Fast/Thermal Reactor Supply-Based Exchange

The primary difference between the request and supply-based cases is that the commodity assignment of assemblies is known, rather than being decided by the outcome of the exchange. The supply-based exchange decides which supporting facilities will receive used fuel.

The levels of fidelity modeled will mirror the request-based case:

Category	Subcategory
Reactor	batch assembly
Fuel Cycle	Once-Through UOX + MOX F/Th Recycle UOX + MOX F/Th Recycle + Thorium F Recycle
Location	None Coarse Fine

Commodities

The same commodities will be used as in the request case.

Facilities

Reactors

Reactors representing AP-1000 and BN-600-like generating units will be used to determine used fuel supply. In order to simplify the generation of supply, each reactor is assumed to be fueled by its preferred commodity with a randomly chosen initial enrichment.

The primary difference between reactors of the request and supply cases is that reactors in the supply case are offering known assembly types, whereas reactors in the request case are requesting an array of assembly types. Accordingly, the assembly types in the supply case must be chosen. If the instance is of high reactor fidelity, the assembly types will be assigned according to the reactor’s distribution parameter. If the instance is of low reactor fidelity, the distribution parameters serve as commodity assignment probabilities for the reactor’s entire batch.

Parameters

Reactor parameters will include all those of the request instance plus

\(d_{th}\) : the distribution of thermal reactor assembly commodities

\(d_{f_{mox}}\) : the distribution of fast mox reactor assembly commodities

\(d_{f_{thox}}\) : the distribution of fast thox reactor assembly commodities

Supporting Facilities

The same supporting facilities will be used with the addition of a Repository and the subtraction of the Enrichment Facility.

Parameters

Supporing facility parameters will include all those of the request instance plus

\(r_{repo}\) : the ratio of repositories to other supporting facilities

Commodity Preferences

Preferences are assigned to facility types based on the fuels they would prefer to process. It is assumed that facilities would prefer to process undesireable fuels over shutting down. Further, it is assumed that any processing facility can process used UOX. Finally, it is assumed that there is a incentive for material to be sent to processing facilities over repositories.

Commodity-Preference Mapping for Supporting Facility Types

Facility Type	EUOX	Th MOX	F MOX	F ThOX
Thermal Recycle	1	1	0.5	N/A
Fast MOX Recycle	0.5	0.5	1	N/A
Fast ThOX Recycle	0.3	N/A	N/A	1
Repository	0.01	0.01	0.01	0.01

Constraints

In addition to a raw throughput capacity constraint of 800 t/yr of material, recycle facilities requesting material will supply a fissile content demand constraint with the coefficient and RHS are shown below, where \(\bar{\epsilon} r_{commod}\) is the mean quantity of fissile materail of the primary supplier to given requester, and \(r_{commod}\) is the relative quantity of the supplier as defined in the previous section.

\[conv_{fiss}(\epsilon, q) = \epsilon r_{commod} q\]\[S_{fiss} = \bar{\epsilon} r_{commod} \frac{800 \frac{t}{year}}{12 \frac{month}{year}} = ~66.7 \bar{\epsilon} r_{commod} \frac{t}{month}\]

Repostories will employ a simple, quantity-based supply constraint. To determine an appropriate RHS, I assume a Yucca Mountain statutory limit of 17,000 tonnes and a 30 year lifetime, resulting in ~575 t per year processing capacity. In fuel units, the RHS value becomes

\[S_{repo} = \frac{575 \frac{t}{year}}{12 \frac{month}{year}} = ~48 \frac{t}{month}\]

Fuel Cycles

The same fuel cycles will be modeled as in the request case.

Location Assignment

Location considerations will be handled in the same manner as the request case.

Preference Determination

Preferences will be determined in the same manner as the request case.

Parameter Summary

In addition to all Request Parameters, the following parameters can be set in a run control file for the supply case:

Structured Supply Species Parameters

Handle	Full Name	Possible Values
\(d_{th}\)	thermal reactor assembly distribution	\([x_{uox}, x_{{mox}_{th}}, x_{{mox}_{f}}], x_i \in [0, 1)\)
\(d_{f_{mox}}\)	fast mox reactor assembly distribution	\([x_{uox}, x_{{mox}_{th}}, x_{{mox}_{f}}, x_{{thox}_{f}}], x_i \in [0, 1)\)
\(d_{f_{thox}}\)	fast thox reactor assembly distribution	\([x_{uox}, x_{{mox}_{th}}, x_{{mox}_{f}}, x_{{thox}_{f}}], x_i \in [0, 1)\)
\(r_{repo}\)	repository to supporting facility ratio	\([0, 2]\)