Geothermal geologists analyzed fluid samples collected from 4 distinct wells (Well W, Well… — ACT

Geothermal geologists analyzed fluid samples collected from 4 distinct wells (Well W, Well X, Well Y, and Well Z). Table 1 lists the measured reservoir temperature in degrees Celsius ( $^\circ\text{C}$ ) and the dissolved silica ( $SiO_2$ ) concentration in milligrams per liter ( $\text{mg/L}$ ) for each well.

Table 1:

Well	Reservoir Temperature ( $^\circ\text{C}$ )	Dissolved $SiO_2$ ( $\text{mg/L}$ )
Well W	140	180
Well X	200	400
Well Y	170	250
Well Z	230	520

Figure 1 displays the fluid viscosity ( $\eta$ , in centipoise, $\text{cP}$ ) as a function of dissolved $SiO_2$ concentration at four different temperature curves:
- At $140^\circ\text{C}$ : $\eta = 0.005 \times (\text{dissolved } SiO_2) + 0.10$
- At $170^\circ\text{C}$ : $\eta = 0.003 \times (\text{dissolved } SiO_2) + 0.20$
- At $200^\circ\text{C}$ : $\eta = 0.002 \times (\text{dissolved } SiO_2) + 0.40$
- At $230^\circ\text{C}$ : $\eta = 0.001 \times (\text{dissolved } SiO_2) + 0.50$

Based on Table 1 and Figure 1, rank the geothermal wells in order from lowest fluid viscosity to highest fluid viscosity.

1Well Y
2Well W
3Well Z
4Well X

Answer

The correct order from lowest to highest fluid viscosity is Well Y, Well W, Well Z, and Well X.

By looking up each well's specific reservoir temperature and dissolved

SiO_2

concentration in Table 1 and substituting those values into the corresponding temperature equation from Figure 1, the calculated viscosities are

0.95\text{ cP}

for Well Y,

1.00\text{ cP}

for Well W,

1.02\text{ cP}

for Well Z, and

1.20\text{ cP}

for Well X. Sorting these from lowest to highest yields the sequence: Well Y, Well W, Well Z, Well X.

Step-by-Step Solution

Extract the temperature and dissolved

SiO_2

concentration for each well from Table 1.

Well W:

140^\circ\text{C}

180\text{ mg/L}

; Well X:

200^\circ\text{C}

400\text{ mg/L}

; Well Y:

170^\circ\text{C}

250\text{ mg/L}

; Well Z:

230^\circ\text{C}

520\text{ mg/L}

Both temperature and concentration are necessary to select the corresponding line equation from Figure 1.

Apply the viscosity formulas from Figure 1 corresponding to each well's temperature.

Well W (

140^\circ\text{C}

\eta = 0.005(180) + 0.10 = 0.90 + 0.10 = 1.00\text{ cP}

; Well X (

200^\circ\text{C}

\eta = 0.002(400) + 0.40 = 0.80 + 0.40 = 1.20\text{ cP}

; Well Y (

170^\circ\text{C}

\eta = 0.003(250) + 0.20 = 0.75 + 0.20 = 0.95\text{ cP}

; Well Z (

230^\circ\text{C}

\eta = 0.001(520) + 0.50 = 0.52 + 0.50 = 1.02\text{ cP}

Synthesizing data from both sources determines the numerical fluid viscosity for each well.

Arrange the resulting viscosity values from smallest to largest.

0.95\text{ cP (Well Y)} < 1.00\text{ cP (Well W)} < 1.02\text{ cP (Well Z)} < 1.20\text{ cP (Well X)}

The question specifies ranking from lowest viscosity to highest viscosity.

Key Concept

Synthesizing values from a data table with temperature-dependent functional relationships in a graph.

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