extend model.py

import copy
import math
import time
import numpy as np
import pandas as pd
from numba import jit
from copy import copy
import multiprocessing  as mp

@jit
def v2(t,V1,tm):
    v2=V1*(1-math.exp(-t/tm))+1
    return v2
#体积函数g（t）的导数
@jit
def dg_dt(t,tm):
    return math.exp(-t/tm)/tm
@jit
def IS(t,n_H,n_CLO4,n_H2BO3,n_I,n_IO3,n_I3,n_K,n_Na,V1,tm):
    i=(n_H+n_CLO4+n_H2BO3+n_I+n_IO3+n_I3+n_K+n_Na)/2/v2(t,V1,tm)
    return i
@jit
def Rk4(I):
    i = I
    if i<0.4:
        k4=pow(10,8.884-0.921*pow(i,1/2))
    if i>=0.4:
        k4=1.96e8
    return k4


@jit
def r3(t,n_H,n_H2BO3,V1,tm):
    return 1e11*n_H*n_H2BO3/v2(t,V1,tm)
#反应4生成I2
@jit
def r4(t,n_H,n_I,n_IO3,V1,tm,rk4):
    return rk4*pow(n_H,2)*pow(n_I,2)*n_IO3/pow(v2(t,V1,tm),4)
@jit
def r5(t,n_I,n_I2,n_I3,V1,tm):
    return 5.6e9*n_I*n_I2/v2(t,V1,tm)-7.5e6*n_I3

@jit
def d_n_H_dt(t,n_H,n_H2BO3,n_I,n_IO3,V1,tm,rk4):
    return -r3(t,n_H,n_H2BO3,V1,tm)-6*r4(t,n_H,n_I,n_IO3,V1,tm,rk4)

@jit
def d_n_H2BO3_dt(t,n_H,n_H2BO3,c_H2BO3,V1,tm):
    return dg_dt(t,tm)*c_H2BO3-r3(t,n_H,n_H2BO3,V1,tm)

#I变化的微分方程
@jit
def d_n_I_dt(t,n_I,n_H,n_IO3,n_I2,n_I3,c_I,V1,tm,rk4):
    return dg_dt(t,tm)*c_I-5*r4(t,n_H,n_I,n_IO3,V1,tm,rk4)-r5(t,n_I,n_I2,n_I3,V1,tm)

# IO3变化的微分方程
@jit
def d_n_IO3_dt(t,n_IO3,n_H,n_I,c_IO3,V1,tm,rk4):
    return dg_dt(t,tm)*c_IO3-r4(t,n_H,n_I,n_IO3,V1,tm,rk4)

# I2变化的微分方程
@jit
def  d_n_I2_dt(t,n_I2,n_H,n_I,n_IO3,n_I3,V1,tm,rk4):
    return 3*r4(t,n_H,n_I,n_IO3,V1,tm,rk4)-r5(t,n_I,n_I2,n_I3,V1,tm)
@jit
def  d_n_I3_dt(t,n_I3,n_I,n_I2,V1,tm):
    return r5(t,n_I,n_I2,n_I3,V1,tm)

# K变化的微分方程
@jit
def d_n_K_dt(t,c_K,V1,tm):
    return dg_dt(t,tm)*c_K
# Na变化的微分方程
@jit
def d_n_Na_dt(t,c_Na,V1,tm):
    return dg_dt(t,tm)*c_Na
@jit
def jisuan_Xs(n_I2,n_I3,c_HCL04,c_IO3,c_H2BO3):
    return 2*(n_I2+n_I3)/c_HCL04*(6*c_IO3+c_H2BO3)/6/c_IO3

@jit
def IM(c_HCLO4,c_H2BO3,c_I,c_IO3,R,tm,h):
    #定义离集体初始体积
    V2=1
    #定义环境体积
    V1=R
    #定义离集体初始物质的量

    n_H=c_HCLO4
    n_CLO4 =c_HCLO4
    n_H2BO3=0
    n_I = 0
    n_IO3 = 0
    n_I2=0
    n_I3=0
    n_K=0
    n_Na=0
    #定义溶液初始离子强度
    I=c_HCLO4
    #定义环境初始浓度

    c_Na = c_H2BO3
    c_K = (c_I + c_IO3)
    c_I_s = c_I
    c_IO3_s = c_IO3
    c_H2BO3_s = c_H2BO3
    #定义反应时间
    t=0
    i=0
    while True:
        i=i+1
        #更新离集体体积
        V2=v2(t,V1,tm)

        #更新溶液离子强度
        I=IS(t,n_H,n_CLO4,n_H2BO3,n_I,n_IO3,n_I3,n_K,n_Na,V1,tm)
        kr4=Rk4(I)
        #计算各物质在h时间步内浓度变化



        #计算H浓度变化

        k1 = d_n_H_dt(t,n_H,n_H2BO3,n_I,n_IO3,V1,tm,kr4)
        k2 = d_n_H_dt(t+h/2,  n_H+h/2*k1, n_H2BO3,n_I,n_IO3, V1, tm,kr4)
        k3 = d_n_H_dt(t+h/2, n_H+h/2*k2, n_H2BO3,n_I,n_IO3, V1, tm,kr4)
        k4 = d_n_H_dt(t+h,  n_H+h*k3,  n_H2BO3,n_I,n_IO3, V1, tm,kr4)
        d_n_H=1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4) * h

        #计算H2BO3浓度变化
        k1 = d_n_H2BO3_dt(t,n_H,n_H2BO3,c_H2BO3_s,V1,tm)
        k2 = d_n_H2BO3_dt(t+h/2, n_H, n_H2BO3+h/2*k1, c_H2BO3_s, V1, tm)
        k3 = d_n_H2BO3_dt(t+h/2, n_H, n_H2BO3+h/2*k2, c_H2BO3_s, V1, tm)
        k4 = d_n_H2BO3_dt(t+h, n_H, n_H2BO3+h*k3, c_H2BO3_s, V1, tm)
        d_n_H2BO3 = 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4) * h
        #计算I浓度变化
        k1 = d_n_I_dt(t,n_I,n_H,n_IO3,n_I2,n_I3,c_I_s,V1,tm,kr4)
        k2 = d_n_I_dt(t+h/2, n_I+h/2*k1, n_H, n_IO3, n_I2, n_I3, c_I_s, V1, tm, kr4)
        k3 = d_n_I_dt(t+h/2, n_I+h/2*k2, n_H, n_IO3, n_I2, n_I3, c_I_s, V1, tm, kr4)
        k4 = d_n_I_dt(t+h, n_I+h*k3, n_H, n_IO3, n_I2, n_I3, c_I_s, V1, tm, kr4)
        d_n_I = 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4) * h
        #计算IO3浓度变化
        k1 = d_n_IO3_dt(t,n_IO3,n_H,n_I,c_IO3_s,V1,tm,kr4)
        k2 = d_n_IO3_dt(t+h/2, n_IO3+h/2*k2, n_H, n_I, c_IO3_s, V1, tm, kr4)
        k3 = d_n_IO3_dt(t+h/2, n_IO3+h/2*k3, n_H, n_I, c_IO3_s, V1, tm, kr4)
        k4 = d_n_IO3_dt(t+h, n_IO3+h*k3, n_H, n_I, c_IO3_s, V1, tm, kr4)
        d_n_IO3 = 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4) * h
        #计算I2浓度变化
        k1 = d_n_I2_dt(t,n_I2,n_H,n_I,n_IO3,n_I3,V1,tm,kr4)
        k2 = d_n_I2_dt(t+h/2, n_I2+h/2*k1, n_H, n_I, n_IO3, n_I3, V1, tm, kr4)
        k3 = d_n_I2_dt(t+h/2, n_I2+h/2*k2, n_H, n_I, n_IO3, n_I3, V1, tm,kr4)
        k4 = d_n_I2_dt(t+h, n_I2+h*k3, n_H, n_I, n_IO3, n_I3, V1, tm,kr4)
        d_n_I2 = 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4) * h
        #计算I3浓度变化
        k1 = d_n_I3_dt(t,n_I3,n_I,n_I2,V1,tm)
        k2 = d_n_I3_dt(t+h/2,n_I3+h/2*k1,n_I,n_I2,V1,tm)
        k3 = d_n_I3_dt(t+h/2,n_I3+h/2*k2,n_I,n_I2,V1,tm)
        k4 = d_n_I3_dt(t+h,n_I3+h*k3,n_I,n_I2,V1,tm)
        d_n_I3 = 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4) * h
        #计算K浓度变化
        k1 = d_n_K_dt(t,c_K,V1,tm)
        k2 = d_n_K_dt(t+h/2, c_K, V1, tm)
        k3 = d_n_K_dt(t+h/2, c_K, V1, tm)
        k4 = d_n_K_dt(t+h, c_K, V1, tm)
        d_n_K = 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4) * h
        #计算Na浓度变化
        k1 = d_n_Na_dt(t, c_Na, V1, tm)
        k2 = d_n_Na_dt(t + h / 2, c_Na, V1, tm)
        k3 = d_n_Na_dt(t + h / 2, c_Na, V1, tm)
        k4 = d_n_Na_dt(t + h, c_Na, V1, tm)
        d_n_Na = 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4) * h
        #更新各浓度
        n_H+=d_n_H
        n_H2BO3+=d_n_H2BO3
        n_I += d_n_I
        n_IO3 += d_n_IO3
        n_I2 += d_n_I2
        n_I3 += d_n_I3
        n_K += d_n_K
        n_Na += d_n_Na
        t=t+h



        if n_H/V2<1e-12:
            break

        if t>5*tm:
            break
    Xs=jisuan_Xs(n_I2,n_I3,c_HCLO4,c_IO3,c_H2BO3)

    return Xs

def run(c_HCLO4,c_H2BO3, c_I, c_IO3, R,Xs,h):
    tm=0.01*Xs
    while True:
        Xs_jisuan = IM(c_HCLO4, c_H2BO3, c_I, c_IO3, R, tm, h)

        print(tm, Xs_jisuan)
        A=tm/Xs_jisuan/math.exp(5*Xs_jisuan)
        tm = A*Xs*math.exp(5*Xs)
        if abs(Xs/Xs_jisuan-1) < 1e-4:
            break
    return tm

if __name__=='__main__':
    c_HClO4=0.2934
    c_H2BO3=0.0909
    c_I = 0.0117
    c_IO3 = 0.0023
    R=10
    Xs=0.024544505
    h=1e-11#步长
    tm=run(c_HClO4,c_H2BO3, c_I, c_IO3, R,Xs,h)
    print(tm)