12:166, Zhang

 Spring, 2002

Lecture on

Well Interference and Effect of Boundaries: Superposition Principle

 

·       Superposition Principle

·          A solution of summation of linear equations is the summation of the solutions to each individual equations.

·          Example:  y1 = x1+3;  y2 = 2x2+5;   y = y1+y2 = x1+2x2+8

 

·       Well Interference

·          Drawdown at an observation well (s) due to several pumping wells is equal to the summation of the drawdowns (si) due to each individual pumping wells, i.e.,

 

 

 

Note: The distance from the observation well to the pumping wells (ri) usually varies

 

·       Effect of Hydrogeological Boundaries with Imaginary wells

 

 

 

 where the plus sign is for a well near a barrier (no-flow or impermeable) boundary;

                                the minus sign is for a well near a recharge (constant head) boundary;

                        s – the observed drawdown;

                        sp – the drawdown caused by the pumping well;

                        si – the drawdown caused by the imaginary well;

                        rp – the distance from the pumping well to the observation well;

                        ri – the distance from the imaginary well to the observation well;

 

·        Recovery in a Pumping Well

 

 

 

Where  Ds’is residual drawdown; t is the time since pumping started;

t’ is the time since pumping stopped.

 

·        Specific Capacity – The pumping rate per unit drawdown

·        Well Efficiency

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Reading:                Section 5.7, 5.8 and 5.9 (p.205 – 209) of the text
Homework:           Problem 2 and 9 of Chpt. 5 (p. 216) more on the back.  Due on Fri. March 8                       

 

 

 

 

Homework due on Fri. March 8

 

  1. Plot the results you obtained from Problems 2 and 9 on a semi-log paper and calculate the transmissivity and storotivity. What you should get?

 

  1. Professor Tom Foster stiil needs your help. He just learned that the city drilled another well (see the map below) and plan to pump the two at the same time but with different rates (the first well at 275 gal/min and the second well at 350 gal/min). Calculate the drawdown at his well due to both pumping wells for 100 days and for one year.