DEVELOPMENT OF GENERALIZED WELL SEMI-ANALYTICAL CONING MODELS
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Oil deposits are often found in association with a communicating gas
or water zone. The production of the oil often leads to the coning of
water or gas. This dynamic interaction can be captured by a properly
detailed reservoir simulation, which unfortunately may not always be
practical. To bridge the gap, researchers over the years have developed
both analytical and empirical methods of modelling gas and water coning
in oil reservoir. The fundamental questions have always been: what is
the critical rate of oil production; what is the breakthrough time if
the critical rate is exceeded; and what is the post-breakthrough
Using analytically derived line source vertical and horizontal well
breakthrough time expressions, a method has been developed to estimate
oil critical rate, breakthrough time and post-breakthrough trend for
inclined wells. The Post-breakthrough prediction scheme was extended to
vertical and horizontal wells. Simplified correlations have also been
generated for the easy application of the method without the need of
analyzing complex mathematical functions. Within the accuracy of the
numerical simulation results, the breakthrough times for the inclined
well were consistently and correctly predicted. Literature correlations
and numerical simulation comparisons showed that the post-breakthrough
production predictions tended to underpredict oil production, but the
trends were much more consistent with simulation results than other
correlations studied. To the best of the knowledge of the author, this
is the first semi-analytical coning model of an inclined well, as well
as, the first semi-analytical post-breakthrough trend prediction for
vertical and horizontal wells.
INTRODUCTION AND PROBLEM DEFINITION
Quite often, oil deposits are associated with an underlying water
aquifer and an overriding gas cap. In many situations, the oil reserve
is desired at the surface while the associated fluid is preferred within
the reservoir either because they are not valuable at the surface as in
the case of produced water or the resources to harness the gas if
produced to the surface are not readily available. The reservoir water
or gas may also be required for pressure maintenance in production
optimization within the reservoir. Whatever may be the intention of
prefering to keep the water and/or gas within the reservoir, it is found
in practice a difficult goal to achieve due to coning of the unwanted
fluid(s). Coning is the tendency of the underlying water in contact with
the oil to rise locally towards the producing well due to the greater
pressure depletion near the producing well and the viscous drag the
production of oil is having on the water-oil interface. The same holds
for the gas oil interface in which case the gas projects downwards
towards the producing well’s perforation against gravitational force
arising from gas-oil density difference. The projection is a result of
viscous drag on the fluid interface and the local pressure depletion
around the well due to oil production.
The production of either water or free gas with the oil will result
in the reduction of the rate of oil production and the ultimate recovery
of the oil. The reduction of oil production arises from the simple fact
that some portion of the well bore that would be transporting oil will
have to transport the unwanted fluid. Reduction in recovery arises from
pressure depletion and trapping of oil behind the advancing unwanted
fluid front. Ordinarily without coning, the unwanted fluid pushes the
oil to the well as production progresses but with coning, the unwanted
fluid leaves the oil behind, enters the well and may lead to early
abandonment of the well.
The production of water has other damaging effect on hydrocarbon
production profitability as it increases the spate and damage of
corrosion. Corrosive agents like acid anhydride require the presence of
water for ionization and chemical activity on metallic materials used in
making the production string and other facilities. Obviously, the
handling and disposal cost of produced water increases with the rate of
coning. Depending on the prevailing environmental policy and the
contaminant present in the produced water, this may constitute a huge
cost burden. Gas handling, especially in areas with little market for
gas, can become very demanding with gas coning. Treatment,
pressurization and storage or re-injection may have dear financial
implications. The environmentally-damaging alternative to the gas
handling problem common in some countries is gas flaring. The latter
constitutes enormous economic and environmental hazard.
As can be appreciated, for technical and economic reasons, it is
crucial that coning be minimized or delayed. Thus coning minimization or
delay is an important aspect of reservoir and production
management. Numerous studies1,2,3,4 have been conducted to understand
the initiation and evolution of coning in order to control or minimize
the stated negative consequences.
1.2 STATEMENT OF PROBLEM
Work on coning had generally been pursued along the path of
preventing or delaying cone generation and evolution, the time to
breakthrough if advancement is not checked and the performance of the
well after cone breakthrough. A number of empirical and analytical
have been conducted to model and determine these properties5. As will
be discussed in detail, in the section on literature review,
correlations and models for the determination of critical rate of oil
production, time to breakthrough when producing at super-critical rate
and the performance of the well after breakthrough have been developed
for vertical and horizontal wells.
DEVELOPMENT OF GENERALIZED WELL SEMI-ANALYTICAL CONING MODELS
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