油藏數(shù)值模擬劉月田上機作業(yè)

1、中國石油大學(xué)（北京）研究生油藏數(shù)值模擬課程上機作業(yè)一油藏的儲層參數(shù)分布附圖所示，W1井網(wǎng)格位置為（4,7）,W2井位置為（7,5）。任務(wù)：獨立編制計算機程序完成第五章滲流問題的模擬求解。具體要求：（一）使用顯式和隱式兩種方法。（二）輸出油藏投產(chǎn)后如下時刻的壓力分布、w1井底流壓和w2井產(chǎn)油量：初始時刻、10天、1個月、2個月、1個季度、半年、1年、2年、5年；給出壓力剛好達到穩(wěn)定的時刻及其壓力分布、w1井底流壓和w2井產(chǎn)油量。（三）對照（二）中內(nèi)容,比較分析顯式和隱式兩種方法的計算過程及結(jié)果有何不同。（四）建議計算過程用國際單位制，輸出的結(jié)果中壓力用MPa,產(chǎn)量用mVd。（五）作業(yè)完成形式。要

2、求三個電子文檔：1.綜合結(jié)果報告，word文檔；2顯式求解方法源程序；3隱式求解方法源程序。附圖油藏的儲層參數(shù)分布（1）厚度分布二附圖中數(shù)據(jù)-50，單位：m（2）滲透率分布二附圖中數(shù)據(jù)，單位：10-3卩m2（3）孔隙度分布二（附圖中數(shù)據(jù)X0.02+15）%,無單位。綜合結(jié)果報告一基礎(chǔ)數(shù)據(jù)二顯式法求解以下為運用顯示求解法得到的不同時刻、不同網(wǎng)格壓力分布（1）初始時刻202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202

3、020202020W1井井底流壓P=18.6669MpawfW2井產(chǎn)油量Q=93.5894m3/d2)10天19.39419.33219.21019.07219.01018.98523776019.43219.35919.20018.99118.96718.95177112019.50819.42919.22018.74518.91518.89498967819.63719.58119.44019.22119.07018.80818.38118.50518.6214561668119.80719.77819.69119.51419.27118.82817.89618.51318.7246974

4、6676019.77019.53419.23718.89718.95019.02920202008626119.76419.57219.40919.37219.386208446719.90219.81719.75719.73419.7242068592202020202020W1井井底流壓P=17.4126MpaW2井產(chǎn)油量wfQ=54.2204m3/d(3)1個月19.39419.33219.21019.07219.01018.9852487619.43219.35919.20018.99118.96718.95187213119.50819.42919.22118.74518.91518

5、.8949878919.63719.58119.44019.22119.07018.80818.38118.50518.6214671678219.80719.77819.69119.51419.27118.82817.89618.51318.72479756777119.77019.53419.23718.89718.95019.02920202019737119.76419.57219.40919.37219.386208447719.90219.81719.75719.73419.7242068592202020202020W1井井底流壓P=17.3554MpawfW2井產(chǎn)油量Q=53.

6、8762m3/d4)2個月19.32319.25919.13518.99418.92918.9013753319.36919.29419.13218.92018.89418.8751899619.37719.16618.68818.85518.83319.4572337819.60019.54419.40119.18019.02718.76718.35118.47818.59354946934919.78819.75919.67119.49019.24518.80317.87818.49118.70069464437619.76019.52019.22118.88118.93319.01020

7、202067411719.75819.39819.36019.37420419.56379419.90019.81319.75219.72919.7182018654202020202020W1井井底流壓P=17.3552MpaW2井產(chǎn)油量wfQ=53.8752m3/d(5)1個季度19.32319.25919.13518.99418.92918.9013753319.36919.29419.13218.92018.89418.8751899619.37719.16618.68818.85518.83319.4572337819.60019.54419.40119.18019.02718.76

8、718.35118.47818.59354946934919.78819.75919.67119.49019.24518.80317.87818.49118.70069464437619.76019.52019.22118.88118.93319.01020202067411719.75819.39819.36019.37420419.56379419.90019.81319.75219.72919.7182018654202020202020W1井井底流壓P=17.3552MpawfW2井產(chǎn)油量Q=53.8752m3/d6）半年19.32319.25919.13518.99418.92918

9、.9013753319.36919.29419.13218.92018.89418.8751899619.37719.16618.68818.85518.83319.4572337819.60019.54419.40119.18019.02718.76718.35118.47818.59354946934919.78819.75919.67119.49019.24518.80317.87818.49118.70069464437619.76019.52019.22118.88118.93319.01020202067411719.75819.39819.36019.37420419.56379

10、419.90019.81319.75219.72919.7182018654202020202020W1井井底流壓P=17.3552MpaW2井產(chǎn)油量wfQ=53.8752m3/d（7）1年19.32319.25919.13518.99418.92918.9013753319.36919.29419.13218.92018.89418.8751899619.37719.16618.68818.85518.83319.4572337819.60019.54419.40119.18019.02718.76718.35118.47818.59354946934919.78819.75919.6711

11、9.49019.24518.80317.87818.49118.70069464437619.76019.52019.22118.88118.93319.0102020206741172019.758419.56319.398719.360919.37442019.900119.813819.752619.729519.7184202020202020W1井井底流壓P=17.3552MpaW2井產(chǎn)油量wfQ=53.8752m3/d(8)2年19.32319.25919.13518.99418.92918.9013753319.36919.29419.13218.92018.89418.8751

12、899619.37719.16618.68818.85518.83319.4572337819.60019.54419.40119.18019.02718.76718.35118.47818.59354946934919.78819.75919.67119.49019.24518.80317.87818.49118.70069464437619.76019.52019.22118.88118.93319.01020202067411719.75819.39819.36019.37420419.56379419.90019.81319.75219.72919.718201865420202020

13、2020W1井井底流壓P=17.3552MpaW2井產(chǎn)油量wfQ=53.8752m3/d(9)5年19.32319.25919.13518.99418.92918.9013753319.36919.29419.13218.92018.89418.8751899619.37719.16618.68818.85518.83319.4572337819.60019.54419.40119.18019.02718.76718.35118.47818.59354946934919.78819.75919.67119.49019.24518.80317.87818.49118.70069464437620

14、202019.760619.520719.221418.881118.933119.01072019.758419.56319.398719.360919.37442019.900119.813819.752619.729519.7184202020202020W1井井底流壓P=17.3552Mpawf19.32319.25919.13518.99418.92918.9013753319.36919.29419.13218.92018.89418.8751899619.37719.16618.68818.85518.83319.4572337819.60019.54419.40119.1801

15、9.02718.76718.35118.47818.59354946934919.78819.75919.67119.49019.24518.80317.87818.49118.70069464437619.76019.52019.22118.88118.93319.01020202067411719.75819.39819.36019.37420419.56379419.90019.81319.75219.72919.718201865420202020202010）穩(wěn)定時刻t=36dW1井井底流壓P=17.3552MpawfW2井產(chǎn)油量Q=53.8752m3/dW2井產(chǎn)油量Q=53.875

16、2m3/d三隱式法求解以下為運用顯示求解法得到的不同時刻、不同網(wǎng)格壓力分布（1）初始時刻202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020W1井井底流壓P=18.6669MpawfW2井產(chǎn)油量Q=93.5893m3/dW2井產(chǎn)油量Q=55.3924m3/d19.44819.39119.27819.1519.09619.0759413719.48319.41419.26319.06519.0519

17、.0392561519.55119.47619.27618.81218.99218.97875265919.66819.61619.48219.27319.13518.88518.46718.60618.7299335664419.82419.79719.71519.54919.31918.88917.95918.59918.81932316537519.78619.56619.28318.95419.02019.10420202063463619.78119.60119.44819.41919.4375325419.90919.83119.77519.75619.74782329202020

18、20202)10天W1井井底流壓P=17.4795Mpawf3)1個月19.34119.27819.15519.01518.95118.92488777819.385819.31219.15118.940218.914618.897119.47019.39119.18118.70418.87318.8517224819.61019.55419.41219.19219.04018.78118.36218.49018.6063461541319.79319.76519.67719.49719.25318.81217.88518.50118.71171167153419.76319.52519.22

19、718.88718.94019.01920202065479219.76019.56619.40319.36619.380207722219.90119.81519.75419.7212014719.7321202020202020W1井井底流壓P=17.3713Mpawf19.32519.26219.13818.99718.93118.90482219319.37119.29719.13518.92318.89618.87841346419.45819.37919.16818.69018.85718.8369134919.60119.54519.40319.18119.02918.76918

20、.35218.47918.59587393556119.78919.76019.67219.49119.24618.80417.87918.49218.7013615446719.52119.22218.88118.93319.01120202019.7612189519.75819.56319.39919.36120742419.37519.90019.81319.75219.72919.71820298862020202020204)2個月W1井井底流壓P=17.3573MpawfW2井產(chǎn)油量Q=54.0099m3/dW2井產(chǎn)油量Q=53.8897m3/d5)1個季度19.32319.26

21、19.13518.99418.92918.9016863619.36919.29519.13318.92118.89418.876412319.45719.37719.16618.68818.85518.8342455919.60019.54419.40219.18019.02718.76818.35118.47818.594756814519.78819.7619.67119.49019.24518.80317.87818.49118.7007575548719.76019.52019.22118.88118.93319.01020202067522819.75819.56319.39819

22、.36019.374205189519.90019.81319.75219.72919.7182018664202020202020W1井井底流壓P=17.3555MpawfW2井產(chǎn)油量Q=53.8767m3/d6）半年19.32319.25919.13518.99418.92818.90136529219.36919.29419.13218.92018.89318.87517889619.37719.16618.68818.85518.83319.4572336719.60019.54419.40119.18019.02718.76718.35118.47818.59354946924919

23、.78819.75919.67119.49019.24518.80317.87818.49118.70069463437619.76019.52019.22118.88118.93319.01020202067411719.75819.39819.36019.37420419.56379419.90019.81319.75219.72919.7182018654202020202020W1井井底流壓P=17.3552MpawfW2井產(chǎn)油量Q=53.8750m3/d7)1年19.32319.25919.13518.99418.92818.90136529219.36919.29419.13218

24、.92018.89318.87517889619.37719.16618.68818.85518.83319.4572336719.60019.54419.40119.18019.02718.76718.35118.47818.59354946924919.78819.75919.67119.49019.24518.80317.87818.49118.70069463437619.76019.52019.22118.88118.93319.01020202067411719.75819.39819.36019.37420419.56379419.90019.81319.75219.72919.

25、7182018654202020202020W1井井底流壓P=17.3552MpaW2井產(chǎn)油量wfQ=53.8750m3/d(8)2年19.32319.25919.13518.99418.92818.90136529219.36919.29419.13218.92018.89318.87517889619.37719.16618.68818.85518.83319.4572336719.60019.54419.40119.18019.02718.76718.35118.47818.59354946924919.78819.75919.67119.49019.24518.80317.87818.

26、49118.70069463437619.76019.52019.22118.88118.93319.01020202067411719.75819.39819.36019.37420419.56379419.90019.81319.75219.72919.7182018654202020202020W1井井底流壓P=17.3552MpawfW2井產(chǎn)油量Q=53.8750m3/dW2井產(chǎn)油量Q=53.8750m3/d19.32319.25919.13518.99418.92818.90136529219.36919.29419.13218.92018.89318.87517889619.377

27、19.16618.68818.85518.83319.4572336719.60019.54419.40119.18019.02718.76718.35118.47818.59354946924919.78819.75919.67119.49019.24518.80317.87818.49118.70069463437619.76019.52019.22118.88118.93319.01020202067411719.75819.39819.36019.37420419.56379419.90019.81319.75219.72919.71820186542020202020209)5年W1

28、井井底流壓P=17.3552Mpawf10)穩(wěn)定時刻t=121d19.32319.25919.13518.99418.92818.90136529219.36919.29419.13218.92018.89318.87517889619.37719.16618.68818.85518.83319.4572336719.60019.54419.40119.18019.02718.76718.35118.47818.59354946924919.78819.75919.67119.49019.24518.80317.87818.49118.70069463437619.76019.52019.22

29、118.88118.93319.01020202067411719.75819.39819.36019.37420419.5637942019.900119.813819.752619.729519.7184202020202020W1井井底流壓P=17.3552MpawfW2井產(chǎn)油量Q=53.8750m3/d四顯隱式方法對比1、結(jié)果對比結(jié)果時間、方法P(MPa)1P(MPa)2W井底流壓1Pwf1(MPa)W井產(chǎn)量2Q2(m3/d)初始時刻顯式202018.666993.5894隱式202018.666993.589310天顯式18.745617.896717.412654.2204隱式18

30、.812617.959317.479555.39241個月顯式18.745717.896717.355453.8762隱式18.704417.885517.371354.0099穩(wěn)定時間顯式（36天）18.688317.878317.355253.8752隱式（121天）18.688317.878317.355253.8750穩(wěn)定后顯式18.688317.878317.355253.8752隱式18.688317.878317.355253.8750從上表中可以看出： 顯式計算為有條件收斂，需要取得時間步長足夠小才會收斂；而隱式計算為無條件收斂。如在計算中輸入厶T=0.5d,在顯式計算中，經(jīng)程

31、序運行后，會因無法收斂，產(chǎn)生明顯錯誤的結(jié)果；而在隱式計算中，仍然可以得到合理且收斂的結(jié)果。一般顯式方法求解簡單，穩(wěn)定性差；隱式格式求解過程復(fù)雜，穩(wěn)定性好。因此一般應(yīng)采用隱式計算方法，以獲得較準確的結(jié)果。 顯式方法計算的壓力達到穩(wěn)定的時間為36天，隱式為121天；說明在相同時間步長（并且顯式收斂）時，顯式解法更快的達到穩(wěn)定。 兩種方法都達到穩(wěn)定后，1）隱式一部分地層壓力分布比顯式低一些（由于只保留四位有效數(shù)字，看起來不是很明顯）；2）相應(yīng)的穩(wěn)定產(chǎn)量隱式較顯式稍低； 以上結(jié)論可以說明，在達到同樣的精度時，隱式方法計算結(jié)果更為準確。2、計算過程對比顯式差分方法：假設(shè)第n時間步的值已知，則方程中只有一

32、個未知量，可以直接計算得到。在t=0的初值給定后，便可利用顯式差分方程逐點逐層對整個問題進行計算。求解步驟比較簡單，但是穩(wěn)定性較差，本問題中其穩(wěn)定條件為:得：；?。骸ｋ[式差分方法：每個差分方程中含有五個未知量：、不能獨立求解，需要聯(lián)立方程。其系數(shù)矩陣A為五對角稀疏矩陣。求解過程較復(fù)雜，但穩(wěn)定性較強。無條件穩(wěn)定，時間間隔可以取大一些減少迭代次數(shù)，節(jié)省計算時間。本問題中?。猴@式差分求解程序functionP1,d,Pwf1,Q2=xscfqj（t）Pini=20;u=5e-3;C=2e-4;Q1=30;Pwf2=15;dx=200;dy=200;dt=1.7;n=t*24/dt;re=0.208*

33、dx;rw=0.1;K=02592222001901801850000;259259222200190180185185000;310310240235228210195195000;330330290270250230205197.51801850;350350300280259222200190180185185;340340320290310240235228210195195;355355335315310290270250230205205;0000325300280240210215215;0000340320290260235225225;00003553353152952752

34、550;H=K/50;kxd=(K.*0.02+15)/100;P=Pini*ones(10,11);P1=Pini*ones(10,11);a=zeros(10,11);b=zeros(10,11);c=zeros(10,11);d=zeros(10,11);e=zeros(10,11);fori=2:9forj=2:10a(i,j)=3600e-9*dt*2*H(i,j-1)*K(i,j-1)*K(i,j)/u/C/kxd(i,j)/dx/dx/(H(i,j-1)*K(i,j-1)+H(i,j)*K(i,j);b(i,j)=3600e-9*dt*2*H(i,j+1)*K(i,j+1)*K(

35、i,j)/u/C/kxd(i,j)/dx/dx/(H(i,j+1)*K(i,j+1)+H(i,j)*K(i,j);c(i,j)=3600e-9*dt*2*H(i+1,j)*K(i+1,j)*K(i,j)/u/C/kxd(i,j)/dx/dx/(H(i+1,j)*K(i+1,j)+H(i,j)*K(i,j);d(i,j)=3600e-9*dt*2*H(i-1,j)*K(i-1,j)*K(i,j)/u/C/kxd(i,j)/dx/dx/(H(i-1,j)*K(i-1,j)+H(i,j)*K(i,j);e(i,j)=1-a(i,j)-b(i,j)-c(i,j)-d(i,j);endendtn=1;w

36、hile(tn<n)dP=zeros(10,11);fori=3:6P1(i,2)=c(i,2)*P(i+1,2)+(a(i,2)+e(i,2)*P(i,2)+b(i,2)*P(i,3)+d(i,2)*P(i-1,2);dP(i,2)=P1(i,2)-P(i,2);P1(i,1)=P1(i,2);endP1(2,2)=c(2,2)*P(3,2)+(a(2,2)+e(2,2)+d(2,2)*P(2,2)+b(2,2)*P(2,3);dP(2,2)=P1(2,2)-P(2,2);P1(2,1)=P1(2,2);P1(1,2)=P1(2,2);forj=3:6P1(2,j)=c(2,j)*P(

37、3,j)+a(2,j)*P(2,j-1)+(e(2,j)+d(2,j)*P(2,j)+b(2,j)*P(2,j+1);dP(2,j)=P1(2,j)-P(2,j);P1(1,j)=P1(2,j);endP1(2,7)=c(2,7)*P(3,7)+a(2,7)*P(2,6)+(e(2,7)+b(2,7)+d(2,7)*P(2,7);dP(2,7)=P1(2,7)-P(2,7);P1(1,7)=P1(2,7);P1(2,8)=P1(2,7);fori=3:4P1(i,7)=c(i,7)*P(i+1,7)+a(i,7)*P(i,6)+(e(i,7)+b(i,7)*P(i,7)+d(i,7)*P(i-

38、1,7);dP(i,7)=P1(i,7)-P(i,7);P1(i,8)=P1(i,7);endforj=8:9P1(5,j)=c(5,j)*P(6,j)+a(5,j)*P(5,j-1)+(e(5,j)+d(5,j)*P(5,j)+b(5,j)*P(5,j+1);dP(5,j)=P1(5,j)-P(5,j);P1(4,j)=P1(5,j);endP1(5,10)=c(5,10)*P(6,10)+a(5,10)*P(5,9)+(e(5,10)+b(5,10)+d(5,10)*P(5,10);dP(5,10)=P1(5,10)-P(5,10);P1(4,10)=P1(5,10);P1(5,11)=P

39、1(5,10);fori=6:9P1(i,10)=c(i,10)*P(i+1,10)+a(i,10)*P(i,9)+(e(i,10)+b(i,10)*P(i,10)+d(i,10)*P(i-1,10);dP(i,10)=P1(i,10)-P(i,10);P1(i,11)=P1(i,10);endfori=8:9forj=6:9P1(i,j)=c(i,j)*P(i+1,j)+a(i,j)*P(i,j-1)+e(i,j)*P(i,j)+b(i,j)*P(i,j+1)+d(i,j)*P(i-1,j);dP(i,j)=P1(i,j)-P(i,j);endendforj=5:9P1(7,j)=c(7,j

40、)*P(8,j)+a(7,j)*P(7,j-1)+e(7,j)*P(7,j)+b(7,j)*P(7,j+1)+d(7,j)*P(6,j);dP(7,j)=P1(7,j)-P(7,j);endforj=3:7P1(6,j)=c(6,j)*P(7,j)+a(6,j)*P(6,j-1)+e(6,j)*P(6,j)+b(6,j)*P(6,j+1)+d(6,j)*P(5,j);dP(6,j)=P1(6,j)-P(6,j);endP1(6,9)=c(6,9)*P(7,9)+a(6,9)*P(6,8)+e(6,9)*P(6,9)+b(6,9)*P(6,10)+d(6,9)*P(5,9);dP(6,9)=P1(6,9)-P(6,9);P1(6,8)=c(6,8)*P(7,8)+a(6,8)*P(6,7)+e(6,8)*P(6,8)+b(6,8)*P(6,9)+d(6,8)*P(5,8)-(3600e-9)*2*pi*K(