Pallet Thermal Model (PTM) Validation

Transcription

1 Pallet Thermal Model (PTM) Validation ASME 2017 V&V Symposium Eugen Nisipeanu, PhD Carlos Corrales, MS May, 2017

2 Disclaimer The information shared in this meeting is not for redistribution or reuse and remains solely the property Baxter Healthcare Corporation. Baxter reserves the copyright ownership of this presentation including video images. 2

3 Baxter International Inc. Baxter provides a broad portfolio of essential renal and hospital products, including home, acute and in-center dialysis; sterile IV solutions; infusion systems and devices; parenteral nutrition; advanced surgery products and anesthetics; and pharmacy automation, software and services. The company s global footprint and the critical nature of its products and services play a key role in expanding access to healthcare in emerging and developed countries. Baxter s employees worldwide are building upon the company s rich heritage of medical breakthroughs to advance the next generation of healthcare innovations that enable patient care. 3

4 Objective and Method Decisions have to be made to release or discard a product (aqueous solutions in flexible containers packaged in pallets or single cases) after a recorded ambient temperature excursion during storage or shipping A need was identified to quantify the lag in response time to ambient temperature variations for the solution inside the pallet or case A model is developed to predict product temperature as a function of ambient temperature Since it is not practical to model all the internals of a pallet/case; an equivalent homogeneous medium is modeled that responds in the same way to external temperature variations The homogenized material properties are determined by optimization from data collected as the pallets are exposed to a controlled temperature change 4

5 Pallet/Case Model Equations The general form of the time dependent energy equation is: E in + E g E out = E st where E in - energy into the pallet (from the environment), W E g - energy generated by the pallet, 0 in our case, W E out- energy outflow from the pallet (to the environment), W E st - energy stored by the pallet (to increase/decrease material temperature), W 5

6 Pallet/Case Model Equations And in cartesian form : x T k + x y k T y + z k T z = ρ c p T t x, y, z cartesian coordinate system directions in 3D, m t time, s T pallet temperature, K (computed by the model) k - effective thermal conductivity of the equivalent homogeneous pallet materia W/mK (model input variable) ρ - density of the equivalent homogeneous pallet material, kg/m 3 (derived for each unit size) c p - specific heat of the equivalent homogeneous pallet material, J/kgK (derived for each unit size) 6

7 Pallet/Case Model Boundary Conditions k T x k T y k T z k T z x=0 y=0 z=h z=0 = h side [T amb (t) T 0, t ] = h side [T amb (t) T 0, t ] = h top [T amb (t) T H, t ] = h bottom [T amb (t) T 0, t ] h side, h top, h bottom - heat transfer coefficient with the environment on the pallet side, top and bottom, W/m 2 K (model input variables) H pallet height, m T amb - ambient temperature of the environment surrounding the pallet, K 7

8 Initial Conditions For accurate temperature excursions the initial temperature of the product has to be known. The model uses an initial temperature T in which is set before running it. For long runs (more than a day) the influence from the initial (starting) product temperature tends to be lost. 8

9 Model Parameters k, h side, h top, h bottom from calibration against experimental data (data matching software) T amb k controls rate of heat propagation ( T curve slope) h top 0 1L h hot controls the amount of heat in or out of the 1L pallet hot (T curve magnitude) L-Hot-Corner Edge2 Corner2 Face1 Edge1 Core1 1L-Hot-Face Corner1 Face L-Hot-Core 1L-Hot Experimental Simulated 1L-Hot-Edge L-Hot-Corner 1L-Hot-Face L-Hot Experimental Simulated 30 h20 side k, ρ, c p hside T in 24 e hot (hr) 20 r, c p computed by averaging r = (#units x #cases x size)/pallet volume c p = x sol c p sol + x air c p air T amb and T in from the field Time hot (hr) h bottom For Internal Use 9

10 Typical Pallet Temperature Distribution during Heat Up Locations inside Pallet: Hot Ambient Corners the most exposed to the high ambient temperatures due to proximity to 3 pallet side faces Edges and Faces follow in terms of temperature lag, due to proximity to 2 and 1 pallet side faces, respectively Core the longest lag in temperature from the ambient Temperature distribution in the pallet For Internal Use 10

11 Temperature Variation Much smaller temperature variation inside pallets than the ambient temperature Smaller units more sensitive to ambient Larger units Smaller units For Internal Use 11

12 Worst Case Scenario Concept The solution temperature response stacks up according to the thermal mass of the pallet which is dependent on the container size Pallet Response to Hot Ambient When a validated PTM is not available for the respective container size in the field a Worst Case Scenario concept is used: Use the existing validated PTM corresponding to the immediately lower size than the one in the field (conservative assumption) Pallet Response to Cold Ambient Larger Size Smaller Size Larger Size Product 1 Smaller Size Product 2 Pallet Thermal Mass For Internal Use 12

13 Thermal Model P-Diagram Geometry INPUTS Pallet length, width, depth Container size and type Units/case, cases/pallet Boundary Conditions Heat Transfer Coefficients with the ambient Ambient temperature profile PTM OUTPUTS Plot of Representative Product Temperature along with Ambient Temperature Data Transmittal Report with Model Assumptions Initial Conditions (T 0 ) Product temperature at time 0 corresponding to the reported ambient profile OR storage conditions 12 hours prior to the event investigated Equivalent Material Properties Density, Thermal Conductivity, Specific Heat Solution In red, parameters that are provided! 13

14 Verification & Validation The model was verified and validated according ASME VV20 and the draft version of VV40 (VV for medical devices) credibility of computational model and simulations (CM&S) by performing verification and validation activities at an appropriate level depending on model risk the model risk is assessed based on the influence of the simulation results and the consequences of the decision based on those results for a context of use (COU) model verification discretization error analysis (spatial and temporal) model validation simulation results compared with experimental data For Internal Use 14

15 Methodology of V&V Scope Aqueous solutions in flexible containers exposed to environmental conditions: hot cycles (representative for the summer season) and cold cycles (winter) Context of Use (COU) 1. Investigations performed after ambient temperature recorded excursions (COU1) 2. Qualification of recurring shipping routes (COU2) Model Risk Assessment 1. Model Influence Moderate (PTM main source of solution temperature but final decision considers additional product information and stability data) 2. Decision Consequence The specific assessment must be made during each investigation depending on the product that is analyzed 3. Model Risk Defined as the multiplication of Model Influence and Decision Consequence scores For Internal Use 15

16 Methodology of V&V Level Rank Model Influence Description Major 5 The CM&S output has a major role on the design or safety decision. The model output is the only source of data available to support the decision. Significant 4 The CM&S output has a significant role on the design or safety decision. The model output is the main source of data available to support the decision. Moderate 3 The CM&S output has a moderate role on the design or safety decision. The model output, along with other (experimental, historical) data, is available to support the decision. Minor 2 Negligible 1 The CM&S output has a minor role on the design or safety decision. The model output one of multiple other sources of data available to support the decision. The CM&S output has a negligible role on the design or safety decision. The model output is minimal compared to a wealth of data available to support the decision. Level Rank Decision Consequence (Severity of Harm) Description Catastrophic 5 Poor decision may result in patient death Critical 4 Poor decision may result in permanent impairment or life-threatening injury Serious 3 Poor decision may result in injury or impairment requiring professional medical intervention Minor 2 Poor decision may result in temporary injury or impairment not requiring professional medical intervention Negligible 1 Poor decision may result in inconvenience or temporary discomfort PN = IxC Action Medium to high credibility activities are required 4-10 Low to medium credibility activities are required 1-3 None to low credibility activities are required For Internal Use 16

17 Methodology of V&V Model Credibility Verification Activities Software Quality Assurance procedures were assumed to be performed by the vendor; Baxter internal network software installation verification Numerical Algorithm was verified by comparison to an exact solution (Transient Heat Conduction in a Semi-Infinite Slab) For Internal Use 17

18 Methodology of V&V Discretization error estimation GCI = F s r p f 3 f 2 GCI - grid convergence index F s safety factor f 2, f 3 numerical solution on the baseline and coarse mesh r grid refinement factor p - observed order of accuracy The discretization error for the baseline case due to space discretization refinement is the main contributor to the total discretization error Smaller GCI at lower temperature gradients as expected in the field Use Error peer review, temperature curves physically predictable Numerical Solver Error Simulation independent on convergence criteria For Internal Use 18

19 Methodology of V&V Validation Activities Governing Equations: Energy (conduction in the pallet and convection with the ambient) Sensitivity Analysis: Container position within the pallet, vibration, air flow conditions, multiple aqueous solutions (similar density and viscosity) Sample Characterization: Multiple measurements on two different types of flexible containers with representative aqueous solutions and for all available sizes Test Conditions: Measurements in temperature controlled chambers Measurement Uncertainty: Measurements with the same thermocouple with known accuracy, in multiple days and with different thermocouples at symmetric locations For Internal Use 19

20 Methodology of V&V Input/Output: Similar inputs between experiment and simulation type/size of the container and solution, packaging type, monitoring location, cycle type Output comparison: Temperature at corner locations for hot and cold cycles, single cases and pallets, multiple containers capacities Metric for comparison Cumulative Excursion Time (CET) = the sum of time intervals where the temperature is above (hot cycles) or below (cold cycles) a prescribed value %Error CET = i=1 t i model t exp i=1 i i=1 t exp i x 100% t i model - time interval the model predicts a temperature above (for hot cycles) or below (for cold cycles) a set temperature limit within a given ambient temperature cycle t i exp - time interval the experiment measures a temperature above (for hot cycles) or below (for cold cycles) a set temperature limit within a given ambient temperature cycle %Error CET - relative cumulative excursion time For Internal Use 20

21 Output Comparison Samples - Hot Cycle For Internal Use 21

22 Output Comparison Samples - Cold Cycle For Internal Use 22

23 Conclusions The PTM can be used to predict product temperature during ambient temperature excursions per COU1 and shipping qualification per COU2 According to the discretization error analysis, the main source of error is the spatial discretization mainly in the presence of steep temperature gradients which are not likely to happen in the field as the product reaches extreme values. A conservative approach of Worst Case Scenario was validated to over-predict the CET For Internal Use 23

24 Aknowldgements Chloe Funkhouser, Mike Wehrli, Audel Gutierrez, Quentin Henneaux, Peter De Beule, Thomas Dudar, Joseph Moore, Jonathan Sanabria For Internal Use 24