# Temperature of a producing geothermal well

## Input(s)

$$T_{o}$$: Inflowing Fluid Temperature $$\left({ }^{\circ} \mathrm{F}\right)$$

$$T_{b h}$$: Downhole Reservoir Temperature $$\left({ }^{\circ} \mathrm{F}\right)$$

a: Geothermal Gradient $$\left({ }^{\circ} \mathrm{F} / \mathrm{ft}\right)$$

A: Diffusion Depth (ft)

y: Distance from the Bottom of the Well ( $$\mathrm{ft}$$ )

$$t$$: Function of Time (d)

## Output(s)

T: Temperature of a Producing Geothermal Well $$\left({ }^{\circ} \mathrm{F}\right)$$

## Formula(s)

$\mathrm{T}=\left(\mathrm{T}_{\mathrm{bh}}-\mathrm{ay}\right)+\mathrm{aA}\left(1-\mathrm{e}^{-\mathrm{y} / \mathrm{A}}\right)+\left(\mathrm{T}_{\mathrm{o}}-\mathrm{T}_{\mathrm{bh}}\right) \mathrm{e}^{-\mathrm{y} / \mathrm{A}}$

## Reference(s)

Ramey Jr, H. J. (1981). Reservoir Engineering Assessment of Geothermal Systems. Department of Petroleum Engineering, Stanford University. Page: 6.2.

## Related

### Total heat loss of a geothermal well

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