WATER AND GAS CONING IN HORIZONTAL AND VERTICALWELLS

D.G. HATZIGNATIOU F. MOHAMED

this article begins on the next page FFPETROLEUM SOCIETY OF CIM & AOSTRA PAPER NO. 94-26S ATMA-23 Water and Gas Coning in Horizontal and Vertical Wells D.G. Hatzignatiou F. Mohamed University of Alaska This paper is to be presented at the 45th annual technical meeting of the Petroleum Society of CIM organized by the Petroleum Society of CIM, co-sponsored by AOSTRA in Calgary, Canada, June 12-15, 1994. Discussion of this paper is invited and may be presented at the meeting if filed in writing with the technical program chairman prior to the conclusion of the meeting. This paper and any discussion filed will be considered forpublication in CIM journals. Publication rights are reserved. This is a pre-print and is subject to correction. ABSTRACT In this paper the coning of water or gas in vertical and horizontal wells is examined. The existing analytical solutions and correlations do not predict accurately the water breakthrough for horizontal wells; also solutions or correlations for predicting the gas breakthrough time do not exist A three-dimensional, three-phase, black- oil, commercial simulator is used to examine the effects of various rock and fluid properties, well configurations, reservoiranisotropy on the breakthrough time and to derive correlations which can be used to predict the time at which gas or water cones into a vertical or horizontal well. A correction is applied to the simulator breakthrough times to incorporate the effects of numerical dispersion. The results obtained from the newly derived correlations are compared with existing analytical and numerical solutions for a number of cases; these comparisons indicate that the correlations developed in this work can be used to predict the water or gas breakthrough time in vertical and horizontal wells quiteaccurately. INTRODUCTION Water and/or gas coning is a serious problem in many reservoirs with wells producing from an oil zone underlying a gas cap, overlying an aquifer or both. Coning occurs in a well on production, when the water or gas zone moves up towards the wellbore in the form of a cone. Eventually, the water or gas breaks through into the well and water from the aquifer and/or gas from the gas cap is produced along with oil. The water or gas production increases progressively after breakthough time and may reduce significantly the crude oilproduction. The main factors affecting the water and/or gas coning tendency are the density difference between oil and gas or oil and water, the viscosity of water or gas, formation permeability, pressure drawdown, flow rate, etc. More specifically, the tendency of a fluid to cone is directly proportional to the density difference between the fluid and crude oil, but

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Water and Gas Coning in Horizontal andVertical Wells

D.G. HatzignatiouF. Mohamed

University of Alaska

This paper is to be presented at the 45th annual technical meeling of Ihe Petroleum Society of elM organized by the Petroleum Society of CIM,co-sponsored by AOSTRA in Calgary, Canada, June 12-15, 1994. Discussion of Ihis paper is invited and may be presented at the meeting if filedIn writing with the technical program chairman prior to Ihe conclusion of the meeting. This paper and any discussion filed will be considered forpubricalion in elM journals. Publication rights are reserved. This is a pre-print and is subject to correction.

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ABSTRACT

In this paper the coning of water or gas in verticaland horizon tal wells is examined. The existing analyticalsolutions and correlations do nat predict accurately thewater breakthrough for horizontal wells; also solutionsor correlations for predicting the gas breakthrough timedo not exist. A three-dimensional, three-phase, black-oil, commercial simulator is used to examine the effectsof various rack and fluid properties, well configurations,reservoir anisotropy, etc. on the breakthrough time andto .: " . ,'e correlations which can be used to predict thetime at which gas or water cones into a vertical orhorizontal well, A correction is applied to the simulator

,breakthrough times to incorporate the effects of: numerical dispersion. The results obtained from the. newly derived correlations are compared with existing,analytical and numerical solutions for a number of cases;these comparisons indicate that the correlationsdeveloped in this work can be used to predict the wateror gas breakthrough time in vertical and horizontal wellsquite accurately.

INTRODUCTION

Water and/or gas coning is a serious problem inmany reservoirs with wells producing from an 011 zoneunderlying a gas cap, overlying an aquifer or both,Coning occurs in a well on production, when the wateror gas zone moves up towards the wellbore in the formof a cone.

Eventually, the water or gas breaks through intcthe well and water from the aquifer and/or gas fromthe gas cap is produced along with oil. The water orgas production increases progressively afterbreakthough time and may reduce significantly thecrude oil production.

The main factors affecting the water and/or gasconing tendency are the density difference between oiland gas or oil and water, the viscosity of water orgas, formation permeability, pressure drawdown,flow rate, etc. More specifically, the tendency of fluid to cone is directly proportional to the densit~difference between the fluid and crUde oil, but

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inversely proportional to the fluid viscosity andreservoir permeability.

The water and/or gas coning can be reduced by (i)decreasing the well production rate; (ii) improving theproductivity of the well; (iii) using horizontal insteadof vertical wells to produce the formation; (iv)selectively partially penetrating the well at the top ofthe reservoir in the case of water coning, at thebottom of the reservoir in the case of gas coning, andclose to the center of the pay zone in the case ofsimultaneous water and gas coning; (v) recompletingthe well at a different elevation t.o increase thedistance between the gas-oil or water-oil contact andthe perforated interval; and (vi) infill drilling.

Most of the research efforts in the area of waterand gas coning have concentrated on estimating thecritical oil rate and the post breakthrough wellbehavior. In ti,e subsequent parts of this section someof these studies will be discussed for both vertical andhorizontal wells.

Vertical Wells

One of the first papers published on the coningphen~mena was by Muskat and Wyckoff1. They solvedLaplace's equation for single phase, steady-state,incompressible flow and presented an approximatesolution of the critical flow rate in isotropicformations. The analytical solution of Ref.1 wassimplified by Meyer and Garder2 for radial- flow,whereas Chaney et al.3 and Chierici et al.4 usedpotentiometric models to obtain the critical flow rate.Ref. 4 studied the effect of reservoir geometrY andwell configurations on critical coning rate and optimumperforation interval for simultaneous gas and waterconing. Schols5 developed an empirical expression forthe critical rate from experiments conducted on Hele-Shaw models.

An approximate theory for the critical oil rate inanisotropic formations was presented by consideringthe oil-water interface to be a streamline6 .Similarly, Chaperon 7 presented a solution for thecritical rate of vertical wells in anisotropicformations in a closed system and reported that whenthe vertical permeability decreases, critical rateincreases slightly, but the elevation of the criticalcone does not change appreciably.

Two methods, one analytical and one numerical,were presented by Hoyland et al.8 t.o predict thecritica[ rate for water coning in anisotropic,

26-2

homogeneous formations. The analytical solution wasbased on 'the assumption of an infinitely conductivewellbore and the results of Ref. 8 were presented in agraphical form of dimensionless critical rate, qeD,versus dimensionless radius, rD, as a function of thefractional well penetration for both isotropic andanisotropic fOmlations.

Addingt.on 9 developed generalized correlations forthe critical coning rate and the gas-liquid ratio (GLR)after gas breakthrough using a three-dimensionalsimulation study of the Prudhoe Bay field. The authorshowed that his correlations can also be applied inheterogeneous reservoirs by using an averageformation permeability. Ref. 9 computed the averageoil column height above the perforations, hgb' as

(1 )

and the GLR after gas breakthrough as

1og(GLR) = m(hap - hgb) +1og(S g.) (2)where

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and

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A correlation for predicting the water cone risefrom static conditions until breakthrough was alsodeveloped by Sobocinski and Cornelius 1 0 for ahomogeneous, incompressible system with no gas cap,producing at a constant rate. Cone breakthrough timeand critical rate can be determined from dimensionlesscorrelating groups reported by Ref. 10. Bournazeland Jeanson11 conducted laboratory experiments andreported a correlation for the water breakthroughtime in vertical wells similar to the correlation of Ref.10. Finally, Refs. 12-17 also presented results onwat.er or gas coning for vertical wells based onlaboratory or simulation studies.

Horizontal Wells

Efros 1 8 was the first to study gas coning andreport a correlation for critical rate in horizontalwells whereas, Chaperon7 presented a solution forcritical rate for horizontal wells in anisotropic