get_hydraulic_head: Get hydraulic head

In gopalpenny/anem: Analytical element models for simple aquifers

Description

Get hydraulic head at location, accounting for the cumulative effect of wells at location, the aquifer type (confined or unconfined), resting head, and cumulative effect of all wells. This function is a wrapper around get_potential_differential() to get the actual hydraulic head instead of the differential potential.

Usage

get_hydraulic_head(loc, wells, aquifer)

Arguments

loc	coordinates vector as c(x,y), with units of [m] or as data.frame with columns $x and $y
wells	wells object with each row containing rate Q [m^3/s], diam [m], radius of influence R [m], & coordinates x [m], y [m]
aquifer	Afuifer object containing aquifer_type, h0, Ksat, bounds, z0 (for confined case only)

Value

The output is the hydraulic head loc, accounting for the cumulative effect of all wells (dP), which is given as hydraulic head [units=m] if aquifer_type="confined" or discharge potential [m^2] if aquifer_type="unconfined". Then the head at loc is:

aquifer_type="confined"

h=h_0+dP

aquifer_type="unconfined"

h=√{h_0^2+dP}

Examples

well1 <- define_wells(x=0,y=0,Q=1e-3,diam=0.75,R=300)
well2 <- define_wells(x=0.5,y=0.25,Q=-2e-3,diam=0.8,R=300)
aquifer <- define_aquifer(aquifer_type="confined",Ksat=0.00001,h0=0,z0=30)


get_hydraulic_head(well1,loc=c(5,5),aquifer)
get_hydraulic_head(well2,loc=c(5,5),aquifer)
wells <- rbind(well1,well2)

get_hydraulic_head(wells,loc=c(5,5),aquifer=aquifer)

grid_pts <- expand.grid(x=seq(0,10,by=5),y=seq(0,10,by=5))
aquifer_unconfined <- define_aquifer(aquifer_type="confined",Ksat=0.00001,h0=50,z0=30)
get_hydraulic_head(well1,loc=grid_pts,aquifer=aquifer_unconfined)
get_hydraulic_head(well2,loc=grid_pts,aquifer=aquifer_unconfined)
get_hydraulic_head(wells,loc=grid_pts,aquifer=aquifer_unconfined)
get_hydraulic_head(NULL,loc=grid_pts,aquifer=aquifer_unconfined)

# Ensure potentials are even when pumping is symmetric (and opposite sign)
well1 <- define_wells(x=0,y=0,Q=1e-3,diam=0.5,R=300)
well2 <- define_wells(x=1,y=1,Q=-2e-3,diam=0.5,R=300)
well3 <- define_wells(x=0,y=0.5,Q=2e-3,diam=0.5,R=300)
well4 <- define_wells(x=0.5,y=1,Q=-2e-3,diam=0.5,R=300)
wells_even <- rbind(well1,well1,well2,well3,well4)
grid_pts_even <- data.frame(x=c(0,0.5,1),y=c(1,0.5,0))
get_hydraulic_head(wells_even,loc=grid_pts_even,aquifer=aquifer_unconfined)

gopalpenny/anem documentation built on Dec. 20, 2020, 5:27 a.m.