agarwal_dmo.m

%% Demo example for the agarwal time 
% This demonstrates the interpretation of a recovery test after a constant
% rate or variable rate test.
%
% MIT License
% Copyright (c) 2017 Philippe Renard - University of Neuchâtel (CHYN)

%%
%
% This demo contains two examples: the first shows the interpretation of a
% recovery test after a constant rate test with real field data, the second
% is a synthetic example comparing the interpretation of the recovery after
% a multiple rate test with a standard Theis interpretation or with the
% Agarwal technique.

%% Field example: recovery after constant rate
%
% The data set for this example comes from: 
% Todd D.K.(1980), Ground Water Hydrology, John Wiley & Sons, New York,
% Batu, V., Aquifer Hydraulics: A Comprehensive Guide to Hydrogeologic
% Data Analysis, John Wiley, New York, 1998.
% Example 4-12, Pages 183-186
%
% The data are from an observation well located 60 m away from the pumping
% well. Let us first load the data and plot them.

[t,s]=ldf('agt_ds1.dat');
clf
plot(t,s,'-o')
title('Recovery data in the observation well')
xlabel('Time since pump stopped in seconds')
ylabel('Residual drawdown in m')


%% 
% We then define the values of the parameters that are required for the
% interpretation: 

tp=240*60;           % Duration of pumping
qp=2500/24/60/60;    % pumping rate
r= 60;               % distance to the pumping well

%% 
% Once the data have been loaded and the parameter defined, they can
% be interpreted. First, we calculate the Agarwal time. Then we use it to
% estimate the parameter p and fit the Theis solution to the data. The
% result is controlled graphically with the trial function.

[ta,sa] = agarwal_time( t, s, tp);   % compute the Agarwal time
p=ths_gss(ta,sa);
p=fit('ths',p,ta,sa);
ths_rpt(p,ta,sa,[qp,r],'Interpretation of recovery test with Agarwal time')


%% 
% The folowing values are obtained:
% T = 1.3e-2 m2/s and S = 1.9 e-4
%
% They are identical to the values found by Batu (1998):
% T  = 1.3 e-2 m2/s and S = 1.9 e-4