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xinxiao
2026-03-13 11:24:41 +08:00
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算例7-油水两相流-不同裂缝制度不同/grid_discretization_SP_model.m
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function r = grid_discretization_SP_model(modelflag, r, f, frac_information, fellip, nf)
% 数据读取
nx = r.nx; ny = r.ny; nz = r.nz; NTG = r.NTG; cell_mid_coords = r.cell_mid_coords;
% 基质孔渗
rock_density = 2700; % 岩石密度，kg/m^3
kx = 5*1e-3 * ones(nx*ny*nz, 1); % 达西，D
ky = 5*1e-3 * ones(nx*ny*nz, 1);%
kz = 5*1e-3 * ones(nx*ny*nz, 1);%
pori = 0.01 * ones(nx*ny*nz, 1);%
prpor = 20; % 参考压力，MPa
cpor = 1.0e-5;% 基质压缩系数，,MPa
% 有效网格
valid_grids = ones(nx*ny*nz, 1);
invalid_layer = []; % 将第二层无效网格
for i = 1:length(invalid_layer)
grid_numbering_range = ((invalid_layer(i)-1)*nx*ny+1:invalid_layer(i)*nx*ny)';
valid_grids(grid_numbering_range,1) = 0;
end
% SRV区域定义
% % % base_x=23:78; nx_SRV=length(base_x);
% % % base_y=15:36; ny_SRV=length(base_y);
% % % base_z=1:1;nz_SRV=length(base_z);
% % % SRV=[];
% % % for k=1:nz_SRV
% % % for j=1:ny_SRV
% % % for i=1:nx_SRV
% % % SRV=[SRV;(base_z(k)-1)*nx*ny+(base_y(j)-1)*nx+base_x(i)];
% % % end
% % % end
% % % end
% % % % SRV渗透率赋值
% % % kx(SRV)=0.001*1e-3 * ones(length(SRV), 1);
% % % ky(SRV)=0.001*1e-3 * ones(length(SRV), 1);
% % % kz(SRV)=0.001*1e-3 * ones(length(SRV), 1);
% 裂缝孔渗
Kf = 10000*1e-3*ones(1,nf);% 裂缝渗透率
Wf = 1e-2*ones(1,nf);% 裂缝开度
Porf = 0.30*ones(1,nf);% 裂缝孔隙度
prporf = 20;% 裂缝系统参考压力
cporf = 1.0e-5;% 裂缝系统压缩系数
% 应力敏感
stress_factor_fracture = 0.000; % 1/MPa 0.001
stress_factor_matrix = 0.000; % 1/MPa
stress_factor_ref_pressure = 20; % 一般取为原始地层压力MPa
%
Rpt = 2;cf = 1;ca = 1;
%% 结合基质、裂缝的几何及物性信息开展前处理
% r = GridProp(modelflag, nx, ny, nz, dx, dy, dz, kx, ky, kz, f, fellip, Kf, Wf, pori, prpor, cpor, Porf, prporf, cporf, cf, ca,co, NTG);
r = GridProp_new(modelflag, r, kx, ky, kz, f, frac_information, fellip, Kf, Wf, pori, prpor, cpor, Porf, prporf, cporf, cf, ca, valid_grids);
r.rock_density = rock_density;
r.valid_grids = valid_grids;
r.stress_factor_fracture = stress_factor_fracture;
r.stress_factor_matrix = stress_factor_matrix;
r.stress_factor_ref_pressure = stress_factor_ref_pressure;
end
算例7-油水两相流-不同裂缝制度不同/main1.m
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function [ r, Times, OutputRs, Wellpara, trun ] = main1()
%% ==================================PART 1: 模型选取========================================
% 1-- classical EDFM
modelflag = 1;% 此处固定为1即可
%% ==================================PART 2: 基质网格定义=====================================
dx=[10*ones(1,100) ];nx=size(dx,2);
dy=[10*ones(1,50) ];ny=size(dy,2);
dz=[10*ones(1,1)];nz=size(dz,2);
NTG= 1*ones(nx*ny*nz,1);
r = GridProp_pre(dx,dy,dz,nx,ny,nz,NTG);
%% ==================================PART 3: 裂缝分布数据输入=====================================
% 四种输入方式: 1表示工程应用输入；2表示向量输入；3表示工程应用输入，包括基准点、倾角、方位角、抬升角；4表示从.fab文件读取
input_style = 1;
%% 输入方式1：工程应用输入
%仅能刻画具有双对称性质的矩形缝或椭圆缝
% 基准点坐标（1），方位角（2），倾角（3），抬升角（4），缝长（椭圆长轴长）（5），缝高（椭圆短轴长）（6），类型1是矩形缝、2是椭圆缝（7）
if input_style==1
input_content={
[255,255,5],90,90,0,200,10,1;
[355,255,5],90,90,0,200,10,1;
[455,255,5],90,90,0,200,10,1;
[555,255,5],90,90,0,200,10,1;
[655,255,5],90,90,0,200,10,1;
[755,255,5],90,90,0,200,10,1;
};
[f,fellip] = sort_fracture(input_content);
flowBarrierFlags = [];
m=size(f,1);n=size(fellip,1);nf=(m+n)/5;
frac_information = fractureInformation_input_engineering_vector(f,fellip,flowBarrierFlags);
end
%% 输入方式2：向量输入
%首先对矩形缝进行研究，裂缝参数包括三个向量和两个参数的取值范围，如果是其它类型缝，则是两个参数间的函数关系
%因此一个5行三列的矩阵可以确定一条裂缝
%向量分量可为非整数，以此保证参数范围的取值为整数即可，
%故可先随意确定为整数的参数范围，再根据缝长缝高去确定向量分量的取值
% 矩形缝
if input_style==2
f=[
0,1200,0;10,-20,0;0,0,10;0,60,0;0,3,0;
0,1200,0;10,20,0;0,0,10;0,15,0;0,3,0;
150,1500,0;20,-10,0;0,0,10;0,20,0;0,3,0;
550,1300,0;10,10,0;0,0,10;0,10,0;0,3,0;
650,1400,0;10,-20,0;0,0,10;0,55,0;0,3,0;
605,705,0;10,0,0;0,0,10;-20,20,0;0,3,0;
];
% 椭圆缝
% fellip=[320,210,10;10,2,0;0,0,2;0,0,8;0,0,5;
% 280,300,10;10,2,0;0,0,2;0,0,10;0,0,4;];
% 300,205,10;10,0,0;0,0,2;0,0,10;0,0,5];
fellip=[];
m=size(f,1);n=size(fellip,1);nf=(m+n)/5;%裂缝条数
frac_information = fractureInformation_input_engineering_vector(f,fellip);
end
%% 输入方式3：二维输入
% load('fractures_generated.mat');
% fractureLines = fractures_generated;
if input_style==3
fractureLines = [
105,150;105,350;
205,150;205,350;
305,150;305,350;
405,150;405,350;
505,150;505,350;
605,150;605,350;
705,150;705,350;
805,150;805,350;
905,150;905,350;
];
fellip=[]; % 椭圆缝
fractureHeights = [
10;10;10;10;10;10;10;10;10];
% 椭圆缝
fellip=[];
flowBarrierFlags = [];% flowBarrierFlags = [1;2;3;4];
[f,frac_information] = input_fracture_2D(fractureLines,fractureHeights,flowBarrierFlags);
m=size(f,1);n=size(fellip,1);nf=(m+n)/5;%裂缝条数
end
%% 输入方式4：从.fab文件读取 Frac_PT
if input_style==4
end
%% ==================================PART 4: 基质网格及裂缝物性参数输入=====================================
% 1-- 单重介质
% 2-- 双重介质（双孔双渗）
grid_model = 1;
if grid_model == 1
r = grid_discretization_SP_model(modelflag, r, f, frac_information, fellip, nf);
end
if grid_model == 2
r = grid_discretization_DP_model(modelflag, r, f, frac_information, fellip, nf);
end
%% 生成向量化变成所需要的算子
os = OperatorRS(r.N, r.nex, r.nc);
%% ==================================PART 5: 模型类型选取及初始状态设定=========================================
% 1-- 气水两相流
% 2-- 油水两相流
flow_model = 2;
if flow_model == 1
[f,state0] = gas_water_flow(r);
end
if flow_model == 2
[f,state0] = oil_water_flow(r);
end
if flow_model == 3
[f,state0] = multi_component_flow(r);
end
%% ==================================PART 6: 井制度schedule设定================================================
%将直井、水平井与多段压裂水平井分开处理
%% 直井、常规水平井定义
% Wellcpara: wellname(1) nperf，射孔点数量(2) index(3) rw(4) skin(5) welltype(6)
% welltype=1 直井，welltype=2 水平井沿x方向，welltype=3 水平井沿y方向 welltype=4 多段压裂水平井
% 直井、水平井，该种井型的处理是将射孔段安排在基质网格
% 对于直井、斜井、水平井，采取与eclipse一致的方式，给出其在基质网格中位置
% 每个射孔点由下px,py,pz确定，分别表示该射孔点在x方向，y方向的网格编号，及层数即z反方向上的网格编号（最初是以垂直向上建立的基质网格）
well1={
% 'w1', 2, [20 10 1;20 10 2;], 0.178/2, 0, 1;
% 'w2', 2, [80 10 1;80 10 2;], 0.178/2, 0, 1;
% 'w3', 1, [20 40 1;], 0.178/2, 0, 1;
% 'w4', 1, [80 40 1;], 0.178/2, 0, 1;
% 'w2', 3, [67 20 1;67 20 2;67 20 3], 0.178/2, 0, 1;
};
well1 = handle_well1(well1,r);
%% 压裂水平井定义
% 多段压裂水平井：射孔段设置在裂缝单元上，可以给出该射孔点所在的坐标，然后去寻找该点所在的裂缝单元编号
num_fracture_wells = 6;
welloc = cell(num_fracture_wells,1);
perfnum = cell(num_fracture_wells,1);
welloc{1,1}=[
255,255,5;];
welloc{2,1}=[
355,255,5;];
welloc{3,1}=[
455,255,5;];
welloc{4,1}=[
555,255,5;];
welloc{5,1}=[
655,255,5;];
welloc{6,1}=[
755,255,5;];
for i = 1:num_fracture_wells
perfnum{i,1} = findWelloc(r, welloc{i,1});%在用以Wellc0之中
end
% perfnum2 = findWelloc(r, welloc2);
well2={
'w1_f1', length(perfnum{1,1}), perfnum{1,1}, 0.178/2, 0,4;
'w1_f2', length(perfnum{2,1}), perfnum{2,1}, 0.178/2, 0,4;
'w1_f3', length(perfnum{3,1}), perfnum{3,1}, 0.178/2, 0,4;
'w1_f4', length(perfnum{4,1}), perfnum{4,1}, 0.178/2, 0,4;
'w1_f5', length(perfnum{5,1}), perfnum{5,1}, 0.178/2, 0,4;
'w1_f6', length(perfnum{6,1}), perfnum{6,1}, 0.178/2, 0,4;
};
Wellc = handle_well1_well2(well1,well2,welloc,r); %加井和射孔位置
%% 井制度设置（开关井、定压/定产、便于吞吐等）
number_phases = 4;
well_schedules = cell(number_phases,1);
time = zeros(number_phases,1);
% 不同方式对应的收敛难度、需要不一样，需分阶段调控，
% 例如在注入阶段需要小一些，如果需要做早期试井，dtmax、dtmin都需要小一些
dtmax = zeros(number_phases,1);
dtmin = zeros(number_phases,1);
% (1)well state: 'open'表示该井是开的；'close'表明该井一直是关的，如果只是阶段性关井，就用'open'定流量0生产
% (2)well type: 'pro'表示是生产井；'inj'表示是注入井;
% (3)protype：'const_q'是定流量；'const_pwf'则是定压
% (4)value：定的流量值或者井底压力值
% (5)value：此代码该值与（3）值相同
time(1) = 10; dtmax(1) = 0.5; dtmin(1) = 0.001;
well_schedules{1,1} = {
'w1_f1','open','inj','const_pwf',40,40;
'w1_f2','open','inj','const_pwf',40,40;
'w1_f3','open','inj','const_pwf',40,40;
'w1_f4','open','inj','const_pwf',40,40;
'w1_f5','open','inj','const_pwf',40,40;
'w1_f6','open','inj','const_pwf',40,40;
};
time(2) = 10; dtmax(2) = 0.5; dtmin(2) = 0.001;
well_schedules{2,1} = {
'w1_f1','open','pro','const_q',0,0;
'w1_f2','open','inj','const_pwf',40,40;
'w1_f3','open','pro','const_q',0,0;
'w1_f4','open','inj','const_pwf',40,40;
'w1_f5','open','pro','const_q',0,0;
'w1_f6','open','inj','const_pwf',40,40;
};
time(3) = 10; dtmax(3) = 0.5; dtmin(3) = 0.001;
well_schedules{3,1} = {
'w1_f1','open','pro','const_pwf',10,10;
'w1_f2','open','pro','const_q',0,0;
'w1_f3','open','pro','const_pwf',10,10;
'w1_f4','open','pro','const_q',0,0;
'w1_f5','open','pro','const_pwf',10,10;
'w1_f6','open','pro','const_q',0,0;
};
time(4) = 200; dtmax(4) = 1; dtmin(4) = 0.001;
well_schedules{4,1} = {
'w1_f1','open','pro','const_pwf',10,10;
'w1_f2','open','pro','const_pwf',10,10;
'w1_f3','open','pro','const_pwf',10,10;
'w1_f4','open','pro','const_pwf',10,10;
'w1_f5','open','pro','const_pwf',10,10;
'w1_f6','open','pro','const_pwf',10,10;
};
%% ======================================PART 7: Solver设置===========================================
yitap = 5; % 50-500psi
yitas = 0.04; % 0.05-0.5
omega = 0.5; % 0-1
Nmax = 50;
epsave = 1e-6;
epsmax = 1e-6;
%% ======================================PART 8: 正式计算===========================================
[Times, OutputRs, Wellpara, trun] = solver_NR(r, flow_model, f, os, state0, yitap,yitas,omega,Nmax,epsave,epsmax,dtmin,dtmax,Wellc,time,well_schedules);
run_time=toc;
trun.run_time=run_time;
end
算例7-油水两相流-不同裂缝制度不同/oil_water_flow.m
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function [f,state0] = oil_water_flow(r)
% =======================油相体积密度、体积系数、粘度等===============================
density_o_sc = 800; % kg/m3
% 第一种模式，直接输入参考压力、体积系数、压缩系数、粘度
oil_model =1;
if oil_model == 1
pro = 30; % reference pressure, MPa
Boi = 1.1; % gas phase volume factor
co = 1e-3 ;% gas phase compressibility, 1/MPa
voi = 10; % gas viscosity, cp
cvo = 0; % 气相粘度随压力变化的线性系数，cp/MPa
[Ppr,BO,MUO] = cal_oil_prop(pro,Boi,co,voi,cvo);
end
if oil_model == 2
Ppr = [ 0.1013
2.0946
4.0878
6.0811
8.0743
10.0676
12.0608
14.0540
16.0473
18.0405
20.0338
22.0270
24.0203
26.0135
28.0068
30.0000
];
% BO = 0.01*ones(size(Ppr,1),1);
BO = [ 1.18297
0.0557041
0.0278168
0.0182594
0.0134665
0.0106154
0.00874829
0.00744907
0.00650639
0.0058006
0.0052587
0.0048336
0.00449378
0.00421751
0.0039895
0.00379871
];
% MUG = 0.01*ones(size(Ppr,1),1);
MUO = [0.0127683
0.0130191
0.0133973
0.013872
0.014437
0.015088
0.0158182
0.0166173
0.0174719
0.0183671
0.0192882
0.0202219
0.0211575
0.0220865
0.0230024
0.0239008
];
end
% ========================水相体积系数、粘度===============================
density_w_sc = 1000; % kg/m3
prw = 30; % reference pressure, MPa
Bwi = 1.000; % water phase volume factor, 无因次
cw = 4.0e-4 ;% water phase compressibility, 1/MPa
vwi = 1; % water viscosity, cp
cvw = 0; % 水相粘度随压力变化的线性系数，cp/MPa
% =============================基质相渗===============================
ifpcow = 0; % 是否考虑毛管力
PRM=[
0.0000 0.0000 1.0000 3.8916
0.2000 0.0000 1.0000 3.8916
0.3160 0.0002 0.6784 0.5796
0.4350 0.0004 0.6215 0.3724
0.5620 0.0010 0.5456 0.2425
0.6140 0.0020 0.3939 0.0608
0.7020 0.0280 0.1399 0.0372
0.8120 0.1721 0.0515 0.0137
0.8750 0.3395 0.0297 0.0104
0.9060 0.4395 0.0 0.0090
1.0 0.4395 0.0 0.0090
];
SW=PRM(:,1);KRW=PRM(:,2);KRO=PRM(:,3);PCOW=PRM(:,4);
% =============================裂缝相渗===============================
PRF=[
0.0000 0.0000 1.0000 3.8916
0.2000 0.0000 1.0000 3.8916
0.3160 0.0002 0.6784 0.5796
0.4350 0.0004 0.6215 0.3724
0.5620 0.0010 0.5456 0.2425
0.6140 0.0020 0.3939 0.0608
0.7020 0.0280 0.1399 0.0372
0.8120 0.1721 0.0515 0.0137
0.8750 0.3395 0.0297 0.0104
0.9060 0.4395 0.0 0.0090
1.0 0.4395 0.0 0.0090
];
SWF = PRF(:,1);KRWF = PRF(:,2);KROF = PRF(:,3);PCOWF=PRF(:,4);
%%
% ===================== 高速非达西流 Forchheimer 方程 ====================
beta_non_Darcy_flow = 0; % 1e-8
% ===================== 启动压力梯度 ====================
p_grad_threshold = 0.00; % MPa/m
%% 结合流体性质参数生成相应的数据体
f = fluidPVT_oil_water_flow(Ppr, BO, MUO, Bwi, prw, cw, vwi, cvw, SW, KRO, KRW, PCOW, SWF, KROF, KRWF, PCOWF, density_o_sc, ifpcow, r.rpt);
f.beta_non_Darcy_flow = beta_non_Darcy_flow;
f.Dwsi = density_w_sc;
f.Dosi = density_o_sc;
f.p_grad_threshold = p_grad_threshold;
%% 初值条件 Initial Condition Section
% =================压力、饱和度初值======================================= %
%压力初值要考虑重力，给出油藏下表面压力值
P = [20 * ones(r.nmc, 1); 20 * ones(r.nfc, 1)];
% plow=25; % P =plow-1e-6*800*9.8*r.z;
Sw = [0.2 * ones(r.nmc, 1); 0.2 * ones(r.nfc, 1)];
state0 = initialRS_oil_water_flow(P, Sw);
end
算例7-油水两相流-不同裂缝制度不同/plotWellResponse.m
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function [] = plotWellResponse(Times,Wellpara)
% 输入
wellNumber = 1; % 井号
dataType = 'OPR'; % 类型，产气速度 GPR，产气速度 OPR, 产水速度 WPR，井底流压 BHP，压力导数 dPWF
%
t = Times;
n= size(Times,1);
% para = cell2mat(Wellpara);
nw = wellNumber;%选井号
% n = length(para);
data = zeros(n,1);
if strcmp(dataType, 'GPR')
for i = 1 : n
data(i) = Wellpara{i}{1,nw}.qg;
figureYlegend = 'Gas production rate, m^3/d';
end
plot(t,data,'k^-');hold off; xlabel('Time, day');ylabel(figureYlegend);
end
if strcmp(dataType, 'OPR')
for i = 1 : n
data(i) = Wellpara{i}{1,nw}.qo;
figureYlegend = 'Oil production rate, m^3/d';
end
plot(t,data,'k^-');hold off; xlabel('Time, day');ylabel(figureYlegend);
end
if strcmp(dataType, 'WPR')
for i = 1 : n
data(i) = Wellpara{i}{1,nw}.qw;
figureYlegend = 'Water production rate, m^3/d';
end
plot(t,data,'k^-');hold off; xlabel('Time, day');ylabel(figureYlegend);
end
if strcmp(dataType, 'BHP')
for i = 1 : n
data(i) = Wellpara{i}{1,nw}.pwf;
figureYlegend = 'BHP, MPa';
end
plot(t,data,'k^-');hold off; xlabel('Time, day');ylabel(figureYlegend);
end
if strcmp(dataType, 'dPWF') % dpwf/dlnt = t*dpwf/dt
for i = 1 : n
if i == 1
data(i) = (Wellpara{i+1}{1,nw}.pwf-Wellpara{i}{1,nw}.pwf)/(log(t(i+1))-log(t(i)));
elseif i == n
data(i) = (Wellpara{i}{1,nw}.pwf-Wellpara{i-1}{1,nw}.pwf)/(log(t(i))-log(t(i-1)));
else
data(i) = (Wellpara{i+1}{1,nw}.pwf-Wellpara{i-1}{1,nw}.pwf)/(log(t(i+1))-log(t(i-1)));
end
figureYlegend = 'Pressure derivative, MPa';
end
plot(t,data,'k^-');hold off; xlabel('Time, day');ylabel(figureYlegend);
set(gca, 'XScale', 'log');
set(gca, 'YScale', 'log');
end
end