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wells-20080109.c
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/* WELLSUB.C - Wells functions
* Velimir V. Vesselinov - Monty SP (c) 1992
*/
#include <math.h>
#include <stdio.h>
#include "design.h"
#include "wells.h"
/* Prototypes of the functions in this file */
void Load_Problem( struct Problem_Info *pi, struct Aquifer_Data *ad, struct Well_Data *wd, struct Point_Data *pd );
void Save_Problem( struct Problem_Info pi, struct Aquifer_Data ad, struct Well_Data *wd, struct Point_Data *pd );
void Save_Well_S( char *fileName, struct Aquifer_Data ad, struct Well_Data *wd );
void Save_Point_S( char *fileName, struct Aquifer_Data ad, struct Point_Data *pd );
void Calc_Wells( struct Aquifer_Data ad, struct Well_Data *wd );
void Calc_Points( struct Aquifer_Data ad, struct Well_Data *wd, struct Point_Data *pd );
void Calc_Save_Grid( float time, struct Aquifer_Data ad, struct Well_Data *wd, struct Grid_Data *gd, char *fileName );
float Theis( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd );
float Theis_unc( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd );
float Hantush( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd );
float Hantush_unc( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd );
float Ei( float u );
float W( float ra, float rb );
float K0( float x );
int matherr( struct exception *except );
int main( int argn, char *args[] )
{
struct Problem_Info pit;
struct Aquifer_Data adt;
struct Well_Data wdt;
struct Point_Data pdt;
if( argn < 4 )
{
printf( "Usage: wells in_problem_file out_well_drawdown out_point_drawdown\n" );
exit( 1 );
}
strcpy( pit.file, args[1] );
Load_Problem( &pit, &adt, &wdt, &pdt );
strcpy( pit.file, "debug.wel" );
Save_Problem( pit, adt, &wdt, &pdt );
Calc_Wells( adt, &wdt );
Save_Well_S( args[2], adt, &wdt );
Calc_Points( adt, &wdt, &pdt );
Save_Point_S( args[3], adt, &pdt );
}
void Load_Problem( struct Problem_Info *pi, struct Aquifer_Data *ad, struct Well_Data *wd, struct Point_Data *pd )
{
FILE *infile;
char buf[50];
int i, j;
if ( ( infile = fopen( (*pi).file, "r" ) ) == NULL )
{
printf( "Problem file could not be read!\n" );
return;
}
fscanf( infile, "%[^:]s", buf ); fscanf( infile, ":%[^\n]60s\n", (*pi).name );
fscanf( infile, "%[^:]s", buf ); fscanf( infile, ": %i\n", &(*ad).co_aquifer );
fscanf( infile, "%[^:]s", buf ); fscanf( infile, ": %i %i %f %f %f\n", &(*ad).co_x_axis, &(*ad).co_y_axis, &(*ad).origin_x, &(*ad).origin_y, &(*ad).origin_angle );
fscanf( infile, "%[^:]s", buf ); fscanf( infile, ": %f\n", &(*ad).h );
fscanf( infile, "%[^:]s", buf ); fscanf( infile, ": %f\n", &(*ad).m );
fscanf( infile, "%[^:]s", buf ); fscanf( infile, ": %f\n", &(*ad).k );
fscanf( infile, "%[^:]s", buf ); fscanf( infile, ": %f\n", &(*ad).S );
fscanf( infile, "%[^:]s", buf ); fscanf( infile, ": %f\n", &(*ad).B );
fscanf( infile, "%[^:]s", buf ); fscanf( infile, ": %i\n", &(*wd).nW );
for( i = 0; i < (*wd).nW; i++ )
{
fscanf( infile, "%s %f %f %f %i\n", &(*wd).id[i], &(*wd).x[i], &(*wd).y[i], &(*wd).r[i], &(*wd).nQ[i] );
for( j = 0; j < (*wd).nQ[i]; j++ )
fscanf( infile, "%f %f\n", &(*wd).t[i][j], &(*wd).Q[i][j] );
}
fscanf( infile, "%[^:]s", buf ); fscanf( infile, ": %i\n", &(*pd).nP );
for( i = 0; i < (*pd).nP; i++ )
{
fscanf( infile, "%s %f %f %i\n", &(*pd).id[i], &(*pd).x[i], &(*pd).y[i], &(*pd).nT );
for( j = 0; j < (*pd).nT[i]; j++ )
fscanf( infile, "%f\n", &(*pd).t[i][j] );
}
fclose( infile );
}
void Save_Problem( struct Problem_Info pi, struct Aquifer_Data ad, struct Well_Data *wd, struct Point_Data *pd )
{
FILE *outfile;
int i, j;
if ( ( outfile = fopen( pi.file, "w" ) ) == NULL )
{
printf( "Problem file could not be opened!\n" );
return;
}
fprintf( outfile, "Problem name: %s\n", pi.name );
fprintf( outfile, "Aquifer type : %i\n", ad.co_aquifer );
fprintf( outfile, "Boundary information: %i %i %g %g %g\n", ad.co_x_axis, ad.co_y_axis, ad.origin_x, ad.origin_y, ad.origin_angle );
fprintf( outfile, "Initial Head : %g\n", ad.h );
fprintf( outfile, "Aquifer Tickness : %g\n", ad.m );
fprintf( outfile, "Permeability : %g\n", ad.k );
fprintf( outfile, "Storage coefficient : %g\n", ad.S );
fprintf( outfile, "Leakage coefficient : %g\n", ad.B );
fprintf( outfile, "--- Number of wells: %i\n", (*wd).nW );
for( i = 0; i < (*wd).nW; i++ )
{
fprintf( outfile, "%s %g %g %g %i\n", (*wd).id[i], (*wd).x[i], (*wd).y[i], (*wd).r[i], (*wd).nQ[i] );
for( j = 0; j < (*wd).nQ[i]; j++ )
fprintf( outfile, "%g %g\n", (*wd).t[i][j], (*wd).Q[i][j] );
}
fprintf( outfile, "--- Number of points: %i\n", (*pd).nP );
for( i = 0; i < (*pd).nP; i++ )
{
fprintf( outfile, "%s %g %g %i\n", (*pd).id[i], (*pd).x[i], (*pd).y[i], (*pd).nT[i] );
for( j = 0; j < (*pd).nT[i]; j++ )
fprintf( outfile, "%g\n", (*pd).t[i][j] );
}
fclose( outfile );
}
void Save_Well_S( char *fileName, struct Aquifer_Data ad, struct Well_Data *wd )
{
FILE *outfile;
int i, j;
if ( ( outfile = fopen( fileName, "w" ) ) == NULL )
{
printf( "Well drawdowns could not be saved!\n" );
return;
}
for( i = 0; i < (*wd).nW; i++ )
{
fprintf( outfile, "%s %g %g %i\n", (*wd).id[i], (*wd).x[i], (*wd).y[i], (*wd).nQ[i] );
for( j = 0; j < (*wd).nQ[i]; j++ )
fprintf( outfile, "%g %g %g %g\n", (*wd).t[i][j], (*wd).Q[i][j], (*wd).s[i][j], ad.h - (*wd).s[i][j] );
}
fclose( outfile );
}
void Save_Point_S( char *fileName, struct Aquifer_Data ad, struct Point_Data *pd )
{
FILE *outfile;
int i, j;
if ( ( outfile = fopen( fileName, "w" ) ) == NULL )
{
printf( "Data could not be saved!\n" );
return;
}
for( i = 0; i < (*pd).nP; i++ )
{
fprintf( outfile, "%s %g %g %i\n", (*pd).id[i], (*pd).x[i], (*pd).y[i], (*pd).nT[i] );
for( j = 0; j < (*pd).nT[i]; j++ )
fprintf( outfile, "%g %g %g\n", (*pd).t[i][j], (*pd).s[i][j], ad.h - (*pd).s[i][j] );
}
fclose( outfile );
}
void Calc_Wells( struct Aquifer_Data ad, struct Well_Data *wd )
{
int i, j, code1, code2, code3;
float x, y, xc, yc, ca, sa,
(*fp)( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd );
switch( ad.co_aquifer )
{
case CONFINED:
fp = Theis;
break;
case UNCONFINED:
fp = Theis_unc;
break;
case LEAKY:
fp = Hantush;
break;
case LEAKY_UNCONFINED:
fp = Hantush_unc;
break;
}
if( ad.co_x_axis != NO_BOUNDARY || ad.co_y_axis != NO_BOUNDARY )
{
ca = cos( ad.origin_angle );
sa = sin( ad.origin_angle );
code1 = code2 = code3 = 0;
if( ad.co_x_axis != NO_BOUNDARY )
code1 = ( ad.co_x_axis == TYPE_1 ) ? -1 : 1;
if( ad.co_y_axis != NO_BOUNDARY )
code2 = ( ad.co_y_axis == TYPE_1 ) ? -1 : 1;
if( ad.co_x_axis != NO_BOUNDARY && ad.co_y_axis != NO_BOUNDARY )
code3 = ( ad.co_x_axis != ad.co_y_axis ) ? -1 : 1;
}
for( i = 0; i < (*wd).nW; i++ )
{
for( j = 0; j < (*wd).nQ[i]; j++ )
{
(*wd).s[i][j] = fp( (*wd).x[i], (*wd).y[i], (*wd).t[i][j], ad, wd );
if( ad.co_x_axis != NO_BOUNDARY || ad.co_y_axis != NO_BOUNDARY )
{
xc = (*wd).x[i] - ad.origin_x;
yc = (*wd).y[i] - ad.origin_y;
x = xc * ca + xc * sa;
y = yc * ca - yc * sa;
if( code1 )
{
xc =x * ca - -y * sa + ad.origin_x;
yc = -y * ca +x * sa + ad.origin_y;
(*wd).s[i][j] += code1 * fp( xc, yc, (*wd).t[i][j], ad, wd );
}
if( code2 )
{
xc = -x * ca -y * sa + ad.origin_x;
yc =y * ca + -x * sa + ad.origin_y;
(*wd).s[i][j] += code2 * fp( xc, yc, (*wd).t[i][j], ad, wd );
}
if( code3 )
{
xc = -x * ca - -y * sa + ad.origin_x;
yc = -y * ca + -x * sa + ad.origin_y;
(*wd).s[i][j] += code3 * fp( xc, yc, (*wd).t[i][j], ad, wd );
}
}
}
}
}
void Calc_Points( struct Aquifer_Data ad, struct Well_Data *wd, struct Point_Data *pd )
{
int i, j, code1, code2, code3;
float x, y, xc, yc, ca, sa,
(*fp)( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd );
switch( ad.co_aquifer )
{
case CONFINED:
fp = Theis;
break;
case UNCONFINED:
fp = Theis_unc;
break;
case LEAKY:
fp = Hantush;
break;
case LEAKY_UNCONFINED:
fp = Hantush_unc;
break;
}
if( ad.co_x_axis != NO_BOUNDARY || ad.co_y_axis != NO_BOUNDARY )
{
ca = cos( ad.origin_angle );
sa = sin( ad.origin_angle );
code1 = code2 = code3 = 0;
if( ad.co_x_axis != NO_BOUNDARY )
code1 = ( ad.co_x_axis == TYPE_1 ) ? -1 : 1;
if( ad.co_y_axis != NO_BOUNDARY )
code2 = ( ad.co_y_axis == TYPE_1 ) ? -1 : 1;
if( ad.co_x_axis != NO_BOUNDARY && ad.co_y_axis != NO_BOUNDARY )
code3 = ( ad.co_x_axis != ad.co_y_axis ) ? -1 : 1;
}
for( i = 0; i < (*pd).nP; i++ )
{
for( j = 0; j < (*pd).nT[i]; j++ )
{
(*pd).s[i][j] = fp( (*pd).x[i], (*pd).y[i], (*pd).t[i][j], ad, wd );
if( ad.co_x_axis != NO_BOUNDARY || ad.co_y_axis != NO_BOUNDARY )
{
xc = (*pd).x[i] - ad.origin_x;
yc = (*pd).y[i] - ad.origin_y;
x = xc * ca + xc * sa;
y = yc * ca - yc * sa;
if( code1 )
{
xc =x * ca - -y * sa + ad.origin_x;
yc = -y * ca +x * sa + ad.origin_y;
(*pd).s[i][j] += code1 * fp( xc, yc, (*pd).t[i][j], ad, wd );
}
if( code2 )
{
xc = -x * ca -y * sa + ad.origin_x;
yc =y * ca + -x * sa + ad.origin_y;
(*pd).s[i][j] += code2 * fp( xc, yc, (*pd).t[i][j], ad, wd );
}
if( code3 )
{
xc = -x * ca - -y * sa + ad.origin_x;
yc = -y * ca + -x * sa + ad.origin_y;
(*pd).s[i][j] += code3 * fp( xc, yc, (*pd).t[i][j], ad, wd );
}
}
}
}
}
void Calc_Save_Grid( float time, struct Aquifer_Data ad, struct Well_Data *wd, struct Grid_Data *gd, char *fileName )
{
FILE *out;
int i, j, code1, code2, code3;
char buf[30];
float s, xg, yg, dx, dy, x, y, xc, yc, ca, sa,
(*fp)( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd );
if ( ( out = fopen( fileName, "w" ) ) == NULL )
{
printf( "Grid file could not be opened!" );
return;
}
fprintf( out, "DSAA\n" );
fprintf( out, "%i %i\n", (*gd).nx, (*gd).ny );
fprintf( out, "%.3g %.3g\n", (*gd).xmin, (*gd).xmax );
fprintf( out, "%.3g %.3g\n", (*gd).ymin, (*gd).ymax );
fprintf( out, "%.3g %.3g\n", 0.0, 0.0 );
switch( ad.co_aquifer )
{
case CONFINED:
fp = Theis;
break;
case UNCONFINED:
fp = Theis_unc;
break;
case LEAKY:
fp = Hantush;
break;
case LEAKY_UNCONFINED:
fp = Hantush_unc;
break;
}
dx = ( (*gd).xmax - (*gd).xmin ) / ( (*gd).nx - 1 );
dy = ( (*gd).ymax - (*gd).ymin ) / ( (*gd).ny - 1 );
ca = cos( ad.origin_angle );
sa = sin( ad.origin_angle );
code1 = code2 = code3 = 0;
if( ad.co_x_axis != NO_BOUNDARY )
code1 = ( ad.co_x_axis == TYPE_1 ) ? -1 : 1;
if( ad.co_y_axis != NO_BOUNDARY )
code2 = ( ad.co_y_axis == TYPE_1 ) ? -1 : 1;
if( ad.co_x_axis != NO_BOUNDARY && ad.co_y_axis != NO_BOUNDARY )
code3 = ( ad.co_x_axis != ad.co_y_axis ) ? -1 : 1;
for( yg = (*gd).ymin, j = 0; j < (*gd).ny; j++, yg += dy )
{
printf( "\rRow %4i of %4i", j + 1, (*gd).ny );
for( xg = (*gd).xmin, i = 0; i < (*gd).nx; i++, xg += dx, fprintf( out, "%12g ", s ) )
{
s = fp( xg, yg, time, ad, wd );
if( code1 || code2 )
{
xc = xg - ad.origin_x;
yc = yg - ad.origin_y;
x = xc * ca + xc * sa;
y = yc * ca - yc * sa;
}
else
continue;
if( code1 )
{
xc = x * ca - -y * sa + ad.origin_x;
yc = -y * ca + x * sa + ad.origin_y;
s += code1 * fp( xc, yc, time, ad, wd );
}
if( code2 )
{
xc = -x * ca - y * sa + ad.origin_x;
yc = y * ca + -x * sa + ad.origin_y;
s += code2 * fp( xc, yc, time, ad, wd );
}
if( code3 )
{
xc = -x * ca - -y * sa + ad.origin_x;
yc = -y * ca + -x * sa + ad.origin_y;
s += code3 * fp( xc, yc, time, ad, wd );
}
}
fprintf( out, "\n" );
}
fclose( out );
}
float Theis( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd )
{
float dx, dy, r, T, sub1, sub2, sub3, s;
int i, n, nR;
T = ad.m * ad.k; /* transmissivity */
sub1 = 12.5663706 * T; /* 4 * PI = 12.5663706 */
sub2 = ad.S / ( 4.0 * T );
s = 0;
for( i = 0; i < (*wd).nW; i++ )
{
dx = x - (*wd).x[i]; dy = y - (*wd).y[i]; r = dx * dx + dy * dy; /* squared radial distance */
sub3 = (*wd).r[i] * (*wd).r[i]; /* squared well radius */
if( r < sub3 ) r = sub3;
sub3 = r * sub2;
s += (*wd).Q[i][0] * Ei( sub3 / ( time - (*wd).t[i][0] ) ) / sub1; /* initial drawdown */
nR = (*wd).nQ[i]; /* number of step pumping rate changes */
for( n = 1; n < nR && (*wd).t[i][n] < time; n++ ) /* loop through all the pumping rates */
s += ( (*wd).Q[i][n] - (*wd).Q[i][n - 1] ) * Ei( sub3 / ( time - (*wd).t[i][n] ) ) / sub1;
}
return( s );
}
float Theis_unc( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd )
{
float dx, dy, r, h2, sub1, sub2, sub3, s;
int i, n, nR;
h2 = ad.h * ad.h;
sub1 = 6.2831853 * ad.k;
sub2 = ad.S / ( 4.0 * ad.k * ad.m );
s = 0;
for( i = 0; i < (*wd).nW; i++ )
{
dx = x - (*wd).x[i]; dy = y - (*wd).y[i]; r = dx * dx + dy * dy;
sub3 = (*wd).r[i] * (*wd).r[i];
if( r < sub3 ) r = sub3;
sub3 = r * sub2;
s += ad.h - sqrt( h2 - (*wd).Q[i][0] * Ei( sub3 / ( time - (*wd).t[i][0] ) ) / sub1 );
nR = (*wd).nQ[i];
for( n = 1; n < nR && (*wd).t[i][n] < time; n++ )
s += ad.h - sqrt( h2 - ( (*wd).Q[i][n] - (*wd).Q[i][n - 1] ) * Ei( sub3 / ( time - (*wd).t[i][n] ) ) / sub1 );
}
return( s );
}
float Hantush( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd )
{
float dx, dy, r, T, sub1, sub2, sub3, sub4, s;
int i, n, nR;
T = ad.m * ad.k;
sub1 = 12.5663706 * T;
sub2 = ad.S / ( 4.0 * T );
s = 0;
for( i = 0; i < (*wd).nW; i++ )
{
dx = x - (*wd).x[i]; dy = y - (*wd).y[i]; r = sqrt( dx * dx + dy * dy );
if( r < (*wd).r[i] ) r = (*wd).r[i];
sub3 = r * r * sub2;
sub4 = r / ad.B;
s += (*wd).Q[i][0] * W( sub3 / ( time - (*wd).t[i][0] ), sub4 ) / sub1;
nR = (*wd).nQ[i];
for( n = 1; n < nR && (*wd).t[i][n] < time; n++ )
s += ( (*wd).Q[i][n] - (*wd).Q[i][n - 1] ) * W( sub3 / ( time - (*wd).t[i][n] ), sub4 ) / sub1;
}
return( s );
}
float Hantush_unc( float x, float y, float time, struct Aquifer_Data ad, struct Well_Data *wd )
{
float dx, dy, r, h2, sub1, sub2, sub3, sub4, s;
int i, n, nR;
h2 = ad.h * ad.h;
sub1 = 6.2831853 * ad.k;
sub2 = ad.S / ( 4.0 * ad.k * ad.m );
s = 0;
for( i = 0; i < (*wd).nW; i++ )
{
dx = x - (*wd).x[i]; dy = y - (*wd).y[i]; r = sqrt( dx * dx + dy * dy );
if( r < (*wd).r[i] ) r = (*wd).r[i];
sub3 = r * r * sub2;
sub4 = r / ad.B;
s += ad.h - sqrt( h2 - (*wd).Q[i][0] * W( sub3 / ( time - (*wd).t[i][0] ), sub4 ) / sub1 );
nR = (*wd).nQ[i];
for( n = 1; n < nR && (*wd).t[i][n] < time; n++ )
s += ad.h - sqrt( h2 - ( (*wd).Q[i][n] - (*wd).Q[i][n - 1] ) * W( sub3 / ( time - (*wd).t[i][n] ), sub4 ) / sub1 );
}
return( s );
}
/* The Theis Function - Ei(x)
*/
float Ei( float u )
{
float s1, s2;
if ( u > 60.0 || u == 0.0 ) return( 0.0 );
if ( u < 1.0 )
{
s1 = ( ( ( ( 0.00107857 * u - 0.00976004 ) * u + 0.05519968 ) * u - 0.24991055 ) * u + 0.99999193 ) * u - 0.57721566;
return( s1 - log ( u ) );
}
else
{
s1 = ( ( ( u + 8.57332875 ) * u + 18.05901697 ) * u + 8.63476088 ) * u + 0.267773734;
s2 = ( ( ( u + 9.57332875 ) * u + 25.63295615 ) * u + 21.09965308 ) * u + 3.958496923;
return( ( 1 / u ) * ( s1 / s2 ) * exp( -u ) );
}
}
/* The Hantush Function
* The function is calculated by logarithmic integration using Simpson's rule
* source: W.Kinzelbach - Groundwater modelling
*/
float W( float ra, float rb )
{
float ug, og, hi, sub1, sub2, x2, x4, s2, s4;
int i;
if( ra < 1e-20 )
return( 2 * K0( rb ) );
if( ra > 2000.0 )
return( 0.0 );
ug = log( ra );
og = 10.0;
hi = ( og - ug ) / 24;
sub1 = rb * rb / 4.0; sub2 = hi * 2;
x4 = ug + hi; x2 = ug;
s4 = s2 = 0.0; i = 0;
while( 1 )
{
s4 += exp( - exp( x4 ) - sub1 / exp( x4 ) );
x4 += sub2;
if( i == 10 ) break;
x2 += sub2;
s2 += exp( - exp( x2 ) - sub1 / exp( x2 ) );
i++;
}
return( hi * ( exp( - exp( ug ) - sub1 / exp( ug ) ) + 4 * s4 + 2 * s2 + exp( - exp( og ) - sub1 / exp( og ) ) ) / 3 );
}
/* The Bessel Function Ko(x)
*/
float K0( float x )
{
float x1, x2;
float s1, s2;
if( x >= 60.0 )
return( 0.0 );
else if( x >= 2.0 )
{
x1 = 2.0 / x;
s1 = ( ( ( ( ( 0.00053208 * x1 - 0.00251540 ) * x1 + 0.00587872 ) * x1 - 0.01062446 ) * x1 + 0.02189568 ) * x1 - 0.07832358 ) * x1 + 1.25331414;
return( s1 * exp( -x ) / sqrt( x ) );
}
else
{
x1 = x * x / 4.0;
x2 = x * x / 14.0625;
s1 = ( ( ( ( ( 0.00000740 * x1 + 0.00010750 ) * x1 + 0.00262698 ) * x1 + 0.03488590 ) * x1 + 0.23069756 ) * x1 + 0.42278420 ) * x1 - 0.57721566;
s2 = ( ( ( ( ( 0.0045813 * x2 + 0.0360768 ) * x2 + 0.2659732 ) * x2 + 1.2067492 ) * x2 + 3.0899424 ) * x2 + 3.5156229 ) * x2 + 1.0;
return( -log( 0.5 * x ) * s2 + s1 );
}
}
int matherr( struct exception *except )
{
if( except->type == DOMAIN )
{
if( strcmp( except->name, "sqrt" ) == 0 )
{
except->retval = 0.0;
printf( "MATH ERROR: Negative root!" );
return 1;
}
}
else
{
printf( "ERROR!" );
return 0;
}
}