含水率与时间关系数学模型的建立及应用

Building and application of a mathematical model for water cut and time relationship.

对油藏条件作不同假设，可以建立不同数学模型，对一些油藏开发经验公式进行理论证明，并探讨其适用条件。建立了已见水油藏含水率与时间关系的数学模型，假设条件为：①总容积不变，只包含油、水两相流体；②产水递增率与产油量递减率之和为经验常数；③平均含水饱和度与时间呈线性关系。用该模型对相对渗透率比值与饱和度的经验关系式进行理论推导，由于油和水的粘度只是压力、温度等因素的函数，不随其饱和度而变化，因此在一定温度、压力条件下，其比值是常数。据此认为，相对渗透率比值与饱和度的经验关系式适用条件为：油、水两相同时渗流，产量递减不明显，产油量递减率与产水递增率之和为常数。用含水率与时间关系的数学模型预测二连阿南油田的综合含水率，在油田全面含水稳定生产的情况下，预测的含水率与实际数据符合较好。图２参５（陈志宏摘）

Various assumptions for reservoir conditions are made to build various mathematical models. Some reservoir development empirical equations have been proved theoretically and the conditions for their applications are discussed. A mathematical model describing the relation of water cut and time for a watered out reservoir is established. The relevant assumptions made are ①total volume of the reservoir is constant and the reservoir contains only two phases of water and oil; ②the sum of water cut increase rate and the production declining rate is an empirical constant; ③average water saturation has a linear relation with time. The viscosities of oil and water are functions of pressure and temperature. Therefore, the viscosity ratio of oil and water is a constant under definite pressure and temperature and has no relation with the saturation. This model is used to derive the empirical expression of viscosity ratio and saturation. According to this it is considered that the conditions under which the empirical expression can be used are: oil and water flow simultaneously, no apparent production declining, the sum of production declining rate and water cut increasing rate is a constant. This model is used to predict the comprehensive rate of water content of A'nan oil field in Erlian basin . Under the condition of stable overall water cut, the water cut predicted conforms with those actual data fairly well. Subject