Speaker | Transcript |
| Hello, I'm Chris Gotwalt and |
| today I'm going to be |
| presenting with Markus Schafheutle |
| and Laura Castro-Schilo |
| on an industrial application of |
| structural equations models, or |
| SEM. This talk showcases one of |
| the things I enjoy most about |
| my work with JMP. In JMP |
| statistical development, we have a |
| bird's eye view of what is |
| happening in data analysis |
| across many fields, which gives |
| us the opportunity to cross |
| fertilize best practices across |
| disciplines. |
| In JMP Pro 15, we added a new |
| structural equations modeling |
| platform. This is the dominant |
| data analytic framework in a |
| lot of social sciences because |
| it flexibly models complex |
| relationships in multivariant |
| settings. One of the key |
| features is that variables may |
| be used as both regressors and |
| responses at the same time as a |
| part of the same model. |
| Furthermore, it occurred to me |
| that with these complicated |
| models they are represented with |
| diagrams that, at least on the |
| surface, look like diagrams |
| representing manufacturing |
| processes. I wasn't the only one |
| to make this connection. Markus, |
| who was working with a |
| chemical company, thought the |
| same thing. He was working on a |
| problem with a chemical company |
| with a two column twin |
| distillation manufacturing |
| process where they wanted to |
| minimize energy costs which were |
| largely going to steam |
| production, while still making |
| product that stayed within |
| specification. He reached out to |
| his JMP sales engineer, |
| Martin Demel, who then connected |
| Markus to Laura and I. |
| We had a series of meetings |
| where he showed and described |
| the data, the problem and the |
| goals of the company. We were |
| able to model the data |
| remarkably well. Our model was |
| validated by sharing the results |
| as communicated with the JMP |
| profiler to the company's |
| internal experts and then with |
| the first principle simulator |
| and then with new physical data |
| from the plant. This was a clear |
| success as a data science |
| project. However, I would like |
| to add a caveat. The success |
| required the joint effort of |
| Laura, who is a top tier expert |
| in structural equations |
| modeling. Prior to joining JMP, |
| she was faculty in quantitative |
| psychology at the University of |
| North Carolina, Chapel Hill, one |
| of the top departments in the |
| US. She is also the inventor of |
| the SEM platform in JMP Pro. |
| This exercise was challenging |
| even for her. She had to write a |
| JSL program that itself wrote |
| a JSL program that specified |
| this model, for example. |
| The model we fit was perhaps |
| the largest and most |
| sophisticated SEM model of all |
| time. I want to call out the |
| truly outstanding and |
| groundbreaking work that |
| Laura's done both with the SEM |
| platform generally and in this |
| case study in particular. Now |
| I'm going to hand it over to |
| Markus, who is going to give |
| background to the problem the |
| customer wanted to solve, then |
| Laura is going to talk about |
| SEM and her model for this |
| problem. I'll do a brief |
| discussion of how we set up the |
| profiler and then Markus will |
| wrap up and talk about the |
| takeaways from the project and |
| the actions that the customer |
| took based on our results. |
| Thank you, Chris, for the |
| introduction. |
| Before I start with the problem, |
| I want to make you familiar with |
| the principles of distillation. |
| Distillation is a process which |
| separates a mixture of liquids |
| most of the time and separates |
| them into their individual |
| components. So how does this |
| work? Here, you see a schematic |
| view of a lab distillation |
| equipment. You see here is a |
| flask where the crude mixture, |
| which has to be separated, is |
| inside. You heat this up, here |
| in this case, with an oil bath |
| and stir it and then it starts |
| boiling. So the lowest boiling |
| material starts first and then the |
| vapor goes up here and pauses |
| here the thermometer to reach |
| the boiling temperature and then |
| further goes into these cooler |
| here where it condensates and |
| then the condensates drop here |
| into the other little flask. |
| So as I said, it's built |
| from...for separating a mixture |
| of liquids with different |
| boiling points, and those are |
| separated by boiling point. |
| For example, everybody knows |
| that perhaps if you want to make |
| schnapps from a mash, you just |
| make the mash inside of this |
| flask, heat it up, and then you |
| distill the alcohol over here |
| and get the schnapps. |
| As it looks very simple |
| here in the lab, in the |
| industry it's a bit more |
| complicated. Because let's |
| say the equipment is not |
| only bigger but more |
| complex and mainly because |
| of of the engineering part |
| of of the story. |
| So in this study, the |
| distillation was not done |
| batchwise as you've seen before, |
| but in a continuous manner. This |
| means the crude mixture is |
| pumped somewhere in the middle of |
| the column and then the low |
| boiling material goes up as a |
| vapor to the top of the column |
| and there it leaves the column |
| and the other higher boiling |
| material flows downward and |
| leaves the column on the bottom. |
| And to make it a bit more |
| complicated, in our case the |
| bottom stream is then pumped |
| into a second column and |
| distilled again, so to |
| separate another material |
| from the main..from... |
| from the residual stuff. So |
| actually we separated the |
| original crude mixture into |
three parts | Distillate 1, |
| Distillate 2 and what's |
| left, then the bottom stream |
| of the second still. |
| And to make it even more |
| complex, we used the heat of the |
| distillate of this second column |
| to heat the first column in |
| order to save energy for this. |
| So in a schematic view, |
| this looks like this. |
| Here you have Still 1 and |
| there's Still 2. And here we |
| have the raw material mix which |
| is actually assembly of |
| distillates from the |
| manufacturing and what we want |
| to do is to separate the value |
| material from the rest. So we |
| pumped this crude mix into the |
| first stills. As I said somewhere |
| in the middle it separates in |
| the low boiling point, which is the |
| first value material we want to |
| have, and the rest leaves the |
| first still on the bottom. Then |
| it's stored immediately here in |
| a tank and then from here it's |
| pumped again into the second |
| still, again somewhere in the |
| middle, and it separates into |
| the second value material and |
| away stream, which was then |
| redeposited. To heat the stuff, |
| we start on this side because |
| this is the higher boiling |
| material, so we need higher |
| temperatures and this means also |
| more energy. So we pump in the |
| steam here, heat this still here, |
| and the material leaving here on |
| the top has the temperature of |
| the boiling of this material, so |
| we used the residual heat to |
| heat the first still. And if |
| there's a little gap between |
| what's coming up from here and |
| what we need for for |
| distillation here in the first |
| still, we can add a little |
| extra steam to keep |
| everything running. |
| So this is a very high level |
| view of the things, and if you |
| want to go a bit more into the |
| details, here it's kind of the |
| same picture. But here I show |
| you with all the different tags |
| which we have here for all the |
| readouts and quality control and |
| temperature control and so on |
| and so forth. So what you see |
| here? We start here, for feed one |
| into the first still. |
| And then we separate into the top |
| stream where we control the |
| density, which is a quality |
| characteristic. And in the |
| bottom stream, the bottom stream |
| goes in this intermediate tank. |
| And then from here it's fitted |
| again into the second still and |
| also and separated here in the |
| bottom stream for top stream. |
| And again we are testing here |
| density for quality control. |
| Here also we add the steam to |
| heat all these things up and |
| the top flow then goes via heat |
| exchanger into the first still |
| and heat that up again. And here |
| we have the possibility to add |
| some extra steam to have |
| everything in balance here. |
| So what we see is on a local |
| basis you have a lot of |
| correlation, so this is done |
| here with the color code of the |
| arrows. So for example, the feed |
| here together with the feed |
| density, which is a measure for |
| the composition here of this |
| feed. So together with these two |
| are defining the top stream and |
| quality here, and that |
| bottom stream more or less. So you |
| have some local predictions. Also |
| over here the material going in |
| here and here defines stuff over |
| here. But if you want to have a |
| total description of the entire |
| equipment, then it gets tricky |
| because you can do local least square |
| correlations here. You can do it |
| here. You can do it separately |
| for the steam or also here. But |
| as you see, we have a start of |
| the mass stream coming here, going |
| through first still, through the |
| second still, to here and we have |
| an energy stream which starts |
| more or less here, going through |
| here via the heat exchanger also |
| down here. So it's a kind of a |
| circuit, which we have here, and |
| all these things are correlating |
| more or less in a kind |
| of circuit and this gives gives |
| us the difficulty that we |
| actually didn't know what the Xs |
| and the Ys were. |
| And that was the reason where we |
| started to think about other |
| possibilities to model this. |
| So the target for this study was |
| to find the optimal flow and |
| steam settings for all these |
| varying incoming factors |
| here, and in a way that we |
| are able to stay everything |
| in spec. So the distillate |
| quality should stay in spec but |
| also internal operational |
| specs and also the spec for |
| the final waste stream. |
| And the most interesting part, |
| at least money |
| wise, we want to minimize |
| the consumption of the |
| speed...sorry, of the steam. |
| So what we actually needed |
| was first of all, a good model |
| which describes this and that |
| was the point where Laura came |
| into the game here and developed |
| this structural equation model. |
| And we also need the kind of |
| profiler which enables us to |
| figure out what are the best |
| settings, the optimal settings |
| for all these incoming |
| variations, which we may have |
| here in order to stay within all |
| these specs. And that was the |
| point where Chris came in, |
| building on the model from Laura, |
| a profiler, which we can use for |
| doing all the predictions we |
| need. So now I want to pass |
| over to Laura to describe the |
| model she built from this |
| data here. Laura, please. |
| Thank you, Markus. I'm Laura |
| Castro-Schilo and I'm going |
| to tell you about the steps |
| we followed to model the |
| distillation process using |
| the structural equation |
| models platform. |
| So when Markus first came and |
| talked to us about his project, |
| there were three specific |
| features that made me realize |
| that SEM would be a good tool |
| for him. The first is that |
| there was a very specific |
| theory of how the processes |
| affect each other, and we saw |
| that on the diagram that he |
| showed. |
| An important feature of that |
| diagram is that all variables |
| had dual roles. In other words, |
| you can see that arrows point at |
| the nodes of the diagram, but |
| those nodes also point at other |
| variables, so there wasn't a |
| clear distinction between what |
| was an input and what was an |
| output. Rather, variables had |
| both of those roles. |
| Lastly, it was important to |
| realize that we were dealing |
| with processes that were |
| measured repeatedly. In other |
| words, we had time series data |
| and so all of these features |
| made me realize that SEM would |
| be a good tool for Markus. Now, |
| if you're not familiar with SEM, |
| might wonder why. SEM is a very |
| general framework that affords |
| lots of flexibility for dealing |
| with these types of problems. |
| I've listed in this slide a |
| number of different features |
| that make SEM a good tool, but |
| since we're not going to be able |
| to go through all of these, I |
| also included a link where you |
| can go with learn more about SEM |
| if you're interested. Now I'm |
| going to focus on two of the |
| points I have here. The first |
| is that SEM allows us to test |
| theories of multivariate |
| relations among variables, |
| which was exactly what Markus |
| wanted to do. |
| Also, there are very useful |
| tools in SEM called path |
| diagrams. These diagrams are |
| very intuitive and they |
| represent the statistical models |
| that we're fitting. |
| So let's talk about that point a |
| little more. Here is an example |
| of a path diagram that we could |
| draw in the SEM platform to |
| represent a simple linear |
| regression, and the diagram is |
| drawn with very specific |
| features. For example, we're |
| using rectangles to represent |
| the variables that we have |
| measured. Here, it's X and Y. We |
| also have a one-headed arrow to |
| represent regression effects. And |
| notice the double-headed arrows |
| that start and end on the same |
| variables represent variances. |
| Now, if these were to start and |
| end on a different variable, |
| those double-headed arrows would |
| then represent a covariance. In |
| this case, we just have the |
| variance of X and the residual |
| variance of Y, which is the part |
| that's not explained by the |
| prediction of X. |
| So this is the path diagram |
| representation of a simple |
| linear regression. But of course |
| we could also look at the |
| equations that are represented |
| by that diagram. And notice that |
| for Y, this equation is that of |
| simply a linear regression. And |
| I've omitted here the means and |
| intercepts just for simplicity. |
| It's important to note that |
| all of the parameters in |
| the equations are |
| represented in the path |
| diagram, so these diagrams |
| really do convey the |
| precise statistical model |
| that we're fitting. |
| Now in SEM, the diagrams or |
| models that we specify imply a |
| very specific covariance |
| structure. This is the |
| covariance structure that we |
| would expect given the simple |
| linear regression model. So you |
| can see we have epsilon X as the |
| variance of X. We also have the |
| variance of Y, which is a |
| function of both the variance of |
| X and the residual variance of |
| Y, and we also have an |
| expression for the covariance of |
| X and Y. And generally speaking, the |
| way that model fit is assessed |
| in SEM is by comparing the model |
| implied covariance structure to |
| the actual observed sample |
| covariance of the data, and if |
| these two are fairly close to |
| each other, we would then say |
| that the model fits very well. |
| So a number of different models |
| can be fit in SEM. |
| And today our focus is |
| going to be specifically |
| on time series models. |
| When we talk about time series, |
| we're speaking specifically about |
| a collection of data where there |
| is dependence on previous data |
| points, and these data are |
| usually collected across equally |
| spaced time intervals. |
| And the way that time series |
| analysis deals with the |
| dependencies in the data is by |
| regressing on the past. So one |
| type of these models are called |
| autoregressive processes or |
| ARP. And you can see here, where |
| Y represents a process that is |
| measured at time T, the auto |
| regressive models consist on |
| regressing that process on |
| previous observations of that |
| process up to time T minus P. |
| So if we're talking |
| specifically about an |
| autoregressive one process, |
| then you can see we have the |
| process YT regressed on its |
| immediately adjacent past YT |
| minus one. |
| And the way that we would |
| implement this in SEM is simply |
| by specifying, as we saw before, |
| the regression of YT on YT minus |
| one. So notice that here the |
| regression equation is very |
| similar to what we saw in |
| the previous slide, and so |
| it's no surprise that the |
| path diagram looks the same. |
| And we can extend this AR(1) |
| model to one that includes two |
| lags, in other words, an |
| autoregressive of order two. And |
| here we see we have the process |
| YT that is being regressed on |
| both T minus 1 and T minus 2. |
| And if we look at the path |
| diagram that represents that |
| model, we see that we have an |
| explicit representation for the |
| process at the current time, but |
| also at the lag one and lag two. |
| A very specific aspect of this |
| diagram is that the paths for |
| adjacent time points are set to |
| be equal to each other, and this |
| is an important part of the |
| specification that allows us to |
| specify the model correctly. So |
| notice here we're using beta 1 |
| to represent this lag 1 |
| effects and we also have to |
| set equality constraints on |
| the residual variances. |
| Lastly, we also have the effect |
| of YT minus 2 as it's |
| predicting YT, and so here's the |
| lag 2 effects. |
| Now all of these models are |
| univariate time series models, |
| and you can fit them using the |
| structural equation modeling |
| platform in JMP or you could |
| also use the time series |
| platform that we have available. |
| However, the problem we were |
| dealing with with Markus' data |
| require more complexity. It |
| required us to look at |
| multivariate time series models |
| and a type of these models are |
| called vector autoregressive |
| models. And what I'd like to |
| show you is one of these models |
| of order two. |
| So we have a process for X and |
| another one for Y, and the same |
| autoregressive effects that we |
| saw before are included here. |
| Notice we have our equality |
| constraints which are really |
| important for proper |
| specification. But we also have |
| the cross lagged effects which |
| tell us how the processes |
| influence each other. And notice |
| here gamma 1 and gamma 1 and |
| also gamma 3, gamma 3, |
| suggesting here that we have to |
| put equality constraints on |
| those lag 1 effects across |
| processes. |
| We also have to incorporate the |
| covariances across the processes |
| so we have their covariance at |
| time T minus 2. But we also have |
| the residual covariances at time |
| T minus 1 and T and notice these |
| have to have equality |
| constraints again to have proper |
| specification. So I'm going |
| to show you in this video how |
| we would fit a bivariate time |
| series model just like the |
| one I showed you, using JMP |
| Pro. We're going to start by |
| manipulating our data so that |
| they're ready for SEM. First, |
| we standardize these two |
| processes because they are in |
| very different scales. |
| Then we create lagged variables |
| to represent explicitly the time |
| points prior to time T. So we're |
| going to have |
| T minus 1 and T minus 2. |
| We launched the SEM platform and |
| we're going to input the Xs |
| then the Ys so that it's |
| easier to specify our models. |
| And now I sped up the video |
| so that you can quickly see |
| how the model is specified. |
| Here we're adding the |
| cross lagged effects |
| for lag 1. |
| And then directly using the |
| interactivity of the diagram, we |
| add the lag 2 effects. |
| And what remains is to |
| specify all the equality |
| constraints that are required |
| for these models within |
| process and across processes. |
| We name our model. |
| And lastly, we're |
| going to run it. |
| As you could see, even just a |
| bivariate time series model that |
| only incorporates two processes |
| requires a number of equality |
| constraints and nuances in the |
| specification that make it |
| relatively challenging. However, |
| in the case of the distillation |
| process data, we had a lot more |
| than two processes. We were |
| actually dealing with 26 of |
| these processes and in total we |
| had about 45,000 |
| measurements, which were taken |
| at 10 minute intervals. |
| And so our first approach was |
| to explore the univariate |
| time series models using the |
| time series platform in JMP. |
| And when we did this, we |
| realized that for most |
| processes an AR(1) or AR(2) |
| model fit best, and so this |
| made me realize that really |
| at the very least we needed |
| to fit multivariate models in |
| SEM that incorporated at |
| least two lags. |
| We also had to follow a number |
| of preprocessing steps for |
| getting the data ready into SEM. |
| On the one hand, we had a lot of |
| missing data, and even though |
| SEM can handle missing data just |
| fine, with models that are as |
| complex as these ones, it became |
| computationally very very |
| intensive. And so we decided to |
| select a subset of data where we |
| had complete data for all of the |
| processes and that left us with |
| about 13,000 observations. |
| Also, as we saw in the video, we |
| had large scale differences |
| across the processes, so we had |
| to standardize all of them. And |
| lastly we created lag variables |
| to make sure that we could |
| specify the models in SEM. |
| Now for model specification, |
| equality constraints in |
| particular are very very big |
| challenge because it would take |
| a lot of time to specify them |
| manually and it would be, of |
| course, tedious and error-prone. |
| So our approach for dealing with |
| this was to generate a JSL |
| script that would then generate |
| another JSL script for launching |
| the SEM platform. |
| And what you see here is the |
| final model that we fit in the |
| platform and thankfully, after |
| estimating this model, we are |
| able to obtain a covariance |
| structure that is implied by the |
| model and that was the piece of |
| information that I could pass |
| over to Chris Gotwalt, who |
| then used the information from |
| that matrix in order to create a |
| profiler that Markus could use |
| for his purposes. |
| So Chris, why don't you tell us |
| how you created that profiler? |
| Thank you, Laura. Now I'm going |
| to show the highlights of how |
| I was able to take the model |
| results and turn them into a |
| profiler that the company |
| could easily work with. |
| So Laura ran her model on the |
| standardized data and sent me a |
| table containing the same model |
| intercepts and she also included |
| the original means and standard |
| deviations that were used to |
| standardize the data. On the |
| right we have the sim model |
| implied covariance matrix, which |
| includes the covariances between |
| the present values and the |
| lagged values from the immediate |
| past. This information describes |
| how all the variables relate to |
| one another. In this form, |
| though the model is not ready to |
| be used for prediction. To see |
| how certain variables change |
| as a function of others, we have |
| to use this information to |
| derive the conditional |
| distribution of the response |
| variables, given the variables |
| that we want to use as inputs. |
| So essentially we need the |
| conditional mean of the |
| responses given the inputs. So |
| to do that, we need to implement |
| this formula right here. |
| And to do that, we use the SWEEP |
| Operator in JSL, the SWEEP |
| Operator is a mathematical tool |
| that was created by SAS CEO and |
| co-founder Jim Goodnight. It's |
| was published in the American |
| Statistician in 1979. The SWEEP |
| Operator is probably the single |
| most important contribution to |
| computational statistics in the |
| last 100 years. Most JMP users |
| don't know that the SWEEP |
| Operator is used by every single |
| JMP statistical platform in |
| many ways. We use it for matrix |
| inversion, the calculations that |
| sums of squares and also can be |
| exploited as simple and elegant |
| way to compute conditional |
| distributions if you know |
| how to use it properly. |
| I created a table with columns |
| for all the variables. The two |
| rows in the table are the |
| minimums and maximums of the |
| original data, which lets the |
| profiler know how to set up the |
| ranges. I added formula columns |
| for the response variables using |
| the swept version of the |
| variance matrix from Laura's |
| model and put those formulas |
| into the back here in the data |
| table or the far right. |
| Here's what one of the formulas |
| looked like. I pulled in the |
| results from the analysis as |
| matrices. Laura's model included |
| the estimated covariance between |
| the current Ys in the last two |
| preceding values because it was |
| a large multivariate |
| autoregressive model of order 2. |
| Predicting the present by |
| controlling the two previous |
| values of the input variables |
| was going to be very cumbersome |
| to operationalize. So I made |
| a simplifying assumption that |
| these two values were to be |
| the same, which collapsed the |
| model into a form that was |
| easier to use. To do this, I |
| simply use the same column |
| label when I was addressing |
| into the lag one, and |
| lag two entries for term. |
| Without machinery in place, |
| I created a profiler for the |
| response columns of |
| interest. I set up |
| desirability functions that |
| reflected the company's |
| goals. So they wanted to |
| match a target on on |
| A2TopTemp, maximize A2BotTemp, |
| and so on, ultimately |
| wanting to minimize the sum |
| of the steam that came out |
| of the two columns. |
| So you can lock certain |
| variables in the profiler by |
| control clicking on a pain. The |
| lock variables will have their |
| value drawn via a solid red |
| line, and then once we've done |
| that we can enter values for |
| them, and when we run the |
| optimizer or maximize |
| desirability, the locked |
| variables will be held fixed. |
| This way we find settings of the |
| variables that we can control |
| that keep the product being made |
| to specification while |
| minimizing energy costs. |
| It's fair to say that it would |
| be difficult for someone else to |
| repeat Laura's modeling approach |
| on a new problem, and it would |
| be difficult for another person |
| to set up a profiler like I did |
| here. If enough people see this |
| presentation and want us to add a |
| platform that makes this kind of |
| analysis easier in the future, |
| you should let us know by |
| reaching out to Technical |
| Support via support@JMP.com. |
| Now I'm going to hand it back |
| over to Markus who will talk |
| about what the customer did with |
| the model and our conclusions. |
| Thank you, Chris. |
| So with the prediction Profiler, |
| which Chris just presented, we |
| used that to, let's say, make a |
| predictive landscape, which |
| makes us understanding how |
| the best settings should be in |
| order to achieve all the |
| necessary quality specs. And so |
| what the three factors which |
| are, let's say, are varying with |
| limited extent to our influence, |
| and what's the |
| feed for the Still 1 and the |
| feed for the Still 2 and also |
| the quality or the composition |
| of the feed into one. |
| And what we've turned out as in |
| their model as well, is the |
| cooling water temperature was |
| also playing an important role |
| in this scenario. All the other |
| variables are of smaller importance |
| so that we neglected them in |
| this first approach. |
| Here you see the landscape. |
| It's kind of a variability |
| chart, so to say, so we have |
| here the feed density for the |
| Still 1, the feed into Still 1 |
| and the feed into Still 2 |
| and all possible combinations, |
| more or less. And here you see then |
| the settings which are predicted |
| to be best in order to stay |
| within the specifications. And |
| here are some of these I have |
| specifications as well, so we |
| have to stay inside them. |
| So it's, for example, it's the |
| steam flow for Still 2, the |
| reflux there, the boiler up and |
| the same things for the |
| Still 1. And here on the right |
| side, you see the |
| predicted outcomes, so the |
| quality specs, so to say. So the |
| temperature of the top flow in |
| Still 1 that the density |
| of the distillate, the density |
| of the distillate of Still 2, |
| and so on and so forth. So what |
| you see is here, if you have a |
| look here on the desirability, |
| which is the bottom row here, |
| there's big areas where |
| we cannot really achieve a good |
| performance of our system. And if |
| you have a look into the details |
| you see, OK, here we are off spec, |
| here we are off spec, here on |
| some points, we are off spec, and so on |
| and so forth. But what else it sees |
| is that this in spec/off spec thing |
| is also governed not only by |
| these three components down |
| here, but also by the river |
| temperature, and for the moment |
| it's highlighted the lowest |
| river temperature; it's 1 |
| degree. So this you see here |
| with it, we are staying most of |
| the time in specs, though there |
| only are rare |
| combinations of these three |
| factors where we aren't. But if |
| we are increasing the river |
| temperature, for example for 24 |
| degrees, then the areas where we |
| are off spec are...become much |
| more predominant. Also here it's |
| very hard to stay within this |
| specifications. So what we |
| learned from the model |
| is that we have problems to stay |
| in our specifications when the |
| river temperature is above 7 |
| degrees C. So then then the |
| the question was why is |
| that? And the engineers |
| often...suspected is that |
| this was because of the |
| cooling capacity of the |
| coolant. But before we went |
| into the real trial, we |
| compared our SEM model versus a |
| thermodynamic model based |
| on Chem CAD. |
| And what it pointed out was |
| that both models are |
| pointing in the same |
| direction, so there were no |
| no real discrepancies |
| between the both. |
| OK, this made us in an |
| optimistic mood and so we did |
| some real trials |
| and with the best |
| settings, and let's say, |
| approved the the predicted |
| things from the models. |
| And so it turned out, as I said |
| already, that what the engineer |
| suspected that the cooling |
| capacity of the cooler is not |
| sufficient. And so when you have |
| at higher river temperature, |
| then the heat transfer is too |
| small, and so the equipment... |
| equipment doesn't really run |
| anymore. So the next step now is |
| to use these data from from this |
| study here to justify another |
| investment which builds |
| a cooler here with a better |
| heat exchange capacity. |
| So thanks to Laura and Chris, we |
| could set up here the investment. |
| If you have questions so |
| please feel free to ask now. |
| Thank you. |