Productivity Prediction And Water Cresting & Coning Dynamic Of Branched Horizontal Well In Bottom Water Reservoir

For the advantage of expanding the drainage area in formation, the branched horizontal well technologe can be used to increase the well’s productivity. The branched horizontal well can improve economic benefit depend on the well reasonable work system, which can effective control of the water cresting or coning in bottom water reservoir. The productivity and water increasing dynamic are the basis of optimization the shape, the structure, the number of branches, the production rate and work system of branched horizontal well in a bottom water reservoir. In this paper, to address the series of problems existing in branched horizontal well seepage flow of bottom water reservoir, the branched horizontal well bore and oil reservoir are the main study objectives. Based on theories about variable mass conduit flow and oil and gas seepage flow, research is conducted on coupling issues of branched horizontal well bore conduit flow and seepage flow in bottom water reservoir, critical rate, critical differential pressure, water breakthrough time and dynamic for branched horizontal well.Simple analytic formulas for horizontal and branched horizontal well productivity prediction are classified and studied. With the prerequisite of infinite conductivity assumption in simple analytic formula and the simplification of drainage mass, methods including equal filtrational resistance, mirror image, potential function superposition theory and conformal transformation are used to derive stable simple analytic equation, which is fit for rapid productivity estimate of some particular horizontal well pattern of bottom water reservoir.By means of point source exact solution, unstable seepage flow model for branched horizontal well which is arbitrarily distributed in 3D space is established. Given the special situation of lower boundary constant pressure, stable productivity analytic computational formula for branched horizontal well is ultimately obtained after studying the transition from unstable seepage flow to stable seepage flow with constant pressure supply.Starting from horizontal well bore variable mass conduit flow model, combined with the complicated structure of branched well, an new pressure drop calculation model is built, in which joint influence of frictional pressure drop, acceleration drop, gravity drop, pressure drop by wall inflow and the pressure drop incurred by the junction/integration of main and branch are taken into account.Theories of point source, mirror image and potential function theories are adopted to study potential distribution function of branched horizontal well which is arbitrarily distributed in 3D space in bottom water reservoir. Besides, by coupling well bore pressure drop model with reservoir seepage model, the coupling model of reservoir seepage and well bore flow for bottom water reservoir with branched horizontal well is set up. The solution of the coupling model is obtained and the productivity and well bore pressure dorp of branched horizontal well is studiedOn the foundation of analysis of water cresting law in bottom water reservoir, research is made on bottom water rising dynamic process, and a new critical condition for bottom water rising is put forward. Allowing for the new critical condition, with methods of mirror image and potential gradient superposition adopted, an amended formula for computing critical rate and breakthrough time is drawn. In the amended formula, single and multiple factors such as formation heterogeneity, barrier, well bore pressure drop and well bore slant are taken into consideration in terms of their integrated effect on the reasonable production parameters and breakthrough time for bottom water reservoir horizontal well.In bottom water reservoir, critical rate, potential pressure difference computational formula for branched horizontal well which is arbitrarily distributed in 3D space is deduced. In addition, breakthrough time computational formula is built, making the breakthrough time calculation in infinitesimal sections of branched horizontal well and breakthrough dynamic prediction such as the order of breakthrough location available. In this formula, many factors are considered, such as reservoir physical properties which are formation permeability, porosity and oil saturation, well bore parameters which are well bore diameter, skin factor, location, well bore pressure drawdown which are friction, acceleration, blend and junction pressure drop, and dynamic parameters of development which are bottom well bore pressure, practical production rate, water displacement efficiency, water displacement vertical and plane conformance efficiency, etc.Finally, Visual Basic and Matlab are utilized to compile a calculation program. Moreover, by using to some field cases and by comparing and analyzing some common formulas, the formulas derived in this paper are well testified.