Free-Fall-Effect Calculation Ensures Better Cement-Operation Design

Abstract

Summary A cement-operation simulator was developed that takes the free-fall effect into account. This simulator allows prediction of well-fluid behavior and pressure, making proper field-operation design possible. The proposed mathematical model was derived from mass and momentum conservation laws by means of a macroscopic balance that reduces field equations to a ID model The resulting initial value problem is solved numerically with the Runge-Kutta method. Special care is taken to control the interfaces between two different fluids while the system is in free fail. A microcomputer program has been implemented with a user interface that permits complex well geometries. Other models are compared with the program to demonstrate its software capabilities. Introduction In most oilwell primary cement jobs, the cement-slurry densities initially exceed the drilling-fluid density in the well. This density difference causes a force imbalance that accelerates flow of the entire fluid column while the heavier fluid is pumped down the string. Therefore, the fluids in the well fall faster than the pump rate, creating a low-pressure region between the wellhead and pump rate, creating a low-pressure region between the wellhead and the free-falling column. The pressure in this region, improperly called a "vacuum," corresponds to the water-vapor pressure. Arnold called this dynamic phenomenon the free fall or U-tube effect. When free fall begins. the average fluid-column velocity changes. Usually, the system accelerates until it reaches a new and temporary state of equilibrium where the average velocity is kept constant. If the system fluids are considered incompressible, the rate of return will equal the rate of free fall. So when equilibrium is attained, the rate of return is constant and differs from the pump rate . Initially, during the acceleration period, the flow rate of the free-falling column exceeds the pump rate. When the hydrostatic imbalance decreases (e.g., because the cement slurry passes to the annulus), decelerating begins. During this period, the free-fall rate decreases to a minimum value, lower than the pump rate, that may constitute another temporary state of equilibrium. The low-pressure zone increases initially, while the freefall rate exceeds the pump rate. Later, when the free-fall rate is less than the pump rate, the low-pressure zone diminishes. then disappears. Correct pressure and flow-rate predictions are important to plan the field operation properly. Acceleration and deceleration plan the field operation properly. Acceleration and deceleration of the flow rate make displacement rate design difficult. If plug flow is desired, care must be taken to avoid problems when the free-fall flow rate exceeds the pump rate. On the other hand. the decrease in the system rate can prevent turbulent cement-slurry or spacer flow in the annulus. Many authors have studied the causes and effects of this dynamic phenomenon, but few models exist to simulate wellbore behavior during cementing operations. Beirute proposed a model based on the assumption that the free-fall rate determines the equilibrium for the dynamic pressure equation; he uses an iterative procedure based on the bisection method to find the roots of his procedure based on the bisection method to find the roots of his algebraic equation. Wahlmeier and Lam presented only the validation and some results of their model but showed little of their basic assumptions. A mathematical model is derived based on the mass and momentum conservation laws to calculate fluid behavior in the well during free fall. Field equations are reduced to a ID model by, use of Eulerian area averaging. The system of equations is reduced to an ordinary differential equation on the basis of the assumption that the system fluids are incompressible. The resulting initial value problem is solved numerically by use of the Runge-Kutta method. SIMENTAR, the cement-operation simulator based on this mathematical model, has been implemented. This paper briefly reviews the theory, software capability, and validation of this simulator.