Copyrrghl 1987, Soctety 01 Pelroleum EngineersTh!s paper was prepared Ior presenlal, ?n at the sPE Cahfornm Regional L4eelmg held m Venlura, Cahforma. Aprd 8-10. 5987 Th,s paper was selected for presenta!fon by an SPE Program COnIM!llee Iollowng rewew of mformalmn conlamed m an abstract submdted by Ihe author(sJ Conlenls of !he paper, as p,esenled. have nO! been rev!cmed by the SOC1e!y of Petroleum Engineers and are sublecl m correclton by the aull?orisl The malcrml as presented. does nol m?cessiwly refk?cl any push ton of the Soclely of Peholeum Engineers. IIS officers. or members Papers pmsenled a[ SPE mee!mgs are sub]ec! 10 pubhcahon rewew by Edrlor,al Commt!lees of Ihc Soctety of Petroleum Engineers Perm!ss,on 10 copy !s restncled to an abslracl of no! more I..an 300 words Illuslrallons may not be cop!ed The abslracl should conlam conspicuous acknowletigment of where and by whonl lhe paper E presented Wrde Pubhcal, ons Manager SPE P O BOX 833836 Richardson, TX 75083 .3S36 Telex. 730989 SPEDAL
Summary. In this paper, lumped-parameter models are presented for confined and unconfined liquid-dominated geothermal reservoirs without recharge and compared to production data from the Svartsengi geothermal field in Iceland. They show that recharge or water influx is likely to affect the field's drawdown with time. Three petroleum reservoir water-influx methods are then presented for steady-state, pseudosteady-state, and unsteady-state aquifers encroaching into the geothermal reservoir. History matching shows that the reservoir/aquifer system is best described as unsteady state and radial, with the aquifer boundary taken at infinite distance. Introduction Geothermal and hydrocarbon reservoirs are in some respects similar, and yet different. In this paper, we examine one of their similarities: the recharge or influx of water from surrounding aquifers. Two types of high-temperature reservoirs represent most geothermal systems: vapor-dominated and liquid-dominated. The Geysers field in northern California is a typical vapor-dominated reservoir, and the Wairakei field in New Zealand is a typical liquid-dominated reservoir. The main feature that distinguishes these types of reservoirs is their pressure gradient. In vapor-dominated systems, the pore space is filled with steam, so the pressure gradient is vaporstatic. In liquid-dominated systems. pressure gradient is vaporstatic. In liquid-dominated systems. the pore space is liquid-filled, so the pressure at any depth is dominated by the water column weight to surface i.e. hydrostatic. The volume of high-temperature geothermal reservoirs must be large to sustain steam production for electric power generation, typically several cubic kilometers of power generation, typically several cubic kilometers of reservoir rock and fluid. This requirement and the volcanic nature of geothermal energy mean that exploited geothermal reservoirs must be thick, usually 1 to 2 km [0.6 to 1.2 miles]. In the natural state, geothermal reservoirs are dynamic rather than static. This means that there is convection within the reservoir and advection to the surface and surrounding formations, hot springs and fumaroles are manifestations of geothermal systems. The fluids lost from a geothermal system must be supplied from below or from adjacent aquifers. Therefore, aquifers surrounding, geothermal resources are likely to encroach into the reservoir when the pressure falls as a result of production. In this paper, we study the application of water-influx methods in geothermal reservoir evaluation. We use a lumped-parameter material-balance model and several water-influx models to match the production history of the Svartsengi geothermal field in Iceland. Basic Reservoir Models The modeling approach used in this paper is often described as lumped-parameter. An early application of this approach to geothermal systems is that of Whiting and Ramey, who studied the Wairakei field in New Zealand. A later lumped-parameter study is that of Brigham and Neri, who studied a part of the vapor-dominated Larderello system in Italy. Other similar studies are those of Castanier et al. and Fradkin et al . An overview of lumped-parameter models is given by Grant et al. and Grant. Olsen reviewed uses of lumped-parameter and water-influx models in geothermal reservoir engineering. There are two components to our model of the Svart-sengi geothermal field, the reservoir and the aquifer. They are brought together in the material-balance equation (1) where the current mass, Wc, equals that initially in the reservoir, Wi, minus what has been produced, Wp, plus any water influx, We. In lumped-parameter modeling, the reservoir is treated as one element with some average properties. Of primary interest in our work is the reservoir production primary interest in our work is the reservoir production mechanism. Is fluid produced because of expansion or because of a fall in liquid level? The initial fluid in place in liquid-dominated reservoirs may be compressed water. In this case, when the reservoir is penetrated by wells and produced, the water expands because of its compressibility. We call this a confined reservoir. For a reservoir of volume V, the fluid mass in place is given by (2) SPERE P. 77
This paper was selectad for presentation by the OTC Program Committee following review of information mntained in an abatract submitted by tha author(s). Contents of tha paper, as presented, hava not been reviewed by tha Offshore Technology Conference and are subject to correot~n by tha author(s). The mater[~, = wsent~d, does not neces=rilY reffeã nv oosition of the OfLshoreTochnoloov Conference or Ikeofficers. Permission to copy la restricted to an abstract of not mora than 300 words. Illustrations may not be copied. The abstract shb~ld contain conaplcuoua acknowf&dgmant of where and by whom the PaPer ia presented.
ABSTRACT
The 22-26m thick oil zone in the Troll West Oi[ Province, offshore Norway, is planned to be developed by 18800m long horizontal wells. The viability of such wells has been proven by long-term testing. To obtain economic oil production the wells will be completed in the lower part of the oil rim close to the oil-water contact. The high water production which is expected can, to some extent, be controlled by gas reinfection. A flexible gas injection scheme will therefore be implemented.
Allowing wells to produce free gas together with the oil (super
Depletion models for liquid-dominated geothermal reservoirs are derived and presented. The depletion models are divided into two categories: conflned and unconfined. For both cases depletion models with no recharge (or influx), and depletion models including recharge, are used to match field data from the Svartsengi high temperature geothermal field in Iceland.The influx models included with the mass and energy balances are adopted from the petroleum engineering literature. The match to production data from Svartsengi is improved when influx was included. The Schilthuis steady-state influx gives a satisfactory match. The Anite aquifer method of Fetkovitch, and the unsteady state method of Hurst gave reasonable answers, but not as good.The best match is obtained using Hurst simplified solution when h = 1 . 3~1 0~ 7n-l . From the match the cross-sectional area of the aquifer was calculated as 3.6 km2.The drawdown was predicted using the'Hurst simplified method, and compared with predicted drawdown from a boiling model and an empirical log-log model. A large difference between the models was obtained. The predicted drawdown using the Hurst simplified method falls between the other two.Injection has been considered by defining the net rate as being the production rate minus the injection rate. No thermal or transient effects were taken into account. Prediction using three different net rates shows that the pressure can be maintained using the Hurst simplified method if there is significant fluid reinjection.
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