Multi-Objective Search for Three-Dimensional Connectivity Paths between Wells in Fractured-Vuggy Reservoirs
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摘要: 深层海相碳酸盐岩油气藏储集体类型复杂多样，非均质性强，井间连通关系评价困难. 针对传统静动态方法主观性强、多解等问题，基于三层结构设计，采用地震多属性数据刻画不同类型储集空间，提出改进A*算法搜索符合地质构造的井间连通路径，根据优化目标研究自适应交叉变异概率改进NSGA Ⅲ算法自动获取井间三维沟通路径，细致刻画静态连通情况. 以塔河油田S80单元典型井组为研究对象，实验结果表明改进优化算法能有效提升多目标算法的全局搜索能力，自动搜索路径与地震资料分析、示踪剂测试情况基本吻合，能较好反映井间不同尺度缝洞空间配置关系，为缝洞型油藏注水开发阶段指导工作制度调整、提高采收率提供技术支撑.Abstract: The deep marine carbonate reservoirs have complex reservoir types and strong heterogeneity, so it's difficult to evaluate the well connectivity.This paper designs a three-layer structure to address the subjectivity and multiple solutions problems about traditional static and dynamic inter-well connected evaluation methods. The improved A* algorithm is proposed to search for the inter-well connected paths by geological formations. The improved NSGA Ⅲ algorithm with self-applicable cross-variance probability according to the optimization objective is proposed to obtain three-dimensional multi-connected paths automatically which can carefully characterize the static connectivity. The experiment takes the S80 unit typical well group as the object in the TAHE oilfield. The results show that the adaptive cross-variance probability can effectively improve the multi-objective algorithm global search capability. The automatic search paths match with the seismic multi-attribute data analysis and tracer testing.Therefore, the algorithm can better reflect the spatial configuration relationship of fractures and cavities at different scales between wells. Furthermore, it can also provide technical support for adjusting the work system and improving the recovery in the field development of fractured-vuggy reservoirs in the water-injecting development stage.
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图 5 井间连通路径多层搜索策略框架图
Fig. 5. Multi-layer search strategy framework for inter-well connection paths
图 9 TK636H井组三维连通路径搜索结果
Fig. 9. 3D communication path search results of well group TK636H
图 10 TK636H-TK747井对搜索路径分类结果
a. 第一类路径；b. 第二类路径；c. 第三类路径
Fig. 10. Search path classification results of the well pair TK636H-TK747
图 11 TK636H井组缝洞发育特征
a. 三维路径图；b. 裂缝展布图；c. 溶洞展布图
Fig. 11. Fractured-vuggy development characteristics of well group TK636H
图 12 TK636H井组示踪剂曲线图
a. TK636H-S80井对；b. TK636H-TK611井对；c. TK636H-TK747井对
Fig. 12. Tracer curve of well group TK636H
表 1 融合地震多属性井间三维连通路径搜索算法
Table 1. Search algorithm for 3D inter-well connection paths with fused seismic multi-attribute
输入：控制参数：种群大小$ NP $，最大演化次数$ GE{N}_{\mathrm{m}\mathrm{a}\mathrm{x}} $，交叉概率最大最小值$ {p}_{c\mathrm{m}\mathrm{a}\mathrm{x}}、{p}_{c\mathrm{m}\mathrm{i}\mathrm{n}} $，变异概率最大最小值$ {p}_{m\mathrm{m}\mathrm{a}\mathrm{x}}、{p}_{m\mathrm{m}\mathrm{i}\mathrm{n}} $
输出：最终种群$ {P}_{GE{N}_{\mathrm{m}\mathrm{a}\mathrm{x}}} $1: 生成初始种群$ {P}_{GEN}=\left\{\overrightarrow{{x}_{1}}, \overrightarrow{{x}_{2}}, \dots, \overrightarrow{{x}_{NP}}\right\} $，并初始化演化代数$ GEN\leftarrow 0 $，生成参考点$ Z $
2: 根据改进A*算法搜索路径通过公式(8)(9)计算目标函数适应值$ f\left(\overrightarrow{{x}_{i}}\right)(i=\mathrm{1, 2}, \dots, NP) $
3: while $ GEN < GE{N}_{\mathrm{m}\mathrm{a}\mathrm{x}} $ do
4: 计算父代种群中的互异路径条数$ d $
5: 通过公式(11)(12)(13)计算交叉变异概率
6: 交叉变异产生子代种群$ {Q}_{GEN} $
7: 合并父子代种群$ {R}_{GEN} $← $ {P}_{GEN}\bigcup {Q}_{GEN} $
8：非支配排序$ \left({F}_{1}, {F}_{2}, \dots \right)=Non\_dominated\_sort\left({R}_{GEN}\right) $
9： 初始化$ {S}_{GEN}\leftarrow \mathrm{\varnothing }, i=1 $
10: do
11: $ {S}_{GEN}\leftarrow {S}_{GEN}\bigcup {F}_{i} $, $ i=i+1 $
12: while $ \left|{S}_{GEN}\right| $≤$ NP $
13: 关键层$ {F}_{l}\leftarrow {F}_{i+1} $
14: if $ \left|{S}_{GEN}\right|=NP $ then
15: $ {P}_{GEN+1}\leftarrow {S}_{GEN} $
16: break
17: else
18: $ {P}_{GEN+1}={\cup }_{j=1}^{l-1}{F}_{j} $
19: 从$ {F}_{l} $挑选个体数$ K=NP-\left|{P}_{GEN+1}\right| $
20: 自适应归一化$ Normalization\left({S}_{GEN}\right) $
21: 参考点关联$ [\pi \left(s\right), d(s\left)\right]\leftarrow Associate({S}_{GEN}, Z) $, $ \pi \left(s\right) $为参考点序号，$ d\left(s\right) $为个体到参考线的距离
22: 通过小生境保留$ {F}_{l} $层选择$ K $个个体$ {P}_{GEN+1}\leftarrow Niching(K, \pi, d, Z, {F}_{l}) $
23: $ GEN=GEN+1 $
24: end while
25: return $ {P}_{GE{N}_{\mathrm{m}\mathrm{a}\mathrm{x}}} $
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表 2 算法参数设置
Table 2. Algorithm parameter setting
算法 $ NP $ $ {P}_{c} $ $ {P}_{c\mathrm{m}\mathrm{a}\mathrm{x}} $ $ {P}_{c\mathrm{m}\mathrm{i}\mathrm{n}} $ $ {P}_{m} $ $ {P}_{m\mathrm{m}\mathrm{a}\mathrm{x}} $ $ {P}_{m\mathrm{m}\mathrm{i}\mathrm{n}} $ $ GE{N}_{\mathrm{m}\mathrm{a}\mathrm{x}} $ NSAG Ⅲ 200 0.6 - - 0.05 - - 30 改进算法 200 - 0.8 0.4 - 0.1 0.01 30
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表 3 TK636H井组示踪剂测试结果
Table 3. Tracer test results of well group TK636H
生产井 背景浓度(cd) 突破时间(d) 突破浓度(cd) 井距(m) 推进速度(m/d) 累积浓度(cd) S80 91.2 12 326.8 691 57.6 24 588.7 TK611 101.4 11 244.5 1631 148.3 19 852.4 TK747 144.7 17 374.1 1191 70.1 20 641.2
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