Matlab编程天然气压缩因子计算模型.docx

1、Matlab编程天然气压缩因子计算模型1程序目的利用AGA8-92DC模型计算天然气的压缩因子，该程序主要应用于在输气和配气正常进行的压力P和温度T范围内的管输气的压缩因子计算2数学模型：AGA8-92DC模型2.1模型介绍此模型是已知气体详细的摩尔分数组成和相关压力、温度来计算气体压缩因子。输入变量包括绝对压力、热力学温度和摩尔组成。摩尔组成是以摩尔分数表示下列组分：CO2、N2、H2、CO、CH4、C2H6、C3H8、i-C4H10、n-C4H10、i-C5H12、n-C5H12、n-C6H14、n-C7H16、n-C8H18。2.2 模型适用条件绝对压力：0MPaP12MPa热力学温度：

2、263KT338K高位发热量：30MJm-3HS45 MJm-3相对密度：0.55d0.80天然气中各组分的摩尔分数应在以下范围内：CH4：0.7xCH41.0N2：0xN20.20CO2：0xCO20.20C2H6：0xC2H60.10C3H8：0x C3H80.035C4H10：0x C4H100.015C5H12：0x C5H120.005C6H14：0x C6H140.001C7H16：0x C7H160.0005C8H18和更高碳数烃类：C8H18：0x C8H180.0005H2：0x H20.10CO：0x CO0.03如果已知体积分数组成，则应将其换算成摩尔分数组成。所有摩尔分

3、数大于0.00005的组分都不可忽略。2.3 模型描述2.3.1 已知条件绝对压力P、热力学温度T、组分数N；各组分的摩尔分数，i = 1N ；查附表1、2、3得到的以下数据：58种物质的状态方程参数， ， ；14种识别组分的特征参数， ；14种识别组分的二元交互作用参数， 。2.3.2 待求量压缩因子 Z2.3.3 计算步骤a) 第二维利系数B的计算：二元参数Eij和Gij，由以下两式计算：b) 计算系数，n = 1358用以下方程求解混合方程，计算混合物参数U，G，Q。c) 计算混合物体积参数K；d) 计算对比密度摩尔密度为：式中，P为绝对压力，Mpa；R为摩尔气体常数；T为热力学温度，K

4、。对比密度r同摩尔密度m相关：e) 利用AGA8-92DC方程，对压缩因子进行迭代计算迭代过程：给出Z0的初始值为1，先计算出m，将m、K和已知量带入AGA8-92DC方程方程，得到新的Z值，当（Z-Z0）的绝对值小于0.000001时，停止迭代，得到Z值。3 程序代码function Z = YSYZ( T,p,x)%计算天然气给定组分的压缩因子% x为天然气组分，按照CO2 N2 H2 CO CH4 C2H6 C3H8 i-C4H10 n-C4H10 i-C5H12 n-C5H12% n-C6H14 n-C7H16 n-C8H18的顺序输入%T 为温度，单位为K%P为压力，单位为兆帕N=1

5、4;R=8.314;%状态参数值b=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,6,6,7,7,8,8,8,9,9;k=0,0,0,0,0,0,0,0,0,0,0,0,3,2,2,2,4,4,0,0,2,2,2,4,4,4,4,0,1,1,2,2,3,3,4,4,4,0,0,2,2,2,4,4,0,2,2,4,4,0,2,0,2,1,2,2,2,2;c=0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,1,1,1,

6、1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,0,1,1,1,1,0,1,0,1,1,1,1,1,1;g=0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0;f=0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

7、0,0,0;q=0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,0,0,1;s=0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;w=0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

8、0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;a=0.153832600,1.341953000,-2.998583000,-0.048312280,0.375796500,-1.589575000,. -0.053588470,0.886594630,-0.710237040,-1.471722000,1.321850350,-0.786659250,. 2.291290e-9,0.157672400,-0.436386400,-0.044081590,-0.003433888,0.032059050,. 0.0248

9、73550,0.073322790,-0.001600573,0.642470600,-0.416260100,-0.066899570,. 0.279179500,-0.696605100,-0.002860589,-0.008098836,3.150547000,0.007224479,. -0.705752900,0.534979200,-0.079314910,-1.418465000,-5.99905e-17,0.105840200,. 0.034317290,-0.007022847,0.024955870,0.042968180,0.746545300,-0.291961300,

10、. 7.294616000,-9.936757000,-0.005399808,-0.243256700,0.049870160,0.033733797,. 1.874951000,0.002168144,-0.658716400,0.000205518,0.009776195,-0.020487080,. 0.015573220,0.006862415,-0.001226752,0.002850908;u=0.0,0.5,1.0,3.5,-0.5,4.5,0.5,7.5,9.5,6.0,12.0,12.5,-6.0,2.0,3.0,2.0,2.0,11.0,-0.5,. 0.5,0.0,4.

11、0,6.0,21.0,23.0,22.0,-1.0,-0.5,7.0,-1.0,6.0,4.0,1.0,9.0,-13.0,21.0,8.0,. -0.5,0.0,2.0,7.0,9.0,22.0,23.0,1.0,9.0,3.0,8.0,23.0,1.5,5.0,-0.5,4.0,7.0,3.0,0.0,1.0,0.0;%特征参数值M=44.0100,28.0135,2.0159,28.0100,16.0430,30.0700,44.0970,58.1230,58.1230,72.1500,72.1500,86.1770,100.2024,114.2310;E=241.960600,99.7

12、37780,26.957940,105.534800,151.318300,244.166700,298.118300,324.068900,337.638900,365.599900,370.682300,402.636293,427.722630,450.325022;G=0.189065,0.027815,0.034369,0.038953,0.0,0.079300,0.141239,0.256692,0.281835,0.332267,0.366911,0.289731,0.337542,0.383381;Q=0.690,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,

13、0.0,0.0,0.0,0.0,0.0;K=0.4557489,0.4479153,0.3514916,0.4533894,0.4619255,0.5279209,0.5837490,0.6406937,0.6341423,0.6738577,0.6798307,0.7175118,0.7525189,0.7849550;F=zeros(N);S=zeros(N);W=zeros(N);F(3)=1;%交互作用参数值Ex=1.0,1.022740,1.281790,1.5,0.960644,0.925053,0.960237,0.906849,0.897362,0.726255,0.85976

14、4,0.855134,0.831229,0.808310;. 1.022740,1.0,1.086320,1.005710,0.971640,0.970120,0.945939,0.946914,0.973384,0.959340,0.945520,1.0,1.0,1.0;. 1.281790,1.086320,1.0,1.1,1.170520,1.164460,1.034787,1.3,1.3,1.0,1.0,1.0,1.0,1.0;. 1.5,1.005710,1.1,1.0,0.990126,1.0,1.0,1.0,1.0049,1.0,1.0,1.0,1.0,1.0;. 0.96064

15、4,0.971640,1.170520,0.990126,1.0,1.0,0.994635,1.019530,0.989844,1.00235,0.999268,1.107274,0.88080,0.880973;. 0.925053,0.970120,1.164460,1.0,1.0,1.0,1.022560,1.0,1.013060,1.0,1.005320,1.0,1.0,1.0;. 0.960237,0.945939,1.034787,1.0,0.994635,1.022560,1.0,1.0,1.0049,1.0,1.0,1.0,1.0,1.0;. 0.906849,0.946914

16、,1.3,1.0,1.019530,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 0.897362,0.973384,1.3,1.0,0.989844,1.01306,1.0049,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 0.726255,0.959340,1.0,1.0,1.00235,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 0.859764,0.945520,1.0,1.0,0.999268,1.00532,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 0.855134,1.0,1.

17、0,1.0,1.107274,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 0.831229,1.0,1.0,1.0,0.88088,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 0.808310,1.0,1.0,1.0,0.880973,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;Gx=1.0,0.982746,1.0,1.0,0.807653,0.370296,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 0.982746,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.

18、0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.95731,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 0.807653,1.0,1.95731,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 0.370296,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0

19、,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.

20、0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;Ux=1.0,0.835058,1.0,0.9,0.963827,0.969870,1.0,1.0,1.0,1.0,1.0,1.066638,1.077634,1.088178;. 0.835058,1.0,0.408838,1.0,0.886106,0.816431,0.915502,1.0,0.993556,1.0,1.0,1.0,1.0,1.0

21、;. 1.0,0.408838,1.0,1.0,1.156390,1.616660,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 0.9,1.0,1.0,1.0,1.156390,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 0.963827,0.886106,1.156390,1.0,1.0,1.0,0.990877,1.0,0.992291,1.0,1.00367,1.302576,1.191904,1.205769;. 0.969870,0.816431,1.616660,1.0,1.0,1.0,1.065173,1.25,1.25,1

22、.25,1.25,1.0,1.0,1.0;. 1.0,0.915502,1.0,1.0,0.990877,1.065173,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 1.0,1.0,1.0,1.0,1.0,1.25,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 1.0,0.993556,1.0,1.0,0.992291,1.25,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 1.0,1.0,1.0,1.0,1.0,1.25,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 1.0,1.0,1.0,1.0,1

23、.00367,1.25,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 1.066638,1.0,1.0,1.0,1.302576,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 1.077634,1.0,1.0,1.0,1.191904,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;. 1.088178,1.0,1.0,1.0,1.205769,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0;Kx=1.0,0.982361,1.0,1.0,0.995933,1.00851,1.0,1.0,1.0

24、,1.0,1.0,0.910183,0.895362,0.881152; 0.982361,1.0,1.03227,1.0,1.00363,1.00796,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.03227,1.0,1.0,1.02326,1.02034,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 0.995933,1.00363,1.02326,1.0,1.0,1.0,1.007619,1.0,0.997596,1.0,

25、1.002529,0.982962,0.983565,0.982707; 1.00851,1.00796,1.02034,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.007619,0.986893,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,0.997596,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,

26、1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 1.0,1.0,1.0,1.0,1.002529,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 0.910183,1.0,1.0,1.0,0.982962,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 0.895362,1.0,1.0,1.0,0.983565,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0; 0.881152,1.0,1.0,1.0,0.982707,1.0,1.0,1.0,1.0,1.0,1.0,1

27、.0,1.0,1.0;Z0=1;M0=0;B=0;%参数Eij、Gij以及第二维利系数的计算sum1=0;sum2=0; for n=1:18 sum=0; ZJCS=(T-u(n); for i=1:14 for j=1:14 Eij(i,j)=Ex(i,j)*(E(i)*E(j)0.5); Gij(i,j)=Gx(i,j)*(G(i)+G(j)/2; Bij(i,j)=(Gij(i,j)+1-g(n)g(n)*(Q(i)*Q(j)+1-q(n)q(n)*(F(i)*F(j)0.5)+1-f(n)f(n)*(S(i)*S(j)+1-s(n)s(n)*(W(i)*W(j)+1-w(n)w(n)

28、; sum=sum+x(i)*x(j)*Bij(i,j)*(K(i)*K(j)1.5); end end B=B+a(n)*ZJCS*sum; end%K值的计算 F0=0; G0=0; Q0=0; U0=0;for i=1:N F0=F0+(x(i)2)*F(i); Q0=Q0+x(i)*Q(i); sum1=sum1+x(i)*G(i); sum2=sum2+x(i)*(E(i)2.5);endfor i=1:(N-1) for j=2:N G0=G0+x(i)*x(j)*(Gx(i,j)-1)*(G(i)+G(j); U0=U0+(Ux(i,j)5)-1)*(E(i)*E(j)2.5);

29、 endendG0=sum1+2*G0;U0=(sum22)+2*U0)0.2;sum1=0;for i=1:N sum1=sum1+x(i)*(K(i)2.5);endsum2=0;for i=1:(N-1) for j=2:N sum2=sum2+x(i)*x(j)*(Kx(i,j)5)-1)*(K(i)*K(j)2.5); endendK0=(sum12)+2*sum2)0.2);%对比密度的计算pr=p*(K03)/(Z0*R*T); SUM1=0;SUM2=0; %计算Cn的值，共有46个值for n=13:18 Cn=a(n)*(G0+1-g(n)g(n)*(Q02)+Q0-q(n

30、)q(n)*(F0+1-f(n)f(n)*(U0u(n)*(T-u(n); SUM1=SUM1+Cn;endfor i=13:58 Cn=a(i)*(G0+1-g(i)g(i)*(Q0*Q0+Q0-q(i)q(i)*(F0+1-f(i)f(i)*(U0u(i)*(T-u(i); SUM2=SUM2+Cn*(b(i)-c(i)*k(i)*(prk(i)*(prb(i)*exp(-c(i)*(prk(i);end% Z的计算Z=1+B*(pr/(K03)-pr*SUM1+SUM2;%迭代过程while abs(Z-Z0)=0.000001 Z0=(Z+Z0)/2; pr=p*(K03)/(Z0*R*T); SUM2=0; for n=13:58 Cn=a(i)*(G0+1-g(i)g(i)*(Q0*Q0+Q0-q(i)q(i)*(F0+1-f(i)f(i)*(U0u(i)*(T-u(i); SUM2=SUM2+Cn*(b(i)-c(i)*k(i)*(prk(i)*(prb(i)*exp(-c(i)*(prk(i); end Z=1+B*(pr/(K03)