Using foam in horizontal well drilling: A cuttings transport modeling approach

Foam is a frequently used compressible fluid in drilling applications. Cuttings transport with foam has been a focus of interest for years. Few studies have been conducted on vertical well configuration and successfully applied. However, less is known about the performance of foam in highly inclined and horizontal wells. In this study, a layered model is developed for describing cuttings transport in horizontal wells. Due to the presence of a cuttings bed, generalized rheological model parameters for foam are modified analytically as a function of fluid properties and complex conduit geometry. Using these parameters, friction between the fluid and the wellbore, between the layers and slip between the cuttings and the fluid are determined. Model performance is examined using experimental data established at The University of Tulsa's low pressure-ambient temperature flow loop. Results showed that, developed model can predict developed cuttings bed thickness and pressure loss in the wellbore with an error of less than 20%. It has been observed that very high foam flow velocities are required in order to prevent a thick bed development in the wellbore. Also, low-viscosity fluids show better performance on preventing bed development inside the wellbore than high-viscosity fluids at the same flow rates.     

Friction factors for hydraulic calculations considering presence of cuttings and pipe rotation in horizontal/highly-inclined wellbores

Pressure loss calculations have a vital role for determining hydraulic horsepower requirements and to predict bottomhole treating pressure. One of the major concerns in developing hydraulic programs is to estimate the frictional pressure losses while cuttings are present in the annulus during pipe rotation. An experimental work has been carried out in a cuttings transport flow loop capable of operating at various inclinations. The pressure drop in the test section was recorded for variable flow rates, cuttings concentrations, pipe inclinations and rotation speeds. Existence of cuttings increase the pressure drop due to decrease in flow area inside the wellbore. As there are cuttings in the system, pipe rotation decreases the frictional pressure loss considerably in particular if the pipe is making an orbital motion in the eccentric annulus. Cuttings bed thickness defined as the ratio of cuttings bed area to the wellbore area is expressed in terms of dimensionless parameters obtained from dimensional analysis. Empirical expressions and charts for friction factor are proposed for low and high viscosity fluids in terms of combined Reynolds number and stationary cuttings bed thickness.     

A homogeneous model for gas–liquid flow in horizontal wells

Radial influx or outflux stands for the major difference between fluid flow in a pipe and fluid flow in a well. A homogeneous model for gas–liquid flow in a horizontal well is presented in this paper. In addition to frictional and gravitational components of total pressure drop, accelerational pressure drops due to fluid expansion and radial influx or outflux are considered. Effect of radial influx or outflux on wall friction is also taken account for. With a segmented approach, the new model and several existing pipe flow models have been applied to predict pressure drop along a wellbore, and predictions are compared with experimental data. It is found that the new homogeneous model outperforms existing models for gas–liquid flow in horizontal wells.     

A Derivation of the Averaging Model for Cuttings Transport: Multi-Region Model

Abstract

The aim of this paper is to derive a mathematical model for cuttings transport in horizontal wellbores using the volume averaging method, which is a technique used to derive transport equations for multiphase systems and one of the main approaches in two-phase flow modeling.

The theoretical derivation of the cuttings transport problem is for a two-region system composed of a fluid bed and a stationary bed of drill cuttings, which is considered as a porous medium. A one-equation model for fluid bed was derived and was used to obtain the multi-region model. This model can be used to study the hydraulic transport of solid particles in horizontal wellbores.     

Analytical model for interfacial waves in vertical core flow

The vertical annular pipe flow of two immiscible liquids with very different viscosities provides an efficient and low cost method for producing heavy oils in vertical wells using water as a lubricant. The core flow pattern is becoming attractive in the current Brazilian deep water production scenario. Understanding interfacial phenomena present in this flow pattern is crucial for appropriate design of the production system. Assuming that in this axisymmetric flow there is no net force associated with interfacial tension, a differential equation governing the shape of the liquid–liquid interface is derived. An analytical solution is proposed for the prediction of the wave geometry, which depends only on pipe geometry, physical properties and flow rates of the fluids. The comparison between the model predictions and recent experimental data shows a reasonable agreement.     

Influence of sand production on pressure drawdown in horizontal wells: Theoretical evidence

Poorly consolidated reservoirs are susceptible to sand production that tends to increase the pressure drawdown along the well length. This problem, which has not received adequate attention in the literature of petroleum engineering, is quantitatively assessed in this paper. Different flow regimes typically encountered in two-phase transport systems of liquid and solid are discussed. In an effort to evaluate the degree of influence the presence of sand exerts on pressure drop, a suitable relation applicable for heterogeneous flow is employed to compute the energy gradient of the mixture. The difference in the energy gradient of pure oil and mixture is examined for horizontal pipelines in terms of volumetric solid concentration and flow velocity. The study demonstrates that for a specific sediment size and pipe roughness, the effect of sand movement on pressure drop cannot be ignored in many cases of poorly consolidated reservoirs, being 5.1–168% times greater than the pressure drop resulting from pure oil under the same flow condition.     

Analytical model for tracer transport in reservoirs having a conductive geological fault

Geological faults are frequently found in oil reservoirs and their presence dramatically impacts the underground fluid motion. Tracer tests provide a mean to dynamically characterize the conduit or barrier behavior of the fault. Although diverse analytical models have been developed to describe tracer transport in a geological conductive fault, only few of them capture the fact that injection and production wells are regularly located outside the fracture plane. In many cases, the tracer path length outside the fault structure is significant. In this work the system is represented by three coupled regions associated to the injector-to-fault, fault, and fault-to-production-well zones. The coupling is simplified by considering linear flow and aligned regions. This model includes hydrodynamic dispersion, an important phenomenon not considered in previous work. One-dimensional advective–dispersive tracer transport is assumed in each region. Border conditions require tracer mass conservation. The initial condition is a Dirac delta pulse at the injection site. The equations are analytically solved in Laplace space and the inverse transform is evaluated numerically by the Stehfest algorithm. Four specific cases have been studied; they comprehend a long and a short fault path length having low or high dispersivity respectively. The pulse behavior and the tracer breakthrough curve, as well as their sensitivity to fault dispersion, fault length and fault fluid velocity are analyzed. Clear differences in the pulse profile and breakthrough curve shape are found in relation to the case when no fault is present.     

Transient gas–liquid two-phase flow in pipes with radial influx or efflux

A simplified model for transient gas–liquid flow in pipes with radial influx or efflux has been developed in this paper. The resulting governing equations are essentially hyperbolic with U_tp+c_s and U_tp−c_s as their eigenvalues. A finite-difference scheme based on the split coefficient matrix (SCM) approach is applied to solve the mass and momentum balance equations. Sample numerical simulation runs are performed. Simulation results agree with experimental observations and clearly show the features of variation in pressure drop, liquid holdup, and two-phase velocity during transient and steady state flow periods.     

Two-Region Average Model for Cuttings Transport in Horizontal Wellbores I: Transport Equations

Abstract

The aim of this article is to derive a mathematical model without length-scale restrictions for cuttings transport in horizontal wellbores using the non-local forms of the volume averaging method, which is a technique used to derive transport equations for multiphase systems and one of the main approaches in two-phase flow modeling. The theoretical derivation of the cuttings transport problem is for a two-region system composed of a fluid bed (ω region) and a stationary bed (η region) of drill cuttings that it is considered as a porous medium. The volume-averaged mathematical model obtained in this work consists of the mass and momentum equations for the ω and η regions. The model was the starting point to obtain one-equation models for both regions. The one-equation models together with adequate jump conditions can be used to predict the hydrodynamics of the ω and η regions. The mathematical derivations of the momentum and mass flux transfer jump conditions are presented in Part II of this article.     

Two-Region Average Model for Cuttings Transport in Horizontal Wellbores II: Interregion Conditions

Abstract

The theoretical derivation of the cuttings transport problem for a two-region system composed of a fluid bed and a stationary bed of drill cuttings, which was considered as a porous medium, was presented in part 1 of this article. The aim of this article is to derive the momentum and mass flux interregion conditions (jump conditions) that contain terms representing the excess surface due to accumulation, convection, stress, and bulk in addition to a term representing the exchange with the surrounding regions. The averaged equations obtained in part 1 of this article and the interregion conditions obtained in this work allow modeling the two-region system described above.     

Numerical study of dispersed oil–water turbulent flow in horizontal tube

In this paper, the three-dimensional flow of two immiscible liquids in a horizontal pipe has been investigated numerically. The transient numerical simulations of two-phase dispersed flow in a pipe (of ID = 0.0024 m) have been carried out using commercial CFD package FLUENT 6.2 in conjunction with multiphase model. Oil–water system is selected as the two-phase system in this work. The k − ε model was used to describe the turbulence in continuous phase. The numerical results in terms of the phase distribution profiles and average in-situ hold-up are presented and discussed. The predicted results are seen to be in good agreement qualitatively as well as quantitatively with the previous experimental results available in the literature.     

Double-porosity model for tracer transport in reservoirs having open conductive geological faults: Determination of the fault orientation

Conductive geological faults in oil reservoirs have a major impact in the efficiency of fluid-flooding and enhanced oil recovery schemes. Inter-well tracer tests are a traditional mean to determine underground communication channel properties, and therefore have the potential to estimate fault features. In this work an analytical model is developed to describe inter-well tracer tests in reservoirs with open conductive faults. Specifically, a fault that intersects the flow path between the injection and production wells without reaching them is treated. In open faults fluid can be exchanged along the fault to external regions. In addition, the present model captures two new relevant aspects of the process: (i) the fault region is a fractured media, and (ii) a Danckwert's discharge condition is established at production well. To treat open faults a new source-coupling scheme is designed for linking the three independent path regions in which the system is discomposed. The first region comprehends the path from the injector to the fault, the second represents the zone along the fault, and the third one the path from the fault to the production well. The involved coupled advection-dispersion equations are analytically solved by the Laplace technique and numerically inverted. There are twelve parameters in the model; from them five concern the fault properties. By exploring their effect on the tracer breakthrough curve it is found that the curve is mainly sensitive to the tracer fault path length and the fault fluid velocity. The two factors describing the fracture-matrix coupling become important only when the fluid velocity in the fault is relatively low. No relevant sensitivity is found on the fault dispersivity. An outstanding attractive feature of the new model is its capacity to determine the fault orientation, which is not possible by the standard characterization means. The model has been successfully applied to data from a real reservoir tracer test performed in Loma Alta Sur Field. Here, the orientation of two faults have been determined.     

A Three-Region Hydraulic Model for Solid-Liquid Flow with a Stationary Bed in Horizontal Wellbores

Abstract

This paper presents a numerical study of cuttings transport in horizontal wellbores. A three-region hydraulic averaging model considers at the bottom of the horizontal pipe a region made with a stationary bed of drill cuttings which behaves as a porous medium. Above this bed there is a two-region fluid with fully suspended solid–liquid flow composed with different concentrations of cuts. The results of the pressure gradient as a function of the average velocity for different bed mobile heights are presented. Pragmatically, it is important to know the behavior of the pressure to establish strategies for drilling horizontal wells.     

Experimental study on interfacial waves in vertical core flow

The vertical annular pipe flow of two immiscible liquids with very different viscosities (also known as core flow) provides an efficient and low cost method for producing heavy oils in vertical wells using water as a lubricant. This liquid–liquid flow pattern is becoming attractive in the current Brazilian deep water production scenario. Understanding interfacial phenomena present in this flow pattern is crucial for appropriate design of the production system. New experimental data on wavespeed, wave length, amplitude and wave profile of interfacial waves and holdup in heavy oil–water core flow (crude oil with 500 mPa s viscosity and 930 kg/m³ density) inside a 2.84-cm-i.d. vertical glass tube at room temperature are presented and analyzed. The in-situ volumetric fraction of the oil is determined from the kinematic wave assumption and agrees very well with the measurements obtained via a proposed optical technique.     

水平井筒分层流型压降计算模型研究

井筒流动是一种沿井筒不断有流体流入的变质量流体流动 ,因此其压降计算有别于常规管流。在混合损失计算模型的基础上 ,应用动量守恒原理推导出了新的水平井筒气液两相分层流型压降计算模型。该模型较全面地考虑了井筒流动各方面的参数 ,将井筒压力损失划分为摩擦损失、加速损失、重力损失和混合损失等 4部分 ,其中加速损失主要源于径向流入引起的加速损失 ,以及由于持液率的变化引起气、液流速变化而导致的加速损失。计算实例表明 ,水平井筒气液两相流动中的井筒压降均随着管壁入流量和轴向流量的增加而增大 ;入流角对井筒压降的影响主要表现为混合损失占井筒损失的比例随入流角的增加而增加 ;新的水平井筒压降模型与油藏渗流相耦合 ,可为水平井产能研究提供理论指导。     

A semi-analytical solution for a two-dimensional capacitance model in solute transport

A two-dimensional capacitance model is presented for the analysis of solute transport in heterogeneous porous media where the transport processes are affected by mass transfer between the flowing volume in macropores and the stagnant volume in micropores. The semi-analytical solutions for both penetrating and nonpenetrating sources are obtained using double Laplace transforms and numerical inversions. The modeling results reveal the strong influences of dispersive and convective properties of porous media in the transverse direction on the overall transport that cannot be replicated by the current one-dimensional transport models. The solution may provide a useful tool to interpret some transport situations within common field geometries.     

水平井筒油水两相流压降计算模型

水平井的应用已越来越广,由于其增产效果明显,特别是对于底水油藏,能有效地延缓地水锥进的速度,从而为油田创造巨大的经济效益。以前人们都普遍把水平井视为无限导流,即：从根端段到指端段几乎没有压降消耗。但是随着水平井的技术越来越成熟,大位移水平井开始出现,水平井筒中的压降已不容忽视。对水平井筒油水两相变质量分层流动进行了微元分析,考虑壁面入流对其中油水两相变质量分层流动压降的影响,运用连续性方程和动量守恒方程,得出了水平井筒油水两相变质量分层流动的基本模型和压降计算模型,通过模型求解揭示了在壁面入流条件下沿水平井筒的压降分布。     

Linear stability analysis and experimental verification of stratified air–water flow in a horizontal bend

Stratified flow in gas–liquid systems is a basic flow configuration which occurs frequently in industries due to the large density differential between the phases that helps to sustain stable stratification for relatively wide ranges of flow rates. The study on stability of stratified flow and the development of transitional criteria to various flow patterns have been very actively pursued for straight pipes, resulting in a broad understanding of the underlying mechanisms. Beside straight pipes, pipelines contain other fittings, which pose abrupt changes to the flow direction, and hence their impact on the flow stability needs to be ascertained.This study attempts to extend the linear stability analysis of stratified flows in a straight pipe to a horizontal bend. A model for the effect of a horizontal elbow on the transition from stratified to non-stratified patterns using the two-fluid approach is presented. The Inviscid Kelvin–Helmholtz (IKH) and Viscous Kelvin–Helmholtz (VKH) stability criteria for stratified flow transition are derived.Experiments are carried out using air and water in a 0.05 m diameter horizontal pipe work containing an intermediate bend of 0.5 m radius of curvature and the flow pattern observed in the bend is compared with the stability theory. The results show that the IKH and VKH stability criteria for stratified flow in a bend have identical forms as their counterparts in an inclined straight pipe, except that the tilt of the liquid lump in the bend which depends on the liquid velocity replaces the inclination angle for a straight pipe. The stable region is over-predicted by the IKH criterion while the VKH criterion shows good agreement for transition from stratified to slug flow if the liquid surface gradient is taken into account in the solution of the flow parameters under fully developed conditions.The work presented in this paper is of tremendous help to oil production engineers who need to know and control the flow regime transitions in order to avoid problems associated during production. These problems are mainly due to the generation of slug flow which leads to severe unwanted jigging.     

基于连续拟稳定法的页岩气体积压裂水平井产量计算

水平井体积压裂是开发页岩气藏的关键技术。体积压裂后,未改造区域的流动为受微纳米孔隙介质控制的非线性渗流,而改造区域的流动则是由微米级裂缝网络控制的达西渗流。综合考虑页岩气藏体积压裂后的多尺度流动、页岩气解吸附、扩散等特点,建立了耦合未改造区域和改造区域流动的稳态产量计算模型;在此基础上,首次运用连续拟稳定法,考虑压力波不稳定扩散,结合物质平衡方程建立了页岩储层体积压裂水平井非稳态产量计算方法,并对页岩气体积压裂水平井非稳态产量的影响因素进行了分析。结果表明：基于连续拟稳定法建立的产量预测模型具有求解过程简单、计算速度快,与数值模拟结果吻合程度高的特点;页岩气的解吸效应主要影响生产中后期的产量;随着体积压裂区半径、压裂区渗透率、扩散系数、朗格缪尔体积的增大,页岩气井产能增大,且增加幅度逐渐减小;朗格缪尔压力对产量的影响较小。该方法为页岩气体积压裂水平井非稳态产量的计算提供了理论依据。