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MHE_PI_reduced.py
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MHE_PI_reduced.py
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# -*- coding: utf-8 -*-
"""
Created on Fri Apr 6 13:20:42 2018
@author: Brandon
"""
#from __future__ import division # compatibility with python 2.7
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import time
#%%
#Timespace for MPC and MHE###########################
tf =1.0 # sec, length of simulation
npt = 11 # number of time discretizations
nit = 1 # number of itterations to solve
ti = np.linspace(0,tf,npt) # times for plotting
#Simulation Timespace############################### (Added)
npt_sim = 21
tf_sim =1.0
# Define time space for MPC
tf_mpc = 1.0
npt_mpc = npt*tf_mpc
# Define Rod Discretizations
TVD_d = 4800 # ft, lenth of rod
npx =10 # number of rod discretizations
npx_m = 5
dx = TVD_d/(npx-1) # #ft lenth of rod discretizations
dx_m = TVD_d/(npx_m-1)
xi = np.linspace(0,TVD_d,npx) # possitions allong rod (for plotting)
xi_m= np.linspace(0,TVD_d,npx_m)
#Set Points
SPM_in = np.ones(npt)*10
#BuildModel####################################################################
mpc = GEKKO()
sim = GEKKO()
mhe = GEKKO()
#Horizon Window
mhe.time = np.linspace(0,tf,npt)
time_mpc = np.linspace(0,tf,npt)
time_mpc = np.append(time_mpc, [1.1,1.4,2,2.5,3,3.5,4,4.5,5,5.5,6.5,7])
mpc.time = time_mpc#np.linspace(0,tf_mpc,npt_mpc)
sim.time = np.linspace(0,tf_sim,npt_sim)
################################
# Conventional Rod Pump Unit Geometry
# API geometry dimension values
Ag=210.0
Cg=120.3
Ig=120.0
Pg=148.5
Hg=237.88
Gg=86.88
Rg=47.0
#lengths from FIG. 1 - Beam Pumping Unit Shown as a Four-Bar Linkage
L_1 = Rg
L_2 = np.sqrt((Hg-Gg)**2.0+Ig**2.0)
L_3 = Cg
L_4 = Pg
L_5 = Ag
starting_height = 3/4
#Setpoints
level_height = 3
SP = starting_height*TVD_d-level_height
dSP = 0.1
#Simulation########################################
for m in [sim,mpc,mhe]:
#Constants
m.API = m.Const(value = 45) #API gravity of fluid, unitless
m.c = m.Const(value = 0.000013) #Compressibility, psi^-1
m.k = m.Const(value = 15) #Permeability, md
m.Bo = m.Const(value = 1.2) #FVF, rb/STB
m.A_d = m.FV(value = 2, ub = 8, lb = 1) #Drainage Area, Acres
m.sw = m.Const(value = 0.2) #Water Saturation
m.porosity = m.FV(value = 0.08, ub = .12, lb = 0.07) #Porosity, unitless
m.gamma_E = m.Const(value = 1.78) #Euler Constant
m.C_a = m.Const(value = 31.6) #Drainage Area Shape Factor (Circular)
m.rw = m.Const(value = 0.328) #Welbore radius, ft
m.S = m.FV(value = 0, ub = 10, lb = -5) #unitless
m.u_visc = m.Const(value = 1.5) # Viscosity, cp
m.h_pz = m.Const(value = 8) #pay zone thickness, ft
m.D_t = m.Const(value = 2.5) # tubing diameter, in
m.St_length = m.Const(value = 85) # rod pump stroke length, in
m.g = m.Const(value = 32.2) # acceleration due to gravity, ft/s^3
m.g_conv= m.Const(value = 32.2) # lbf conversion , lb-ft/s^2-lbf
m.rho_r = m.Const(value = 490) # lbs/ft^3, density of rod steel
m.rho_w = m.Const(value = 62.3 ) # lbs/ft^3, density of water at standard conditions
m.a = m.Const(value =18996.06 ) # ft/s speed of sound in steel
m.D_r = m.Const(value = 1.0) # in, diameter of rod string
m.Ac = m.Const(value= m.D_r.value**2/4.0*np.pi) # in^2, cross sectional area of rod
m.nu = m.Const(value = 0.01) # unitless, damping coefficient
m.pi = m.Const(value=np.pi)
m.E = m.Const(value = 32025000.0) # psi sucker rod modulus of elasticity
m.alpha = m.Const(value = 0.0) # pump parameter, unitless
m.beta = m.Const(value = 1.0) # pump parameter, unitless
m.L_1 = m.Const(value =L_1) # unit geometry
m.L_2 = m.Const(value =L_2) # unit geometry
m.L_3 = m.Const(value =L_3) # unit geometry
m.L_4 = m.Const(value =L_4) # unit geometry
m.L_5 = m.Const(value =L_5) # unit geometry
if m == sim:
m.dx = m.Const(value = dx) # ft delta x
else:
m.dx = m.Const(value = dx_m)
#Prime Mover Constants (Torque Balance)
m.tau_p = m.Const(value = 3) #tau
m.k_gain = m.Const(value = 1) #one to one ratio between torque and SPM
##Economic
m.Weight_lb_ft = m.Const(value = m.rho_r.value*m.Ac.value*m.g.value/m.g_conv/144) #Weight of rod string, lbf/ft
m.Capex = m.Const(value = 200000) #Cost of Pumping Rod Unit,$?
m.P_o = m.Const(value = 50) #Price of Oil, $/STB
m.r = m.Const(value= .12/365) #Daily Discount Rate, %
m.P_th = m.Const(value = 100) #tubing head pressure, psi
m.TVD = m.Const(value = 4800) #true vertical depth, ft
m.E_cost = m.Const(value = 0.13/3600) #Cost of Electricity, cents/Kws
#Calculated Constants #DO NOT MODIFY#
m.Wr = m.Const(value = m.TVD.value*m.Weight_lb_ft.value) #Weight of entire rod string, lbm
m.D_a = m.Const(value = 2*12*m.rw.value) #Annulus Diameter, in
m.gamma = m.Const(141.5/(m.API.value+131.5)) #Specific gravity of Fluid
m.P_startpump = m.Const(value = 0.433*m.gamma.value*m.TVD.value) #Average Reservoir Pressure at Pump start up
m.Pi = m.Const(value = .433*m.TVD.value) #Initial Reservoir Pressure, psi
m.A_t = m.Const((np.pi/4)*m.D_t.value**2) #Cross sectional Area of tubing, in^2
m.A_a = m.Const((np.pi/4)*m.D_a.value**2) #Cross Sectional Area of Annulus, in^2
m.Wf = m.Const(value = m.TVD.value*m.rho_w.value*m.gamma.value*m.g.value/m.g_conv.value*(m.A_t.value-m.Ac.value)/144) # lbf, weight of fluid in tubing
#MV's
m.SPM_in = m.MV(value = 15, lb = 5, ub = 15) #Rod Pump Pumping Speed/Torque, spm
#Variables
m.V_i= m.Var(value = 7758*m.A_d.value*m.h_pz.value*m.porosity.value*(1-m.sw.value)/m.Bo.value) #OOIP, stb
m.Vp = m.Var(value = m.V_i.value*(np.exp(m.c.value*(m.Pi.value-m.P_startpump.value))-1)) #initial volume produced prior stb
if m == sim or m == mpc:
m.h = m.CV(value = 1.0*m.TVD.value*starting_height)
else:
m.h_mv = m.MV(value = 1.0*m.TVD.value*starting_height, lb = 0, ub = 4800)
m.h = m.Var(value = 1.0*m.TVD.value*starting_height, lb = 0, ub = 4800) # Height, ft
m.Equation(m.h_mv == m.h)
m.NPV = m.Var(value = -1.0*m.Capex.value) #Net Present Value, $
m.y = m.Var( lb = -1, ub = 1) # SIGN(x)
m.sa = m.Var(value = 0, lb = 0) # slack variable a
m.sb = m.Var(value = 0, lb = 0) # slack variable b
m.tsi = m.Var(value = 0.0) # mulation time
m.SPM = m.Var(value = 15) #SPM, strokes/min
#omega = m.Var(value = 0)
m.theta = m.Var(value = 0) # rad i.e sec^-1 crank angle of surface unit
if m == sim:
m.u = [m.SV(value = 9.22) for i in range(npx)] # relative position of each rod segment
m.v = [m.Var(value = 0.0) for i in range(npx)] # velocity of reach rod segment
m.f = [m.SV(value = 0.0) for i in range (npx)] # load at each rod segment
else:
m.u = [m.SV(value = 9.22) for i in range(npx_m)] # relative position of each rod segment
m.v = [m.Var(value = 0.0) for i in range(npx_m)] # velocity of reach rod segment
m.f = [m.SV(value = 0.0) for i in range (npx_m)] # load at each rod segment
m.P = m.Var(value = 1e-6) # unitless, load at the pump
## State Variables
m.P_res = m.Var(value = m.P_startpump.value*1.0) #Current Reservoir Pressure , psi
m.P_wf = m.Var(value = 0.433*m.gamma*m.h.value) #Bottomhole Flowing Pressure, psi
m.q_in = m.Var(value = (1/86400)*m.k.value*m.h_pz.value*(m.P_res.value-m.P_wf.value)/(141.2*m.Bo.value*m.u_visc.value*((1/2)*np.log(4*m.A_d.value/(m.gamma_E.value*m.C_a.value*m.rw.value**2)) + m.S.value))) #IPR-VLP Flow rate, STB/s
m.q_out = m.Var(value = 0) # Outgoing Flow Rate, STB/s
m.t = m.Var(value = 0) #Time, days
m.W_rod = m.Var(value = (1.0962)*m.q_out.value*(m.P_th.value-m.P_wf.value + .433*m.gamma.value*m.TVD.value) + (4.7053e-7)*m.Wr.value*m.St_length.value*m.SPM.value) #Work supplied by electric Motor, KW
#Intermediates
m.hs = m.Intermediate(m.sqrt(L_1**2 +L_2**2 + 2 *L_1 *L_2 *m.cos(m.theta)))
#Equations
##AlgebraicEqns
m.Equation(m.V_i == 7758*m.A_d*m.h_pz*m.porosity*(1-m.sw)/m.Bo)
m.Equation(m.P_wf == 0.433*m.gamma*m.h)
m.Equation(m.P_res == m.Pi-(1/m.c)*m.log((m.Vp/m.V_i)+1))
m.Equation(m.q_in == (1/86400)*m.k*m.h_pz*(m.P_res-m.P_wf)/(141.2*m.Bo*m.u_visc*((1/2)*m.log(4*m.A_d/(m.gamma_E*m.C_a*m.rw**2)) + m.S))) #STB/s
m.Equation(m.W_rod == (1.0962)*m.q_out*(m.P_th-m.P_wf + .433*m.gamma*m.TVD) + (4.7053e-7)*m.Wr*m.St_length*m.SPM)
#Prime Mover Equations- Torque Balance and Kinematic Eqns
m.Equation(m.SPM.dt() == -(1/m.tau_p)*m.SPM + (m.k_gain/m.tau_p)*m.SPM_in)
m.Equation((2*m.pi/60)*m.SPM == m.theta.dt())
m.Equation(m.u[0] == (1/12)*L_5*(m.asin(L_1*m.sin(m.theta)/m.hs)+m.acos((m.hs**2+L_3**2-L_4**2)/(2*L_3*m.hs)))) # position of polished rod, inches
if m == sim:
[m.Equation(m.v[i+1].dt()== m.a**2 * (m.u[i+2] - 2.0*m.u[i+1] + m.u[i])/m.dx**2 - m.pi*m.a*m.nu/(2.0*m.TVD)*m.v[i+1] - (1-m.rho_w*m.gamma/m.rho_r)*m.g) for i in range(npx-2) ]# wave equation
else:
[m.Equation(m.v[i+1].dt()== m.a**2 * (m.u[i+2] - 2.0*m.u[i+1] + m.u[i])/m.dx**2 - m.pi*m.a*m.nu/(2.0*m.TVD)*m.v[i+1] - (1-m.rho_w*m.gamma/m.rho_r)*m.g) for i in range(npx_m-2) ]# wave equation
m.Equation(m.q_out == m.A_t * m.u[-1].dt()*12/231/42 * (1+m.y)/2) # rate of fluid production, barrels/
# Equations for calculating rod loading
# Load at surface
m.Equation(m.f[0] == m.E*m.Ac*1/2/m.dx *(-m.u[2] + 4*m.u[1] -3*m.u[0]))
# Load at pump
if m == sim:
m.Equation(m.f[npx-1] == m.E*m.Ac* m.P)
# load at intermediate points
[m.Equation(m.f[1+i] == m.E*m.Ac*1/2.0/dx*(m.u[i+2] - m.u[i])) for i in range(npx-2)]
# pump boundary
m.Equation( m.u[npx-1]*m.alpha + (m.u[npx-1] - m.u[npx-2])/dx == m.P)
#add in signum for lifting and lowering conditions
else:
m.Equation(m.f[npx_m-1] == m.E*m.Ac* m.P)
# load at intermediate points
[m.Equation(m.f[1+i] == m.E*m.Ac*1/2.0/dx*(m.u[i+2] - m.u[i])) for i in range(npx_m-2)]
# pump boundary
m.Equation( m.u[npx_m-1]*m.alpha + (m.u[npx_m-1] - m.u[npx_m-2])/dx == m.P)
#add in signum for lifting and lowering conditions
m.Equation(m.v[-1] == m.sb - m.sa )
m.Equation(m.P == -((m.Wf- (m.A_t - m.Ac)*m.P_wf)/m.E/m.Ac) * (1 + m.y)/2 ) # -P_wf*A_t
##DifferentialEans
m.Equation(m.t.dt() == 1)
m.Equation(m.Vp.dt() == m.q_in)
m.Equation(m.NPV.dt() == (m.P_o*m.q_out-m.E_cost*m.W_rod)*m.exp(-m.r*m.t))
m.Equation(m.h.dt() == (1617/2)*(m.q_in - m.q_out)/(m.A_a -m.A_t))
m.Equation(m.tsi.dt()==1.0) # create time variable
if m == sim:
[m.Equation(m.u[i].dt()==m.v[i]) for i in range(npx)] # velocity of rod string
else:
[m.Equation(m.u[i].dt()==m.v[i]) for i in range(npx_m)] # velocity of rod string
# Set Objectives ##################################################
if m == sim:
m.Obj((m.sa*(1+m.y) + m.sb*(1-m.y))) # objective function to make signum work.
elif m== mhe:
m.Obj((m.sa*(1+m.y) + m.sb*(1-m.y))) # objective function to make signum work.
m.Equation((m.sa*(1+m.y) + m.sb*(1-m.y))<=1e-4)
else:
m.Obj((m.sa*(1+m.y) + m.sb*(1-m.y))) # objective function to make signum work.
#m.Equation((m.sa*(1+m.y) + m.sb*(1-m.y))<=1e-3)
#SetGlobalOptions(Simulation)##############################################################
sim.options.IMODE = 5 # 4 = Dynamic Simulation (Seqential)
sim.options.NODES = 2 # 3 = 3 Nodes, 2 = No collocation nodes
sim.options.SOLVER = 3 # 1 =APOPT, 3 = IPOPT
sim.options.time_shift = npt_sim-1 # time shift forward for multiple simulations
sim.options.MAX_ITER = 450
#SetLocalOptions###############################################################
#N/A
sim.SPM_in.FSTATUS = 1 # accept measurments
sim.SPM_in.STATUS = 0 # don't let optimizer change (simulation)
#MHE###########################################################################
#Parameters (Holds Measured values from MHE)
fm = mhe.Param(value = sim.f[0].value)
#SetGlobalOptions(MHE)##########################################################
mhe.options.IMODE = 5 # 4 = Dynamic Simulation (Seqential)
mhe.options.NODES = 2 # 3 = 3 Nodes, 2 = No collocation nodes
mhe.options.SOLVER = 3 # 1 =APOPT, 3 = IPOPT
mhe.options.time_shift = npt-1 # time shift forward for multiple simulations
mhe.options.MAX_ITER = 1000
mhe.Obj((mhe.f[0] - fm)**2)
#SetLocalOptions (MHE)###############################################################
##FV #Variable to estimate
mhe.h_mv.FSTATUS = 0
mhe.h_mv.STATUS = 1
#mhe.h.DMAX = 0.5
mhe.h_mv.DMAX = 0.5#0.05
mhe.h_mv.DCOST = 0.01
#MV
mhe.SPM_in.FSTATUS = 1
mhe.SPM_in.STATUS = 0
#SetGlobalOptions(MPC)##########################################################
mpc.options.IMODE = 6 # 4 = Dynamic Simulation (Seqential)
mpc.options.NODES = 2 # 3 = 3 Nodes, 2 = No collocation nodes
mpc.options.SOLVER = 3 # 1 =APOPT, 3 = IPOPT
mpc.options.time_shift = npt-1 # time shift forward for multiple simulations
mpc.options.MAX_ITER = 450
mpc.options.CV_TYPE = 1
#SetLocalOptions###############################################################
##FV
mpc.SPM_in.STATUS = 1
mpc.SPM_in.FSTATUS = 0 # cound be meausured, but we are setting it
mpc.SPM_in.DMAX = .05 # maximum change in SPM per cycle
#mpc.SPM_in.DCOST = .01
# CV's
mpc.h.STATUS = 1 # control h
mpc.h.FSTATUS = 1 # accept measurements
mpc.h.TR_INIT = 2 # create trajectory to setpoint
mpc.h.TAU = .1 # time constant of trajectory to h set point
#Solve#########################################################################
#%%
# Solve the simulation in a loop to simulate a longer horizon
loops = 180 # number of steps forward in time
res = {}
solve_stat = np.zeros(loops)
t_cycle = 0.0
#PID Options ######################################################
e = np.zeros(loops)
ie = np.zeros(loops)
op = np.zeros(loops)
#SPM_output
op[0] = np.ones(1)*sim.SPM_in.value
ophi = 15
oplo = 5
pv = np.zeros(loops)
P = np.zeros(loops)
I = np.zeros(loops)
pv_ave = np.zeros(loops)
#Tuning
kc = 1
tauI = 1
#Initialize Storage Values
sim_ts = np.ones(npt_sim)*sim.tsi.value # simulation time storage
sim_hstor = np.ones(npt_sim)*sim.h.value # height of fluid in annulus storage
sim_q_ins= np.ones(npt_sim)*sim.q_in.value # reservoir influx storage
sim_q_outs = np.ones(npt_sim)*sim.q_out.value # production rate storage
sim_P_ress = np.ones(npt_sim)*sim.P_res.value # reservoir pressure storage
sim_Vps = np.ones(npt_sim)*sim.Vp.value # cumulative volume produced storage
sim_NPVs = np.ones(npt_sim)*sim.NPV.value # NPV storage
sim_W_rods = np.ones(npt_sim)*sim.W_rod.value # work of rod (work to lift fluid) storage
sim_SPMs = np.ones(npt_sim)*sim.SPM_in.value # Strokes per minute/ Torque storage Set Points
sim_SPMr = np.ones(npt_sim)*sim.SPM.value #SPM storage
sim_thetas = np.ones(npt_sim)*sim.theta.value#Theta storage
sim_P_wfs = np.ones(npt_sim)*sim.P_wf.value # bottom hole pressure storage
sim_ys = np.ones(npt_sim)*sim.y.value # sign of du/dt storage
#MHE Storage
mpc_ts = np.zeros(0) # simulation time storage
mhe_us = [np.array(mpc.u[i].value) for i in range(npx_m)] # u relative position storage
mhe_vs = [np.array(mpc.v[i].value) for i in range(npx_m)]
mhe_fs = [np.array(mpc.f[i].value) for i in range(npx_m)] # dynamic load storage
mpc_hstor = np.zeros(0)# height of fluid in annulus storage
mpc_q_ins= np.zeros(0) # reservoir influx storage
mpc_q_outs = np.zeros(0) # production rate storage
mpc_P_ress = np.zeros(0) # reservoir pressure storage
mpc_Vps = np.zeros(0) # cumulative volume produced storage
mpc_NPVs = np.zeros(0) # NPV storage
mpc_W_rods =np.zeros(0) # work of rod (work to lift fluid) storage
mpc_SPMs = np.zeros(0) # Strokes per minute/ Torque storage Set Points
mpc_SPMr = np.zeros(0) #SPM storage
mpc_thetas = np.zeros(0)#Theta storage
mpc_P_wfs = np.zeros(0) # bottom hole pressure storage
mpc_ys = np.zeros(0) # sign of du/dt storage
mpc_Skins = np.zeros(0) #Skin storage
mpc_porosity = np.zeros(0)
mpc_A_d = np.zeros(0)
mhe_Skins = np.zeros(0) #Skin storage
mhe_hstor = np.zeros(0)# height of fluid in annulus storage
mpc_Skins = np.zeros(0)
mpc_Skinss = np.zeros(0)
mpc_h = np.zeros(0)
mpc_hss = np.zeros(0)
###############################################################
for i in range(loops):
# simulate system for 1 second
sim.solve() # (remote = False) for local
if i == 0:
# Create and store results
sim_ts = np.array(sim.tsi.value) # simulation time storage
sim_us = [np.array(sim.u[i].value) for i in range(npx)] # u relative position storage
sim_vs = [np.array(sim.v[i].value) for i in range(npx)]
sim_fs = [np.array(sim.f[i].value) for i in range(npx)] # dynamic load storage
sim_hstor = np.array(sim.h.value) # height of fluid in annulus storage
sim_q_ins= np.array(sim.q_in.value) # reservoir influx storage
sim_q_outs = np.array(sim.q_out.value) # production rate storage
sim_P_ress = np.array(sim.P_res.value) # reservoir pressure storage
sim_Vps = np.array(sim.Vp.value) # cumulative volume produced storage
sim_NPVs = np.array(sim.NPV.value) # NPV storage
sim_W_rods = np.array(sim.W_rod.value) # work of rod (work to lift fluid) storage
sim_SPMs = np.array(sim.SPM_in.value) # Strokes per minute/ Torque storage Set Points
sim_SPMr = np.array(sim.SPM.value) #SPM storage
sim_thetas = np.array(sim.theta.value)#Theta storage
sim_P_wfs = np.array(sim.P_wf.value) # bottom hole pressure storage
sim_ys = np.array(sim.y.value) # sign of du/dt storage
elif i>0:
sim_ts = np.append(sim_ts,sim.tsi.value) # simulation time storage
sim_us = [np.append(sim_us[i],sim.u[i].value) for i in range(npx)] # u relative position storage
sim_vs = [np.append(sim_vs[i],sim.v[i].value) for i in range(npx)]
sim_fs = [np.append(sim_fs[i],sim.f[i].value) for i in range(npx)] # dynamic load storage
sim_hstor = np.append(sim_hstor,sim.h.value) # height of fluid in annulus storage
sim_q_ins= np.append(sim_q_ins,sim.q_in.value) # reservoir influx storage
sim_q_outs = np.append(sim_q_outs,sim.q_out.value) # production rate storage
sim_P_ress = np.append(sim_P_ress,sim.P_res.value) # reservoir pressure storage
sim_Vps = np.append(sim_Vps,sim.Vp.value) # cumulative volume produced storage
sim_NPVs = np.append(sim_NPVs,sim.NPV.value) # NPV storage
sim_W_rods = np.append(sim_W_rods,sim.W_rod.value) # work of rod (work to lift fluid) storage
sim_SPMs = np.append(sim_SPMs,sim.SPM_in.value) # Strokes per minute storage
sim_SPMr = np.append(sim_SPMr,sim.SPM.value) #Strokes per minute storage
sim_thetas = np.append(sim_thetas,sim.theta.value)
sim_P_wfs = np.append(sim_P_wfs,sim.P_wf.value) # bottom hole pressure storage
sim_ys = np.append(sim_ys,sim.y.value) # sign of du/dt storage
solve_stat[i] = t_cycle
##MHE##################################################################
#Insert Measurements to MHE
fm.value = np.array(sim.f[0].value)[0:npt_sim:2] #(Modified)
mhe.SPM_in.value = np.array(sim.SPM_in.value)[0:npt_sim:2] #(Modified)
#Solve
t_start = time.time()
mhe.solve() # (remote = False) for local solve
#Pass values to MPC
pv[i] = mhe.h_mv.NEWVAL
pv_ave[i] = np.average(pv[i-10:i])
#Store new values for plotting
mhe_hstor = np.append(mhe_hstor,mhe.h.value)
# ##PID #####################################################################
# if i<10:
e[i] = pv[i] - SP
# if i>10:
# e[i] = pv_ave[i] - SP
#
# if i >= 1:
ie[i] = ie[i-1] + e[i]*tf
P[i] = kc * e[i]
I[i] = kc/tauI * ie[i]
op[i] = op[0] + P[i] + I[i]
#Anti-reset Wind up
if op[i] > 15:
op[i] = ophi
ie[i] = ie[i] - e[i]*tf
if op[i] < 5:
op[i] = oplo
ie[i] = ie[i] - e[i]*tf
#Pass output to simulation
t_end = time.time()
t_cycle = t_end - t_start
sim.SPM_in.value = np.ones(npt_sim)*op[i]
#######################################################################
# Plotting
plt.clf()
ax=plt.subplot(311)
ax.grid()
plt.plot(sim_ts[0:i*npt_sim],sim_SPMs[0:i*npt_sim],'ro',label='SPM Set Point')
plt.plot(sim_ts[0:i*npt_sim],sim_SPMr[0:i*npt_sim],'bo',label='SPM')
plt.ylabel('Strokes per Minute')
plt.legend(loc=2)
ax=plt.subplot(312)
ax.grid()
plt.plot(sim_ts[0:i*npt_sim],sim_hstor[0:i*npt_sim],'k-',label= 'Height')
plt.plot(sim_ts[0:i*npt_sim], np.ones(i*npt_sim)*SP, label = 'height SP')
#plt.plot(ts[0:i*npt], mpc_hs[0:npt*i], label = 'mpc height')
plt.ylabel('Annular Fluid Height (ft)')
plt.legend(loc='best')
ax = plt.subplot(313)
ax.grid()
plt.plot(sim_ts[0:i*npt_sim], sim_q_outs[0:i*npt_sim], label = 'q_out')
plt.plot(sim_ts[0:i*npt_sim], sim_q_ins[0:i*npt_sim], label = 'q_in')
plt.legend()
plt.ylabel('Flow Rate, STB/s')
plt.xlabel('Time (sec)')
plt.draw()
plt.pause(0.02)
#%%
res['solve_stat'] = solve_stat
res['ts' ] = sim_ts
res['us' ] = sim_us
res['vs' ] = sim_vs
res['fs'] = sim_fs
res['hstor' ] = sim_hstor
res[ 'q_ins' ] = sim_q_ins
res[ 'q_outs' ] = sim_q_outs
res['P_ress' ] = sim_P_ress
res['Vps' ] = sim_Vps
res[ 'NPVs' ] = sim_NPVs
res['W_rods' ] = sim_W_rods
res['SPMs'] = sim_SPMs
res['SPMr'] = sim_SPMr
res['thetas'] = sim_thetas
res['P_wfs'] = sim_P_wfs
res[ 'ys'] = sim_ys
res['h_SP'] = np.ones(loops*npt)*SP
#%%
np.save('PI_MHE_Control_Results_10npt_5npt.npy', res)
#%%
# Load dictionary of results
res = np.load('PI_MHE_Control_Results_10npt_5npt.npy').item()
#%% Plotting from dictionary
plt.figure()
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
ax=plt.subplot(311)
ax.grid()
plt.plot(res['ts'], res['SPMs'], 'r--', label=r'$T_{net}$ (ft-lb)')#, s = 4, c='b' ) # 'ro', for latex
plt.plot(res['ts'], res['SPMr'],'b-', label=r'Actual')#, s = 4, c = 'r') #'bo',
plt.ylabel('SPM', fontsize = 12)
plt.legend(loc= 1,fontsize = 12)
plt.xlim(0,180)
ax=plt.subplot(312)
ax.grid()
plt.plot(res['ts'], res['hstor'],'k-',label= 'Actual')
plt.plot(res['ts'], np.ones(np.size(res['ts']))*(sim.TVD.value*3/4 -3), label = 'SP') # fix
#plt.plot(ts[0:i*npt], mpc_hs[0:npt*i], label = 'mpc height')
plt.ylabel('Fluid Level (ft)', fontsize = 12)
plt.legend(loc=1,fontsize = 12)
plt.xlim(0,180)
ax = plt.subplot(313)
ax.grid()
plt.plot(res['ts'], res['q_outs'], label = r'$q_{out}$')
plt.plot(res['ts'], res['q_ins'], label = r'$q_{in}$')
plt.legend(loc = 1,fontsize = 12)
plt.ylabel('Flow (STB/s)', fontsize = 12)
plt.xlabel('Time (seconds)', fontsize = 12)
plt.xlim(0,180)
plt.draw()
#plt.legend(fontsize = 12)
#plt.ylabel('Fluid Level (ft)', fontsize = 12)
#plt.xlabel('Time (seconds)', fontsize = 12)
plt.tight_layout()
plt.savefig('PI_MHE_Control_K_10_Tau_5.eps', transparent = True, dpi = 1200)
plt.show()
#%%
# timing figure
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
plt.figure()
plt.plot(np.linspace(1,180,179), res['solve_stat'][1:],'r-',label='Solve Time')
plt.plot(np.linspace(1,loops,loops-1), np.ones(loops-1)*np.average(res['solve_stat'][1:]),'b--', label = 'Average')
plt.plot(np.linspace(1,loops,loops-1), np.ones(loops-1),'k:', label = 'Real Time')
plt.xlabel('Control Cycle', fontsize = 12)
plt.ylabel('Computation Time (seconds)', fontsize = 12)
plt.legend(fontsize = 12)
plt.ylim(0,4)
plt.xlim(0,180)
plt.savefig('PI_MHE_Simulation_Timing.eps', dpi = 1200, transparent = True)
plt.savefig('PI_MHE_Simulation_Timing.png', dpi = 200, transparent = True)
plt.show()
print('Average Solve Time '+str(np.average(res['solve_stat'][1:]))+'(s)')
#%%
## Figure 1 ## Height in the Annulus and incoming and outgoing flow rate####
plt.figure(1, figsize = (6,4.5))
plt.subplot(211)
plt.plot(sim_ts, sim_hstor, 'r--', label = 'height in annulus')
plt.plot(sim_ts, np.ones(len(sim_ts))*SP, 'b--', label = 'height Set Point')
plt.ylabel('height, ft')
plt.legend()
plt.subplot(212)
plt.plot(sim_ts, sim_q_ins, 'b--', label = r'$q_{in}$')
plt.plot(sim_ts, sim_q_outs, 'g--', label = r'$q_{out}$')
plt.ylabel('Flow Rate, STB/s')
plt.xlabel('time, sec')
plt.legend()
plt.show()
##Figure 2: Reservoir Pressure Decline and Cumulative Volume Produced####
plt.figure(2, figsize = (6,4.5))
plt.subplot(211)
plt.plot(sim_ts, sim_P_ress, 'k--', label = 'Reservoir Pressure')
#plt.plot(m.time, P_wf.value, 'r--', label = r'$P_{wf}$')
plt.ylabel('Pressure, psi')
plt.legend()
plt.subplot(212)
plt.plot(sim_ts, sim_Vps, '--', label = 'Cumulative Volume Produced')
plt.ylabel('Volume, STB')
plt.xlabel('time, sec')
plt.legend()
plt.tight_layout()
plt.show()
##Figure 3: NPV #########################################
plt.figure(3, figsize = (6,4.5))
plt.plot(sim_ts, sim_NPVs/(1e6), 'g:', label = 'NPV')
plt.xlabel('time, sec')
plt.ylabel('NPV, $ Millions')
plt.legend()
plt.show()
########################################################
#Figure 4# Work of Motor And
plt.figure(4, figsize = (6,4.5))
plt.subplot(311)
plt.plot(sim_ts,sim_W_rods, 'b-', label = 'Work Supplied by Motor' )
plt.ylabel('KiloWatts, KW')
plt.subplot(312)
plt.plot(sim_ts, sim_SPMs, 'r-', label = 'Input' )
plt.ylabel('SPM')
plt.subplot(313)
plt.plot(sim_ts, sim_P_wfs, 'r--', label = r'$P_{wf}$')
plt.ylabel('FBHP, psi')
plt.xlabel('time, sec')
#plt.tight_layout()
plt.show()
##Figure 5 -Doublet Test
plt.figure(5, figsize = (6,4.5))
plt.subplot(211)
plt.plot(sim_ts, sim_hstor, 'r--', label = 'height in annulus')
plt.ylabel('height, ft')
plt.legend()
plt.subplot(212)
plt.plot(sim_ts, sim_SPMs, 'b--', label = r'SPM')
plt.ylabel('strokes/min')
plt.xlabel('time, sec')
plt.legend()
plt.show()