Optimization Of Perforation Distribution Of The Horizontal Well Using Nonlinear Constrained Programming

Optimization of the perforating parameter is very important to stabilize the production and control the water cut in the perforated horizontal well. A model for coupling reservoir-wellbore fluid patterns was deduced from the seepage flow model of reservoir fluid and the fluid flow model of horizontal wellbore. The nonlinear constrained programming was applied to optimize the perforation distribution of the horizontal well under the circumstances of infinite and finite conductivity respectively. This approach is hoped to be the theoretical foundation on which the optimization of the horizontal well is based.A perforated horizontal well located at the center of an infinite and uniformly anisotropic slab reservoir impermeable at both top and bottom was studied. The pressure response of pseudo-radial flow at the top of the wellbore was obtained using Green's function, source function method, principle of superposition and Laplace transform. Based on the continuity of the pressure and the flux along the surface of the wellbore, a model for coupling reservoir-wellbore flow patterns was established to describe the interaction between the reservoir and the perforated horizontal well. Newton-Raphson iterative method is developed to solve the coupled model. The results show the inflow profile is nonuniform, the inflow flux from the toe to the heel of the horizontal well gradually increases, and the calculated production is close to the real production. The analyses of effects of perforation parameters on productivity index indicate that the length of the perforation has a significant influence on productivity index under low perforation density; under the perforation density less than 3shot/m with perforation length of 0.3m, the perforation density has a large effect on the productivity index; the influence of perforation phasing angle becomes apparent in anisotropic formation; and the effect of perforation radius on the productivity becomes negligible for all practical purpose.A program of generalized Lagrange multiplier method was developed and its feasibility was validated. An optimization model is presented, in which the production of the horizontal well is treated as an objective function and the perforation distribution as a decision-making variable. The present model was solved by generalized Lagrange multiplier method under the conditions of infinite and infinite conductivity respectively and compared with that of uniform perforation distribution. The results show that under the infinite conductivity the perforation distribution has little effect on the production of the horizontal and inflow profile has a shape of"U"; the perforation density distribution has a shape of arc, which is larger at both ends of the well and smaller in the middle of the well, if the inflow flux is uniform; under the finite conductivity the inflow profile is nonuniform, which reaches the minimum at the location a distance 4/5 length of the well from the heel, and the closer to the heel of the well, the more the inflow; the perforation density reaches the maximum at the location a distance 3/4 length of the well from the heel and decreases toward the ends the well if uniform inflow is not considered; if the inflow is uniform, the minimum of the density is located at the position a distance 3/4 length of the well from the heel and increases toward the ends of the well. The above research may provide a new guideline for optimization of perforation parameters of horizontal wells.