# Presentation: 070767

## Criticality Safety Methods

** **

*Elliott Whitesides*
- Oak Ridge National Laboratory - Retired
- whitesidesge@yahoo.com

## Criticality Safety MethodsThe Past, the Present, and the Future

** **
**The objective of this paper is:**
** ****to look at the history of nuclear criticality safety calculations, **
** ****examine current methods, and **
** ****take a look at the future.**

## Historical Background Of Criticality Safety

** ****First Recorded Criticality**
** ****Consequences of this Criticality**

## Nuclear Criticality Safety the Early Years

** ****Electromagnetic Separation**
** ****Pu production by irradiating U-238**
** ****Gaseous Diffusion and Thermal Diffusion**

## Early Criticality Safety Calculations

** ****Initial Material Forms with Criticality         Safety Concerns**
-  Solutions
-  Metals
-  Computational Requirements

## Need for Criticality Experiments

** ****The Single Most Important Tool in Criticality                  Calculations is the Availability of Critical Experiments Data **
** ****The Validation of Criticality Calculations**

## Reactor Design Calculations vs. Criticality Safety Calculations or Order vs. Chaos

** ****Same Mathematical Model**
** ****Different Materials**
** ****Different Geometrical Configurations**

## Early Computational Tools for Criticality Safety Calculations

** ****Diffusion Theory**
** ****Solid Angle**
** ****Surface Density**
** ****Density Analog**

## Second Generation Computational Tools for Criticality Safety Calculations

** ****Discrete Ordinates**
** ****Monte Carlo**
** ****N(B****N****)****2**** Method**

## Important Elements for Criticality Safety Calculations	

** ****Critical Experiments**
** ****Benchmarks**
** ****Validation**

## Role of the Discrete Ordinates Method for Criticality Safety Calculations

** ****Capable of Handling Voids**
** ****Capable of Treating Anisotropic Scattering**
** ****Capable of Treating Systems with Highly Absorbing Materials**
** ****Capable of Computing arrays on a single axis**
** ****Limited to the use of multi-group cross sections**

## Role of the Monte Carlo for Criticality Safety Calculations

** ****Capable of Using Point-wise Cross Sections**
** ****Capable of Computing Systems with General Geometry Descriptions**
** ****Early Codes required large computer memories and excessive amounts of computer time**
** ****Computer Technology Development Has Made the Monte Carlo Method the Most Widely Used Method**

## Capabilities of Early Monte Codes,A Review

**O5R**
-  Generalized geometry capable of computing any system described by second-order equations.
-  Utilized cross section data in essentially point-wise form.
-  Its generality was its greatest fault.

## Capabilities of Early Monte Codes,A Review (cont.)

**GEM**
-  Had unique capability to compute array systems made up of nested spheres, cylinders, and rectangular parallelepipeds.
-  Had capability to handle point-wise cross sections, however, in practice utilized essentially group-wise cross sections.
-  Had unique computational method called the MR Method.

## Criticality Safety Calculationsthe Present

**The Discrete Ordinates Method**
**The current generation of Discrete Ordinates Methods have the capability of computing systems in one-, two-, or three- dimensions.**
**Discrete Ordinates calculates the flux as well as the *****k******eff*****.**
**The flux from this method is useful in evaluating the effect of cross section or material uncertainties through the use of perturbation theory.**
**This method computes *****k******eff***** without statistical uncertainty which is important in evaluating small perturbations in a system.**
**Major computational uncertainty - convergence limits.**

## Criticality Safety CalculationsThe Present (cont.)

**The Monte Carlo Method**
**This Method is the most commonly used method to determine Criticality Safety.**
**Current Codes have very general, easy-to-use geometry packages.**
**Current Codes are available to use either point- or group-wise cross sections.**
**The main weakness of the method is the statistical uncertainty associated with the results of the computation.**
**A significant concern with the Monte Carlo Method is the potential problem with under sampling .**

## Role of Cross-Section Representationin Nuclear Criticality Calculations

**Two Cross-Section options are available:**
**Multi-group**
- The Multi-group option is currently the most widely used principally because it is the only method available for use with the Discrete Ordinates method and because of the extensive validation work that has been documented.

## Role of Cross-Section Representationin Nuclear Criticality Calculations (cont.)

**Point-wise**
-  The use of the point-wise option is growing in usage.Some systems require the use of Point-wise cross sections (i.e. systems in which Fe, Ni, and Cr play an important neutronic part).
-  A potential, often overlooked, problem with point-wise cross sections is the problem of under sampling for materials with many closely spaced resonances.

## A Complete Criticality Calculation Approach

** ****No Single Method is sufficient.**
** ****Each Method Plays an important role.**
** ****Simplified methods such as Solid Angle, Surface Density, Density Analog, and the N(B****N****)****2**** Methods serve effectively to determine problem bounds.**

## The Future

**Computer Technology:**
**Larger Memories, Faster Speed, means Greater Capability**
**Computational Uncertainties Can Be Reduced**
**Cross Sections:**
**Cross Section Uncertainties Remain a Major Problem **
**Uncertainty Analysis - the Next Great Stride**
**Geometrical Capabilities:**
**Geometrical capabilities have been and will continue to be expanded both in the Discrete Ordinates and the Monte Carlo Method**

## Summary

**Nuclear Criticality Safety Calculations Present a                 Unique Computational Challenge**
**Nuclear Criticality Safety Experiments Must be Continued**
**'Mining' and Benchmarking of Existing Experimental Data Will Be Essential**
**Cross-Section Measurements are Needed to Resolve Uncertainties of Existing Data**
**Continued Method Development Will Be Important**