| With the development of horizontal well drilling technology, combined distribution pattern of horizontal well and vertical well provide a new method which can develop low permeability reservoir in an efficient and scientific way and enhance profit of oilfield. In this paper, on the basis of previous studies, comprehensively adopted higher mathematics, complex functions, percolation mechanics and the oil/gas field development knowledge theory and so on, steady-flow theory of horizontal well, multilateral horizontal well, mixed well pattern of horizontal well or multilateral horizontal well and vertical well are studied, The study includes:(1) The mechanics of fluid flow of horizontal well and multilateral horizontal well; (2) productivity calculation method of horizontal or multilateral horizontal well and vertical well mixed well patterns in the condition of single-phase steady flow; (3) The potential of a row horizontal well and a vertical well in XY plate are deduced respectively; (4) The mechanics of fluid flow of staggered mixed pattern of horizontal well and vertical well.The following conclusions are made from studies above:(1) We obtained deliverability equations of horizontal well and multilateral horizontal well by study steady-flow characteristic of them. All of these researches lay a foundation for well pattern research.(2) Productivity of mixed well pattern of horizontal well or multilateral horizontal well and vertical well is constructed. From the formula show that:productivity of mixed well pattern is higher than vertical well pattern, so as to oil and gas field development scheme provides certain theory basis, which provide theoretical basis for oilfield development design.(3) The equivalence percolation resistance law is accurate enough than conformal transformation to be used in productivity calculation of horizontal well and vertical well horizontal mixed well pattern.(4) The influences of the horizontal well length, the thickness of reservoir, vertical well spacing, formation heterogeneity and oil well location are analyzed.(5) The potential of a row horizontal well and a vertical well in XY plate are deduced respectively, which is important for mixed well pattern research.(6) The mechanics of fluid flow theory of staggered mixed pattern of horizontal well and vertical well is constructed. The accurate productivity of the pattern in pseudo 3-dimension is given and a new concept of optimum shape factor of the well pattern is advanced. The relationship of optimum shape factor against dimensionless length of horizontal well is presented by regression equation.(7) By drawing charts concluded that: the relationship of optimum shape factor of the well pattern against dimensionless length of horizontal well is independent of the area pattern unit and formation thickness, so it is very important to oilfield development design. |