In [144]:

    

import numpy as np
import pandas as pd
import math
import cmath
from scipy.optimize import root
from scipy.integrate import odeint
from __future__ import division
from scipy import *
from pylab import *
import matplotlib.pyplot as plt
%matplotlib inline


    

In [145]:

    

xo = 0.5
xk = 0.3
gamma = 0.8
A = 2
yr = 0.1 #kg kgCO2 −1

tao = np.linspace(0,5)
print(tao)
print(np.shape(tao), type(tao))


    

    




[0.         0.10204082 0.20408163 0.30612245 0.40816327 0.51020408
 0.6122449  0.71428571 0.81632653 0.91836735 1.02040816 1.12244898
 1.2244898  1.32653061 1.42857143 1.53061224 1.63265306 1.73469388
 1.83673469 1.93877551 2.04081633 2.14285714 2.24489796 2.34693878
 2.44897959 2.55102041 2.65306122 2.75510204 2.85714286 2.95918367
 3.06122449 3.16326531 3.26530612 3.36734694 3.46938776 3.57142857
 3.67346939 3.7755102  3.87755102 3.97959184 4.08163265 4.18367347
 4.28571429 4.3877551  4.48979592 4.59183673 4.69387755 4.79591837
 4.89795918 5.        ]
(50,) <class 'numpy.ndarray'>

In [146]:

    

tao1 = (xo - xk) / (gamma * A * yr) 
tao1


    

    
Out[146]:





1.2499999999999998

In [147]:

    

tao2 = tao1 + xk / (gamma * A * yr) * np.log(xk / xo + (1 - xk / xo) * np.exp(xo / xk * A))
tao2


    

    
Out[147]:





5.879695601713209

In [148]:

    

def concentracion(tao):
    
    if tao == 1:
        x = x0 - gamma * A * yr * tao * exp(-A*z)
        return x
    if tao == 2:
        x = x0 - (xo - xk) * exp(-A * (z - zk))
        return x
    if tao == 3:
        x = x0 / (1 + ((xo/xk) * exp(gamma * A * yr / xk * (tao - tao1)) - 1) * exp(-xo/xk * A*z))
        return x


    

In [149]:

    

zk = xk / (A * xo) * np.log((xo * np.exp(gamma * A * yr / xk * (tao - tao1)) - xk) / (xo - xk))
zk


    

    




C:\Users\Agnès\Anaconda3\lib\site-packages\ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in log
  """Entry point for launching an IPython kernel.






    
Out[149]:





array([        nan,         nan,         nan, -1.34814669, -0.70396795,
       -0.50630908, -0.38276556, -0.29130864, -0.21784477, -0.15589928,
       -0.10195478, -0.05388602, -0.01031013,  0.02972326,  0.06689549,
        0.10171164,  0.13455655,  0.16573011,  0.1954706 ,  0.2239704 ,
        0.25138712,  0.27785142,  0.30347285,  0.32834414,  0.35254444,
        0.37614186,  0.39919539,  0.42175649,  0.44387025,  0.46557642,
        0.48691022,  0.50790296,  0.52858263,  0.54897428,  0.56910048,
        0.5889816 ,  0.60863604,  0.62808054,  0.6473303 ,  0.66639922,
        0.68529996,  0.70404416,  0.72264248,  0.74110472,  0.75943992,
        0.7776564 ,  0.79576186,  0.81376343,  0.8316677 ,  0.8494808 ])

In [150]:

    

tao2 = tao1 + xk / (gamma * A * yr) * np.log(xk / xo + (1 - xk / xo) * np.exp(xo / xk * A))
tao2


    

    
Out[150]:





5.879695601713209

In [151]:

    

e = gamma * yr* tao * (1- np.exp(-A))
np.shape(e)
type(e)


    

    
Out[151]:





numpy.ndarray

In [152]:

    

plt.plot(tao, e)


    

    
Out[152]:





[<matplotlib.lines.Line2D at 0x12d86682400>]






    

In [153]:

    

e = gamma * yr* (tao - tao1 * np.exp(-A * (1 - zk)))


    

In [154]:

    

e = xo - xk / A * np.log(1 + xk / xo * (np.exp(xo / xk * A) - 1)) * np.exp(gamma * A * yr / xk * (tao1 - tao))


    

In [155]:

    

def rendimiento(tao):
    if tao <= tao1 and tao < tao2:
        e = gamma * yr* tao * (1- np.exp(- A))
        print("tao < tao1 and tao < tao2")
        return e
    if tao > tao1 and tao <= tao2:
        zk = xk / (A * xo) * np.log((xo * np.exp(gamma * A * yr / xk * (tao - tao1)) - xk) / (xo - xk))
        e = gamma * yr * (tao - tao1 * np.exp(- A * (1 - zk)))
        print("tao >= tao1 and tao < tao2")
        return e
    if tao > tao2:
        e = xo - xk / A * np.log(1 + xk / xo * (np.exp(xo / xk * A) - 1) * np.exp(gamma * A * yr / xk * (tao1 - tao)))
        print("tao >= tao2")
        return e


    

In [156]:

    

tao = 9
print("tao1 = {} tao2 = {}".format(tao1, tao2))
rendimiento(tao)


    

    




tao1 = 1.2499999999999998 tao2 = 5.879695601713209
tao >= tao2






    
Out[156]:





0.4653356509957497

In [157]:

    

ttao = [i for i in range(5)]
ttao


    

    
Out[157]:





[0, 1, 2, 3, 4]

In [158]:

    

ttao = [i for i in np.linspace(0,5)]
ttao


    

    
Out[158]:





[0.0,
 0.10204081632653061,
 0.20408163265306123,
 0.30612244897959184,
 0.40816326530612246,
 0.5102040816326531,
 0.6122448979591837,
 0.7142857142857143,
 0.8163265306122449,
 0.9183673469387755,
 1.0204081632653061,
 1.1224489795918369,
 1.2244897959183674,
 1.3265306122448979,
 1.4285714285714286,
 1.5306122448979593,
 1.6326530612244898,
 1.7346938775510203,
 1.836734693877551,
 1.9387755102040818,
 2.0408163265306123,
 2.142857142857143,
 2.2448979591836737,
 2.3469387755102042,
 2.4489795918367347,
 2.5510204081632653,
 2.6530612244897958,
 2.7551020408163267,
 2.857142857142857,
 2.9591836734693877,
 3.0612244897959187,
 3.163265306122449,
 3.2653061224489797,
 3.36734693877551,
 3.4693877551020407,
 3.5714285714285716,
 3.673469387755102,
 3.7755102040816326,
 3.8775510204081636,
 3.979591836734694,
 4.081632653061225,
 4.183673469387755,
 4.285714285714286,
 4.387755102040816,
 4.4897959183673475,
 4.591836734693878,
 4.6938775510204085,
 4.795918367346939,
 4.8979591836734695,
 5.0]

In [159]:

    

caso1 = [rendimiento(tao) for tao in np.linspace(0,15)]
caso1


    

    




tao < tao1 and tao < tao2
tao < tao1 and tao < tao2
tao < tao1 and tao < tao2
tao < tao1 and tao < tao2
tao < tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2






    
Out[159]:





[0.0,
 0.021175462451348267,
 0.042350924902696534,
 0.0635263873540448,
 0.08470184980539307,
 0.10586240724665469,
 0.12693119197306726,
 0.14783738881474864,
 0.1685261464121838,
 0.18894922443715043,
 0.20906060982884964,
 0.22881410899010135,
 0.24816182896433522,
 0.26705309024678237,
 0.28543355559493905,
 0.30324446322126325,
 0.32042190154796807,
 0.33689608714873753,
 0.35259062034949884,
 0.36742169991480716,
 0.38130372981839566,
 0.3941960908220593,
 0.406090123152443,
 0.41699047089218877,
 0.4269147321107626,
 0.43589255261409354,
 0.44396415365496233,
 0.45117844370314303,
 0.457590892189559,
 0.46326134405019936,
 0.46825193197286874,
 0.4726252062684879,
 0.4764425591202635,
 0.479762978345391,
 0.48264213103884324,
 0.48513175212947535,
 0.48727929723524216,
 0.48912781199630445,
 0.4907159692896542,
 0.4920782292572582,
 0.49324508303711023,
 0.4942433480260757,
 0.49509648943078877,
 0.4958249491782092,
 0.49644646866322384,
 0.49697639621796236,
 0.4974279736363982,
 0.4978125986875685,
 0.49814006243866604,
 0.49841876152514436]

In [160]:

    

caso1


    

    
Out[160]:





[0.0,
 0.021175462451348267,
 0.042350924902696534,
 0.0635263873540448,
 0.08470184980539307,
 0.10586240724665469,
 0.12693119197306726,
 0.14783738881474864,
 0.1685261464121838,
 0.18894922443715043,
 0.20906060982884964,
 0.22881410899010135,
 0.24816182896433522,
 0.26705309024678237,
 0.28543355559493905,
 0.30324446322126325,
 0.32042190154796807,
 0.33689608714873753,
 0.35259062034949884,
 0.36742169991480716,
 0.38130372981839566,
 0.3941960908220593,
 0.406090123152443,
 0.41699047089218877,
 0.4269147321107626,
 0.43589255261409354,
 0.44396415365496233,
 0.45117844370314303,
 0.457590892189559,
 0.46326134405019936,
 0.46825193197286874,
 0.4726252062684879,
 0.4764425591202635,
 0.479762978345391,
 0.48264213103884324,
 0.48513175212947535,
 0.48727929723524216,
 0.48912781199630445,
 0.4907159692896542,
 0.4920782292572582,
 0.49324508303711023,
 0.4942433480260757,
 0.49509648943078877,
 0.4958249491782092,
 0.49644646866322384,
 0.49697639621796236,
 0.4974279736363982,
 0.4978125986875685,
 0.49814006243866604,
 0.49841876152514436]

In [161]:

    

Tao = np.linspace(0,15)

plt.plot(Tao, caso1)
plt.title("Modelo Lack")
plt.xlabel(" $tao $ ")
plt.ylabel("Rendimiento e")
#plt.legend(('$xk=0.3$'),loc=0)


    

    
Out[161]:





Text(0,0.5,'Rendimiento e')






    

In [228]:

    

def rendimiento(tao):
    if tao <= tao1 and tao < tao2:
        e = gamma * yr* tao * (1- np.exp(- A))
        print("tao < tao1 and tao < tao2")
        return e
    if tao > tao1 and tao <= tao2:
        zk = xk / (A * xo) * np.log((xo * np.exp(gamma * A * yr / xk * (tao - tao1)) - xk) / (xo - xk))
        e = gamma * yr * (tao - tao1 * np.exp(- A * (1 - zk)))
        print("tao >= tao1 and tao < tao2")
        return e
    if tao > tao2:
        e = xo - xk / A * np.log(1 + xk / xo * (np.exp(xo / xk * A) - 1) * np.exp(gamma * A * yr / xk * (tao1 - tao)))
        print("tao >= tao2")
        return e


    

In [232]:

    

def rendementparametre(xk,A):
    Tao = np.linspace(0,15)

    plt.plot(Tao, caso1)
    plt.title("Modelo Lack")
    plt.xlabel(" $tao $ ")
    plt.ylabel("Rendimiento e")
    return


    

In [233]:

    

rendementparametre(0.1,1)


    

In [234]:

    

rendementparametre(0.2,2)


    

In [235]:

    

rendementparametre(0.4,4)


    

In [216]:

    




    

    
Out[216]:





4.583946341135364

In [217]:

    




    

    
Out[217]:





numpy.ndarray

In [218]:

    




    

    
Out[218]:





[<matplotlib.lines.Line2D at 0x12d879905c0>]






    

In [219]:

    




    

In [220]:

    




    

In [221]:

    




    

In [222]:

    




    

    




tao1 = 1.2499999999999998 tao2 = 5.879695601713209
tao >= tao2






    
Out[222]:





0.48928938945393036

In [223]:

    




    

    
Out[223]:





[0, 1, 2, 3, 4]

In [224]:

    




    

    
Out[224]:





[0.0,
 0.10204081632653061,
 0.20408163265306123,
 0.30612244897959184,
 0.40816326530612246,
 0.5102040816326531,
 0.6122448979591837,
 0.7142857142857143,
 0.8163265306122449,
 0.9183673469387755,
 1.0204081632653061,
 1.1224489795918369,
 1.2244897959183674,
 1.3265306122448979,
 1.4285714285714286,
 1.5306122448979593,
 1.6326530612244898,
 1.7346938775510203,
 1.836734693877551,
 1.9387755102040818,
 2.0408163265306123,
 2.142857142857143,
 2.2448979591836737,
 2.3469387755102042,
 2.4489795918367347,
 2.5510204081632653,
 2.6530612244897958,
 2.7551020408163267,
 2.857142857142857,
 2.9591836734693877,
 3.0612244897959187,
 3.163265306122449,
 3.2653061224489797,
 3.36734693877551,
 3.4693877551020407,
 3.5714285714285716,
 3.673469387755102,
 3.7755102040816326,
 3.8775510204081636,
 3.979591836734694,
 4.081632653061225,
 4.183673469387755,
 4.285714285714286,
 4.387755102040816,
 4.4897959183673475,
 4.591836734693878,
 4.6938775510204085,
 4.795918367346939,
 4.8979591836734695,
 5.0]

In [225]:

    




    

    




tao < tao1 and tao < tao2
tao < tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao1 and tao < tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2
tao >= tao2






    
Out[225]:





[0.0,
 0.024041249659867737,
 0.7190914533309968,
 0.718579163809553,
 0.7179856386328294,
 0.7172858071202229,
 0.7164525039367247,
 0.7154541878287507,
 0.7142532926478884,
 0.7128045965993925,
 0.7110533931746522,
 0.7089333394989181,
 0.7063638773622033,
 0.7032471177307396,
 0.6994640639179353,
 0.3422169643639321,
 0.36113676813322215,
 0.378934489364718,
 0.39547915297515,
 0.41065899741032463,
 0.4243921053446273,
 0.4366350926454827,
 0.4473880158319006,
 0.4566943655439216,
 0.4646361475721564,
 0.4713251864255304,
 0.4768924922334224,
 0.48147761541705325,
 0.4852194768336529,
 0.48824948300646315,
 0.4906870935567196,
 0.49263756209496956,
 0.49419135465912917,
 0.49542471233898844,
 0.49640089297803586,
 0.4971717372028536,
 0.49777931571338624,
 0.49825750797968005,
 0.49863343155527706,
 0.49892868792607403,
 0.4991604198386353,
 0.4993421914103874,
 0.4994847102707726,
 0.4995964137138029,
 0.49968394057592386,
 0.49975250873476684,
 0.49980621564599303,
 0.49984827671470905,
 0.49988121381246126,
 0.4999070040309815]

In [226]:

    




    

    
Out[226]:





[0.0,
 0.024041249659867737,
 0.7190914533309968,
 0.718579163809553,
 0.7179856386328294,
 0.7172858071202229,
 0.7164525039367247,
 0.7154541878287507,
 0.7142532926478884,
 0.7128045965993925,
 0.7110533931746522,
 0.7089333394989181,
 0.7063638773622033,
 0.7032471177307396,
 0.6994640639179353,
 0.3422169643639321,
 0.36113676813322215,
 0.378934489364718,
 0.39547915297515,
 0.41065899741032463,
 0.4243921053446273,
 0.4366350926454827,
 0.4473880158319006,
 0.4566943655439216,
 0.4646361475721564,
 0.4713251864255304,
 0.4768924922334224,
 0.48147761541705325,
 0.4852194768336529,
 0.48824948300646315,
 0.4906870935567196,
 0.49263756209496956,
 0.49419135465912917,
 0.49542471233898844,
 0.49640089297803586,
 0.4971717372028536,
 0.49777931571338624,
 0.49825750797968005,
 0.49863343155527706,
 0.49892868792607403,
 0.4991604198386353,
 0.4993421914103874,
 0.4994847102707726,
 0.4995964137138029,
 0.49968394057592386,
 0.49975250873476684,
 0.49980621564599303,
 0.49984827671470905,
 0.49988121381246126,
 0.4999070040309815]

In [227]:

    




    

    
Out[227]:





Text(0,0.5,'Rendimiento e')






    

In [ ]:

    




    

In [ ]: