Enrichment – `pyne.enrichment`¶

The enrichment module contains tools for defining and manipulating enrichment cascades. The Cascade class is a simple container for storing parameters that define an enrichment setup. These include feed, product, and tail materials, target enrichments, and separation factors. The main functions in this module compute the total flow rate and separation factors from an initial cascade. Other helper functions compute relative flow rates and nuclide-specific separation factors.

class pyne.enrichment.Cascade(self, **kwargs)¶

This class is a container for enrichment cascade parameters that define the perfomance of a separations plant. Instances of this class are passed into and out of many enrichment functions.

Parameters

kwargsoptional: Any keyword argument which is supplied is applied as an attribute to this instance.

M¶: The number of stripping stages.

Mstar¶: This is the mass separation factor \(M^*\). On initialization, this should be in the ballpark of the optimized result of the Mstar value. However, this must always have a value between the weights of the j and k key components.

N¶: The number of enriching stages.

alpha¶: The \(\alpha\) attribute specifies the overall stage separation factor for the cascade. This should be set on initialization. Values should be greater than one. Values less than one represent de-enrichment.

j¶: This is an integer in id-form that represents the jth key component. This nuclide is preferentially enriched in the product stream. For standard uranium cascades j is 922350 (ie U-235).

k¶: This is an integer in id-form that represents the kth key component. This nuclide is preferentially enriched in the tails stream. For standard uranium cascades k is 922380 (ie U-238).

l_t_per_feed¶: Total flow rate (\(L_t\)) per feed flow rate. This is a characteristic of the cascade as a whole. As such it is this quatity which is minimized in any real cascade.

mat_feed¶: Feed material to be enriched. Often set at initialization.

mat_prod¶: Product (enriched) material.

mat_tail¶: Tails (de-enriched) material.

swu_per_feed¶: The seperative work units (SWU) per unit mass of feed material.

swu_per_prod¶: The seperative work units (SWU) per unit mass of prod material.

x_feed_j¶: This is the target enrichment of the jth isotope in the feed stream mat_feed. The \(x^F_j\) value should be set prior to solving for the remainder of the cascade. For typical uranium vectors, this value is about U-235 = 0.00711.

x_prod_j¶: This is the target enrichment of the jth isotope in the product stream mat_prod. The \(x^P_j\) value should be set prior to solving for the remainder of the cascade. For typical uranium vectors, this value is about U-235 = 0.05.

x_tail_j¶: This is the target enrichment of the jth isotope in the Tails stream mat_tail. The \(x^T_j\) value should be set prior to solving for the remainder of the cascade. For typical uranium vectors, this value is about U-235 = 0.0025.

pyne.enrichment.alphastar_i()¶

Calculates the stage separation factor for a nuclide i of atomic mass \(M_i\).

\[\alpha^*_i = \alpha^{(M^* - M_i)}\]

Parameters

alphafloat: Stage separation factor.
Mstarfloat: Mass separation factor.
M_ifloat: Atomic mass of the ith nuclide.

Returns

astar_ifloat: As calculated above.

pyne.enrichment.default_uranium_cascade()¶

Returns a copy of a default uranium enrichment cascade, which has sensible initial values for this very common case.

The values of this instance of Cascade are as follows:

duc = pyne.enrichment.Cascade(N=30.0, M=10.0, alpha=1.05, Mstar=236.5, 
        j=922350, k=922380, x_feed_j=0.0072, x_prod_j=0.05, x_tail_j=0.0025,
        l_t_per_feed=0.0, swu_per_feed=0.0, swu_per_prod=0.0, 
        mat_feed=pyne.material.Material({922340: 5.5e-05, 922350: 0.0072, 
                                         922380: 0.992745}, 1.0, 
                                        'Natural Uranium', 1.0), 
        mat_prod=pyne.material.Material({}, -1.0, '', -1.0), 
        mat_tail=pyne.material.Material({}, -1.0, '', -1.0))

Returns

ducCascade: As defined above.

pyne.enrichment.feed()¶

Calculates the feed quantity in kg from either the product or tails.

Parameters

x_feedfloat: Feed enrichment.
x_prodfloat: Product enrichment.
x_tailfloat: Feed enrichment.
productfloat, optional: Quantity of product in kg
tailsfloat, optional: Quantity of tails in kg

Returns

feedfloat: Feed quantity

pyne.enrichment.multicomponent()¶

Calculates the optimal value of Mstar by minimzing the seperative power. The minimizing the seperative power is equivelent to minimizing \(L_t/F\), or the total flow rate for the cascade divided by the feed flow rate. Note that orig_casc.Mstar represents an intial guess at what Mstar might be. This function is appropriate for feed materials with more than 2 nuclides (i.e. multicomponent).

Parameters

orig_cascCascade: A cascade to optimize.
solverstr, optional: Flag for underlying cascade solver function to use. Current options are either “symbolic” or “numeric”.
tolerancefloat, optional: Numerical tolerance for underlying solvers, default=1E-7.
max_iterint, optional: Maximum number of iterations for underlying solvers, default=100.

Returns

cascCascade: A new cascade object, copied from the original, which has been optimized to minimize flow rates. Correct values of product and tails materials are also computed on this instance.

pyne.enrichment.prod_per_feed()¶

Calculates the product over feed enrichment ratio.

\[\frac{p}{f} = \frac{(x_f - x_t)}{(x_p - x_t)}\]

Parameters

x_feedfloat: Feed enrichment.
x_prodfloat: Product enrichment.
x_tailfloat: Tails enrichment.

Returns

pfratiofloat: As calculated above.

pyne.enrichment.product()¶

Calculates the product quantity in kg from either the feed or tails.

Parameters

x_feedfloat: Feed enrichment.
x_prodfloat: Product enrichment.
x_tailfloat: Product enrichment.
feedfloat, optional: Quantity of feed in kg
tailsfloat, optional: Quantity of tails in kg

Returns

productfloat: Product quantity

pyne.enrichment.solve_numeric()¶

Calculates the total flow rate (\(L_t\)) over the feed flow rate (\(F\)).

Parameters

orig_cascCascade: A cascade to compute the l_t_per_feed, swu_per_feed, swu_per_prod, mat_prod, and mat_tail attributes for.
tolerancefloat, optional: Numerical tolerance for solvers, default=1E-7.
max_iterint, optional: Maximum number of iterations for underlying solvers, default=100.

Returns

cascCascade: A new cascade object, copied from the original, with the appropriate attributes computed.

pyne.enrichment.solve_symbolic()¶

Computes the cascade parameters based on a given initial state.

Parameters

orig_cascCascade: A cascade to compute the l_t_per_feed, swu_per_feed, swu_per_prod, mat_prod, and mat_tail attributes for.

Returns

cascCascade: A new cascade object, copied from the original, with the appropriate attributes computed.

pyne.enrichment.swu()¶

Calculates the SWU required to reach a given quantity of an enrichment level. One of feed, product, or tails must be provided.

Parameters

x_feedfloat: Feed enrichment.
x_prodfloat: Product enrichment.
x_tailfloat: Feed enrichment.
feedfloat, optional: Quantity of feed in kg
productfloat, optional: Quantity of product in kg
tailsfloat, optional: Quantity of tails in kg

Returns

SWUfloat: SWU required

pyne.enrichment.tail_per_feed()¶

Calculates the tails over feed enrichment ratio.

\[\frac{t}{f} = \frac{(x_f - x_p)}{(x_t - x_p)}\]

Parameters

x_feedfloat: Feed enrichment.
x_prodfloat: Product enrichment.
x_tailfloat: Tails enrichment.

Returns

tfratiofloat: As calculated above.

pyne.enrichment.tail_per_prod()¶

Calculates the tails over product enrichment ratio.

\[\frac{t}{p} = \frac{(x_f - x_p)}{(x_t - x_f)}\]

Parameters

x_feedfloat: Feed enrichment.
x_prodfloat: Product enrichment.
x_tailfloat: Tails enrichment.

Returns

tpratiofloat: As calculated above.

pyne.enrichment.tails()¶

Calculates the tails quantity in kg from either the feed or product.

Parameters

x_feedfloat: Feed enrichment.
x_prodfloat: Tails enrichment.
x_tailfloat: Tails enrichment.
feedfloat, optional: Quantity of feed in kg
productfloat, optional: Quantity of product in kg

Returns

tailsfloat: Tails quantity

pyne.enrichment.value_func()¶

Calculates the value or separation potential of an assay.

\[V(x) = (2x - 1) \log{\frac{x}{x - 1}}\]

Parameters

xfloat: assay enrichment.

Returns

valfloat: As calculated above.

Enrichment – pyne.enrichment¶

Enrichment – `pyne.enrichment`¶