Oil Cracking Unit: Difference between revisions
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{{Infobox Test
|name=Oil Cracking Unit
|image=OilCrackingUnit.png|alt= A five block long, three block deep, three block tall multiblock made from light grey-blue metallic blocks with rivets. The second and fourth row are copper blocks with diagonal stripes instead. Front and center is an electronic panel with red light, and a light grey hatch marked with a wrench directly below. On the left and right sides are two hatches with four blue arrows pointing in and out. Another hatch with arrows pointing in is centered on the top, between the copper coils.
|mod=Gregtech 5
|type=Tile Entity
|tooltip= Controller Block for the Oil Cracking Unit
|quest=Oil Cracker<div/>Let's Get Crackin!
|tier=HV
|machinesize=5x3x3
|pollutionoutput= None
|blastresistance= 6
|hardness= 1-5
|gteuusage=240+ eu/t
|gtvoltagein= As Energy Hatch
|gtamperage=1-2A per Energy Hatch
}}
== Introduction ==
The '''Oil Cracking Unit''' is a specialized [[multiblock]] that uses Steam or Hydrogen to crack oil-based fuels. Compared to a [[Chemical Reactor]], an Oil Cracking Unit gets an additional 25-50% output bonus for the same recipes but runs them at a higher [[tier]] with similar EU cost/speed. Steam has a 50% bonus output, Hydrogen 25% bonus and 20% less Hydrogen compared to a Chemical Reactor. The Oil Cracking Unit can be further upgraded with improved [[coil]]s and has an advanced variant in the [[Mega Oil Cracker]]. Beyond power production, this multiblock can make Toluene, a component of [[Rocket]] fuel, crack Radox, and break down Naquadah into various noble gasses / radioactive elements.
==
An Oil Cracking Unit is a hollow 5x3x3 (WxHxD) structure that requires:
== Usage ==
The Oil Cracking Unit must have a steady supply of Steam or Hydrogen to work. If there are no [[Steam_Age#Boilers|Steam Boiler]]s available, a [[Fluid Heater]] can make steam from EU and water. IC2 steam is not compatible with this multiblock. Lacking an Input Bus, circuits must be set with a Programmed Circuit item, which is placed in the bottom-right slot of the Controller. Upgraded [[coil]]s reduce power consumption by 10% per tier, up to a maximum discount of 50% with HSS-G Coil Blocks. In practice, this overclocks and will make recipes run faster for about the same power consumption.
== Maximizing Output Calculation and Conclusion ==
This section is the challenging part of mathematical theory! Here, we will use the language of linear algebra to calculate the best output method, providing a theoretical basis for petrochemical production lines. If you wish to skip the theoretical part, please
We know that each type of desulfurized fuel can be cracked and distilled into chemicals and two other types of fuels. Therefore, after one cracking and distillation, the fuel is not entirely consumed, and we need to calculate the cracking of the remaining fuel by using linear algebra.
The initial approach, which is to maximize the
This article is only a theoretical calculation, valuable for reference,
The following mathematical theory may be too hard to comprehend. With the general principle understood, it's suggested to directly use the calculator below if you're not into complicated maths.
▲This article is only a theoretical calculation, valuable for reference, but there is no need to completely mimic the methods described here.
=== Variable Definitions and Interpretations ===
First, let's define each variable:
<math>\kappa</math>: The ratio of the final product from cracking and distillation per barrel of crude oil
<math>\delta</math>: The crude oil distillation ratio.
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<math>\alpha</math>: The yield rate of the target product from each type of fuel under a specific cracking combination.
Here, κ is a scalar, while δ and α are column vectors up to three dimensions. Note that we generally use the row vector of δ^T
If the definitions seem to be not clear enough, just download the calculator.
=== Calculation Formula ===
Now, let's give the specific calculation formula. After inputting a certain amount (a large amount) of a type of crude oil, the first cracking and distillation are performed:
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The conversion ratio of the target product in this instance is
<math>\kappa_0 = \delta^T \alpha</math>
<math>\delta^T A</math>
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The conversion ratio of the target product up to this point is
<math>\kappa_1 = \kappa_0 + \delta^T A \alpha = \delta^T (I + A) \alpha</math>
<math>\delta^T A^2</math>
This process can be repeated many times, theoretically infinitely, leading to
<math>\kappa_n = \delta^T \sum_{i=0}^{n} A^i \alpha</math>
Taking n to infinity, we get
<math>\kappa = \delta^T \
The infinite sum is similar to a geometric series, and using Taylor's theorem for multivariate functions, we can obtain
<math>\sum^{\infty}_{n=0} A^n = (I - A)^{-1}</math>
(Note: The negative exponent represents the matrix inversion operation.)
Thus, the formula simplifies to
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We need to maximize κ under all conditions that meet the constraints (such as not using hydrogen cracking or heavy cracking, etc.). Please note, the type of oil might affect the outcome, but we have not encountered this situation yet.
When stirring to make diesel but not directly distilling heavy fuel, the fuel cracking matrix A changes. This situation might occur when using heavy oil for electricity generation and cracking heavy fuel to obtain petrochemical by-products in the early to mid-stages. In such cases, the light fuel output in the matrix should be set to zero, and the heavy fuel should be reduced by 0.2 times the light fuel output. Similarly, in δ (crude oil distillation), the light fuel output and 0.2 times the light fuel output in heavy fuel should be removed.▼
You can also modify the matrix to get results under different constraints.
▲
For example, in the matrix of the example, if this operation is performed, then:
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<math>A = \left( \begin{array}{ccc} 0 & 0.1 - 0.1 & 0.125 - 0.1 \times 0.2 \\ 0 & 0 - 0 & 0.1 - 0 \times 0.2 \\ 0.05 & 0 - 0.05 & 0 - 0.05 \times 0.2 \end{array} \right) = \left( \begin{array}{ccc} 0 & 0 & 0.105 \\ 0 & 0 & 0.1 \\ 0.025 & 0 & -0.01 \end{array} \right)</math>
(in old version without buffs on OCU)
As light fuel does not produce any chemical products, we can eliminate the second row and second column, making it a second-order matrix and completely ignoring light fuel in subsequent calculations (as it's no longer present).▼
▲As light fuel does not produce any chemical products, we can eliminate the second row and second column, making it a second-order matrix and completely ignoring light fuel in subsequent calculations (as it's no longer present). But this doesn't really matter.
===== Calculator =====▼
Well, there's a calculator which was mainly contributed by core.exe: [https://github.com/core-exe/GTNHPetroOptim GTNHPetroOptim]
It needs Python to run. Feel free to manipulate the parameters in the code and derived the result you want by yourself.
[[Category:Multiblocks]][[Category:Gregtech]]
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