Evaluating the Transport of Solids Generated by Shale Instabilities in ERW Drilling
- A.L. Martins (Petrobras S.A.) | M.L. Santana (Petrobras S.A.) | Wellington Campos (Petrobras S.A.) | E.F. Gaspari (Petrobras S.A.)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- December 1999
- Document Type
- Journal Paper
- 254 - 259
- 1999. Society of Petroleum Engineers
- 1.6 Drilling Operations, 4.2 Pipelines, Flowlines and Risers, 5.3.2 Multiphase Flow, 4.1.2 Separation and Treating, 1.11 Drilling Fluids and Materials, 1.10 Drilling Equipment, 1.6.6 Directional Drilling, 1.7.7 Cuttings Transport, 4.1.5 Processing Equipment
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The problem of cuttings transport in the inclined sections of extended reach wells (ERW) is a major concern in the oil-well drilling industry. This article presents an innovative time-dependent mathematical model, along with a computer implementation of it, which is based on the well-known two-layer model approach. An innovative feature of this model consists in the consideration of the added amount of solids that comes from the crumbling and cave-in of the wellbore. The unstable effects of this added amount of solids is taken into account through a variable representing the added volume of cuttings per unit time and length. A finite volume approach is used to solve the system of differential equations. The paper represents a first step on the integrated analysis of cuttings transport and wellbore stability problems.
The strategy of using ERW is being adopted worldwide as an attractive way of developing oilfields. Cuttings transport and wellbore stability are critical aspects in the drilling of highly inclined extended reach wells through unstable shales, which may be exposed to the drilling fluid during long time.
These two problems are addressed by two classical sciences (two phase flow and rock mechanics) and treated separately. The study of steady-state stratified solid-liquid annular flows has been the subject of several researchers in the last decades1-3 in an attempt at describing the complex phenomena involved in the cuttings transport in high angle wells. On the other hand, considerable research effort has been conducted in the past aiming the quantification of mechanical4,5 and chemical6,7 effects which may cause wellbore instabilities.
The main objectives of this paper are to introduce some ideas about the dependence of these two problems and to quantify the removal of solids generated by wellbore instabilities.
The tool for this development is a computer program for the evaluation of cuttings circulation based on an innovative time dependent model for cuttings transport simulation. The computer program can calculate the variables which govern cuttings transport for the highly inclined section of an extended reach well, considering other source of solids besides the bit.
Using the computer simulator, a series of analysis is performed in order to quantify the effects of the main variables as well as of the subtle increase of solids a given section of the well in the time-dependent behavior of cuttings transport.
Cuttings Transport Simulation and the Two-Layer Model
The two-layer model has been originally proposed for the representation of drilled cuttings transport in high angle wells,8 based on the good results of this approach for the simulation of other industrial processes, such as specific gas-liquid flows,9 and hydraulic transport of solids in pipes.10 The model proposed by the authors is illustrated in Fig. 1 and is based on the following hypothesis:
The bottom layer represents the cuttings bed, which deposits in the annulus due to the action of gravitational forces. In this layer a fixed solids concentration of 52% is assumed.
The top layer only contains the carrier fluid.
There is no slip between the solid and liquid phases in each of the layers.
There is no mass transfer between the solid and liquid phases.
The solid-liquid system is incompressible and its rheological parameters are the same of the fluid.
The height of the interface between the two layers is constant in the annular section studied and, consequently, a hydrostatic distribution of pressure in a cross section is assumed.
The solids are characterized by an average diameter and by their sphericity.
This model8 can be formulated by a system of two algebraic equations, based on momentum conservation laws for the bed and the fluid layers. The solution for the two unknowns, bed height and friction losses, require iterative approaches due to the nonlinearity of the system.
Martins11 expanded the previous model, considering solids in the upper layer and four different flow patterns in the annulus: stationary bed, moving bed, heterogeneous suspension and pseudo homogeneous suspensions. The model is an adaptation of the proposal of Doron et al.12 for annular flows. This model is formulated by a system of four algebraic and one integral equations based on mass conservation laws for each phase, momentum conservation laws for each layer and a turbulent diffusion concept to describe solids distribution in the upper layer. This model has became the basis of PETROBRAS cuttings transport simulator which is widely used in the design and troubleshooting while drilling complex trajectory wells.
Several improvements were made to the model, based on the feedback from field operators. Such improvements include specific correlations for interfacial stresses prediction,13 corrections for rotation effects,2 use of different rheological models for characterizing the fluid flow14 and the introduction of a permeability equation to describe flow through the bed.14
Among the changes in the basis model, proposed by Gavignet and Sobey,8 the introduction of a solid phase in the upper layer and the inclusion of an equation for liquid flow through the bed showed negligible difference in the final results. For this reason, these changes will not be kept in the time-dependent formulation. All the others proved to be very useful for the adequate representation of cuttings transport while drilling high angle wells.
An expressive contribution was given by Nguyen and Rahman15 by the introduction of the three layer model concept to the analysis of cuttings transport. This concept, also brought from the hydrotransport industry16 may be useful to improve the understanding of the role of rheology on cuttings transport.
The Time-Dependent Formulation
The present work consists on a first step on time-dependent solid-liquid stratified flow modeling. The concept of the two-layer model is kept, but now, unlike any previous approach for cuttings transport analysis, transient conservation laws are derived to describe the phenomena. Eccentricity is an input parameter in the model. It directly affects all the area and perimeter expressions, as described in Gavignet and Sobey.8 Eccentricity can be predicted by mechanistic models17,18 using commercial softwares.
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