Nonlinear Well Productivity And Well Testing

Recently, with the development of non-conventional reservoirs, more attention is paid on nonlinear flow in porus media. The flow theory based on Darcy model becomes perfect gradually, but the nonlinear flow still needs further research. It has profound significance to study well productivity and well testing on evaluating this kind of formation.Based on the review of domestic and international documents, nonlinear flow mechanics of two different kinds (low velocity nonlinear flow and high velocity nonlinear flow) are summarized. Based on capillary model and boundary layer theory, a new mathematical model is proposed by introducing two parameters: c₁ and c₂ .Comprehensive explanation is made on start-up gradient and nonlinear flow and verification of the new model is made by the experimental data. High velocity nonlinear flow model proposed by Barree and Conway is analyzed on k_mrandÏ„.Based on two new nonlinear models, low velocity productivity of vertical well, vertical fractured well, horizontal well and high velocity productivity of vertical well is studied. The results show that c₁ and c₂ are essential to low velocity well productivity. Well productivity is increasing with the decrease of c₁ or c₂ when the sum of c₁ and c₂ is not constant while well productivity is increasing with the decrease of c₁ and the increse of c₂ when the sum of c₁ and c₂ is constant. Vertical fratured well and horizontal well can decrease the start-up pressure and have high productivity than vertical well. k_mrandÏ„is important to high velocity well productivity. Well productivity is increasing when the increase of k_mrorÏ„.Based on two new nonlinear models, low velocity nonlinear homogeneous media and double media well testing models and high velocity nonlinear homogeneous media, double media and triple media well testing models are established and solved by finite different method. The well testing curves of different models are compared and the effect of related parameters is discussed, the nonlinear buildup well testing curve is also discussed. The results show that the pressure and pressure deviation curves become upward in radical flow period for low velocity homogeneous media while the depth of concave decreases for low velocity double media in contrast with Darcy model. The degree of upward and depth of concave is increasing with the increase of c_1Dor c_2Dwhen the sum of c_1Dand c_2Dis not constant while the degree of upward and depth of concave is increasing with the increase of c_1Dand the decrese of c_2Dwhen the sum of c_1Dand c_2Dis constant. The hump has changed for high velocity nonlinear homogeneous media, double media and triple media well testing compared with Darcy model. The degree of pressure curve ascending and hump augment is increasing with the decrease of k_mror increase ofÏ„D.