Productivity Evaluation And Completion Parameter Optimization Of Perforating Completed Horizontal Wells

Productivity evaluation and completion parameter optimization of the horizontal well has been the highlight of horizontal well technology. Horizontal wells are one of the most important strategic tools in increasing productivity significantly, delaying water or gas coning, enhancing oil recovery and improving exploitation effect by enhancing the reservoir contact area and creating smaller drawdown. As result of advantages and widespread application of horizontal wells in field development, the state of applications of horizontal well technology require better completion designs to optimize production rate. Concentrating on an openhole or a perforating completed horizontal well in a homogeneous anisotropic infinite slab reservoir confined by top and bottom no-flow boundaries, a comprehensive semi-analytical model coupling the flow equations in the reservoir and wellbore is developed to investigate the effect of well completion on horizontal well performance. Based on the coupling model, the sensitivity analysis performed for a perforating completed horizontal well and optimal theories, mathematical optimization models for completion parameters are established and solved by sequential quadratic programming (SQP) algorithm to maximize production and obtain uniform inflow rate along the wellbore.Openhole completion horizontal well or perforations for perforating completed horizontal well are modeled as line sources in a homogeneous anisotropic infinite slab reservoir with no-flow at both top and bottom boundaries. The method of source and Green's functions, Newman's product method, Laplace and its inverse transform, the method of images and principle of superposition are used to derive the long-time asymptotic solutions of the pressure response in real time domain for single-phase flow in the reservoir along the well surface. The additional pressure drop due to formation damage and non-Darcy flow are addressed and incorporated into long-time asymptotic equations of pressure response. The wellbore flow model considers the pressure losses inside the well due to friction and acceleration and the effect of influx from the reservoir into the horizontal well. A comprehensive semi-analytical model which couples the reservoir and wellbore flow equations and takes into account formation damage, non-Darcy flow is presented and can be used to evaluate the productivity, perform sensitivity analysis and optimize perforating completed parameters. This study will provide the knowledge of basic theory for production rate, sensitivity analysis and optimization for completion parameters of a horizontal well.Sensitivity analysis performed for completion parameters of an openhole completed horizontal well shows, the productivity index is maximum when the well is located at the center of the reservoir; increasing well length increases the productivity index but there exists an optimum length; the productivity index decreases with increment of drilling damage thickness for same ratio of damamge permeability to formation permeability; increment of ratio of damamge permeability to formation permeability for same damage thickness results in significant reduction of productivity index; increment of damage thickness results in less reduction of productivity index for less ratio of damage permeability to formation permeability; reduction of productivity index with increment of damage thickness becomes severe for larger ratio of damage permeability to formation permeability; the impact of non-Darcy flow upon productivity index becomes obvious for higher flow rate.Sensitivity analysis performed for completion parameters of a perforating completed horizontal well indicates, perforation phase angle has significant effect on productivity index, 180o phasing angle is the best, and the difference in effect of phase angle on productivity index becomes unconspicuous for higher perforation density but obvious for low perforation density; perforation density has significant impact on productivity index, increasing perforation density enhances productivity index but the gain in productivity index becomes negligible beyond the density of 6 shot/m; the increment of perforation penetration improves productivity of the well and perforaton length has more important influence on productivity index especially for low perforating density; whether perforations terminated inside or extended beyond damaged zone has more important influence on productivity of the well, the reduction of productivity index due ot the further increase of damage zone thickness becomes moderate for damaged zone penetrated by perforations; the smaller the damage zone permeability, the smaller the well productivity, damage zone has more severe influence on well productivity for perforations terminated inside the damaged zone; drilling damage leads to significant reduction of well productivity when the ratio of damage permeability to formation permeability is smaller than 0.5, however, the ratio beyond 0.5 guarantees relatively high well productivity; when the ratio of perforating crushed zone permeability to formation permeability is larger than 0.4, perforating damage impact on well productivity is not severe; the influence of non-Darcy flow has obvious influence on productivity index for higher flow rate.On the basis of the comprehensive semi-analytical model, the sensitive analysis of the performance of perforating completed horizontal well and optimal theories, mathematical optimization models in which the productivity index is treated as an objective function, the perforation locations as decision-making variables and the inflow profile as constraints are presented to maximize the productivity index or lead to uniformity of specific inflow along the wellbore. The establishment of optimization models provides the theoretical basis of optimizing perforating parameters of horizontal wells.A program based on SQP algorithm in optimal theories is developed and verified by some typical nonlinear programmings with constraints. Then, the program is used to solve optimization models assisting in investigating how perforation distribution affects the performance of a horizontal well under infinite and finite conductivity. The results shows the perforating completed horizontal well is located at the center of the reservoir and perforated by 180o phasing angle, perforations are penetrated drilling damages zone, and the perforation density with a shape of"U"curve is distributed along the wellbore, the well productivity becomes maximum; the perforation density with a shap of"∩"curve will result in a uniform inflow rate along the wellbore; the variable perforation density along full length of the wellbore does not significantly improve the well productivity; increasing perforation density in each open segment for selective completion of the well improves well productivity but using high perforation density near the heel end of the well significantly enhance the well productivity. Last, the guidelines of perforating parameters optimization are developed.