Modeling and Measurement of Thermal Process in Experimental Borehole in Matlab&Simulink and Comsol Multiphysics

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1 Modeling and Measurement of Thermal Process in Experimental Borehole in Matlab&Simulink and Comsol Multiphysics STEPAN OZANA, RADOVAN HAJOVSKY, MARTIN PIES, BLANKA FILIPOVA Department of Cybernetics and Biomedical Engineering VSB-Technical University of Ostrava 17. listopadu 15/2172 CZECH REPUBLIC {stepan.ozana radovan.hajovsky martin.pies Abstract: - The article deals with the measurement, modeling and simulation of thermal process within the experimental borehole located at mining dump Hedvika. The model is based on Heat equation, solved in Matlab and Comsol Multiphysics. The purpose of this model is to verify simulated data with the one retrieved from sensoric network around and within the experimental borehole. Experiment that provided all the necessary data has been running at Hedvika mining dump which is still one of the thermally active mining dumps in the surroundings of Ostrava with subsurface fires in it. The temperature of the mining dump can increase dramatically any time. The great benefit would be the knowledge of when and where fast temperature changes occur. Key-Words: - borehole, Matlab, Comsol Multiphysics, mining dump, modeling, simulation 1 Introduction The issue of mining dumps is very extensive. The heaps are made from waste and tailings from coal mines. Waste rocks can catch fire spontaneously any time and mining dump starts to burn. Temperatures can change immediately. Fast change of temperature has a bad effect on the environment, whether it is the fauna, flora, or the surrounding buildings and humans. and arise as a secondary product of combustion. It is dangerous for living organisms due to exhaust fumes and high temperature that can reach to the buildings on the ground. It is one of the main reasons why the presented data model is being developed. Currently we are monitoring temperature changes in the mining dump. It is a large network made up of tens of sensors. The sensors measure temperatures at depths of 3 and 6 meters. Temperature distribution throughout the heap is determined with using mathematical interpolated methods based on the temperature measurements. Current situation illustrated in Fig. 1 has been changed by adding one more experimental borehole with more additional equipment than the other borehole have at these days. All of the data, as the same as for the other sensors, is transferred to the MySQL database by GPRS, then it is accessed and processed by Matlab and Simulink environment. The basic model (one-chamber) is solved in Matlab only, then 3D model has been created with the use of Comsol Multiphysics that allows to solve more complex tasks by FEM (finite elements method) [6]. Fig. 1. Current sensoric network at Hedvika mining dump [7]. 2 Mathematical background The thermal process within the experimental borehole can be analytically identified by use of Heat equation which is then solved either in Matlab (FDM, FEM) or Comsol Multiphysics (FEM) [1], [3]. 2.1 Heat equation The basic form of heat equation used in this paper to analyze the dynamic model of thermal process is according (1). ISBN:

2 where and ( ) (1) stands for a short denotation of w D m/s Darcy s flow K D m 2 permeability L m length T K temperature 2.2 Analysis of heat sources The environment of the experimental borehole includes solid and leeks filled up with a liquid phase. The liquid phase could consist of both liquid and gas elements. Heat transfer is carried out by two ways: convection and conduction. The first way is bound for presence of media flow, the direction of heat transfer is determined by the direction of this flow and the magnitude of particular relative heat flux is according (2). qk wd * t * ct * T (2) Darcy s relative flow of liquid phase (for laminar flow) is given by (3). wd KD * p (3) L * The relative heat flux for the heat transfer is given by (4) q V * grad( T) (4) and partial differential equation for thermal field includes the term (5) a c * (5) usually referred to as thermal conductivity coefficient and other parameters refers to as c J/kg/deg relative heat capacity c t J/kg/deg relative heat capacity of liquid component q k W/m 2 relative heat flux (convection) q v W/m 2 relative heat flux (conduction) W/m/deg relative heat conductivity N.s/m 2 dynamic viscosity kg/m 3 density p Pa pressure difference The equation for computing Darcy s flow includes permeability K D that deps on porosity of the environment. Therefore besides relative density, thermal capacity and thermal conductivity the porosity has to be entered into the model. The values of thermal conductivity coefficient for common materials are rarely mentioned in the literature resources, it is often determined as a result of additional computational techniques [2], [4], [5]. 3 Modeling of the thermal process in experimental borehole Modeling of thermal process in experimental was firstly carried out as one-chamber model and this model then was exted into three-chamber model that summarizes heat sources into three volumes. 3.1 Modeling of the basic one-chamber model in Matlab The Matlab code shown below shows the solution of basic one-chamber model, by use of FDM (finite difference model). This solution was used to determine basic parameters of the model and mainly helped to turn the solution towards Comsol Multiphysics. Fig. 2 shows borehole cylindrical model (type of single U-pipe) with placement of corresponding variables: borehole parts, temperature variables and four-variable functions, borehole essential parameters (e. g. thermal conductivity λ or borehole resistance RB), parameters of temperature initial condition (IC), and temperature boundary conditions (BC) based on geometrical configuration of this borehole model (finite length circular cylinder). ISBN:

3 Fig. 2. Borehole cylindrical model (type of single U-pipe) [6]. 3.2 Modeling of three-chamber model in Comsol Multiphysics The main purpose of this experiment is to measure heating, resp. cooling of a small area in close surroundings of the experimental borehole by use of temperature sensors Pt100. Inside there are three interconnected chambers with cooling media. The overall height of the apparatus is 4 meters, having its top 1 meter under the ground, which works out 5 meters of the depth altogether, as it can be seen from Fig. 2. Around the borehole itself there is a cross-cylindrical system of sensors for temperature measurement, the distance between sensors are 0.3 meter horizontally and they are located in three levels vertically, corresponding to the centers of particular chambers. It is supposed that temperature changes caused by enforced cooling happen at least 100 times faster than temperature changes caused by burning of the mining dump. Before the start of the experiment the temperature in the borehole surroundings can be considered as constant (and can be measured within the borehole). By control intervention the temperature in a close surroundings of the borehole will be affected, ant the temperature tr lines can be stored. Fig. 3. Setting up the heat equation in Comsol Multiphysics environment. ISBN:

4 Fig. 5. Top view of the experiment setup. Fig. 6. Detail of chamber outlets with Pt100 temperature sensor. Fig. 4. Transverse view of the experiment setup. Fig. 7. Meshed geometry in Comsol Multiphysics. ISBN:

5 Fig. 8. 3D plot of temperature over the time in x- direction Setting of the partial differential equation describing the model into Comsol Multiphysics can be seen in Fig. 3. The experimental setup of the apparatus that provides the data to be compared to simulated results is illustrated in Fig. 4, Fig. 5 and Fig. 6. The created model is linear time invariant with variant space parameters. Therefore, is not necessary to deal with absolute values of temperature, but it is enough to compute relative temperature differences related to initial or steady state. The top and sides of the modeled object will have zero Dirichlet boundary condition that determine the ambient temperature, or Neumann condition computed from zero (relative) ambient temperature, simulated temperature of cooled object and heat transfer coefficient (iteration computation). Meshed geometry ready to compute is illustrated in Fig. 7. There can be many plots resulting from the computation, such as the one in Fig. 8 representing energy spread over x-axis and time. The sequence of computation is as follows: setting of zero initial condition setting of zero Dirichlet boundary condition input of step change of the power is brought to the system retrieving particular values of at given points (corresponding to measured points) calculation of from 4 Conclusion The paper presented main idea of modeling experimental borehole. This model can be then exted and applied for large areas of mining dumps provided we have sufficient information about crucial parameters of area of interest. The verification between simulated and measured data is just in the primal phase, but it has been proven that the concept of the model and the methodology of experiment are valid. The most crucial fact that has to be explored in detail in future phases of the project is heat sources represented by the component. The Comsol Multiphysics appears to be the most appropriate tool for solution of such complex model due to the fact that it allows to model nonlinear phenomena even in heterogeneous materials with time and space variant coefficient, while the partial differential equation(s) are already predefined in this environment. Of course, it lets user easily define 1D, 2D or 3D plots with computed signals. 5 Acknowledgment The paper was supported by TACR TA Enhancement of quality of environment with respect to occurrence of ogenous fires in mine dumps and industrial waste dumps, including its modeling and spread prediction. References: [1] Phillips G. M., Taylor P. J.: Theory and Applications of Numerical Analysis. Elsevier Academic Press. London, ISBN [2] Filipova B., Hajovsky R. Using MATLAB for modeling of thermal processes in a mining dump. Recent advances in fluid mechanics and heat & mass transfer. Proceedings of the 9th IASME/WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment. WSEAS Press, pp , ISBN [3] Stoer J., Bulirsch R. Introduction to Numerical Analysis. Springer Science + Business Media, New York, USA, ISBN [4] Vitasek E. Numericke metody. SNTL, Praha [5] Lixin L., Revesz P. Interpolation methods for spatio-temporal geographic data. Computers, Environment and Urban Systems. Volume 28, Issue 3, pp , Elsevier, [6] Vojcinak P., Vrtek M., Hajovsky R. Evaluation and Monitoring of Effectiveness of Heat Pumps via COP Parameter, In International Conference on Circuits, Systems, Signals pp , ISBN [7] Hajovsky R., Ozana S., Nevriva P. Remote Sensor Net for Wireless Temperature and Gas Measurement on Mining Dumps. In 7th WSEAS International Conference on Remote Sensing (REMOTE '11). Penang, Malaysia: WSEAS Press, pp ISBN ISBN:

6 Appix clear all,close all maxdel=10; %maximum of slices dt=1; %integration step maxtime=100; %number of integration steps case "integer" h=5; %length of the step in coordinates q=1; %input heat source" h2=h*h; %square of step in coordinates %initial values: i=1:1:maxdel;j=1:1:maxdel;k=1:1:maxdel; Q(i,j,k)=0; %zero initial value i=1:1:maxdel;j=1:1:maxdel;k=1:1:maxdel; qt(i,j,k)=0; %zero initial value n=1:1:maxtime;i=1:1:maxdel; G(i,n)=0; %reset of regult matrix %integration start for n=1:1:maxtime; %cycle for integration steps %second derivatives in the sides (going through starting point) j=1:1:maxdel; k=1:1:maxdel; d2qdx2(1,j,k)=(q(1,j,k)-2*q(2,j,k)+q(3,j,k))/h2; %second derivative of the energy perpicular to x-axis i=1:1:maxdel;k=1:1:maxdel; d2qdy2(i,1,k)=(q(i,1,k)-2*q(i,2,k)+q(i,3,k))/h2; %second derivative of the energy perpicular to y-axis i=1:1:maxdel;j=1:1:maxdel; d2qdz2(i,j,1)=(q(i,j,1)-2*q(i,j,2)+q(i,j,3))/h2; %second derivative of the energy perpicular to z-axis %second derivatives inside the objects (sides excluded) i=2:1:maxdel-1;j=1:1:maxdel;k=1:1:maxdel; d2qdx2(i,j,k)=(q(i-1,j,k)- 2*Q(i,j,k)+Q(i+1,j,k))/h2; %second derivative of the energy in x-axis i=1:1:maxdel;j=2:1:maxdel-1;k=1:1:maxdel; d2qdy2(i,j,k)=(q(i,j-1,k)- 2*Q(i,j,k)+Q(i,j+1,k))/h2; %second derivative of the energy in y-axis %second derivatives in the sides (going out of starting point) j=1:1:maxdel;k=1:1:maxdel; d2qdx2(maxdel,j,k)=(q(maxdel-2,j,k)- 2*Q(maxdel-1,j,k)+Q(maxdel,j,k))/h2; %second derivative of the energy in the side x=maxdel i=1:1:maxdel;k=1:1:maxdel; d2qdy2(i,maxdel,k)=(q(i,maxdel-2,k)- 2*Q(i,maxdel-1,k)+Q(i,maxdel,k))/h2; % second derivative of the energy in the side y=maxdel i=1:1:maxdel;j=1:1:maxdel; d2qdz2(i,j,maxdel)=(q(i,j,maxdel-2)- 2*Q(i,j,maxdel-1)+Q(i,j,maxdel))/h2; % second derivative of the energy in the side z=maxdel %input heat source k=1:1:maxdel; k=1:1:maxdel; qt(1,1,k)=(1-exp(0.05*(-n+1)))-0.1*q(1,1,k); %time derivatives i=1:1:maxdel;j=1:1:maxdel;k=1:1:maxdel; dq(i,j,k)=d2qdx2(i,j,k)+d2qdy2(i,j,k)+d2qdz2(i,j,k )+qt(i,j,k); %notation of derivatives in all points %integration in time for k=1:1:maxdel; for j=1:1:maxdel; for i=1:1:maxdel; Q(i,j,k)=Q(i,j,k)+dt*dQ(i,j,k); % Q(i,j,k)is a vector deping on n index G(i,n)=Q(i,3,2); %preparation for plottingin x axisx %3D plotting figure(1),surface (G); axis ([1 maxtime 1 maxdel 0 15]); xlabel('time'),ylabel('x axis') zlabel('energy'),grid i=1:1:maxdel; j=1:1:maxdel;k=2:1:maxdel-1; d2qdz2(i,j,k)=(q(i,j,k-1)- 2*Q(i,j,k)+Q(i,j,k+1))/h2; %second derivative of the energy in z-axis ISBN: