Hydraulic systems calculation model

Abstract To better understand the coupling of thermal (T), hydraulic (H) and mechanical (M) processes (T-H-M processes) and their influence on the system behaviour, models allowing T-H-M coupling are developed. These models allow simulations in the near-field of the system. Such a model has been developed within the simulator RockFlow/RockMech. This paper concentrates on the thermal and hydraulic processes. For those processes, the material parameters and state variables are highly non-linear and mostly functions of temperature, saturation and pressure. This paper shows how these dependencies are formulated mathematically and are implemented into RockFlow/RockMech. The implementation allows phase changes between the fluid phases (gas and liquid) to occur explicitly. The model allows the simulation of very low permeability clays with high capillary pressures. An example for code validation is shown, where low permeability clay is desaturated, lastly, current work on the calculations performed in the near field study (BMTl) of the DECOY ALEX III project is outlined. 

Numerical models have been developed for calculating the probable maximum seiche in the form of the amplitude of oscillation as a function of time at any point within a bay of arbitrary shape. These models usually require as input a specification of the overall geometry (bathymetry and coastal topography) and of the forcing wave system. They also require as input the time dependence of the excitation (tsunami wave, surge wave, wind wave etc.) at the open boundary or source location. The amplitude time history of the seiches for the location of the plant should then be calculated. Hydraulic model studies and/or field results should be used to validate the calculation model selected. 

The evaluation of the parameters for this flow regime requires the calculation of the Reynolds number and hydraulic diameter for each continuous phase. The hydraulic diameter can be determined only if the holdup of each phase is known. This again illustrates the importance of understanding the fluid mechanics of two phase systems. Once the hydraulic diameter is known, the Reynolds number can be evaluated with the knowledge of the in situ phase velocity, and the parameters of the model equations can be evaluated. 

JAEA conducted an improvement of the RELAP5 MOD3 code (US NRC, 1995), the system analysis code originally developed for LWR systems, to extend its applicability to VHTR systems (Takamatsu, 2004). Also, a chemistry model for the IS process was incorporated into the code to evaluate the dynamic characteristics of process heat exchangers in the IS process (Sato, 2007). The code covers reactor power behaviour, thermal-hydraulics of helium gases, thermal-hydraulics of the two-phase steam-water mixture, chemical reactions in the process heat exchangers and control system characteristics. Field equations consist of mass continuity, momentum conservation and energy conservation with a two-fluid model and reactor power is calculated by point reactor kinetics equations. The code was validated by the experimental data obtained by the HTTR operations and mock-up test facility (Takamatsu, 2004 Ohashi, 2006). 

The main variable of design for a CSTR is the hydraulic retention time (HRT), which represents the ratio between volume and flow rate, and it is a measure of the average length of time that a soluble compound remains in the reactor. Capital costs are related to HRT, as this variable directly influences reactor volume [83]. HRT can be calculated by means of a mass balance of the system in that case, kinetic parameters are required. Some authors obtained kinetic models from batch assays operating at the same reaction conditions, and applied them to obtain the HRT in continuous operation [10, 83, 84]. When no kinetic parameters are available, HRT can be estimated from the time required to complete the reaction in a discontinuous process. One must take into account that the reaction rate in a continuous operation is slower than in batch systems, due to the low substrate concentration in the reactor. Therefore, HRT is usually longer than the total time needed in batch operation [76]. 

Pressure drop unit are used to simulate hydraulic operations, as for example the pressure drop in a pipeline or in a distribution network. Adiabatic operation or heat transfer with the surroundings can be treated. In flowsheeting the module is generally tailored to simulate the transport of fluids in process plants. It can cover a large variety of physical conditions, as for example three-phase calculations in different flow regimes. However, special applications are better modelled by dedicated software, as the network of utilities (water and steam), or pipeline systems in oil gas production. 

For the HM base case the mean mechanical properties have been used to calculate the hydraulic aperture distributions over the depth of the model. The continuum model and the applied methodology for the HM coupling in fractured rock does not allow the modelling of a fully HM-coupled system, hence the HM-modified hydraulic conductivity tensors were calculated at the mid point values of several depth ranges (Table 1). The results were assigned uniformly to the formation within each depth range (25m=>0m-50 m, 75 m => 50 m - 100 m, 175 m => 100 m -250 m, 375 m => 250 m - 500 m and 750 m 500 m - 1000 m). The variation in the calculated aperture values decreases as depth increases, which allows for the larger depth bands at the base of the model. 

To get better the understanding of the system, the mechanical behaviour of the clay has been taken into account. The initial conditions are null total stresses everywhere. So, in-situ mechanical stresses are not taken into account. The results of our THM calculation show only stresses induced by thermal-hydro-mechanical couplings. The contact between the EB and the canister is once again supposed to be perfect, so that no radial displacement of the clay is allowed at that boundary. Biot s poroelastic model is chosen to represent clay behaviour. It takes partial saturation into account via an equivalent pressure which includes capillary effects, involving both gas and liquid, Dangla (1998). Biot s model is added as fourth equation to the system. The associated main variable is total stress state. The couplings with thermal-hydraulics behaviour are introduced by... 

The numerical solution method for the above fluid-solid coupling model is an iterative computation process. To reduce the computational complexity, the solid deformation and fluid flow are regarded as two coupled equation systems, solved by FEM. The equilibrium in solid matrix is solved using Eq.(6) with an added coupling item apS j and the pore pressure is treated as an equivalent initial stress term. The flow equation (5) is solved with an added term of volume strain, reflecting the effect of solid deformation on fluid flow. It can be treated as a source or converge. In each iterative loop, the solid matrix deformation is solved firstly. The stress and strain results are then taken as inputs for the flow calculation with modified hydraulic parameters. After flow model is solved, the pore pressure values are transferred into solid matrix deformation model and begins next iterative loop. In this way, the flow and deformation of oil reservoir can be simulated. 

In addition, the efficiency of electric contact between bipolar plates and gas diffusion layers was measured using special test station comprising a hydraulic press with a temperature control, current supply and control systems. The purpose of provided measurements is the comparative analysis of parameters of different bipolar plates and gas diffusion layers, and also obtaining of the necessary data for use in calculations on mathematical model. Resistance tests of gas diffusion layers and bipolar plates were performed both in a longitudinal direction (four-contact method) and in a transverse direction. 

Validation of the hydraulic model was achieved using a steady-state solution of the groundwater flow and exfiltrating rate calculated by the groundwater modelling system FEFLOW. These calculations are carried out at a transect in Nieschen (see Section 8.3.2.3). Detailed geologic and hydraulic data and long term measurements enables an exact parameterization of the exemplary ditch types. 

Event-tree and fault-tree models are built on the basis of results from physical models as implemented in a thermal-hydraulics or integral code. For instance, calculations with a deterministic thermal-hydraulics code provide information on the minimum requirements for safety and emergency functions, i.e. on the minimum number n of safety systems needed to cope... 

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