Volumetric Source Models Of Binary System And Its Appliction

The binary system is employed to describe reservoirs with natural fractures or fracture networks created by volume fracturing.Theory of fluids flow in those reservoirs is widely used in well testing,production predicting,fractures predicting and development plan optimal designing.Domestic and foreign researchers have made numerous studies for the theories and applications of binary system.However,most of those studies are focused on straight wells,vertical fractures and horizontal wells,and rarely involve fractured horizontal wells.Moreover,shale gas reservoirs could be characterized as binary system after volume fracturing;the flow model should be deeply studied.Laplace transformation is the most important method to deal with flow models of binary system if combined with the numerical inversion method.Unfortunately,equations which express flow in horizontal wellbore or high velocity non-Darcy flow cannot be solved through Laplace transformation due to the non-linear relation of pressure and flow rate in the equations.As a result,this kind of flow becomes a challenging problem in traditional flow theory.Nevertheless,semi-analytical method to solve the non-linear flow problems in real space is mature,it operate by divide the time,calculate flow rate in each time interval.As a result,a basic solution in real space becomes the foundation to carry out the semi-analytical methods.This result enlightens us to seek a way to solve flow model of binary system in real space(without taking Laplace transformation).Consequently,the non-linear flow problems could be combat by following the mature semi-analytical method.For regular binary system and shale gas reservoirs,volumetric source idealization is applied to discuss non-steady flow problem.In this method,theories and techniques of Advanced Mechanics of Fluids Flow in Porous Media,Reservoir Engineering,Partial Different Equations,Numerical Analysis,Computing Mathematics and Computer Programming are considered,so the non-steady flow models are established,and then basic volumetric source functions are derived.Furthermore,applications on productivity analyses for different types of wells are illustrated,and finally the main theoretical algorithm is programed.In this study some important results were obtained as follows:(1)Based on flow mechanics of regular binary system and shale gas reservoirs,three-dimensional non-steady flow models were proposed with volumetric source idealization.The models were solved both in real space and in Laplace space by taking appropriate integral transformation,so basic volumetric source functions were derived and its application were elaborated.(2)Pressure response models of different type of wells(straight wells,vertical fractures,horizontal wells,fractured horizontal wells)with different assumptions(uniform-flux,infinite-conductivity and finite-conductivity)were derived with basic volumetric source functions.Results of volumetric source models and traditional models were compared and achieved preferably coincidence,which shows validity and reveals the advantages of new models.(3)Semi-analytical methods were developed to calculate production of fractured horizontal wells in naturally fractured reservoirs,which flow in horizontal wellbore or high velocity non-Darcy flow were considered.Correlations of parameters of hydraulic fractures were analyzed,and then a new optimization design method was proposed based on the results.(4)Based on the volumetric source flow models and its main algorithms,software for calculating production of fractured horizontal wells and optimizing parameters of hydraulic fractures were exploited by utilizing Visual Basic 6.0,and the software could be applied in both homogeneous and binary systems.It has been proved volumetric source methods can be well adopted to solve flow problems in binary system.Moreover,volumetric source methods show the same advantages as what shows in homogeneous reservoirs:better property of basic source functions,more concise in calculation,better adaptability of basic source 'function,better efficient in application on complex well/fracture configuration cases.Therefore,this paper can offer instructive value for the exploitation of naturally fractured reservoirs and shale gas reservoirs.