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{{:Infobox:Kovarex enrichment process}}
{{:Infobox:Kovarex enrichment process}}
Der Kovarex-Anreicherungsprozess ist eine Methode zur Wiederaufbereitung von Uran in einer [[Centrifuge/de|Zentrifuge]]. Obwohl der Prozess eine große Menge des seltenen [[Uranium-235/de|Uran-235]] erfordert, kann es ein guter Weg sein, um das vorhandene [[uranium ore/de|Uranerz]] besser zu nutzen.


== Zweck ==
The '''Kovarex enrichment process''' is a method for reprocessing uranium in a [[centrifuge]]. Although the process requires a large amount of (much rarer) Uranium-235 to start, it can be a good way to get more use out of the available [[uranium ore]].
Bei der [[Uranium processing/de|Uranverarbeitung]] wird aus 10 Einheiten [[uranium ore/de|Uranerz]] 1 Einheit [[Uranium-235/de|Uran-235]] mit einer Wahrscheinlichkeit von etwa 0,7% gewonnen. Weiterhin fällt dabei [[Uranium-238/de|Uran-238]] mit einer Wahrscheinlichkeit von 99,3% an, was zu einer [[:Wikipedia:Binomial_distribution|Binomialverteilung]] führt, deren Resultat allerdings auch nicht garantiert ist.
Somit werden nach ungefähr 143 Verarbeitungszyklen 1 Einheit [[Uranium-235/de|Uran-235]] und 142 Einheiten [[Uranium-238/de|Uran-238]] produziert.
Dies ist derzeit das einzige wahrscheinlichkeitsbasierte Handwerksrezept im Spiel.


[[Uranium-235/de|Uran-235]] ist notwendig, um [[Uranium fuel cell/de|Uran-Brennstoffzellen]] und [[Atomic bomb/de|Atombomben]] in beträchtlichen Mengen für Letztere herzustellen.
== Purpose ==
Die Wahrscheinlichkeitsverteilung der [[Uranium processing/de|Uranverarbeitung]] führt dazu, dass es nur langsam produziert wird und große Lagerbestände mit [[Uranium-238/de|Uran-238]] als Nebenprodukt entstehen. Das Kovarex-Verfahren bietet dem Spieler somit eine wesentlich schnellere  (und deterministische) Methode zur Herstellung von [[Uranium-235/de|Uran-235]] sowie eine Verwendung für das überschüssige [[Uranium-238/de|Uran-238]].
[[Uranium processing]] takes 10 uranium ore and returns 1 [[Uranium-235]] with 0.007 (0.7%) probability, or 1 [[Uranium-238]] with 0.993 (99.3%) probability, leading to an [[:Wikipedia:Binomial_distribution|expected]] (not guaranteed!) 1 unit of Uranium-235 per approximately 143 processing cycles (or about a 1:142 ratio of U-235 to U-238). This is currently the only probability-based crafting recipe in the game.


Es sei darauf hingewiesen, dass [[Uranium-238/de|Uran-238]] nicht nutzlos ist. Es ist notwendig - und auch ausreichend vorhanden - um [[Uranium_rounds_magazine/de|Uran-Munition]], [[Uranium cannon shell|Uran-Kanonenmunition]] und explosive [[Explosive_uranium_cannon_shell|explosive Uran-Kanonenmunition]] herzustellen.
Uranium-235 is necessary to create [[Uranium fuel cell]]s and [[Atomic bomb]]s, in considerable quantities for the latter, but the probability distribution of uranium processing leads to it being produced slowly and creating large stockpiles of U-238 as a byproduct. The Kovarex process thus provides the player with a considerably faster (and deterministic) method of producing U-235, as well as a use for the surplus U-238.
Weiterhin wird es als sekundärer Bestandteil bei der Herstellung von [[Uranium fuel cell/de|Uran-Brennstoffzellen]] benötigt.
Daher ist es nicht ratsam, das Kovarex-Verfahren zu verwenden, um '''alles''' auf Lager befindliche [[Uranium-238/de|Uran-238]] in [[Uranium-235/de|Uran-235]] umzuwandeln. (Obwohl im Falle eines Mangels die [[Used up uranium fuel cell|verbrauchte Uranbrennstoffzellen]] in einer bescheidenen Menge von [[Uranium-238/de|Uran-238]] wiederaufbereitet werden kann).


== Voraussetzungen für die Einleitung (Uranverarbeitung) ==
It should be noted that U-238 is not useless; it is necessary (and sufficient) to manufacture [[Uranium rounds magazine]]s, [[Uranium cannon shell]]s, and [[Explosive uranium cannon shell]]s, and is required as a secondary ingredient in Uranium fuel cells. Therefore, it is not advisable to use the Kovarex process to convert ''all'' stockpiled U-238 into U-235. (Although, in case of shortage, [[Used up uranium fuel cell]]s can be [[Nuclear fuel reprocessing|reprocessed]] into a modest amount of U-238.)
Im Gegensatz zu allen anderen Herstellungsprozessen im Spiel stellt die Uranverarbeitung U-235 und U-238 nach Wahrscheinlichkeiten und nicht in garantierten deterministischen Mengen her. Darüber hinaus erfordert das Kovarex-Verfahren eine Massenlagerung von 40 Einheiten des seltenen Uran-235-Isotops, um es in einer einzigen Zentrifuge zu initiieren. Daher erfordert die Planung des Uranabbaus und der -verarbeitung für den Kovarex-Prozess einige Überlegungen, die an anderer Stelle im Spiel nicht anzutreffen sind.


=== Erwartungswert ===
== Requirements for initiation (Uranium processing) ==
Da U-235 in Zentrifugen erzeugt wird, die eine Uranverarbeitung mit ''p = 0,007'' ausführen, ist die erwartete Anzahl von Verarbeitungszyklen zur Gewinnung einer einzelnen Einheit ''E(1,p) = 1 ÷ p = ~143''. Die erwartete Anzahl von Zyklen zur Gewinnung von 40 Einheiten beträgt dann ''E(40,p) = 40 × E(1,p)'' = was etwa 5714 Zyklen entspricht. Beachten Sie, dass das Ausführen dieser vielen Zyklen auch den Abbau von 57140 Einheiten Uranerz erfordert. Eine nicht unbedeutende Aufgabe.
Unlike all other crafting processes in the game, Uranium processing creates U-235 and U-238 based on probability, rather than in guaranteed deterministic amounts. Additionally, the Kovarex process requires a bulk stockpile of 40 units of the rare Uranium-235 isotope to initiate in a single centrifuge. Therefore, planning uranium mining and processing for the Kovarex process takes certain considerations not encountered elsewhere in the game.


Angesichts der Unsicherheit bei der Verarbeitung in der Zentrifuge, kann jedoch auch das nicht garantiert werden, dass nach dieser Anzahl von Zyklen '''wirklich''' 40 Einheiten [[Uranium-235/de|Uran-235]] erreicht werden. Tatsächlich liegt die Wahrscheinlichkeit, dass 5714 Zyklen mindestens 40 Einheiten [[Uranium-235/de|Uran-235]] erzeugen, nur bei etwa 52%.
=== Expected value ===
As U-235 is created in centrifuges running Uranium processing with ''p = 0.007'', the expected number of processing cycles to gain a single unit is ''E(1,p) = 1 ÷ p = ~143''. The expected number of cycles to gain 40 units is then ''E(40,p) = 40 × E(1,p)'' = '''~5,714 cycles'''. Note that running this many cycles requires mining 57,140 Uranium ore, a non-trivial task.


=== Vertrauensniveau ===
However, given the nature of probability, it is impossible to guarantee that 40 units will be reached in this number of cycles; as a matter of fact, some mathematics yields that the probability that 5,714 cycles will produce ''at least'' 40 units of U-235 is only about 52%.
[[File: Kovarex-prob-chart.png | 300px | thumb | right | Wahrscheinlichkeit, 40 Einheiten U-235 von der Uranverarbeitung nach Zyklenanzahl zu erreichen (zum Vergrößern anklicken)]]


Weitere mathematische Berechnungen ermöglichen es, die Anzahl der Uranverarbeitungszyklen zu berechnen, die ausgeführt werden müssen, um mindestens 40 U-235-Einheiten mit einem bestimmten Zuverlässigkeitsgrad (Wahrscheinlichkeit des Erreichens) zu erhalten.
=== Confidence levels ===
[[File:Kovarex-prob-chart.png|300px|thumb|right|Probability of reaching 40 U-235 from Uranium processing by number of cycles (click to enlarge)]]


Wie im vorherigen Abschnitt erörtert, liegt das Vertrauensniveau, der 5714 Zyklen entspricht (für die der "erwartete Wert" von U-235 40 ist) zufällig bei etwa 52% (oder anders ausgedrückt bei dieser Anzahl von Zyklen kann man davon ausgehen, 40 U-235 etwas weniger als einmal von 2 Versuchen zu erreichen).
Some further mathematics enables one to calculate the number of Uranium processing cycles one must run to obtain ''at least'' 40 units of U-235 (given ''p = 0.007'') with a given level of confidence (probability of achieving the set goal).


In der folgenden Tabelle sind einige Beispiele für Vertrauensstufen aufgeführt, die für den Spieler von Interesse sein können. Die benutzerdefinierten Werte finden Sie in der Tabelle rechts.
As discussed in the previous section, the level of confidence corresponding to 5,714 cycles (for which the ''expected value'' of U-235 gained is 40) happens to be about 52% (or, in other words, with this number of cycles, one can expect to fail to reach 40 U-235 a bit less than once out of every 2 tries).
 
Some further example confidence levels that may be of interest to players are given in the table below. Consult the chart to the right for custom values.


{| class="wikitable" style="text-align: center;"
{| class="wikitable" style="text-align: center;"
!style="width: 120px;" |Vertrauensniveau
!style="width: 120px;" |Confidence level
!style="width: 100px;" |Erwartungswert
!style="width: 100px;" |Failures
!Zyklen
!Cycles required
|-
|-
| 10% || 9 von 10 || 4,595
| 10% || 9 out of 10 || 4,595
|-
|-
| 50% || 1 von 2 || 5,667
| 50% || 1 out of 2 || 5,667
|-
|-
| 90% || 1 von 10 || 6,894
| 90% || 1 out of 10 || 6,894
|-
|-
| 95% || 1 von 20 || 7,272
| 95% || 1 out of 20 || 7,272
|-
|-
| 99% || 1 von 100 || 8,015
| 99% || 1 out of 100 || 8,015
|-
|-
|}
|}


== Trivia ==
== Trivia ==
* Der hier im Spiel aufgeführte "Kovarex-Anreicherungsprozess" ist nach Michal Kovařík, dem führenden Designer von Factorio und Mitinhaber von Wube, benannt, dessen Online-Name "kovarex" ist.
* The Kovarex enrichment process is named after [[development-team|Michal Kovařík]], lead designer of Factorio and co-owner of Wube, whose online nick is ''kovarex'' (which he usually spells lowercase). [https://www.reddit.com/r/factorio/comments/67bj3p/015_kovarex_uranium_enrichment_is_too_good_with/dgq2ij3/?context=1]
Siehe hierzu: [https://www.reddit.com/r/factorio/comments/67bj3p/015_kovarex_uranium_enrichment_is_too_good_with/dgq2ij3/?context=1]
 
* In the real world, [[:Wikipedia:Uranium-235|Uranium-235]] is the only fissile isotope of uranium and makes up approximately 0.72% of naturally-occurring uranium, with the other 99.28% being [[:Wikipedia:Uranium-238|Uranium-238]]. The in-game representation is thus highly accurate in this regard. Uranium is commonly [[:Wikipedia:Enriched_uranium|enriched]] in centrifuges to increase the percentage of 235U for use in fission reactions.
* Uranium munitions are made from [[:Wikipedia:depleted uranium|depleted uranium]], a byproduct of uranium enrichment, which is mostly 238U whose natural admixture of the 235U isotope has been lowered even further through the enrichment process. Depleted uranium is minimally radioactive and the reason for its use in munitions is its very high density and other mechanical properties, not radioactivity / toxicity.


* In der realen Welt ist [[:Wikipedia:Uranium-235|Uran-235]] das einzige spaltbare Isotop des Urans und macht etwa 0,72% des natürlich vorkommenden Urans aus, wobei die übrigen 99,28% Uran-238 ausmachen. Siehe: [[:Wikipedia: Uran-238|Uran-238]]. Die Darstellung im Spiel ist somit in dieser Hinsicht ziemlich genau. Uran wird in Zentrifugen häufig angereichert, um den prozentualen Anteil von Uran-235 für Spaltreaktionen zu erhöhen.
== History ==
{{History|0.15.2|
* No longer usable with productivity modules.}}


* Uranmunition oder auch DU-Munition wird aus "abgereichertem Uran" hergestellt, einem Nebenprodukt der Urananreicherung.
{{History|0.15.0|
Siehe dazu: [[Wikipedia: depleted Uran]].
* Introduced}}
Das "abgereicherte Uran" ist minimal radioaktiv und der Grund für seine Verwendung als Munition ist seine sehr hohe Dichte und weitere mechanische Eigenschaften, nicht die Radioaktivität oder Toxizität.


== Siehe auch ==
== See also ==
* [[uranium processing/de|Uranverarbeitung]]
* [[Uranium-235]]
* [[Uranium-235/de|Uran-235]]
* [[Uranium processing]]
* [[Uranium-238/de|Uran-238]]


{{IntermediateNav}}
{{IntermediateNav}}
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Revision as of 15:16, 27 January 2019

Kovarex enrichment process.png
Kovarex enrichment process

Recipe

Time.png
60
+
Uranium-235.png
40
+
Uranium-238.png
5
Uranium-235.png
41
+
Uranium-238.png
2

Total raw

Time.png
60
+
Uranium-235.png
40
+
Uranium-238.png
5

Prototype type

recipe

Internal name

kovarex-enrichment-process

Required technologies

Kovarex enrichment process (research).png

Produced by

Centrifuge.png

The Kovarex enrichment process is a method for reprocessing uranium in a centrifuge. Although the process requires a large amount of (much rarer) Uranium-235 to start, it can be a good way to get more use out of the available uranium ore.

Purpose

Uranium processing takes 10 uranium ore and returns 1 Uranium-235 with 0.007 (0.7%) probability, or 1 Uranium-238 with 0.993 (99.3%) probability, leading to an expected (not guaranteed!) 1 unit of Uranium-235 per approximately 143 processing cycles (or about a 1:142 ratio of U-235 to U-238). This is currently the only probability-based crafting recipe in the game.

Uranium-235 is necessary to create Uranium fuel cells and Atomic bombs, in considerable quantities for the latter, but the probability distribution of uranium processing leads to it being produced slowly and creating large stockpiles of U-238 as a byproduct. The Kovarex process thus provides the player with a considerably faster (and deterministic) method of producing U-235, as well as a use for the surplus U-238.

It should be noted that U-238 is not useless; it is necessary (and sufficient) to manufacture Uranium rounds magazines, Uranium cannon shells, and Explosive uranium cannon shells, and is required as a secondary ingredient in Uranium fuel cells. Therefore, it is not advisable to use the Kovarex process to convert all stockpiled U-238 into U-235. (Although, in case of shortage, Used up uranium fuel cells can be reprocessed into a modest amount of U-238.)

Requirements for initiation (Uranium processing)

Unlike all other crafting processes in the game, Uranium processing creates U-235 and U-238 based on probability, rather than in guaranteed deterministic amounts. Additionally, the Kovarex process requires a bulk stockpile of 40 units of the rare Uranium-235 isotope to initiate in a single centrifuge. Therefore, planning uranium mining and processing for the Kovarex process takes certain considerations not encountered elsewhere in the game.

Expected value

As U-235 is created in centrifuges running Uranium processing with p = 0.007, the expected number of processing cycles to gain a single unit is E(1,p) = 1 ÷ p = ~143. The expected number of cycles to gain 40 units is then E(40,p) = 40 × E(1,p) = ~5,714 cycles. Note that running this many cycles requires mining 57,140 Uranium ore, a non-trivial task.

However, given the nature of probability, it is impossible to guarantee that 40 units will be reached in this number of cycles; as a matter of fact, some mathematics yields that the probability that 5,714 cycles will produce at least 40 units of U-235 is only about 52%.

Confidence levels

Probability of reaching 40 U-235 from Uranium processing by number of cycles (click to enlarge)

Some further mathematics enables one to calculate the number of Uranium processing cycles one must run to obtain at least 40 units of U-235 (given p = 0.007) with a given level of confidence (probability of achieving the set goal).

As discussed in the previous section, the level of confidence corresponding to 5,714 cycles (for which the expected value of U-235 gained is 40) happens to be about 52% (or, in other words, with this number of cycles, one can expect to fail to reach 40 U-235 a bit less than once out of every 2 tries).

Some further example confidence levels that may be of interest to players are given in the table below. Consult the chart to the right for custom values.

Confidence level Failures Cycles required
10% 9 out of 10 4,595
50% 1 out of 2 5,667
90% 1 out of 10 6,894
95% 1 out of 20 7,272
99% 1 out of 100 8,015

Trivia

  • The Kovarex enrichment process is named after Michal Kovařík, lead designer of Factorio and co-owner of Wube, whose online nick is kovarex (which he usually spells lowercase). [1]
  • In the real world, Uranium-235 is the only fissile isotope of uranium and makes up approximately 0.72% of naturally-occurring uranium, with the other 99.28% being Uranium-238. The in-game representation is thus highly accurate in this regard. Uranium is commonly enriched in centrifuges to increase the percentage of 235U for use in fission reactions.
  • Uranium munitions are made from depleted uranium, a byproduct of uranium enrichment, which is mostly 238U whose natural admixture of the 235U isotope has been lowered even further through the enrichment process. Depleted uranium is minimally radioactive and the reason for its use in munitions is its very high density and other mechanical properties, not radioactivity / toxicity.

History

  • 0.15.2:
    • No longer usable with productivity modules.

See also