1、中國石油大學（北京）研究生油藏數值模擬課程上機作業一油藏的儲層參數分布附圖所示，W1井網格位置為（4,7）,W2井位置為（7,5）。任務：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）輸出油藏投產后如下時刻的壓力分布、w1井底流壓和w2井產油量：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定的時刻及其壓力分布、w1井底流壓和w2井產油量。（三）對照（二）中內容,比較分析顯式和隱式兩種方法的計算過程及結果有何不同。（四）建議計算過程用國際單位制，輸出的結果中壓力用MPa,產量用mVd。（五）作業完成形式。要

2、求三個電子文檔：1.綜合結果報告，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分布（1）厚度分布二附圖中數據-50，單位：m（2）滲透率分布二附圖中數據，單位：10-3卩m2（3）孔隙度分布二（附圖中數據X0.02+15）%,無單位。綜合結果報告一基礎數據二顯式法求解以下為運用顯示求解法得到的不同時刻、不同網格壓力分布（1）初始時刻202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202

3、020202020W1井井底流壓P=18.6669MpawfW2井產油量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）穩定時刻t=36dW1井井底流壓P=17.3552MpawfW2井產油量Q=53.8752m3/dW2井產油量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、不同網格壓力分布（1）初始時刻202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020W1井井底流壓P=18.6669MpawfW2井產油量Q=93.5893m3/dW2井產油量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井產油量Q=54.0099m3/dW2井產油量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井產油量Q=53.8750m3/dW2井產油量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井產油量Q=53.8750m3/d四顯隱式方法對比1、結果對比結果時間、方法P(MPa)1P(MPa)2W井底流壓1Pwf1(MPa)W井產量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穩定時間顯式（36天）18.688317.878317.355253.8752隱式（121天）18.688317.878317.355253.8750穩定后顯式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，經程

31、序運行后，會因無法收斂，產生明顯錯誤的結果；而在隱式計算中，仍然可以得到合理且收斂的結果。一般顯式方法求解簡單，穩定性差；隱式格式求解過程復雜，穩定性好。因此一般應采用隱式計算方法，以獲得較準確的結果。 顯式方法計算的壓力達到穩定的時間為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定。 兩種方法都達到穩定后，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字，看起來不是很明顯）；2）相應的穩定產量隱式較顯式稍低； 以上結論可以說明，在達到同樣的精度時，隱式方法計算結果更為準確。2、計算過程對比顯式差分方法：假設第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，但是穩定性較差，本問題中其穩定條件為:得：；取：。隱式差分方法：每個差分方程中含有五個未知量：、不能獨立求解，需要聯立方程。其系數矩陣A為五對角稀疏矩陣。求解過程較復雜，但穩定性較強。無條件穩定，時間間隔可以取大一些減少迭代次數，節省計算時間。本問題中取：顯式差分求解程序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(