变表皮系数试井解释模型建立及应用

Establishment and application of well testing model considering variable skin factor

 李文会¹ 刘鹏程¹ 李中超²

中国地质大学（北京）能源学院，北京 100083 中国石化中原油田分公司勘探开发研究院，河南 濮阳 457001）

School of Energy Resources, China University of Geosciences, Beijing 100083, China Research Institute of Exploration and Development, Zhongyuan Oilfield Company, SINOPEC, Puyang 457001, China)

 目前大部分试井数学模型将表皮系数视为常数，然而这仅是一种简化的处理。在实际生产过程中，注入或产出的流体可能冲刷岩石颗粒或者携带杂质颗粒进入地层，因此表皮系数是随时间变化的。文中将受影响区域的平均渗透率定义为一个时间的函数，利用经典表皮系数的定义，建立了表皮系数与时间的关系式，称之为变表皮系数；将该变表皮系数代替传统试井解释模型内视为常数的表皮系数，建立变表皮系数试井解释数学模型；利用拉普拉斯变换求解出该模型在拉氏空间内的解，并利用Stehfest数值反演计算出实空间的解；做出无量纲井壁压力和压力导数随时间变化的双对数图，并分析了变表皮系数表达式中各参数对无量纲井壁压力及压力导数的影响。文中利用胜利油田胜2区块一口井的实测试井数据进行实例分析，说明了该模型的适用性。

 At present, skin factor is regarded as a constant in most of mathematical models of well test, but this is only a simplified treatment. In the actual production process, fluid of injection or production may scour rock particles or carrying particles into formation, hence, the actual skin factor changes with time. The average permeability of damaged area is defined as a time function in this paper. Using the traditional definition of skin factor, the relationship between the skin factor and time is established, and this skin factor is called variable skin factor. The variable skin factor is introduced to replace the constant skin factor in traditional well test interpretation models, then a new model considering variable skin factor is established. This model can be solved by Laplace transformation in Laplace domain, after that the solution is inversed by the method of stehfest numerical inversion. The dimensionless wellbore pressure and pressure derivative changes with dimensionless time plots are drawn by double logarithm, and the effects of all the parameters on the variable skin factor expression are analyzed on the dimensionless wellbore pressure and pressure derivative. Finally, the well testing data in Sheng-2 Block, Shengli Oilfield, are carried to prove the applicability of the model.

10.6056/dkyqt201604018