User:Ssms2017/sandbox/Alternative Energy: Political, Economic, and Social Feasibility

Steam Accumulators are energy storage devices that store steam when there is excess steam and release steam when the demand for steam is greater than the boiler's ability to supply the demanded steam. Thus, they are an efficient energy storage device when used in the industrial scene and power plants to adjust differences between consumption rates and steam production. Furthermore, if the accumulator is being charged with lower steam consumption the pressure in the accumulator increases. Likewise, if the accumulator is charged with excess steam production steam condenses. Allowing steam accumulators to increase the energy efficiency of the steam supply is such an area.

Purpose
Steam accumulators serve the purpose of withholding steam under high pressure. The main purpose of steam accumulators is to release steam when the demand for steam is greater than the plant’s ability to supply the amount of steam required or when the demand is low. Thus, the steam accumulators meet fluctuating and sudden steam loads to meet specific steam demands on an industrial scale. This process is accomplished by withholding steam when needed or releasing steam based on specific demands.

Basic Function
The direct storage of saturated or superheated steam in pressure vessels is not economical due to it having a low volumetric energy density. Therefore, steam accumulators are a sensible heat storage in pressurized saturated liquid water. They are profitable because the high volumetric storage capacity of liquid water makes it sensible for heat caused by its high specific heat capacity.

The production of steam is made by lowering the pressure of saturated liquid during discharge. Since water is being used as both a working medium and storage medium high discharge rates are plausible. Thus, the capacity is limited by the volume of the pressure vessel. The volume of specific thermal energy density depends on the variation of the saturation temperature caused by the pressure drop during the discharge. These characteristic values are in the range of 20-30kWh/m^3.

In the charging phase, the temperature of liquid water can be increased due to condensation of superheated steam. The mass of the volume can be increased by feeding saturated liquid water into the system. If superheated steam is used during this phase the pressure in the vessel can increase during the charging phase. Due to the small amount of variation of liquid storage mass. If saturated liquid enters the steam accumulator the pressure remains at a constant rate.

Advantages
Steam accumulators are used in various power plants around the globe due to their advantages.


 * They don't need to be sized due to the steam boiler being based on peak demand.
 * Instant availability of the demanded amount of steam.
 * Performance is very flexible and controllable.
 * Saves large amounts of energy due to the boiler working gradually and rationally.
 * The constant flow of pressure steam and steam quality.
 * Avoids stress related to the structure of the boiler on high steam demands.

Challenges
Steam accumulators face challenges as well; the most common is producing wet steam. Wet steam is produced by a pressure drop occurring causing the pressure to lower. Forcing the boiler to shut off due to low water levels produces wet steam. The aspects of wet steam could affect the operation.


 * Reduces thermal efficiency of the steam.
 * Causes erosion as water moves through the steam lines.
 * Condenses faster due to radiant heat losses.
 * Causes water hammer due to the lack of ability of the steam traps to remove the condensate.
 * Affects the quality of the product steam.

Design
Steam pressure transients and water level position within the accumulator depend on the initial boundary conditions. These are initial water masses, steam inflow and outflow rates, inlet steam temperature, pressure, evaporation, and condensation rates. The design calculates the capacity for a specific volume and maximum and minimum pressure values. The variable inlet steam flow rates, outlet steam flow rates, and enthalpies allows the accumulator to predict the transient pressure changes under the operating conditions.

Model
The model of a steam accumulator is based on the following balances.

Liquid Mass Balance:

$$\frac{dM_1}{dt}=\dot{m_{1B}}+\dot{m_{PT1}}$$

Steam Mass Balance:

$$\frac{dM_2}{dt}=\dot{m_{2B}}+\dot{m_{PT2}}$$

Liquid Mass Balance:

$$\frac{dH_1}{dt}=(\dot{m}h)_{1B}+\dot{m_{PT1}h''}-\dot{Q_{21}}+V_1\frac{dp}{dt}$$

Steam Energy Balance:

$$\frac{dH_2}{dt}=(\dot{m}h)_{2B}+\dot{m_{PT2}h''}-\dot{Q_{21}}+V_2\frac{dp}{dt}$$

The net mass balance between the liquid water inlet and the outlet flows is calculated as $$\dot{m_{1B}}=\dot{m_{1,in}}-\dot{m_{1,out}}$$; the steam inlet and outlet mass flow rates is calculated as $$\dot{m_{2B}}=\dot{m_{2,in}}-\dot{m_{2,out}}$$. These mass flow rates depend on the difference between calculated pressure and prescribed pressure in the volume within the accumulator. The net energy balances between the inlet and outlet flows at the steam accumulators boundaries differ between liquid water and steam. The net energy balance for liquid water is calculated as $$(\dot{m}h)_{1B}=\dot{m_{1,in}h_{1,in}}-\dot{m_{1,out}h_{1,out}}$$and the net energy balance for steam is calculated as $$(\dot{m}h)_{2B}=\dot{m_{2,in}h_{2,in}}-\dot{m_{2,out}h_{2,out}}$$. On condition of steam or water outlet flow, the calculated enthalpy for the corresponding phase within the steam accumulator equals the outlet which is calculated as such $$\dot{m_{PT1}}=\dot{m_c}-\dot{m_e}$$ and $$\dot{m_{PT2}}=\dot{m_e}-\dot{m_c}$$. Volume balance is also used and calculated as $$V_1+V_2=V$$.

The evaporation rate of the steam accumulator is calculated as

$$\dot{m_e}=\frac{\rho_1V_1(h_1-h')}{\tau_er}$$ for $$h_1>h'$$

and $$\dot{m_e}=0$$ if water within the accumulator is saturated or subcooled.

The condensation rate is very similar in comparison with the evaporation rate the condensation rate is calculated as

$$\dot{m_c}=\frac{\rho_1V_1(h'-h_1)}{\tau_cr}$$

and $$\dot{m_c}=0$$ if water within the accumulator is saturated or superheated.

The heat transfer rate from the superheated steam to the liquid within the accumulator is calculated as $$\dot{Q_{21}}=(ha)_{21}(T_2-T_1)V_1$$

where $$(ha)_{21}$$ is the product of $$h$$ the heat transfer coefficient and the concentration area $$a$$ of the steam-water interface.

Nomenclature
$$a$$	steam-water interface concentration, $$m^2/m^3$$

$$H$$	total enthalpy, J

$$h$$	specific enthalpy, J/kg

$$h$$	heat transfer coefficient, W/($$m^2$$K)

$$M$$	mass, kg

$$\dot{m}$$	mass flow rate, kg/s

$$p$$	pressure, Pa

$$\dot{Q}$$	heat transfer rate, W

$$r$$	latent heat of evaporation/condensation, J/kg

$$T$$	temperature, K

$$t$$	time, s

$$V$$ 	volume, $$m^3$$

$$v$$	specific volume, $$m^3$$/kg

Greek symbols
$$\rho$$	density, kg/$$m^3$$

$$\tau$$	phase change relaxation time, s

Subscripts and superscripts
$$B$$ 	boundary parameter

$$c$$	condensation

$$e$$	evaporation

$$in$$	inlet

$$PT$$	the phase change parameter

$$out$$	outlet

1	water

2	steam

21	interfacial transfer from steam to water

$$\prime$$	saturated

$$\prime\prime$$	saturated steam