Summary
Cooling of rock by water injection frequently causes fracturing of wells. This paper describes a 3D simulation model of thermally induced fracturing. Itis used to show that fractures often tend to grow vertically into permeablezones. Procedures are outlined for confining fracture growth in wells where itwill assist waterflood sweep performance.
Introduction
The performance of water-injection wells in deep, warm reservoirs is usuallydominated by thermally induced fracturing of the formation around the wellbore. Without fracturing, it would not be possible in many cases to maintain highinjection rates, particularly possible in many cases to maintain high injectionrates, particularly when the injected water has a significant solids content, which could block a nonfractured wellbore. At the same time, fracturing caninfluence the vertical and horizontal sweep efficiencies of a waterflood.
Thermally Induced Fracturing.
The mechanism of thermally induced fracturingis as follows. Rock at depth exists in a state of high compressive stress. Atdepths of greater than about 3,000 ft [1000m] the vertical stress (equal to theweight of the overburden rock) is normally greater than the horizontal stress. The magnitude of the horizontal stress varies with direction, with a typicalvalue of the minimum principal horizontal stress being 0. 65 to 0. 8 psi/ft ofdepth [14.5 to 18 kPa/m]. The injection of cool surface water into a warmreservoir leads to cooling and contraction of the rock around the wellbore. Asthe cooled rock pulls inward upon the warm region around it, a tensilecomponent of stress (thermoelastic stress) builds up within it. The value ofthe thermoelastic stress depends on the shape of the cooled region and on rockproperties but may exceed 10 psi/ degrees F of cooling [100 kPa/ degrees C]. When, for example, 50 degrees F [10 degrees C] seawater is injected into areservoir at 10,000-ft [3000-m] depth and 250 degrees F [120 degrees C] initialtemperature, thermoelastic stress will be reduced by up to 2,000 psi [14 MPa], which is a very significant factor in fracture growth. A fracture can propagatefrom the wellbore provided the water bottomhole pressure (BHP) exceeds the netcompressive including thermoelastic stress, in the cooled rock. (Someadditional pressure may be needed in the very early stages of fracture growthto overcome the rock fracture toughness.) The fracture will open against thedirection of least stress, which means that at sufficient depth it will occupya vertical plane perpendicular to the minimum principal stress direction, asillustrated in Fig. 1. As the fracture propagates, subsequent water injectioncools the rock in its vicinity, propagates, subsequent water injection coolsthe rock in its vicinity, which generates thermoelastic stress, which in turnfeeds back into fracture growth. Thermal fracturing thus couples the fluid andheat flow in the reservoir and fracture to the stress and fracture mechanics ofthe rock. Thermally induced fracturing of injection wells often occursspontaneously at design wellhead pressure (WHP), where WHP is typically chosento be high enough to provide an adequate waterflood pressure gradient acrossthe reservoir but low enough to avoid the pressure gradient across thereservoir but low enough to avoid the risk of fracturing into the hot under-and overburden rock. In other cases, particularly where the prefractureinjection rate is low, the well may not fracture spontaneously. In such cases, a high WHP can initially be applied deliberately to propagate a fracture, whichcan subsequently maintain itself as a result of thermal effects when the WHP isreduced. In addition to thermoelasticity, the fluid pressure in the pores ofthe rock close to the wellbore will set up poroelastic stress. Typically, poroelastic stress is compressive (owing to poroelastic stress. Typically, poroelastic stress is compressive (owing to the enhanced pressure aroundinjection wells) and smaller (but not by an order of magnitude) than thethermoelastic stress. The existence and characteristics of thermally inducedfracturing have been reported in a number of field studies. There is aconsiderably larger body of work in the industry, mostly unpublished, in whichnegative or rate-dependent injection-well skins, which are recognized to becaused by fracturing, have been measured from well testing or assumed inreservoir modeling. This has led to a growing awareness among engineers thatmost waterinjection wells in deep reservoirs are fractured and that fracturinghas consequences for injectivity, WHP specifications, waterflood sweepperformance, and injection-water quality requirements.
Simulation of Thermally Induced Fracturing.
Simulation of thermally inducedwaterflood fracturing requires the coupling of fluid and heat flow in thefractured reservoir with thermo- and poroelastic stresses and rock mechanics. If the fracture can be approximated as 2D, extending over the full verticalinterval of the pay zone for its frill length, then simple plane-strainequations may be used to describe the fracture mechanics for-a linear elasticmedium. Perkins and Gonzalez constructed a simplified analytic model of Perkinsand Gonzalez constructed a simplified analytic model of 2D thermally inducedfracturing based on the assumption of elliptical flow fields around thefracture. Models that couple 2D fracture models into a reservoir grid have beendeveloped both for hydraulic fractures and for waterflood-induced fractures. The Dikken and Niko model calculates the thermo- and poroelastic stresses fromthe Goodier displacement potential with methods developed by Koning. Theassumption of large vertical extent is not appropriate, however, in manyexamples of thermally induced fracturing. A sandstone reservoir will very oftenexhibit layering of properties that are central to waterflood fracturepropagation-i.e., permeability, in-situ stress, and elastic modulus. Fracturecontainment by high-compressive-stress barriers (e.g., in under- or overburdenlayers) is an important feature of hydraulic fracturing 10 and applies equallyto waterflood-induced fractures. The elastic modulus, the most important factorin determining the thermoelastic stress produced by a given temperaturedistribution, may vary by a factor of two to five between layers. Permeability, which in many reservoirs varies by a factor of 10 to 100 between layers, isprobably the largest influence on the propagation of thermally inducedfractures. It is possible to envisage propagation of thermally inducedfractures. It is possible to envisage injected water cooling ahigh-permeability streak, which then forms the site of fracturing. In addition, thermal fractures that develop from a limited interval of perforation, or asmall section of a deviated wellbore, are bound to be 3D for at least part oftheir lifetimes. A small number of 3D fracture-mechanics models have beenwritten for hydraulic fracture simulation. The simulator used in this papercombines the rock-mechanics element of one With the fluid and heat-flowcalculation from a 3D reservoir simulator calculating stress with thedisplacement potential method. It can thus perform 3D modeling ofwaterflood-induced fracture propagation. propagation. Numerical Model
A numerical model of thermally induced fracturing must incorporate theessential elements of coupling between the fluid and heat flow and the rockmechanics of the problem.
*Now at Dowell Schlumberger.
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