http://hdl.handle.net/2282/290 Search the Channel search http://teora.hit.no:8443/dspace/simple-search http://hdl.handle.net/2282/410 Title: Topics in open and closed loop subspace system identification : finite data-based methods <br/> <br/>Authors: Nilsen, Geir Werner <br/> <br/>Abstract: When subspace identification methods for finite closed loop data sets are presented they are often compared to poor subspace identification methods. The methods presented in this thesis are always compared to the results from the prediction error method implemented in Matlab 6.5. The advantage of the subspace identification methods is the computational efficiency and the ability to estimate the system order, or alternatively help the user to choose the correct system order. One of the assumptions in subspace identification is that the input is uncorrelated to the noise at the output. In closed loop systems this assumption is not necessarily fulfilled. This can lead to a bias problem. Only the performance with finite data sets is considered in this thesis.The thesis also presents the classic subspace identification algorithms DSR and N4SID together with an error-in-variable based subspace identification algorithm using the notation used in the outline of the DSR algorithm. The projections used in DSR to estimate the extended observability matrix, and the eigenvalues,are compared to the projections used in the other algorithms. The effect of the parameter choice in DSR when used on finite closed loop datasets is presented. It is especially the estimation of the zeros which is hard using the classic subspace identification algorithms for direct closed loop identification. Solutions to help reducing the bias on the zeros are presented. The closed loop can be modified to either reduce the noise in the feedback or make the noise through the feedback uncorrelated to the noise on the output. The effect of using different types of filters in the feedback loop is considered. The optimal filter used in the feedback is not the noise free output or a 1st order low-pass filter rather the Kalman filter. This leads to a new three-step closed loop subspace identifications algorithm based on the DSR algorithm and the Kalman filter properties. In an initial step DSR is used for identification of the process model, including the Kalman filter gain. The next step is to implement the Kalman filter in the feedback in such a way that the controller uses the filtered output from the filter, not the actual process measurement. The final step is to use DSR to identify the process model when the feedback is filtered through the Kalman filter. The goal for closed loop subspace identification algorithms is to be as easy to use for direct identification on finite closed loop data sets as the original subspace identification algorithms are on finite open loop data sets. In addition the closed loop subspace identification algorithms are to provide results comparable to the results from PEM in closed loop. The DSR_e algorithm is a modification of the existing DSR algorithm fulfilling these requirements. The algorithm is based on the fact that the noise innovation process can be identified directly from the data in a first step. The system identification process is considered in two different ways. The first way is when all information regarding the process is considered as known and a benchmark is performed to see how good the performance can be. In this case DSR_e is comparable to PEM. The other is when the system order has to be estimated from the process data.Methods to estimate the system order of systems operating in a closed loop by subspace identification are presented. The methods are meant to help users without experience in using subspace identification algorithms. In addition a procedure is suggested combining the visual inspection of singular values from DSR_e and the search for the minimum prediction error. Visual inspection of the singular values gave the correct estimate of system order everytime, independent of the choice of past and future horizons in DSR_e. The parameter settings for DSR_e found by searching for the minimum prediction error resulted in estimates comparable to the estimates from PEM. This indicates that this is a good practical approach for the use of DSR_e for direct closed loop system identification. <br/> <br/>Description: Avhandling (dr.ing.) - Høgskolen i Telemark / Norges teknisk-naturvitenskapelige universitet http://hdl.handle.net/2282/382 Title: Multivariable process control in high temperature and high pressure environment using non-intrusive multi sensor data fusion <br/> <br/>Authors: Nygaard, Olav Gerhard Haukenes <br/> <br/>Abstract: The main objective of this thesis is to use available knowledge about a process and combine this with measurement data from the same process to extract more information about the process. The combination of knowledge and measurement data is referred to as Multi Sensor Data Fusion, MSDF. This added information is then used to control the process towards a specified goal. The process studied in this thesis is the process of drilling wells in a petroleum reservoir, while the oil is flowing from the reservoir. In the petroleum industry, this is defined as underbalanced drilling (UBD), where the bottom hole pressure (BHP) in the well is below the pore pressure in the reservoir. Detailed knowledge of the process is of paramount importance when using multi sensor data fusion. Due to this, various process modelling efforts are examined and evaluated, from simple relations between parameters to a finite-element approach of modelling the fluid flow in the well during drilling. Several sensors are used in the various cases, and existing sensors such as pressure sensors and flow sensors are the main data source in the analysis. Future scenario with sensors such as pressure arrays and non-intrusive multiphase flow meters are evaluated. In addition, new positions of existing sensor systems are discussed. The methods available for fusing the knowledge of the process represented as models together with the available data is ranging from artificial intelligent methods such as neural networks, to methods incorporating statistical analysis such as various Kalman filters. History matching techniques using gradient techniques are also examined. The migration of reservoir fluids into the well during UBD influences the BHP of the well. The results in the thesis show that this reservoir influx can be calculated by estimating some of the important reservoir parameters such as reservoir pore pressure or reservoir permeability. These reservoir parameters can be estimated most efficiently by performing an MSDF using a detailed nonlinear model of the well and reservoir dynamic behaviour together with real-time measurements of the fluid flow parameters such as fluid temperature, fluid pressure and fluid flow rates. The unscented Kalman filter shows the best performance when evaluating both estimation accuracy and computational requirements. Regarding available instrumentation for use during UBD, the analysis shows that there is a major potential in introducing new sensors. As new data transmission methods are emerging and making data from sensors distributed along the drillstring available, this can generate a shift in paradigm regarding real-time analysis of reservoir properties during drilling. Controlling the process is an important usage of the information gained from the MSDF analysis. Various control methods for controlling the most important process variables are examined and evaluated. The results show that acceptable pressure control can be obtained when using the choke valve opening as the primary control parameter. However, the choke valve operation has to be closely coordinated with drilling fluid flow rate adjustments. The choke valve opening control is able to compensate for pressure variations during the whole drilling operation. A suggested nonlinear model predictive control algorithm gives best results when looking at the control accuracy, and can easily be expanded to handle multiple control inputs and system constraints. This control algorithm uses a detailed model of the well and reservoir dynamics. The Levenberg-Marquardt algorithm is used to calculate the optimal future control variables. The main drawback of the control algorithm is computational burden. A linear control algorithm, which also is evaluated, uses less computational resources, but has less control accuracy and is more difficult to expand into a multivariable control system. Recommendations for further work are to expand the suggested model predictive control algorithm to handle more control inputs, while reducing the computational burden by incorporating low-order models for describing the future behaviour of the well. <br/> <br/>Description: Avhandling (dr.ing.) - Høgskolen i Telemark / Norges teknisk-naturvitenskapelige universitet. The entire thesis can not be made available electronically due to publisher restrictions. http://hdl.handle.net/2282/381 Title: Degradation of polymeric and particulate organic carbon in biofilms <br/> <br/>Authors: Kommedal, Roald <br/> <br/>Abstract: Polymeric and particulate organic carbon (POM) are fundamental compounds in the global cycling of carbon, and constitute significant amounts of BOD in municipal wastewater. The main objective of this work is to study molecular size effects on degradation dynamics in biofilm systems. Specifically, the effect of substrate molecular weight on degradation kinetics and transport dynamics, location of depolymerisation enzyme activity and depolymerisation intermediate formation dynamics are assessed. A mathematical model for biofilm degradation dynamics is presented, and used for data interpretation and simulations. Dextran, an a-1,6 Glucan, was used as model substrate during batch degradation in a Rototorque biofilm reactor, in addition to batch tests on biofilm sub samples retrieved from the Rototorque, and during pure endo- and exo-Dextranase studies. Oxygen utilisation rate (OUR) estimates and bulk phase TOC mass balances were used to evaluate the effect of variable initial molecular weight on the observed half order removal coefficient (Harremoës, 1978; Rittmann and McCarty, 1980). Size exclusion-HPLC analysis for determination of bulk phase depolymerisation intermediates, and specific enzyme assays were used to evaluate transport dynamics of polymers and location of enzyme activity in the enhanced mixed population biofilm system. Dextran removal rate decrease with increasing Dextran molecular weight. The observed areal half order removal rate coefficient, k1/2,A, demonstrate an approximate 10-fold decrease in the 1-500 kDa range, showing negative logarithmic correlation to the initial MW of Dextran. A less distinct correlation is observed above this transition limit (1-10 MDa). Evaluation of the Thiele moduli, from one step depolymerisation modelling, suggests that the logarithmic reduction in observed removal rate is caused by combined reaction rate and transport limitations. Transport limitations dominates as the polymeric substrate size increase and hinders biofilm matrix diffusion, and the removal rate becomes a surface limited process. Removal of Dextran is biomass dependent in what appears to be a non-linear dependency on biofilm thickness. Expressed as biomass areal density (g/m2), no depolymerisation is observed for thin biofilms (0.7 g/m2), slow for medium (3.7 g/m2) and high for thicker biofilms (5.2 g/m2). Depolymerisation intermediates accumulated in the bulk phase over the entire Dextran size range during pure Dexranase studies, with even size distributions. Final products were oligo-isomaltoses (DP 2-6). Dextran was not depolymerised by a-Glucosidase nor Oligoa- 1,6 Glucosidase. During biofilm reactor and slide sub-sample tests, low MW Dextran intermediates (1-10 kDa) accumulated in the bulk during depolymerisation of 160 kDa Dextran at 250 and 200 mg/l initial concentrations, but were not detected during experiments with 100 mg/l initial concentrations. Intermediate range Dextran (10-100 kDa) did not accumulate in either case. At the same conditions, some assimilable range Dextran (0.2-0.9 kDa) accumulated in the bulk liquid during initial 250 and 200 mg/l batches, but was not detected during 100 mg/l initial Dextran concentrations. The extent of bulk phase accumulation seems to depend on the biofilm growth rate, where more bulk phase accumulation is observed during experiments with starved compared to more actively growing biofilms. More intermediates accumulate during low MW initial standards, compared to higher. These observations indicate that the extent of bulk phase intermediate accumulation is balanced by the rate of depolymerisation, and the substrate uptake rate (growth). Accumulation of intermediate hydrolysis products in biofilm systems is therefore dependent on the slowly biodegradable organic (SBCOD) loading rate. Dextranase was detected in the cellular fraction of the biofilms. The enzyme activity was not detected in any other biofilm sub compartments, implying that the exogenous enzyme remains attached to the cells while working on polymers. These findings support the conceptual model of Confer and Logan (1998), implying that bulk phase intermediate accumulation observed in this study and by others, is not a result of enzymatic activity in the bulk phase, but transport of intermediates from the biofilm matrix. <br/> <br/>Description: Avhandling (dr.ing.) - Høgskolen i Telemark / Norges teknisk-naturvitenskapelige universitet http://hdl.handle.net/2282/377 Title: Gas explosions in process pipes <br/> <br/>Authors: Kristoffersen, Kjetil <br/> <br/>Abstract: In this thesis, gas explosions inside pipes are considered. Laboratory experiments and numerical simulations are the basis of the thesis. The target of the work was to study gas explosions in pipes and to develop numer- ical models that could predict accidental gas explosions inside pipes. Experiments were performed in circular steel and plexiglass pipes. The steel pipes have an inner diameter of 22.3 mm and lengths of 1, 2, 5 and 11 m. The plexiglass pipe has an inner diameter of 40 mm and a length of 1.9 m. Mixtures of propane, acetylene and hydrogen with air at various equivalence ratios were used. Pressure was recorded by Kistler pressure transducers and ‡ame propagation was captured by photodiodes, a SLR camera and a high-speed camera. The experiments showed that acoustic oscillations would occur in the pipes, and that the frequency of these oscillations are determined by the pipe length. Several inversions of the ‡ame front can occur during the ‡ame propagation in a pipe. These inversions are appearing due to quenching of the ‡ame front at the pipe wall and due to interactions of the ‡ame front with the longitudinal pressure waves in the pipe. Transition to detonation was achieved in acetylene-air mixtures in a 5 m steel pipe with 4 small obstructions. Simulations of the ‡ame propagation in smooth pipes were performed with an 1D MATLAB version of the Random Choice Method (RCMLAB). Methods for estimation of quasi 1D burning velocities and of pipe outlet conditions from experimental pres- sure data were implemented into this code. The simulated pressure waves and ‡ame propagation were compared to the experimental results and there are good agreements between the results. Simulations were also performed with the commercial CFD code FLACS. The code was tested for gas explosions in smooth pipes and the results compared to experimental results. To properly handle the longitudinal pressure oscillations in pipes, at least 7 grid cells in each direction of the pipe cross-section and a Courant number (CFLC) of maximum 1 should be used. It was shown that the current combustion model in FLACS gave too high ‡ame speeds initially for gas explosions in a pipe with an inner width of 40 mm. <br/> <br/>Description: Avhandling (dr.ing.) - Høgskolen i Telemark / Norges teknisk-naturvitenskapelige universitet