Dynamic Data Reconciliation of regenerative Heat Exchangers ...

obtained in the previous step, and uses this model as a set of constraints to reconcile allavailable measurements.3. HEAT TRANSFER MODELWe assumed that the flow of gas through the regenerative heat exchanger is distributedevenly among the parallel channels (approximately 10000 of them). Thus the model willfocus on a single channel, and approximate the hexagonal cross section by an equivalentcircular section (figure 3). The partial differential equations describing the system will betransformed into ODE's by discretising the space co-ordinates.Assuming plug flow and no axial conduction in the gas leads to a dynamic balanceequation (Bird et al., 1960):⎡∂Tg∂Tg⎤ ∂P 4 hρgCpg , ⎢ + vg vg ( Tw Tg)t z⎥+ = −⎣ ∂ ∂ ⎦ ∂z Dh(1)Similarly for the tube wall:ρ∂T 1 ∂ ⎛ ∂T ⎞ ∂ T− − = 0∂t r ∂r ⎜r⎟⎝ ∂ ⎠ ∂z2s s ssCps ,rk ks2In order to obtain a numerical solution of this equation system, we discretised the solid andthe gas into cells of constant geometric and physical properties, each cell being approximately1 meter long. In the radial direction, the solid was also discretised into layers approximately 1mm thick (figure 3) exchanging heat by conduction with the neighbouring layers. Bysymmetry of the system, no heat is transferred from one channel to the adjacent one, so thedeepest layer only exchanges heat on one side. An overall heat loss term was added to the gasbalance equation to account for exchange with the ambient.The characteristic time for heat transfer in the radial direction was found to be in the orderof one minute; this is the same order of magnitude as the phenomena to be monitored in theprocess, and therefore it may not be ignored. The temperature gradient in the solid in theradial direction can be as high as 1000 K/m, while it is approximately 30 K/m in the axialdirection. This is why we neglected the conductive heat transfer in the axial direction.The numerical solution of system dynamic equations was obtained by discretising alongthe space co-ordinates, and integration using Euler's method to find the variation of thetemperature field with time. The integration time step is limited to avoid numerical instability.In order to do so, the equations were rewritten as follows.Gas-solid transfer for a cellOn the gas side, an energy balance allows to calculate the heat transfer in a cell:Hout − Hin =−Qexch− Losses(3)where : H in : inlet gas enthalpyH out : outlet gas enthalpy, (H out = H in of the next layer)Q exch : heat transferred from the gas to the refractory brickworkThe average gas temperature of the layer can be obtained from the heat transfer equation:Tg( Hout-Hin-Losses)= + Tw(4)h.S(2)

The application of dynamic data reconciliation to the stove system allowed detecting someprocess malfunctions:• Some sensors do not measure what they are expected to do; this is the case for the dometemperature measurement using a pyrometer; the probe is supposed to measure the bricktemperature, but it is influenced by the emissivity of the gas through which it is aimed.Since the gas emissivity depends mainly from the partial pressure of CO 2 and H 2 O, thebias introduced is not the same when the unit operates on-gas or on-blast.• Some sensors are not appropriate (the oxygen probe saturates when the blast is enrichedwith oxygen).• Some sensors are not ideally located : e.g. the thermocouples located below the supportinggrid do not provide an adequate estimate of the brick temperature when the regeneratoroperates on blast; in fact the thermocouple is surrounded with cold air, and measures thegas temperature more than the solid temperature.• Some measured values were not correctly converted in the process computer, such as thelower heating value for the residual gas used as a fuel.5. CONCLUSIONThe main goal of the present study was to better understand the behaviour of theregenerative heat exchanger, in order to improve its control . The model developed allows tocarry out a sensitivity analysis and to validate the measurement system.It provided also values of key operating parameters of the plant, which are needed foroptimally scheduling of the energy accumulation and delivery. By operating closer to theoperating limits and decreasing the heat losses, significant fuel savings are expected (in arecent paper, Muske and al.(2000) developed a similar model as a support for optimal controland they report savings in the range of 5%).This study shows the feasibility and the possibilities of dynamic validation but it alsoidentifies some practical limitations: selection of initial conditions, inertia phenomenon,...6. SYMBOLSC p specific heatD h hydraulic diameter ofa channelh heat transfercoefficientk thermal conductivityP pressurerSTvzρradial co-ordinategas-solid exchangearea in a celltemperaturegas velocityaxial co-ordinatespecific gravitySubscriptsg gass solidw gas-solid interface7. REFERENCESBird R.B., Stewart W.E., Lightfoot E.N., Transport Phenomena, Wiley New York (1960)BELSIM, VALI III Users Guide, BELSIM s.a., Allée des Noisetiers 1, 4031 Angleur (Belgium) (1999)Cameron D, Fault Detection and Diagnosis, in "Model Based Manufacturing - Consolidated Reviewof Research and Applications", document available in CAPE.NET web site(http://capenet.chemeng.ucl.ac.uk/ ) (1999)Muske K.R., Howse J.W., Hansen G.A., Cagliostro D.J, Model-based control of a thermalregenerator: Part 1 : dynamic model, Computers & Chemical Engineering 24, 2519-2531 (2000)Part 2 : Control and estimation, Computers & Chemical Engineering 24, 2507-2518 (2000)