4.6. Role of sampling in experimental work
4.6.1. Experimental arrangement
The following experimental arrangement was used to determine the effects of the two sampling methods:
The two sampling methods used here were manual ball valves and semi-automatic pneumatic piston valves (Valmet NOVE M2). The construction of the piston valve is illustrated in Fig. 14. Sampling was carried out with the manual valves for the first five months, after which they were replaced by the pneumatic sampling valves for the next four months. The valves were located in the inlet pipe and outlet pipes of the two-stage pressure screen (Fig. 15). The manual valves were mounted conventionally on the wall of the pipe, and the semi-automatic valves in the manner shown in Fig. 14, where the sampling device extends into the process stream. The ranges of the flow parameters in these pipes are presented in Table 9.
All the pipes excluding the feed pipe were equipped with magnetic flow meters, and the volumetric feed flow was calculated from the flow balance. Pulp samples were taken from the feed, accept and reject pipes during steady-state screening for laboratory analysis of their consistency, and the accuracy of the sampling methods was evaluated in terms of the standard deviation and mean of the calculated mass balance error over the screen. 112 mass balances were calculated for the manual sampling method and 96 for the semi-automatic method. White water from the paper machine was used as dilution water between the screening stages. This had a constant, fairly low fibre concentration and its daily average was used in the mass balance calculations.
Figure 14. Schematic diagram of the semi-automatic piston valve used in the experiments (Reisto 1990).
The mass balance error was used to determine the differences between the two valve types in the sampling of the pulp slurry. Two inlet and three outlet flows are shown in Fig. 15, and the mass flow balance is calculated according to:
where
m is mass flow (kg/s),
V is volume flow, (m3/s),
c is consistency, (kg/m3),
the subscripts refer to the flow positions in Fig. 15.
The mass balance error, mbe, as a percentage, is calculated as follows:
Table 9. Pipe diameters and the range of flow parameters in the test series with manual and semi-automatic sampling valves.
| Manual valves | Feed | 1st accept | 2nd accept | Reject | Dilution |
|---|---|---|---|---|---|
| Pipe diameter, mm | 250 | 200 | 150 | 100 | 80 |
| Volume flow, dm 3/s | 37-193 | 30-110 | 8-55 | 3-44 | 0-21 |
| Flow velocity, m/s | 0.7-3.9 | 0.9-3.5 | 0.5-3.1 | 0.4-5.6 | 0.0-4.2 |
| Consistency, % | 0.9-2.0 | 0.5-1.5 | 0.6-1.4 | 1.4-4.8 | 0.1-0.2 |
| Freeness, ml | 111-161 | 52-113 | 40-96 | 253-519 | - |
| Pressure, kPa | 190-230 | 220-290 | 220-290 | 240-340 | - |
| Temperature, °C | 75-85 | - | - | - | - |
| Semi-automatic valves | Feed | 1st accept | 2nd accept | Reject | Dilution |
| Diameter, mm | 250 | 200 | 150 | 100 | 80 |
| Volume flow, dm 3/s | 48-187 | 30-120 | 11-44 | 8-44 | 0-28 |
| Flow velocity, m/s | 1.0-3.8 | 0.9-3.8 | 0.6-2.5 | 1.0-5.6 | 0.0-5.6 |
| Consistency, % | 1.0-2.4 | 0.7-1.7 | 0.7-1.5 | 1.5-4.7 | 0.0-0.1 |
| Freeness, ml | 106-172 | 50-127 | 35-136 | 196-525 | - |
| Pressure, kPa | 190-230 | 230-270 | 220-280 | 250-330 | - |
| Temperature, °C | 78-87 | - | - | - | - |
4.6.2. Statistical analysis
The following equations, together with an assumption of normally distributed sampling errors, were used for statistical evaluation of the sampling methods.
Measurement error is a combination of several error components, and errors in different steps of the analysis procedure will prove cumulative in the final result. Provided that the error components are independent, the uncertainty attached to the result can be determined by the sum of the variances of the components:
where
S02 is the total variance of the measurement,
S12 is the variance of the sampling,
S22 is the variance of the laboratory analysis,
S32 is the variance of the process.
If the standard deviation of a variable is known or can be estimated, the number of samples, n, needed to obtain the mean value of the variable in a given confidence interval can be calculated as:
where
p is the risk level for an errorless interpretation of the result,
tp is the t-value of Student’s distribution at the risk level p,
a denotes the limits of the confidence interval,
S is the standard deviation of the variable.