Question 4 (30 points) Consider a geothermal well with the properties given below: Assume that the well is initially filled with the geothermal water and that the well and its surroundings are at the linear geothermal gradient. The inflowing temperature can be taken equal to the bottomhole temperature. 3a-) (15 points) Determine the temperature in the well at a depth of 500m at 10 days for production. Assume that the inflowing fluid temperature is the same as the bottomhole temperature. 3b-) (15 points) Determine the temperature in the well at a depth of 500m at 10 days for injection. Consider the injection temperature to be 90C and the injection rate to be equal to the production rate