Cyclic steam stimulation in non-fractured reservoirs has been treated extensively in the literature, but there has been little attention paid to the development of analytical models for vertically fractured reservoirs.
One such model" for predicting the heated reservoir volume at the end of any steam injection or production period has been developed, This model accounts for heat losses, hot liquid production, steam injection and down time, in order to predict the temperature distribution in the reservoir at any given time. The isotherm concept is then applied to determine the drainage volume of the heated reservoir. This concept consists of selecting an isotherm such that oil mobility is achieved within its boundaries. An additional feature of the model is that the growth of the steam zone in the reservoir can be estimated.
The development of this model arose from a need to calculate the size and shape of healed volumes to design well spacing and estimate potential oil recovery [or a pilot expansion. The model has also been used to schedule slug sizes during cyclic steam stimulation, Some examples of its use are given.
The Energy Resources Conservation Board1 estimates there is as much as 275 × 109 m3 of bitumen in place in Alberta's Cretaceous sands: the majority of which is at a depth greater than 250 m. Where it is producible, thermal insitu techniques such as steam stimulation are required to mobilize the oil and in many instances fracturing is required to achieve the necessary Steam injectivity. All depths below 250 m, these fractures are for the most part horizontal fractures. Below 400 m, vertical fractures are usual, with a transition from horizontal to vertical in the 250 to 400m interval.
The largest and perhaps the most successful of the vertically fractured steam stimulation recovery projects is the Esso Canada Ltd. Cold Lake project in northwestern Alberta2 but there are many more operators such as BP Canada Ltd., and Shell Canada Ltd, 3 who have used vertical fractures in combination with steam stimulation for bitumen recovery.
For these reserves to be efficiently exploited, the reservoir engineer needs to know how much of the reservoir has been heated with each steam cycle and the shape of the heated volume. Rapid or easy to use performance indicators are also desirable for cycle Optimization or to assess the impact of different operating strategies. Numerical simulators can be used for these purposes but are expensive to run and time consuming. If available, analytical models can be a convenient and simple alternative.
To be useful, an analytical reservoir performance model must account for convective and conductive heat transport white injecting and producing fluids. Several of these models exist for cyclic stimulation, but of the existing analytical models, Wheeler's4 model is the only one for steam injection into a vertical fracture. Unfortunately his model, like most of the Others, does not handle recurrent cyclic operations.
This paper extends Wheeler's theory using the principal at superposition 10 rectify this deficiency.