitioned into three distinct regions or parts i.e., a front-end, middle and back-end. YNT99 = 0.90 + 0.99 − 0.90 OT99 − OT90 NT99 − OT90 NF = OF 1 + DYNT01 + DYNT99 YNT01 = 0.10 − 0.10 − 0.01 OT10 − OT01 OT10 − NT01 DYNT01 = 0.01 − YNT01 DYNT99 = YNT99 − 0.99 Example: maximize the flow of DC1 and DC2 subject to their relative and arbitrary pricing of 0.9 for DC1 and 1.0 DC2 with lower and upper bounds of 0.0 and 100.0 each. For simplicity, the flows for DC3 and DC4 are fixed to a marginal and arbitrary value of 1.0 and the total blend flow cannot exceed 100.0 and its ASTM D86 specifications are D10 ≤ 470, 540 ≤ D90 ≤ 630 and D99 ≤ 680. Old Temperature: OT New Temperature: NT New Yield: YNT Difference in Yield: DYNT In the example is not possible to satisfy the blend with the most valuable DC2 component as its D10, D90 and D99 are all greater than the final blend distillation temperature specification. Furthermore, it is also not possible to fill the blend with all DC1 as its D90 does not comply with the specification. As such, this forces a mixture of DC1 and DC2 and this also requires an adjustment or shifting to the distillation curve for DC1 where only the DC1 material is allowed to have manipulated cutpoint temperature. Figure. ASTM D86 distillation curves, including the final blend, which is determined by the blended TBP interconvertion to ASTM D86. The new and optimized TBP curve for DC1 given its front and back-end shifts is now [(1.053%,312.8), (10.015%,432.9), (31.188%,521.6), (52.361%,565.3), (73.534%,606.4), (94.707%,668.3), (98.995%,689.3)]