The Directional Flame Thermometer (DFT) is often used to measure heat flux during room fire testing. In literature and practice, heat transfer solutions for the DFT have been post processed. It is important to develop real-time capability for calculating heat flux based on measured temperatures as such capability will allow control of fire testing furnaces. In this study, we show that if a user will accept moderate errors in the heat flux, then a simple forward solution methodology allows heat flux measurements to be made in real-time. Essentially, the “inverse” problem is sufficiently well-conditioned to allow for a simple solution. Both a simple spreadsheet type solution and a finite difference code were used to generate the heat flux. The code was verified in both forward and inverse senses. The calculations were verified through a convergence study of both the forward and inverse solutions in spatial discretization (dx) and temporal discretization (dt). The inverse solution showed expected convergence behavior in both spatial and temporal discretization. In all cases, the solution for the front plate produced a maximum error of around 5%, which decreased as the DFT reached a steady state temperature. The forward and inverse models were validated through experimental testing using a radiant heater panel. The inverse model’s calculations were compared to measurements from a Schmidt-Boelter gage. The front plate heat flux measurements of the DFT matched reasonably well with the Schmidt-Boelter gage (2–6% difference) during the majority of the testing. The heat flux was then used to drive a forward simulation, and the forward model’s calculations were compared to actual temperature data acquired by the tests, producing a difference no greater than 4%. The DFT was also placed into a room fire to evaluate its effectiveness in this environment. The DFT was placed near a sand burner and in a panel fire test. The DFT produced reasonable heat flux values, but had more noise than results from those in front of the radiant heater panel (standard deviation of 1500 W/m2 compared to 400–600 W/m2).
Flow laboratories have been used for six decades to evaluate and optimize perforating systems for downhole environments.A key experimental variable is the pressure/flow boundary condition on the target core. Two standard configurations are axial flow, and radial flow. The implications of each configuration have been addressed somewhat in the literature in the context of steady flow with identical but prescribed tunnels. There has never been a careful comparison of the influence of boundary conditions on the actual tunnels.In this paper we summarize the state of understanding regarding these two flow regimes by primarily focusing on the sensitivity of each to perforation damage and cleanup. In addition to addressing the differences under steady flow conditions, we also experimentally investigated the influence of target boundary conditions on the transient flow regime (i.e. during dynamic underbalance perforation cleanup). This was primarily an experimental investigation, supported by numerical simulations to determine baseline flow performance.We find that radial flow provides the most meaningful measure of perforation damage (as indicated by post-shot steady flow). Indeed, radial flow is indispensable to parameterize skin and productivity models as they are currently formulated.Axial flow yields steady production flow which is most sensitive to penetration depth, and relatively insensitive to perforation damage.Finally, and perhaps most significantly, the transient perforation cleanup process is different for radial vs. axial boundaries. The intrinsic inflow characteristic of the tunnel is itself a function of the boundary conditions at shot time.Proper selection of laboratory flow geometry is essential to yield meaningful measurements of perforation damage. In addition to this diagnostic purpose, target boundary conditions play a critical role in the removal of perforation damage, evolution of open tunnel length and diameter, and the resulting perforation flow efficiency.
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