不确定性预测与决策方法及其在油藏管理单元评价中的应用研究
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摘要
油田开发具有高投入、高风险的特点,如何取得最大的经济开采效益一直是各大石油公司追求的目标。为了应对当前油气资源逐年递减和开采难度日益增大的问题,各油田公司在广泛应用新技术的同时,也积极探索新的油藏经营管理模式,提倡精细化管理。加强油田开发指标精细化管理是油田开发精细化管理的重要组成部分。由于油藏深埋地下,内部结构复杂,人们对油藏的认识具有一定的模糊性,再加上开发环境的不确定性,导致一些确定性预测与决策方法可靠性不高。借助于现在比较成熟的不确定性理论(概率论、模糊集理论、粗糙集理论和灰色系统理论)进行油田开发指标的预测与优化,可以为油田开发方案编制及调整提供技术支撑；油田开发各阶段生产目标的制定也需要运用不确定性理论作为工具,进行最优决策。
油藏管理单元作为油藏经营管理主体,其操作行为直接关系到油藏能否平稳有序地进行开发。基于不确定性理论建立的预测与决策方法,编制相应计算机程序,能够提高油藏管理单元决策的时效性。根据油藏开发动态,运用这些精细化管理技术对油田开发指标进行预测或规划,提出油藏管理单元实际可行的阶段生产目标,在此基础上,制定合理的评价体系,可以有效提高目标管理的执行效率。因此,研究基于不确定性理论的开发指标预测决策方法及油藏管理单元评价方法具有重要意义。本文主要做了以下工作：
(1)对用于开发指标预测的灰色模型进行了深入研究。针对灰色模型的适用范围及特点,研究了用于灰色建模的原始数据序列预处理方法,包括单调递增序列、单调递减序列、波动序列的预处理方法；还研究了基于模糊数的灰色预测方法,包括区间模糊数、三角模糊数和梯形模糊数的预测方法。这些方法有效地解决了不同形式的开发指标时间序列预测问题。
(2)对用于开发指标预测的神经网络与不确定性理论(模糊集、粗糙集、灰色系统理论)相融合的预测方法进行了研究。神经网络与模糊集融合可以解决软预测问题,把确定性数据进行模糊化,使神经网络具有更好的泛化能力；而神经网络与粗糙集融合可以消除训练样本的冗余信息,提高神经网络的训练速度；神经网络与灰色系统理论融合可以有效减弱训练样本数据的扰动,提高神经网络的预测能力。这些方法可以解决开发指标多输入多输出的预测问题。
(3)对用于开发指标预测的支持向量机与不确定性理论(粗糙集、灰色系统理论)相融合的预测方法进行了研究。支撑向量机不仅具有神经网络很好的泛化能力,而且能够克服其收敛局部解和过学习情况；不仅适用于样本分类,还能进行多输入单输出预测。支持向量机与粗糙集融合可以排除影响不大的指标数据,提高预测准确性；支持向量机与灰色系统理论融合是用累加序列作为训练样本,可以减弱原始样本数据的扰动。
(4)对用于开发指标优化决策的不确定性规划方法进行了研究。考虑到目标函数之间的不可公度性,目标函数不能直接进行线性相加或加权相加,对多目标规划中的目标函数进行了改进,给出了基于改进目标函数的随机规划和模糊规划模型,并分析了产量优化的不确定性规划模型。
(5)对不确定多属性决策方法进行了系列研究及应用。研究了考虑概率分布的区间数比较方法,提出了区间数比较的期望值法,基于随机模拟可以求得可能性大小；证明了区间数比较的可能度法和优势度法其实都可以用区间数的中点进行判别的结论,并从互补和互反两个角度提出了一种基于相对熵的优势度法；研究了属性值或权重为模糊数的多属性决策问题；以及带有可行区间的多属性决策问题,提出了区间数包含度的概念,这里可行区间是指属性值符合允许范围；还利用粗糙多属性决策方法确定了剩余可采储量品位的决定因素和利用灰色多属性决策方法优选开发方案。
(6)研究了油藏管理单元评价方法,制定了采油作业区开发管理考核评价体系和油藏管理单元开发效果评价体系。利用传统层次分析法和模糊层次分析法之间的同构关系提出了一种传统层次分析法一致性变换方法；根据系统工程方法确定了采油作业区开发管理考核评价指标体系层次结构,用传统层次分析法来确定各评价指标权重,建立了各指标的评分标准；并建立了油藏管理单元开发效果的评价指标及用数据包络分析方法评价其开发效果相对有效性。
Oilfield development has the characteristics of high investment, high risk, and how to obtain the maximum economic effectiveness of exploitation has been a goal pursued by the oil companies. With the current oil and gas resources gradually decreasing and the difficulty of exploitation increasing, oilfield companies widely used the new technologies, and also actively explore the new management mode to promote the delicacy management. Strengthening the management of the oilfield development indicators is an important part of the delicacy management of oilfield development. Owing to the oil reservoir under the deep layers and has the complex internal structure, people's understanding has certain vagueness for it, coupled with the uncertainty of the development environment, leading to some deterministic methods of forecasting and decision-making are unreliable. By means of the now mature uncertainty theories, such as probability theory, fuzzy set theory, rough set theory and grey system theory, forecasting and optimizing the oilfield development indicators, it can provide the technical support for the oilfield development programming and adjustment; the stage production targets of oilfield development require the uncertainty theories as a tool for the optimal decision.
Reservoir management unit (RMU) as the main body of reservoir management, its operation behavior is directly related to the reservoir whether smoothly and orderly developed. The forecasting and decision-making model based on uncertainty theory, by setting up the correspondingly computer programming, can improve the decision-making for RMUs. According to the dynamic of oilfield development, use these techniques of delicacy management to predict the oilfield development indicators or make reasonable planning, and propose the practical and feasible stage production targets. On this basis, formulating a reasonable evaluation system, it can effectively improve the implementation efficiency for the management by objectives. Therefore, the study on the forecasting and decision-making methods of development indicators based on the uncertainty theories is of great significance. In this paper, we mainly do the following:
(1) For grey modeling the pretreatment methods of original data sequence were studied. According to the characteristics and the scope of application of grey model, previously processed for the original data sequence, including the processing methods of monotone increasing sequence, monotone decreasing sequence and fluctuation sequence; Grey forecasting methods based on fuzzy number were also studied, including the forecasting methods of interval fuzzy number, triangular fuzzy number and trapezoidal fuzzy number. These methods could effectively solve the forecasting problems of the different forms of time series for the development indicators.
(2) The forecasting methods combined the neural network (NN) with the theory of fuzzy sets (FS), rough sets (RS) and grey systems (GS) were studied. The integration of NN and FS can solve the soft forecasting problem, by fuzzifying the deterministic data, it make NN has the better generalization ability; The integration of NN and RS can eliminate the redundant information of training samples to improve the neural network training speed; The integration of NN and GS can weaken the perturbation of training sample data to improve the predictive ability of NN. These methods can solve the multi-input multi-output forecasting problem.
(3) The forecasting methods combined the support vector machine (SVM) with the theory of rough sets and grey systems were studied. SVM not only has the good generalization ability as NN, but also can overcome the convergence of local solution and excessive learning; it can be applied not only to sample classification, but also to the multi-input single-output forecasting problems. Combined with RS, SVM can be ruled out the little impact indicators to improve the forecasting accuracy; Combined with GS, the accumulative sequences used as the training samples, SVM can weaken the perturbation of the original sample data.
(4) Taking into account the incommensurability between the objective functions, the objective functions can't be directly linear or weighted sum. The objective function in multi-objective programming was improved, and based on the improved objective function, stochastic and fuzzy programming models were given out, including the expected value model, chance constrained model and dependent-chance model.
(5) Uncertainty multi-attribute decision-making (MADM) methods and their application were studied. The comparison method of two interval numbers with probability distribution was studied, and the law of expectation value was put forward, by means of the stochastic simulation, we can get the value of possibility; it was proved that the law of possible degree and advantage degree can be judged by the midpoint of two interval numbers, and we put forward a kind of advantage degree based on the relative entropy method from the complementary and reciprocal angle; considered the fuzzy MADM problems, whose attribute values or attribute weights are fuzzy numbers; MADM problems with the feasible intervals were also studied, and the concept of inclusion degree of interval number was presented, where the feasible interval is the allowable range for an attribute; Rough MADM method was used to determine the determinants of the remaining recoverable reserves grade, and grey MADM methods were used to choose the best development program.
(6) Set up the evaluation system of development and management for the oil recovery operation units and the evaluation system of development effectiveness for reservoir management units respectively. By the isomorphic relationship between the traditional analytic hierarchy process (AHP) and the Fuzzy AHP, a kind of consistency transformation was proposed for the traditional AHP. Through the systems engineering approach to determine the hierarchy of evaluation indicators, and the AHP was used to determine the weights of all the evaluation indicators. We formulated the scoring methods of various indicators for the oil recovery operation units and used the data envelopment analysis (DEA) method to evaluate the relative efficiency of development effectiveness for reservoir management units.
油藏管理单元作为油藏经营管理主体,其操作行为直接关系到油藏能否平稳有序地进行开发。基于不确定性理论建立的预测与决策方法,编制相应计算机程序,能够提高油藏管理单元决策的时效性。根据油藏开发动态,运用这些精细化管理技术对油田开发指标进行预测或规划,提出油藏管理单元实际可行的阶段生产目标,在此基础上,制定合理的评价体系,可以有效提高目标管理的执行效率。因此,研究基于不确定性理论的开发指标预测决策方法及油藏管理单元评价方法具有重要意义。本文主要做了以下工作：
(1)对用于开发指标预测的灰色模型进行了深入研究。针对灰色模型的适用范围及特点,研究了用于灰色建模的原始数据序列预处理方法,包括单调递增序列、单调递减序列、波动序列的预处理方法；还研究了基于模糊数的灰色预测方法,包括区间模糊数、三角模糊数和梯形模糊数的预测方法。这些方法有效地解决了不同形式的开发指标时间序列预测问题。
(2)对用于开发指标预测的神经网络与不确定性理论(模糊集、粗糙集、灰色系统理论)相融合的预测方法进行了研究。神经网络与模糊集融合可以解决软预测问题,把确定性数据进行模糊化,使神经网络具有更好的泛化能力；而神经网络与粗糙集融合可以消除训练样本的冗余信息,提高神经网络的训练速度；神经网络与灰色系统理论融合可以有效减弱训练样本数据的扰动,提高神经网络的预测能力。这些方法可以解决开发指标多输入多输出的预测问题。
(3)对用于开发指标预测的支持向量机与不确定性理论(粗糙集、灰色系统理论)相融合的预测方法进行了研究。支撑向量机不仅具有神经网络很好的泛化能力,而且能够克服其收敛局部解和过学习情况；不仅适用于样本分类,还能进行多输入单输出预测。支持向量机与粗糙集融合可以排除影响不大的指标数据,提高预测准确性；支持向量机与灰色系统理论融合是用累加序列作为训练样本,可以减弱原始样本数据的扰动。
(4)对用于开发指标优化决策的不确定性规划方法进行了研究。考虑到目标函数之间的不可公度性,目标函数不能直接进行线性相加或加权相加,对多目标规划中的目标函数进行了改进,给出了基于改进目标函数的随机规划和模糊规划模型,并分析了产量优化的不确定性规划模型。
(5)对不确定多属性决策方法进行了系列研究及应用。研究了考虑概率分布的区间数比较方法,提出了区间数比较的期望值法,基于随机模拟可以求得可能性大小；证明了区间数比较的可能度法和优势度法其实都可以用区间数的中点进行判别的结论,并从互补和互反两个角度提出了一种基于相对熵的优势度法；研究了属性值或权重为模糊数的多属性决策问题；以及带有可行区间的多属性决策问题,提出了区间数包含度的概念,这里可行区间是指属性值符合允许范围；还利用粗糙多属性决策方法确定了剩余可采储量品位的决定因素和利用灰色多属性决策方法优选开发方案。
(6)研究了油藏管理单元评价方法,制定了采油作业区开发管理考核评价体系和油藏管理单元开发效果评价体系。利用传统层次分析法和模糊层次分析法之间的同构关系提出了一种传统层次分析法一致性变换方法；根据系统工程方法确定了采油作业区开发管理考核评价指标体系层次结构,用传统层次分析法来确定各评价指标权重,建立了各指标的评分标准；并建立了油藏管理单元开发效果的评价指标及用数据包络分析方法评价其开发效果相对有效性。
Oilfield development has the characteristics of high investment, high risk, and how to obtain the maximum economic effectiveness of exploitation has been a goal pursued by the oil companies. With the current oil and gas resources gradually decreasing and the difficulty of exploitation increasing, oilfield companies widely used the new technologies, and also actively explore the new management mode to promote the delicacy management. Strengthening the management of the oilfield development indicators is an important part of the delicacy management of oilfield development. Owing to the oil reservoir under the deep layers and has the complex internal structure, people's understanding has certain vagueness for it, coupled with the uncertainty of the development environment, leading to some deterministic methods of forecasting and decision-making are unreliable. By means of the now mature uncertainty theories, such as probability theory, fuzzy set theory, rough set theory and grey system theory, forecasting and optimizing the oilfield development indicators, it can provide the technical support for the oilfield development programming and adjustment; the stage production targets of oilfield development require the uncertainty theories as a tool for the optimal decision.
Reservoir management unit (RMU) as the main body of reservoir management, its operation behavior is directly related to the reservoir whether smoothly and orderly developed. The forecasting and decision-making model based on uncertainty theory, by setting up the correspondingly computer programming, can improve the decision-making for RMUs. According to the dynamic of oilfield development, use these techniques of delicacy management to predict the oilfield development indicators or make reasonable planning, and propose the practical and feasible stage production targets. On this basis, formulating a reasonable evaluation system, it can effectively improve the implementation efficiency for the management by objectives. Therefore, the study on the forecasting and decision-making methods of development indicators based on the uncertainty theories is of great significance. In this paper, we mainly do the following:
(1) For grey modeling the pretreatment methods of original data sequence were studied. According to the characteristics and the scope of application of grey model, previously processed for the original data sequence, including the processing methods of monotone increasing sequence, monotone decreasing sequence and fluctuation sequence; Grey forecasting methods based on fuzzy number were also studied, including the forecasting methods of interval fuzzy number, triangular fuzzy number and trapezoidal fuzzy number. These methods could effectively solve the forecasting problems of the different forms of time series for the development indicators.
(2) The forecasting methods combined the neural network (NN) with the theory of fuzzy sets (FS), rough sets (RS) and grey systems (GS) were studied. The integration of NN and FS can solve the soft forecasting problem, by fuzzifying the deterministic data, it make NN has the better generalization ability; The integration of NN and RS can eliminate the redundant information of training samples to improve the neural network training speed; The integration of NN and GS can weaken the perturbation of training sample data to improve the predictive ability of NN. These methods can solve the multi-input multi-output forecasting problem.
(3) The forecasting methods combined the support vector machine (SVM) with the theory of rough sets and grey systems were studied. SVM not only has the good generalization ability as NN, but also can overcome the convergence of local solution and excessive learning; it can be applied not only to sample classification, but also to the multi-input single-output forecasting problems. Combined with RS, SVM can be ruled out the little impact indicators to improve the forecasting accuracy; Combined with GS, the accumulative sequences used as the training samples, SVM can weaken the perturbation of the original sample data.
(4) Taking into account the incommensurability between the objective functions, the objective functions can't be directly linear or weighted sum. The objective function in multi-objective programming was improved, and based on the improved objective function, stochastic and fuzzy programming models were given out, including the expected value model, chance constrained model and dependent-chance model.
(5) Uncertainty multi-attribute decision-making (MADM) methods and their application were studied. The comparison method of two interval numbers with probability distribution was studied, and the law of expectation value was put forward, by means of the stochastic simulation, we can get the value of possibility; it was proved that the law of possible degree and advantage degree can be judged by the midpoint of two interval numbers, and we put forward a kind of advantage degree based on the relative entropy method from the complementary and reciprocal angle; considered the fuzzy MADM problems, whose attribute values or attribute weights are fuzzy numbers; MADM problems with the feasible intervals were also studied, and the concept of inclusion degree of interval number was presented, where the feasible interval is the allowable range for an attribute; Rough MADM method was used to determine the determinants of the remaining recoverable reserves grade, and grey MADM methods were used to choose the best development program.
(6) Set up the evaluation system of development and management for the oil recovery operation units and the evaluation system of development effectiveness for reservoir management units respectively. By the isomorphic relationship between the traditional analytic hierarchy process (AHP) and the Fuzzy AHP, a kind of consistency transformation was proposed for the traditional AHP. Through the systems engineering approach to determine the hierarchy of evaluation indicators, and the AHP was used to determine the weights of all the evaluation indicators. We formulated the scoring methods of various indicators for the oil recovery operation units and used the data envelopment analysis (DEA) method to evaluate the relative efficiency of development effectiveness for reservoir management units.
引文
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