 Optimization of a Dewar Flask Design

In this article we will perform a Dewar flask design optimization using Simulation Master's optimizer.  In a previous article we analyzed a Dewar flask's design that was used to shield down hole electronics from high temperature oil & gas well bores.

In that article we had a fixed design, and treated emissivity of the vacuum chamber surfaces as a random variable.  The heat generated by the electronics in the flask was also treated as a random variable.  Using Monte Carlo simulation, the time the flask could spend in the well was determined with a 95% confidence level.

This article approaches the problem from a different angle.  Let's say we have a requirement that the flask must keep the internal temperature below 435 K for 500 minutes in a 500 K well bore with 95% confidence.  To do this requires adjusting volume of the heat sink.  The flask diameter is fixed, so the length of the heat sink must be changed to meet the requirement.  Overall flask length must be adjusted as well to fit the heat sink.

The problem is to find the optimum heat sink volume to meet the requirement.  Emissivity and heat generated by electronics are random variables and can assume different values each time the model is recalculated.  This eliminates using a normal optimizer such as Excel's Solver since the random inputs will not allow the optimizer to converge on a solution.

Instead, we need to do a Monte Carlo simulation to generate a statistic of the simulation that we can optimize instead of a single point value.

Decision Variables

A decision variable is something that we can control.  For this model, the flask length will be a decision variable.  Heat sink length will be dependent on overall flask length.

So for the design, we have the following:

Insulator length: 150 mm

Electronics length: 800 mm

Heat sink length: ?

Flask length = Insulator length + Electronics length + Heat sink length

In Simulation Master, a decision variable that is used with optimization is defined with the RVOPTDECISION function.  This function is placed in a cell and defines the cell address that will be changed during optimization, the data type (decimal or integer), and the bounds of the decision variable.  In the model, cell A7 is the decision variable definition cell, and cell B7 is the cell that is changed during optimization.

Simulation with Optimization

Using optimization with Monte Carlo simulation is basically a loop within a loop.  The outer loop is the optimization algorithm.  The inner loop is running simulations to generate a statistic value, such as mean, that serves as the objective measure for the optimization algorithm.

The optimization algorithm changes any decision variables to meet the optimization goal.  The goal can be to minimize, maximize, or reach a target value of a simulation statistic (objective measure).

Running the Dewar Flask Design Optimization

The model above was simulated and optimized.  The objective measure is the 5th percentile with a target value of 500 minutes.  Remember the requirement to meet is 500 minutes with 95% confidence.  If the 5th percentile is 500, 95% of the outcomes are greater than 500.

Each time the optimization algorithm calls for a value of the objective measure (5th percentile), the software will perform a Monte Carlo simulation of 500 iterations, and calculate the 5th percentile of the simulation.  Because of the number of times a simulation is run within an optimization loop, it is very computationally intensive versus a regular Monte Carlo simulation.

The optimization loop was run for 25 iterations.

The final simulation results using the latest optimum decision variable value is shown below.

Clicking on the Optimization tab of the results window will show how the objective measure changed during each optimization iteration.  The final optimum value of decision variables is also shown.

In this example, the final value of the 5th percentile of down hole time was 499.95.  This is close enough to the 500 minute requirement for our purposes.  The optimum value of flask length was found to be 1.26 meters.

Conclusion

In our Dewar flask design optimization problem, we have random variables (emissivity and electrical power) that do not allow for traditional optimization.  To accommodate the random variables, we used simulation to generate a statistic of the possible outcomes, and optimized for the statistic.  This allows us to take variation into account while optimizing our design.

Excel is a registered trademark of Microsoft Corporation.  Used with permission from Microsoft.