Working out the universal algorithm of consumed characteristics calculation for control and management of discharged production

The basis of any automation system is devices to control the technological parameters which determine the course of technological process. Such parameters are temperature, pressure, discharge and amount, chemical formulation, concentration, density etc.

As we know, while controlling the technological process the information goes from sensors set on technological conduits to logical controller (the drop of pressure on narrowing device, temperature and pressure in conduit). The values of flow rate of substances and energy loss are determined.

Considering this, in this work was set the target to create the universal algorithm for calculation the flow rate and the software to determine the mentioned above parameters which are fundamental as in the process of tellurium extraction so in other technological processes of metallurgical complex. [1-2].

The task of work included studying the process of measuring the pressure drop on narrowing device and the behavior of measuring substances at this process. The following results were acquired after construction of algorithm for calculation the flow rate of substances and energy with some of them and summarizing some authors’ research data:

1. The algorithm of calculation the flow rate of steam, condensed air, cold and hot water and thermal energy accumulated with steam and hot water was worked out and realized on computer.

2. The behavior model of liquids and gaseous substances at passing through narrowing device of flowmeter was analyzed.

Developed in the course of this work and realized on computer algorithm on IBM provides an opportunity to get precise data for calculation the fundamental consumed characteristics of technological processes of metallurgical complex with maximum speed which lets in turn to optimize and automate the process of control and quality management of discharged production.

The created interface visually reflects calculated data, considers given peculiarities of controlled process and is maximally comforted to consumers’ needs.

The showed below calculation formulas as the methods of calculation are valid for all narrowing devices including standard diaphragm. But the values of flow rate coefficient Q_m and corrective multipliers Q for change of gas or steam density will be different for various narrowing devices. However, most commonly used narrowing device is a diaphragm representing itself a thin disc with round hole with diameter d axis of which coincides with axis of pipe.

Calculation formulas. For the comfort of calculation showed above formulas (19) and (20) for massive Qm and volume Q were modified.

First of all, the square of hole of narrowing device Fo should be found through diameter d coming from equality F0 = πd2/4. It is necessary to keep in mind that initial units of measurement in formulas (19) and (20) are: kilogram (kg), meter (m), and second (s). It is more convenient to measure diameter not in meters but in millimeters and time not in seconds but in hours. Then mentioned formulas should be multiplied by 3600 and divide by 106.

Considering that

(1),

We will get

(2).

In these equations d is in millimeters, p in kg/m³ and (р₁ – р₂) in Pa.

Till present time devices which measure pressure are calibrated in kgs/m² or kgs/sm² and so are the maximum drops of differential pressure gages working in compliance with narrowing devices. So we transformed the equation of flow rate that the pressure drop would be in kgs/m². In order to this we must multiply equation (2) by (9. 81)^1/2.

If 4*10^-3*(9,81)^1/2 = 0,01252 we will get:

(3).

These formulas are basic when calculating narrowing devices.

When measuring volume flow rate of gas it is reasonable to bring the results to normal conditions (p_n=760 mm of m.c., T_n=293 K). Let’s call the adapted flow rate of gas through Q_n and density of dry gas at normal conditions through p_n. Then we can write that

Q_n = Qρ/ ρ_n = Qp₁Т_n / (р_nТ1К), (4),

Where:

k is the coefficient of coercibility 121 characterizing its failure from laws of perfect gas.

Using this expression and also changing density p to ρ_nр₁Т_n/р_nТ₁К in equation of flow rate we will get from formula (2) the following:

Q_n = 2,151*10^-4 α ε d² (p₁(p₁ – p₂)/ρ_нТ₁К)^1/2 (5),

Where:

p₂ is in Pa.

Then from formula (24) we will get:

Q_n = 0,2109 α ε d² (p₁(p₁ – p₂)/ρ_nТ₁К)^1/2 (6),

Where:

p₁ is in kgs/sm²,

(p₁ – p₂ )is in kgs/m².

In both previous equations Q_n is expressed in m³/h, d- in mm, and p_n in kg/m³. Yet it would be more proper to start measuring the massive flow rate of gas Q_m instead of accepted now measuring the volume flow rate Q (as it is done while measuring the low rate of steam). Adjusting of volume flow rate to normal conditions doesn’t always provide necessary accuracy of result (especially when adding different gases).

The flow rate of gas (condensed air). The flow rate of gas is being measured using the following basic formulas:

(7),

Here:

a is the coefficient of flow rate of diaphragm with angular way of selection and sharp entrance edge;

(29),

Here:

Number Re is in limits Re_min ≤ Re ≤ 10⁸,

Re_min has the following values depending on m:

0,05 ≤ m ≤ 0,20 Re_min = 5*10³,

0,20 < m ≤ 0,59 Re_min = 10⁴,

0,59 < m ≤ 0,64 Re_min = 2*10⁴,

m is relative square equals to:

(8),

e              is corrective multiplier for change of density of measuring medium;

(9),

Where:

d₂₀ is the diameter of the hole of diaphragm at temperature 20⁰C, mm;

D₂₀ is the inner diameter of conduit at temperature 20⁰C, mm;

< P is the pressure drop on diaphragm, kgs/m²;

P is the absolute pressure on diaphragm, kgs/sm²;

c is the indicator of adiabatic curve;

K_t is the coefficient showing temperature expansion of the material of diaphragm:

К_t = 1+ β_t (t – 20) (10),

Here:

β_t is the average coefficient of linear thermal expansion of the material of narrowing device; (steel 1Х18н10Т - β_t = 0,165*10^-4);

p_nom is the density of gas at normal conditions, kg/m²;

T is the absolute temperature, К (Т = t + 273,15);

K is the coefficient of gas condensability.

The flow rate of steam. The main formula for calculation the flow rate of steam:

[kg/min] (11),

Here:

[m³/kg] (12),

Where:

t is the temperature of steam, ^oC;

P is the absolute pressure of steam, kgs/sm²;

А₁ - А₅ are coefficients having under pressure 1.6-7 kgs/sm² the following values:

А₁ = -8,394429*10^-3,

А₂ = 1,426259*10^-5,

А₃ = -5,3654771*10^-4,

А₄ = 1,9958847*10^-6,

А₅ = -223,7858.

Assessment of flow rate of thermal energy with steam. Charges of thermal energy with steam are calculated with formula:

Q_п = G_m*H , [kJoule/kg] (13),

Where:

H is the specific enthalpy of superheated steam:

(14).

When Р = 1,6-7 kgs/sm² coefficients B_i has the following values:

В₁ = 2503,798,

В₂ = 1,895008,

В₃ = -12,067877,

В₄ = 3,375952*10^-2,

В₅ = -237066,5.

The flow rate of water. The basic formula of massive flow rate of water looks this way:

[kg/min] (15).

The density of water determined by formula approximates table data in the range of temperature 0-150 ⁰C:

(16).

The assessment of flow rate of thermal energy with hot water is made with formula:

Q_B = Gm*H, [кДж/ч] [kJoule/hour] (17),

Where:

H is the specific enthalpy of water which approximates table data in the range of temperature 0-150 ⁰C and is calculated with formula:

Н = В₁ + В₂t + В₃t² (18),

Here:

B_i are coefficients with the following values:

В₁ В₂ В₃

When t = 0-90⁰С 8,1909182*10^-1 4,1793106 5,6818181*10^-5

When t = 91-150⁰С 7,318027 4,0298544 9,0537089*10^-4

Determination of Reynolds’ number Re. The Reynolds’ number Re for conduit with diameter D while knowing the volume flow rate Q at working conditions is calculated with expressions:

Re = 0,0361 Qρ/(Dμ) - при μ = [кгс*с/м²] [kgs*s/m² ] (19)

And

Re = 0,354Q/(Dv) = Qρ/(Dμ) при μ = [Па*с][Pa*s] и v = [м²/с] [m²/s] (20),

Here:

Q is the volume flow rate;

Μ is the dynamic viscosity of measuring medium at working conditions.

For determination the coefficient of correction of flow rate to the number Re we calculate first flow rate of substances Q at its working parameters and assuming that Re = 10⁶(in this case k_Re = 1, and a_y = a_y^*, a_y^* is the coefficient of flow rate with Re = 10⁶).

The Reynolds’ number Re is determined depending on the value of flow rate Q. Then we find the real number Re with formula:

(21),

Where:

С = (0,5959 + 0,0312m^1,05 – 0,184m⁴) / (1-m²)^1/2,

S = S₁/S₂^1,75.

At the same time S₁ and S₂ are determined with formulas:

S₁ = B Re^*/(a_y^*10⁶) (22),

S₂ = C Re^*/(a_y^*10⁶) (23),

Where:

В = 0,0029 m^1,25/(1-m²)^1/2 (24).

Then we calculate the corrective coefficient to number Re in order to get real amount of flow rate of substances:

k_Re = (C + B(10⁶/Re)^0,75)/(C + B) (25).

So the real flow rate of substances is determined as value equal to:

Q = Q^* k_Re (26).

Thus, in this part of work have been introduced a mathematical model and a program for calculation the consumed characteristics and parameters of technological processes allowing to measure different flow rates of substances and energy, their quantity and levels. Thanks to these developments the management of technological cycle of metallurgical complex can be done more effectively.

The developers provided fast obtaining precise data of the course of the technological process and visual demonstration using created interface of obtained calculated characteristics considering given peculiarities of controlled process. [5]

Acquired information lets optimize the process of management of all technological production and provides significant economical effect at production of rare metals.

LITERATURE

1. Belgibayev B.A., Abitova G.A. Расчет параметров расходомера переменного давления гидрометаллургического производства ОАО «УМЗ». // Materials of international scientific practical conference. – Almaty city, publishing house KazGASA. 2003 – pages 123-125/

2. Abitova G.A., Belgibayev B.A. Программно-аппаратное обеспечение расходомера переменного давления в АСУ гидрометаллургическими процессами ОАО «УМЗ». // The results of international conference (Almaty, March 4-6, 2003). – Almaty city. Publishing house Kazakh University. 2003 – pages 12-15.

3. Abitova G. A. Оптимизация технологических процессов современных промышленных предприятий на основе создания пакета прикладных программ. // Materials of international scientific practical conference. – Ust-Kamenogorsk: publishing house of East Kazakhstan State University, 2002 – pages 192-194.

4. Belgibayev B.A., Abitova G.A. Расчет параметров расходомера переменного давления гидрометаллургического производства ОАО «УМЗ». // Materials of international scientific practical conference. – Almaty: publishing house KazGASA, 2003 – pages 123-125.

5. Abitova G.A., Belgibayev B.A. Программно-аппаратное обеспечение расходомера переменного давления в АСУ гидрометаллургическими процессами ОАО «УМЗ». // The results of international conference – Almaty: publishing house of Kazakh University, 2003 – pages 12-15.