Research On Productivity Prediction Method For Gravel-packed Horizontal Well Considering Sanding Influence

Gravel-packed sand control technology is one vital completion technology for reservoirdevelopment with horizontal well, especially the unconsolidated reservoir and heavy-oilreservoir. A series of problems need to deal with: sand migration and plugging mechanism ingravel pore, variation of formation porosity and permeability at different reservoir stress,influence of sand migration and plugging on gravel porosity and permeability, analysis forfluid-structure interaction between reservoir formation, gravel layer and horizontal well bore.All the answers to these questions will have significant theoretical guidance to accuratepredict well productivity of gravel-packed horizontal well and optimize horizontal wellcompletion with gravel pack.In this paper, the experimental system is designed to evaluate gravel pack impairmentbecause of sand migration and plugging. The gravel impairment experiment at different sandradius ratio and sensitive tests to experimental parameters are carried out using formationsand and gravel sand from real-world scenarios. According to liquid-solid two-phase theory inporous media, considering the impact of sand particulates deposition on vertical direction, andplugging on horizontal direction, the model of plugging concentration of fluidized sand isproposed. According to above model and considering the influence of sand plugging, thegravel layer porosity and permeability varation models are derived, and using theexperimental results, this model is validated and perfected. And then, we propose the variationmodels of reservoir formation porosity and permeability on the base of volume straindefinition. This work illustrates formation porosity and permeability variation at differentreservoir pressure. According to theory of elatic-plastic deformation, mass conservation lawand parameter variation model, the formation seepage model is proposed; the seepage modelin gravel layer is proposed under the consideration of gravel damage caused by sand plugging;According to mass conservation, momentum conservation, and continuous boundaryconditions, the flow pressure drop model in horizontal well bore is derived. Considering thecoupled process between formation deformation, seepage and mass variation, we proposed well productivity predicting model of gravel-packed horizontal well. Finite element method(FEM) is employed for space and time discretization of solid deformation model, reservoirseepage model, and pressure drop model of well blore. The decoupling method is used forsolving models. With solution of one phase fluid-solid coupling problem and two phasecoupling problem, the model solving system is validated.The numerical calculation and analysis show that the calculated well productivity has agood agreement with real-world measured data. The calculated error of initial productivity is7.27%, and the average error of dynamic productivity is6.8%. Due to influence of variousmass flow, fluid production distribution along wellbore is asymmetric U-shaped, and thepressure at heel end is smaller than pressure at the tip end. For sand plugging in gravel layer,the percentage of pressure drop in gravel layer increases and well productivity reduces withwell producing. The sensitive tests show that well bore length, formation permeability, andfluid viscosity have significant influence on well initial well productivity. Formationpermeability and fliud viscosity are the vital factors to determine the period of effective sandcontrol.