# Chapter 6 Appendix

## 6.1 Sequential Guassian Simulation (R Code)

#install.packages(c('gstat','sp','sp','plyr','fields'))

library(gstat)                                 # geostatistical methods by Edzer Pebesma
library(sp)                                    # spatial points addition to regular
# data frames
library(plyr)                                  # manipulating data by Hadley Wickham
library(fields)                                # required for the image plots

nx = 45                                       # number of cells in the x direction
ny = 45                                       # number of cells in the y direction
xsize = 10.0                                   # extent of cells in x direction
ysize = 10.0                                   # extent of cells in y direction

xmin = 0
ymin = 0
xmax = xmin + nx * xsize
ymax = ymin + ny * ysize
x<-seq(xmin,xmax,by=xsize)                     # used for axes on image plots
y<-seq(ymin,ymax,by=ysize)

colmap = topo.colors(100)                      # define the color map and
# descritation

nscore <- function(x) {                        # by Ashton Shortridge, 2008
# Takes a vector of values x and calculates their normal scores. Returns
# a list with the scores and an ordered table of original values and
# scores, which is useful as a back-transform table. See backtr().
nscore <- qqnorm(x, plot.it = FALSE)$x # normal score trn.table <- data.frame(x=sort(x),nscore=sort(nscore)) return (list(nscore=nscore, trn.table=trn.table)) } addcoord <- function(nx,xmin,xsize,ny,ymin,ysize) { # Michael Pyrcz, March, 2018 # makes a 2D dataframe with coordinates based on GSLIB specification coords = matrix(nrow = nx*ny,ncol=2) ixy = 1 for(iy in 1:nx) { for(ix in 1:ny) { coords[ixy,1] = xmin + (ix-1)*xsize coords[ixy,2] = ymin + (iy-1)*ysize ixy = ixy + 1 } } coords.df = data.frame(coords) colnames(coords.df) <- c("X","Y") coordinates(coords.df) =~X+Y return (coords.df) } sim2darray <- function(spdataframe,nx,ny,ireal) { # Michael Pyrcz, March, 2018 # makes a 2D array from realizations spatial point dataframe model = matrix(nrow = nx,ncol = ny) ixy = 1 for(iy in 1:ny) { for(ix in 1:nx) { model[ix,iy] = spdataframe@data[ixy,ireal] ixy = ixy + 1 } } return (model) } sim2vector <- function(spdataframe,nx,ny,ireal) { # Michael Pyrcz, March, 2018 # makes a 1D vector from spatial point dataframe model = rep(0,nx*ny) ixy = 1 for(iy in 1:ny) { for(ix in 1:nx) { model[ixy] = spdataframe@data[ixy,ireal] ixy = ixy + 1 } } return (model) } mydata1=read.csv('Welllocation5SGS_inj.csv') j=1 cumdata <- matrix(0,nrow = 1500,ncol = 4) cumdata <- as.data.frame(cumdata) for (i in 1:1){ sample <- matrix(data.matrix(mydata1[i,2:9]),nrow = 4,ncol = 2) locdata <- data.frame(rbind(matrix(c(23,23),nrow = 1,ncol = 2),sample)) locgrid <- matrix(0,nrow=5,ncol = 2) for (k in 1:5) { locgrid[k,1] <- (locdata[k,1]-1)*xsize + 5 locgrid[k,2] <- (locdata[k,2]-1)*ysize + 5 } m <- 500 s <- 100 location <- log(m^2 / sqrt(s^2 + m^2)) shape <- sqrt(log(1 + (s^2 / m^2))) Perm <- matrix(rlnorm(5,location,shape),nrow = 5,ncol = 1) logperm <- log10(Perm) logperm <- matrix(logperm,nrow = 5,ncol = 1) mydata2 <- data.frame(cbind(locgrid,Perm,logperm)) z <- i*5 cumdata[j:z,1:4] <- mydata2 colnames(mydata2) <- c('X','Y','Perm','logperm') #head(mydata2) j=j+5 coordinates(mydata2) = ~X+Y npor.trn = nscore(mydata2$logperm)              # normal scores transform
mydata2[["NPermeability"]]<-npor.trn$nscore # append the normal scores transform cuts = c(2.4,2.45,2.5,2.65,2.7,2.8,2.9) cuts.var = c(0.05,.1,.15,.20,.25,.3,.35,.4,.45,.5,.55,.6,.65,.7,.75,.8,.85,.9,.95) spplot(mydata2, "logperm", do.log = TRUE, # location map of porosity data key.space=list(x=1.05,y=0.97,corner=c(0,1)),cuts = cuts, scales=list(draw=T),xlab = "X (m)", ylab = "Y (m)",main ="Permeability (Log(K)), in md") coords <- addcoord(nx,xmin,xsize,ny,ymin,ysize) # make a dataframe with #all the estimation locations #summary(coords) # check the coordinates sill = var(mydata2$logperm)                    # calculate the variance of the property
#of interest as the sill
min = min(mydata2$logperm) # calculate the property min and max #for plotting max = max(mydata2$logperm)
zlim = c(min,max)            # define the property min and max in a 2x1 vextor

vm.nug1 <- vgm(psill =0.5*sill, "Sph", 200, anis = c(000, 1.0),nugget=0.5*sill)
condsim.nug1 = krige(logperm~1, mydata2, coords, model = vm.nug1, nmax = 100, nsim = 10)

par(mfrow=c(2,2))
real1 <- sim2darray(condsim.nug1,nx,ny,1)     # extract realization #1 to a
#  2D array and plot
image.plot(10^real1,x=x,y=y,xlab="X(m)",ylab="Y(m)",
zlim = c(min(10^real1),max(10^real1)),
col=colmap,legend.shrink = 0.6);
mtext(line=1, side=3, "Realization #1", outer=F);box(which="plot")

real2 <- sim2darray(condsim.nug1,nx,ny,2)     # extract realization #2 to a
#2D array and plot
image.plot(10^real2,x=x,y=y,xlab="X(m)",ylab="Y(m)",
zlim =c(min(10^real2),max(10^real2)) ,
col=colmap,legend.shrink = 0.6);
mtext(line=1, side=3, "Realization #2", outer=F);box(which="plot")

real3 <- sim2darray(condsim.nug1,nx,ny,3)      # extract realization #3 to a
# 2D array and plot
image.plot(10^real3,x=x,y=y,xlab="X(m)",ylab="Y(m)",zlim = c(min(10^real3),max(10^real3)),
col=colmap,legend.shrink = 0.6);
mtext(line=1, side=3, "Realization #3", outer=F);box(which="plot")

real4 <- sim2darray(condsim.nug1,nx,ny,4)      # extract realization #4 to a
#2D array and plot
image.plot(10^real4,x=x,y=y,xlab="X(m)",ylab="Y(m)",
zlim = c(min(10^real4),max(10^real4)),
col=colmap,legend.shrink = 0.6);
mtext(line=1, side=3, "Realization #4", outer=F);box(which="plot")

}

## 6.2 Calculation of Connectivities (FMM) for 5-Spot Pattern (Python Code)

!pip install pandas
!pip install numpy
!pip install pandas
!pip install seaborn
!pip install scikit-fmm

import os
import pandas as pd
import numpy as np
import skfmm

loc_well = pd.DataFrame(np.array([[30,80,11,19,18,12,87,88]]),
columns=['X1', 'X2', 'X3','X4','Y1','Y2','Y3','Y4'])

input = pd.DataFrame(np.array([(np.arange(1,18))]),
columns=['ConI1I2', 'ConI1I3', 'ConI1I4',
'ConI2I1','ConI2I3','ConI2I4','ConI3I1',
'ConI3I2','ConI3I4''ConI4I1','ConI4I2',
'ConI4I3','ConP1I1','ConP1I2','ConP1I3',
'ConP1I4','PV_flight'])

import timeit
start = timeit.default_timer()
i=1
j=1
ii=str(i)
jj=str(j)
ss='C:\\Users\\243886\\OneDrive - Universitetet i Stavanger\\ML-5spot-SGS\\R&\\En$' pathnew=ss.replace("&", ii) pathnews=pathnew.replace("$", jj)
os.chdir(pathnews)
os.getcwd()
data=pd.read_csv('SPEED.csv')
speed=data
speed = speed.iloc[:,0:100]
phi=np.ones((100,100))
phi[loc_well.loc[i-1,'X1']-1,loc_well.loc[i-1,'Y1']-1]=0
t_va=skfmm.travel_time(phi,speed,dx=10)
TimeFMM_hr=t_va**2/4/3600
input.loc[0,'ConI1I2']=TimeFMM_hr[loc_well.loc[i-1,'X2']-1,loc_well.loc[i-1,'Y2']-1]
input.loc[0,'ConI1I3']=TimeFMM_hr[loc_well.loc[i-1,'X3']-1,loc_well.loc[i-1,'Y3']-1]
input.loc[0,'ConI1I4']=TimeFMM_hr[loc_well.loc[i-1,'X4']-1,loc_well.loc[i-1,'Y4']-1]

######################################################################################

phi=np.ones((100,100))
phi[loc_well.loc[i-1,'X2']-1,loc_well.loc[i-1,'Y2']-1]=0
t_va=skfmm.travel_time(phi,speed,dx=10)
TimeFMM_hr=t_va**2/4/3600
input.loc[0,'ConI2I1']=TimeFMM_hr[loc_well.loc[i-1,'X1']-1,loc_well.loc[i-1,'Y1']-1]
input.loc[0,'ConI2I3']=TimeFMM_hr[loc_well.loc[i-1,'X3']-1,loc_well.loc[i-1,'Y3']-1]
input.loc[0,'ConI2I4']=TimeFMM_hr[loc_well.loc[i-1,'X4']-1,loc_well.loc[i-1,'Y4']-1]

######################################################################################

phi=np.ones((100,100))
phi[loc_well.loc[i-1,'X3']-1,loc_well.loc[i-1,'Y3']-1]=0
t_va=skfmm.travel_time(phi,speed,dx=10)
TimeFMM_hr=t_va**2/4/3600
input.loc[0,'ConI3I1']=TimeFMM_hr[loc_well.loc[i-1,'X1']-1,loc_well.loc[i-1,'Y1']-1]
input.loc[0,'ConI3I2']=TimeFMM_hr[loc_well.loc[i-1,'X2']-1,loc_well.loc[i-1,'Y2']-1]
input.loc[0,'ConI3I4']=TimeFMM_hr[loc_well.loc[i-1,'X4']-1,loc_well.loc[i-1,'Y4']-1]

###################################################################################

phi=np.ones((100,100))
phi[loc_well.loc[i-1,'X4']-1,loc_well.loc[i-1,'Y4']-1]=0
t_va=skfmm.travel_time(phi,speed,dx=10)
TimeFMM_hr=t_va**2/4/3600
input.loc[0,'ConI4I1']=TimeFMM_hr[loc_well.loc[i-1,'X1']-1,loc_well.loc[i-1,'Y1']-1]
input.loc[0,'ConI4I2']=TimeFMM_hr[loc_well.loc[i-1,'X2']-1,loc_well.loc[i-1,'Y2']-1]
input.loc[0,'ConI4I3']=TimeFMM_hr[loc_well.loc[i-1,'X3']-1,loc_well.loc[i-1,'Y3']-1]

###################################################################################
phi=np.ones((100,100))
phi[49, 49]=0
t_va=skfmm.travel_time(phi,speed,dx=10)
TimeFMM_hr=t_va**2/4/3600
input.loc[0,'ConP1I1']=TimeFMM_hr[loc_well.loc[i-1,'X1']-1,loc_well.loc[i-1,'Y1']-1]
input.loc[0,'ConP1I2']=TimeFMM_hr[loc_well.loc[i-1,'X2']-1,loc_well.loc[i-1,'Y2']-1]
input.loc[0,'ConP1I3']=TimeFMM_hr[loc_well.loc[i-1,'X3']-1,loc_well.loc[i-1,'Y3']-1]
input.loc[0,'ConP1I4']=TimeFMM_hr[loc_well.loc[i-1,'X4']-1,loc_well.loc[i-1,'Y4']-1]

##################################################################################

phi=np.ones((100,100))
phi[loc_well.loc[i-1,'X1']-1,loc_well.loc[i-1,'Y1']-1]=0
phi[loc_well.loc[i-1,'X2']-1,loc_well.loc[i-1,'Y2']-1]=0
phi[loc_well.loc[i-1,'X3']-1,loc_well.loc[i-1,'Y3']-1]=0
phi[loc_well.loc[i-1,'X4']-1,loc_well.loc[i-1,'Y4']-1]=0
t_va=skfmm.travel_time(phi,speed,dx=10)
TimeFMM_hr=t_va**2/4/3600
PV=(sum(sum(TimeFMM_hr<TimeFMM_hr[49, 49])))/10000
input.loc[0,'PV_flight']=PV
stop = timeit.default_timer()
print('Time: ', stop - start)

input

## 6.3 XGBOOST Machine Learning Model (R Code)

setwd("C:/Users/243886/OneDrive - Universitetet i Stavanger/ML-5spot-SGS/Rcode")
NPVpl <- data.frame(N)
NPVpl <- NPVpl[, c(1)]
input1 <- data.frame(input)
geoin <- read.csv('INPUTPCA489.csv',nrows = F)
Final_Input <- cbind(input1,NPVpl)
install.packages(c("e1071", "caret", "doSNOW", "ipred", "xgboost"))
install.packages(c('lattice','ggplot2'))
library(caret)
library(doSNOW)
INPUTMEAN <- data.frame(INPUTMEAN)
train <- INPUT
#=================================================================
# Data Wrangling
#=================================================================
# Set up factors.
# Subset data to features we wish to keep/use.

features <- c('MC1','MC2','MC3','MC4','MPV','NPVpl')
c('En1C1','En2C1','En3C1','En4C1','En5C1','En6C1','En7C1','En8C1','En9C1',
'En10C1','En1C2','En2C2','En3C2','En4C2','En5C2','En6C2','En7C2','En8C2'
,'En9C2','En10C2','En1C3','En2C3','En3C3','En4C3','En5C3','En6C3','En7C3',
'En8C3','En9C3','En10C3','En1C4','En2C4','En3C4','En4C4','En5C4','En6C4',
'En7C4','En8C4','En9C4','En10C4','En1PV','En2PV','En3PV','En4PV','En5PV',
'En6PV','En7PV','En8PV','En9PV','En10PV','NPVpl')
train <- train[, features]

#=================================================================
# Split Data
#=================================================================

names(train)[26]<-"NPVpl"
# Use caret to create a 70/30% split of the training data,
# keeping the proportions of the Survived class label the
# same across splits.
set.seed(54321)
indexes <- createDataPartition(train$NPVpl, times = 1, p = 0.7, list = FALSE) profs.train <- train[indexes,] profs.test <- train[-indexes,] # Examine the proportions of the Survived class lable across # the datasets. prop.table(table(train$NPVpl))
prop.table(table(proonebyone.train$NPVpl)) prop.table(table(proonebyone.test$NPVpl))

#=================================================================
# Train Model
#=================================================================
# nrounds max_depth  eta gamma colsample_bytree min_child_weight subsample
#4    4000         6 0.01     0              0.4                2         1
#   nrounds max_depth   eta gamma colsample_bytree min_child_weight subsample
#10    4000         6 0.025     0              0.4             2.25         1
# Set up caret to perform 10-fold cross validation repeated 3
# times and to use a grid search for optimal model hyperparamter
# values.
train.control <- trainControl(method = "repeatedcv",
number = 10,
repeats = 3,
search = "grid")

# Leverage a grid search of hyperparameters for xgboost. See
# the following presentation for more information:
# https://www.slideshare.net/odsc/owen-zhangopen-sourcetoolsanddscompetitions1
tune.grid <- expand.grid(eta = c(0.0025),
nrounds = c(4000),
max_depth = 6,
min_child_weight = c(2.25),
colsample_bytree = c(0.4),
gamma = 0,
subsample = 1)
View(tune.grid)

# Use the doSNOW package to enable caret to train in parallel.
# While there are many package options in this space, doSNOW
# has the advantage of working on both Windows and Mac OS X.
#
# Create a socket cluster using 10 processes.
#
# NOTE - Tune this number based on the number of cores/threads
# available on your machine!!!
#
cl <- makeCluster(10, type = "SOCK")

# Register cluster so that caret will know to train in parallel.
registerDoSNOW(cl)

library(foreach)
install.packages('doParallel')
library(doParallel)
cl <- makeCluster(30)
registerDoParallel(cl)

# Train the xgboost model using 10-fold CV repeated 3 times
# and a hyperparameter grid search to train the optimal model.
library('xgboost')
caret.cv <- train(NPVpl ~ .,
data = profs.train,
method = "xgbTree",
tuneGrid = tune.grid,
trControl = train.control)
stopCluster(cl)
caret.cv$bestTune # Examine caret's processing results # Make predictions on the test set using a xgboost model # trained on all 625 rows of the training set using the # found optimal hyperparameter values. preds <- predict(caret.cv, profs.test) plot(preds,profs.test$NPVpl,col='red',type = 'p',pch=1 ,xlab =
'NPV predicted by ML ($MM)',ylab = 'NPV of the real Test Data ($MM)',
main = 'Test Data vs. ML Prediction')
abline(a=0,b=1,col=4,lwd=3)
mylabel = bquote(italic(R)^2 == .(format(r2, digits = 2)))
text(x = 40, y = 15, labels = mylabel)
caret::R2(preds,profs.test$NPVpl) # Use caret's confusionMatrix() function to estimate the # effectiveness of this model on unseen, new data caret.cv$bestTune

## 6.4 Modyfing the Eclipse Data File + Running the Eclipse Simulator from R Shell (R Code)

setwd("C:/Users/243886/OneDrive - Universitetet i Stavanger/ML-5spot-INJ-SGS/Rcode")
library(readr)
X2D_4Inj_1Prod_R1 <- read_delim("2D_4Inj_1Prod_R.DATA",
"\t", escape_double = FALSE, na = "null",
trim_ws = TRUE)
run <- 'C:/ecl/macros/eclrun.exe eclipse "C:/Users/243886/OneDrive
- Universitetet i Stavanger/ROOPT_Ide/En#/Ensemble.DATA"'

Eclipse <- function(X1,Y1,X2,Y2,X3,Y3,X4,Y4,A1,A2,A3,A4,gam1,gam2,gam3,gam4,En){
wd <- 'C:/Users/243886/OneDrive - Universitetet i Stavanger/ROOPT_Ide/En#'
run1 <- gsub('#',En,run)
newwd <- gsub('#',En,wd)
setwd(newwd)
X1 <- round(X1)
X2 <- round(X2)
X3 <- round(X3)
X4 <- round(X4)
Y1 <- round(Y1)
Y2 <- round(Y2)
Y3 <- round(Y3)
Y4 <- round(Y4)
slope <- c(-0.0005,-0.00025,0,0.00025,0.00050,0.00075,
0.00100,0.00125,0.00150,0.00175,0.00200)
Avalue <- c(100,150,200,250,300)
A_1 <- Avalue[findInterval(A1,Avalue)]
A_2 <- Avalue[findInterval(A2,Avalue)]
A_3 <- Avalue[findInterval(A3,Avalue)]
A_4 <- Avalue[findInterval(A4,Avalue)]

Gam1 <- slope[findInterval(gam1,slope)]
Gam2 <- slope[findInterval(gam2,slope)]
Gam3 <- slope[findInterval(gam3,slope)]
Gam4 <- slope[findInterval(gam4,slope)]

data <- X2D_4Inj_1Prod_R1
g1 <- data[131,1]
g2 <- data[132,1]
g3 <- data[133,1]
g4 <- data[134,1]
g5 <- data[138,1]
g6 <- data[139,1]
g7 <- data[140,1]
g8 <- data[141,1]
G1 <- gsub('101',X1, g1)
G2 <- gsub('102',Y1, G1)
G3 <- gsub('103',X2, g2)
G4 <- gsub('104',Y2, G3)
G5 <- gsub('105',X3, g3)
G6 <- gsub('106',Y3, G5)
G7 <- gsub('107',X4, g4)
G8 <- gsub('108',Y4, G7)
G9 <- gsub('109',X1, g5)
G10 <- gsub('110',Y1, G9)
G11 <- gsub('111',X2, g6)
G12 <- gsub('112',Y2, G11)
G13 <- gsub('113',X3, g7)
G14 <- gsub('114',Y3, G13)
G15 <- gsub('115',X4, g8)
G16 <- gsub('116',Y4, G15)
data[131,1] <- G2
data[132,1] <- G4
data[133,1] <- G6
data[134,1] <- G8
data[138,1] <- G10
data[139,1] <- G12
data[140,1] <- G14
data[141,1] <- G16
#'C:/Users/243886/OneDrive - Universitetet i Stavanger/ROOPT/Ecl'
write.table(data, file ="Ensemble.DATA", sep = "\t",quote = F,
row.names = F,col.names = F)
int <- seq(from=0,to=1485,by=30)
InjectionRatesex <- Injec_up1
InjectionRatesex[seq(from=2,to=400,by=8),5] <- A_1*exp(-Gam1*int)
InjectionRatesex[seq(from=3,to=400,by=8),5] <- A_2*exp(-Gam2*int)
InjectionRatesex[seq(from=4,to=400,by=8),5] <- A_3*exp(-Gam3*int)
InjectionRatesex[seq(from=5,to=400,by=8),5] <- A_4*exp(-Gam4*int)
write.table(InjectionRatesex, 'InjectionRates.inc',quote = F,
row.names = F,col.names = F, na = '')
a1 <- A_1*exp(-Gam1*int)
a2 <- A_2*exp(-Gam2*int)
a3 <- A_3*exp(-Gam3*int)
a4 <- A_4*exp(-Gam4*int)
AA <- a1+a2+a3+a4
shell(run1)
return(aa(AA,newwd))

}

## 6.5 Net Present Value Calculation - Processing the Eclipse Output Data (R Code)

setwd("C:/Users/243886/OneDrive - Universitetet i Stavanger/ML-5spot-INJ-SGS
/R1/En1")
ens <- "ENSEMBLE.RSM"
NPV <- read.delim(ens,  header=FALSE, comment.char="#")
NPVcalc <- NPV[, c(2,5,6)]
colnames(NPVcalc) <- c('Days', 'Oilrate', 'waterrate')
NPVcalc <- na.omit(NPVcalc)
NPVcalc <- NPVcalc[-seq(9,400,by = 2), ]
rownames(NPVcalc) <- 1:nrow(NPVcalc)
days <- as.numeric(levels(NPVcalc$Days))[as.integer(NPVcalc$Days)]
days <- na.omit(days)
l1 <- min(which(days==c(1), arr.ind = TRUE))
l2 <- min(which(days==c(1500), arr.ind = TRUE))
days <- days[c(l1:l2)]
oil <- as.numeric(levels(NPVcalc$Oilrate))[as.integer(NPVcalc$Oilrate)]
oil <- na.omit(oil)
oil <- oil[c(l1:l2)]
water <- as.numeric(levels(NPVcalc$waterrate))[as.integer(NPVcalc$waterrate)]
water <- na.omit(water)
water <- water[c(l1:l2)]
FWCT <- numeric(length = length(water))
FWCT <- water/(water+oil)
t <- seq(0,days[length(which(FWCT<0.85, arr.ind = TRUE))],by = 30)
t[1] <- 1
cashflow <- numeric(length(t)-1)
discashflow <- numeric(length(t)-1)
b <- 0.08
for (j in 1:(length(t)-1)) {
m1 <- t[j]
z1 <- which(days==c(m1), arr.ind = TRUE)
m2 <- t[j+1]
z2 <- which(days==c(m2), arr.ind = TRUE)
cashflow[j] <- (mean(oil[z1],oil[z2])*6.29*75-mean
(water[z1],water[z2])*6.29*19-A[j]*5*6.29)*30
discashflow[j] <- cashflow[j]/((1+b)^(t[j+1]/360))
}
sum(discashflow)

## 6.6 Alghorithem of VOI Calculation in HRDP Method (R Code)

fn_EVII <- function(x_mean,x_sd,z_mean,z_sd,rho,Cost) {
set.seed(1234)
N <- 1000         # Number of grid nodes
rho <- rho          # Correlation Coefficient
x_mean <- x_mean-Cost    # mean of prior
x_sd <- x_sd      # standard Deviation Prior
z_mean <- z_mean-Cost     # standard Deviation signal
z_sd <- z_sd       # standard Deviation signal
range <- quantile(rnorm(10^6,x_mean,x_sd),c(0.000001,0.99999))
xx <- seq(range[[1]],range[[2]],length.out = N+1)
ss <- seq(range[[1]],range[[2]],length.out = N+1)
X <- c(rep(0,N))
S <- c(rep(0,N))
for (i in 1:N) {
X[i] <- (xx[i]+xx[i+1])/2
}

for (i in 1:N) {
S[i] <- (ss[i]+ss[i+1])/2
}
# Prior Plot
z <- S
x <- X

f_x<- dnorm(x, x_mean,x_sd)
f_x_N <- f_x/sum(f_x)

# Signal Plot
f_z <- dnorm(z,z_mean,z_sd)
f_z_N <- f_z/sum(f_z)

# Liklihood Table
Lik <- matrix(0,nrow = N,ncol = N)          # Liklihood table, x in columns and z in rows

for (j in 1:N) {
mean <- z_mean + (rho*z_sd*(x[j]-x_mean)/x_sd)
sd <- ((1-rho^2)*x_sd^2)^0.5
z_di <- dnorm(z, mean,sd)
z_di_N <- z_di/sum(z_di)
Lik[,j] <- z_di_N
}

Prepos <- c(rep(0,N))                     # Preposterior Rows
Pos <- matrix(0,nrow = N,ncol = N)    # Posterior Table
for (j in 1:N) {
Prepos[j] <- sum(Lik[j,]*f_x_N)
for (i in 1:N) {
Pos[i,j] <- Lik[j,i]*f_x_N[i]/Prepos[j]
}
Pos[,j] <- Pos[,j]/sum(Pos[,j])
}

sum <- 0
for (j in 1:N) {
VOI <- Prepos[j]*max(sum(Pos[,j]*x),0)
sum <- sum + VOI
}
EVII <- sum-max(sum(x*f_x_N),0)
return(EVII)
}

## 6.7 Alghorithem of Sensitivity Analysis of VOI to Mean of Prior (R Code)

X <- data.frame(NPV =rnorm(100000,30,5))
Y <- data.frame(NPV = rnorm(100000,40,5))
Z <- data.frame(NPV = rnorm(100000,50,5))
E <- data.frame(NPV = rnorm(100000,60,5))
ee <- data.frame(NPV = rnorm(100000,70,5))

# Now, combine your two dataframes into one.
# First make a new column in each that will be
# a variable to identify where they came from later.
X$type <- 'Mean_PV_Production_Prior = 30' Y$type <- 'Mean_PV_Production_Prior = 40'
Z$type <- 'Mean_PV_Production_Prior = 50' E$type <- 'Mean_PV_Production_Prior = 60'
ee$type <- 'Mean_PV_Production_Prior = 70' # and combine into your new data frame vegLengths vegLengths <- rbind(X,Y,Z,E,ee) ggplot(vegLengths, aes(NPV, fill = type)) + geom_density(alpha = 0.2)  ## 6.8 Alghorithem of Sensitivity Analysis of VOI to Standard Deviation of Prior (R Code) X <- data.frame(NPV =rnorm(100000,50,2.5)) Y <- data.frame(NPV = rnorm(100000,50,5)) Z <- data.frame(NPV = rnorm(100000,50,10)) E <- data.frame(NPV = rnorm(100000,50,15)) # Now, combine your two dataframes into one. # First make a new column in each that will be # a variable to identify where they came from later. X$type <- 'SD_PV_Production_Prior = 2.5'
Y$type <- 'SD_PV_Production_Prior = 5' Z$type <- 'SD_PV_Production_Prior = 10'
E$type <- 'SD_PV_Production_Prior = 15' # and combine into your new data frame vegLengths vegLengths <- rbind(X,Y,Z,E) ggplot(vegLengths, aes(NPV, fill = type)) + geom_density(alpha = 0.2)  ## 6.9 Optimization Alghorithem, Fittness Function: Machine Learning Model (R Code) modelxgb <- readRDS('NEWMODELUP.rds') speed_En1_Re <- read.csv('SPEED.csv',header=T) speed <- speed_En1_Re[,2:46] install.packages(c('GA','fastmaRching')) install.packages(c('parallel','doParallel')) library(doParallel) library(GA) library(fastmaRching) ML_fun_grid <- function(X1,Y1,X2,Y2,X3,Y3,X4,Y4,A1,A2,A3,A4, gam1,gam2,gam3,gam4,speed){ X1 <- round(X1) X2 <- round(X2) X3 <- round(X3) X4 <- round(X4) Y1 <- round(Y1) Y2 <- round(Y2) Y3 <- round(Y3) Y4 <- round(Y4) slope <- c(-0.0005,-0.00025,0,0.00025,0.00050,0.00075,0.00100,0.00125, 0.00150,0.00175,0.00200) Avalue <- c(100,150,200,250,300) A_1 <- Avalue[findInterval(A1,Avalue)] A_2 <- Avalue[findInterval(A2,Avalue)] A_3 <- Avalue[findInterval(A3,Avalue)] A_4 <- Avalue[findInterval(A4,Avalue)] Gam1 <- slope[findInterval(gam1,slope)] Gam2 <- slope[findInterval(gam2,slope)] Gam3 <- slope[findInterval(gam3,slope)] Gam4 <- slope[findInterval(gam4,slope)] con_fm <- c(rep(0,11)) grid <- speed seed <- c(X1,Y1,0,1) fm <- gridFastMarch(grid, seed, spatial.res=10) con_fm[1] <- fm$arrival.time[X2,Y2]^2/4/3600

seed <- c(X3,Y3,0,1)
fm <- gridFastMarch(grid, seed, spatial.res=10)
con_fm[2] <- fm$arrival.time[X1,Y1]^2/4/3600 con_fm[3] <- fm$arrival.time[X2,Y2]^2/4/3600

seed <- c(X4,Y4,0,1)
fm <- gridFastMarch(grid, seed, spatial.res=10)
con_fm[4] <- fm$arrival.time[X1,Y1]^2/4/3600 con_fm[5] <- fm$arrival.time[X2,Y2]^2/4/3600
con_fm[6] <- fm$arrival.time[X3,Y3]^2/4/3600 seed <- c(23,23,0,1) fm <- gridFastMarch(grid, seed, spatial.res=10) con_fm[7] <- fm$arrival.time[X1,Y1]^2/4/3600
con_fm[8] <- fm$arrival.time[X2,Y2]^2/4/3600 con_fm[9] <- fm$arrival.time[X3,Y3]^2/4/3600
con_fm[10] <- fm$arrival.time[X4,Y4]^2/4/3600 seed <- cbind(c(X1,Y1,0,1),c(X2,Y2,0,1),c(X3,Y3,0,1),c(X4,Y4,0,1)) fm <- gridFastMarch(grid, seed, spatial.res=10) fmm_N <- fm$arrival.time^2/4/3600
PV=(sum(sum(fmm_N<fmm_N[23, 23])))*1000/20250
con_fm[11] <- PV

NPV_Ml <- predict(modelxgb,data.frame(ConI1I2=con_fm[1],ConI3I1=con_fm[2],
ConI3I2=con_fm[3],ConI4I1=con_fm[4],
ConI4I2=con_fm[5],
ConI4I3=con_fm[6],ConPI1=con_fm[7],
ConPI2=con_fm[8], ConPI3=con_fm[9],ConPI4=con_fm[10],
PV_flight=con_fm[11],A1=A_1,A2
=A_2,A3=A_3,A4=A_4,gam1=Gam1,gam2=Gam2,gam3=Gam3,gam4=Gam4))
return(NPV_Ml)
}

ML_fun_En <- function(X1,Y1,X2,Y2,X3,Y3,X4,Y4,A1,A2,A3,A4,gam1,gam2,gam3,gam4) {
result <- c(rep(0,10))
for (i in 1:10) {
grid <- my.list[[i]]
result[i] <- ML_fun_grid(X1,Y1,X2,Y2,X3,Y3,X4,Y4,A1,A2,A3,A4,gam1,gam2,gam3
,gam4,speed=grid)
}
mean_result <- mean(result)
return(mean_result)
}

A <- ga(type = "real-valued",
fitness = function(x) + ML_fun_En(x[1],x[2],x[3],
x[4],x[5],x[6],x[7],x[8],x[9],                                                             x[10],x[11],x[12],x[13],x[14],x[15],
x[16]),lower = c(rep(1,8),rep(100,4),
rep(-0.0005,4)), upper = c(rep(45,8),rep(300,4),
rep(0.002,4)),popSize = 50, maxiter = 50,
run = 10,parallel = T)

## 6.10 Optimization Alghorithem, Fittness Function: Eclipse Reservoir Simulator (R Code)

setwd("C:/Users/243886/OneDrive - Universitetet i Stavanger/ML-5spot-INJ-SGS/Rcode")
library(readr)
X2D_4Inj_1Prod_R1 <- read_delim("2D_4Inj_1Prod_R.DATA",
"\t", escape_double = FALSE, na = "null",
trim_ws = TRUE)
run <- 'C:/ecl/macros/eclrun.exe eclipse "C:/Users/243886/OneDrive -
Universitetet i Stavanger/ROOPT_Ide/En#/Ensemble.DATA"'

Eclipse <- function(X1,Y1,X2,Y2,X3,Y3,X4,Y4,A1,A2,A3,A4,gam1,gam2,gam3,gam4,En){
wd <- 'C:/Users/243886/OneDrive - Universitetet i Stavanger/ROOPT_Ide/En#'
run1 <- gsub('#',En,run)
newwd <- gsub('#',En,wd)
setwd(newwd)
X1 <- round(X1)
X2 <- round(X2)
X3 <- round(X3)
X4 <- round(X4)
Y1 <- round(Y1)
Y2 <- round(Y2)
Y3 <- round(Y3)
Y4 <- round(Y4)
slope <- c(-0.0005,-0.00025,0,0.00025,0.00050,0.00075,0.00100,0.00125,
0.00150,0.00175,0.00200)
Avalue <- c(100,150,200,250,300)
A_1 <- Avalue[findInterval(A1,Avalue)]
A_2 <- Avalue[findInterval(A2,Avalue)]
A_3 <- Avalue[findInterval(A3,Avalue)]
A_4 <- Avalue[findInterval(A4,Avalue)]

Gam1 <- slope[findInterval(gam1,slope)]
Gam2 <- slope[findInterval(gam2,slope)]
Gam3 <- slope[findInterval(gam3,slope)]
Gam4 <- slope[findInterval(gam4,slope)]

data <- X2D_4Inj_1Prod_R1
g1 <- data[131,1]
g2 <- data[132,1]
g3 <- data[133,1]
g4 <- data[134,1]
g5 <- data[138,1]
g6 <- data[139,1]
g7 <- data[140,1]
g8 <- data[141,1]
G1 <- gsub('101',X1, g1)
G2 <- gsub('102',Y1, G1)
G3 <- gsub('103',X2, g2)
G4 <- gsub('104',Y2, G3)
G5 <- gsub('105',X3, g3)
G6 <- gsub('106',Y3, G5)
G7 <- gsub('107',X4, g4)
G8 <- gsub('108',Y4, G7)
G9 <- gsub('109',X1, g5)
G10 <- gsub('110',Y1, G9)
G11 <- gsub('111',X2, g6)
G12 <- gsub('112',Y2, G11)
G13 <- gsub('113',X3, g7)
G14 <- gsub('114',Y3, G13)
G15 <- gsub('115',X4, g8)
G16 <- gsub('116',Y4, G15)
data[131,1] <- G2
data[132,1] <- G4
data[133,1] <- G6
data[134,1] <- G8
data[138,1] <- G10
data[139,1] <- G12
data[140,1] <- G14
data[141,1] <- G16
#'C:/Users/243886/OneDrive - Universitetet i Stavanger/ROOPT/Ecl'
write.table(data, file ="Ensemble.DATA", sep = "\t",quote = F,
row.names = F,col.names = F)
int <- seq(from=0,to=1485,by=30)
InjectionRatesex <- Injec_up1
InjectionRatesex[seq(from=2,to=400,by=8),5] <- A_1*exp(-Gam1*int)
InjectionRatesex[seq(from=3,to=400,by=8),5] <- A_2*exp(-Gam2*int)
InjectionRatesex[seq(from=4,to=400,by=8),5] <- A_3*exp(-Gam3*int)
InjectionRatesex[seq(from=5,to=400,by=8),5] <- A_4*exp(-Gam4*int)
write.table(InjectionRatesex, 'InjectionRates.inc',quote = F,
row.names = F,col.names = F, na = '')
a1 <- A_1*exp(-Gam1*int)
a2 <- A_2*exp(-Gam2*int)
a3 <- A_3*exp(-Gam3*int)
a4 <- A_4*exp(-Gam4*int)
AA <- a1+a2+a3+a4
shell(run1)
return(aa(AA,newwd))

}

aa <- function(AA,newwd){
setwd(newwd)
ens <- "ENSEMBLE.RSM"
NPV <- read.delim(ens,  header=FALSE, comment.char="#")
NPVcalc <- NPV[, c(2,5,6)]
colnames(NPVcalc) <- c('Days', 'Oilrate', 'waterrate')
NPVcalc <- na.omit(NPVcalc)
NPVcalc <- NPVcalc[-seq(9,400,by = 2), ]
rownames(NPVcalc) <- 1:nrow(NPVcalc)
days <- as.numeric(levels(NPVcalc$Days))[as.integer(NPVcalc$Days)]
days <- na.omit(days)
l1 <- min(which(days==c(1), arr.ind = TRUE))
l2 <- min(which(days==c(1500), arr.ind = TRUE))
days <- days[c(l1:l2)]
oil <- as.numeric(levels(NPVcalc$Oilrate))[as.integer(NPVcalc$Oilrate)]
oil <- na.omit(oil)
oil <- oil[c(l1:l2)]
water <- as.numeric(levels(NPVcalc$waterrate))[as.integer(NPVcalc$waterrate)]
water <- na.omit(water)
water <- water[c(l1:l2)]
FWCT <- numeric(length = length(water))
FWCT <- water/(water+oil)
t <- seq(0,days[length(which(FWCT<0.85, arr.ind = TRUE))],by = 30)
t[1] <- 1
cashflow <- numeric(length(t)-1)
discashflow <- numeric(length(t)-1)
b <- 0.08
for (j in 1:(length(t)-1)) {
m1 <- t[j]
z1 <- which(days==c(m1), arr.ind = TRUE)
m2 <- t[j+1]
z2 <- which(days==c(m2), arr.ind = TRUE)
cashflow[j] <- (mean(oil[z1],oil[z2])*6.29*75-
mean(water[z1],water[z2])*
6.29*19-AA[j]*5*6.29)*30
discashflow[j] <- cashflow[j]/((1+b)^(t[j+1]/360))
}
return(sum(discashflow))}

Eclipse1 <- function(X1,Y1,X2,Y2,X3,Y3,X4,Y4,A1,A2,A3,A4,
gam1,gam2,gam3,gam4) {
a <- foreach(En=1:50, .export=c("Eclipse")) %dopar% {
Eclipse(X1,Y1,X2,Y2,X3,Y3,X4,Y4,A1,A2,A3,A4,gam1,gam2,
gam3,gam4,En)
}
return(mean(unlist(a)))
}

GA_Eclipse <- ga(type = "real-valued",
fitness = function(x) Eclipse1(x[1],x[2],x[3],
x[4],x[5],x[6],x[7],x[8],x[9]
,x[10],x[11],x[12],x[13],x[14],x[15],x[16])
,lower = c(rep(1,8),rep(100,4),rep(-0.0005,4)),
upper = c(rep(45,8),rep(300,4),rep(0.002,4)),
popSize = 25, maxiter = 20,run = 10,parallel = T,
suggestions = suggestedSol)

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