This article presents the detailed formulation for each of the three steps of a horizontal gravel pack displacement operation, including sand injection and alpha/beta waves propagation. The main core of the model, aiming the definition of alpha wave height, is based on a well known two layer model. Initially developed for hydrotransport applications, this kind of model has been adapted by several authors for drilled cuttings transport analysis. Besides, a comparison between theoretical predictions and pumping charts from a field operation performed in Campos Basin is presented.
Gravel Packing is today the most frequently applied sand control technique in Campos Basin, offshore Brazil. Due to the critical conditions, such as the deep and ultra deepwaters and low frac gradients, a lot of precision is required to assure gravel packing success. Most models available in the industry for horizontal gravel pack design are essentially empirical, resulting in imprecise predictions for extrapolated conditions.
These aspects were the main motivators for the development of a mechanistic model to describe the hole operation. It is a consensus among design and operation engineers that a physically based software is a necessary rigsite tool for determining operational parameters, specially when last minute data have to be considered.
Several authors present experimental results of horizontal gravel packing performed in test facilities: Forrest1 presents a correlation to estimate pack length limits in highly inclined wells based on 45 and 100 ft model tests with viscous fluids and water.
Penberthy2 presents several field tests in a 1,500 ft long simulator to identify the main variables which govern the phenomenon. Extensive field-scale testing has aided in the development of procedures and operational guidelines. Software has also been developed, based on empirical correlations to assist design tasks.
Sanders3 presents a numerical model based on a pseudo three-dimensional approach aiming the simulation of an alternative flow path concept during the horizontal gravel pack displacement. The model solves the equations of volume and momentum conservation for the incompressible slurry in the wellbore. In order to validate the flow path concept both small-scale and large-scale experimental tests using models ranging from 5 to 1,000 ft in length were performed.
For displacement calculation purposes, the horizontal well gravel pack operation can be divided in three different stages: the injection, the alpha wave propagation and the beta wave propagation.
The injection stage, as highlighted in Fig. 1, consists of pumping a fluid-gravel mixture through the pipe until a cross over tool where the flow will be diverted to the open hole annulus. At this moment, there is usually a decrease in the mixture displacement velocity, resulting that the force which sustains the gravel particles is not high enough to maintain them in suspension. Consequently, the solids begin to sediment in the lower portion of the annulus, forming a bed that, for a given flow rate, reaches an equilibrium height. The deposited sand length will propagate till the extremity of the horizontal section, leaving a free channel between the superior wall of the well and the top of the bed. This stage is known as alpha wave propagation and is illustrated in Fig. 2.
When the alpha wave arrives at the extremity of the well, a new step, called the beta wave propagation, begins: since the sand can not flow through the screens, it will start to deposit above the sand deposited in the alpha wave stage, beginning at the extremity of the well and finishing at the crossover tool. Fig. 3 highlights the process.
While during the alpha wave propagation, the fluid flow totally happens through the annular space between the screen and the open hole, in the beta wave the fluid will flow radially through the screen and then axially through the annular gap formed between the screen and the washpipe. Fig. 4 shows the cross section of the horizontal wells when equipped with the gravel pack displacement columns.