Steam Assisted Gravity Drainage (SAGD) is a thermal bitumen production technology widely used in Northern Alberta’s oil sands. A SAGD process consists of bitumen production from subsurface reservoirs and bitumen and water treating in a surface facility. The subsurface part of the process includes twin horizontal wells drilled at the bottom of the formation, known as a well pair, one for steam injection and the other for bitumen production. High temperature steam is continuously injected into an injector well to heat the formation and to separate bitumen from the sands which allows the oil to drain by gravity to a producer well which is located a few meters below the steam injector well. Due to thermal losses in the well and reservoir, the steam is condensed, and a mixture of bitumen and water is pumped into the production pipeline and sent to the surface facilities to be processed and prepared for sale.
Due to subsurface complexity, limited data availability and uncertainty present in measurements and data analysis, a reservoir cannot be deterministically defined. Reservoir properties such as porosity, relative permeability, thermal diffusivity, oil saturation, formation heat capacity, etc. are inevitably associated with uncertainties. The uncertain parameters associated with oil reservoirs affect production forecasts and hence, field development plans which ultimately determine the efficiency of resource extraction and project economics. A rigorous evaluation of reservoir uncertainties allows SAGD operations to evaluate the risk on financial indicators (e.g. NPV) of a SAGD project. To support decision making and predict the reservoir behavior by taking into account the uncertainties, the application of sensitivity/uncertainty analysis to subsurface reservoir proxy modelling is investigated in this study.
Based on the physics of the SAGD process, several analytical and numerical models have been proposed to study reservoir behavior. Although numerical-based reservoir simulators can solve complex problems and they are powerful tools, they require large volumes of input data for a single run. They are based on discretizing the reservoir and performing all calculations for every grid block which requires many hours for computation. On the other hand, analytical or semi-analytical approaches require less computation time and they are very fast in history matching and forecasting production. Therefore, the analytical or semi-analytical models such as physical-based proxies instead of numerical models are found well-applicable for uncertainty analysis purposes.
Proxy models have been derived based on Darcy’s law, oil material balance and heat transfer fundamentals (Butler et al 1981a and 1981b, Butler 1992, Reis 1992). Among those, the analytical model proposed by Reis (1992) is selected in this study due to its accuracy and simplicity. The model was implemented in the Process Ecology’s Xtrema engine for optimal scheduling and planning for field development over the life of a SAGD project.
The oil drainage rate model proposed by Reis was derived based on Butler’s theory for SAGD horizontal wells. The steam chamber was assumed to be an inverted triangle with the lower vertex fixed at the production well. In addition to oil rate, the latent heat injection rate for steam to expand the steam chamber zone, preheat the formation, and heat losses to overburden were determined and through combining the oil production rate and energy balance, he developed a model for the steam-oil ratio.
To illustrate the effect of uncertainties in reservoir properties on SAGD performance, the sensitivity/uncertainty analysis was applied to a reservoir with the properties listed in Table 1. The input uncertainty on reservoir height (pay thickness), reservoir temperature, injection pressure, initial oil saturation, porosity, permeability, thermal diffusivity, heat capacity, and oil viscosity were assumed as a percentage of the true value of the parameter.
The first step to analyze the uncertainty propagation through the model is to identify the main input parameters which contribute the most to the variation in the model response. Through conducting the one-at-a-time method, the consequences of changing a given parameter in the model were quantitatively assessed and the results are presented in Tornado charts (Figure 1). As shown in Figure 1, oil viscosity, reservoir permeability, porosity, initial oil saturation, pay thickness, formation heat capacity, and thermal diffusivity are the most important parameters whereas reservoir initial temperature and injection pressure are insignificant parameters which can be eliminated from further analysis.
After conducting the sensitivity analysis, the Monte Carlo simulation approach along with Latin Hypercube Sampling (LHS) is used for uncertainty analysis and quantitatively determine the uncertainty in model response. The Monte Carlo technique is a probabilistic computer-based approach and it is most common in the uncertainty analysis of processes in the oil and gas industry. The distributions for all uncertain input need to be determined and in this work, it has been assumed that reservoir and oil properties are characterized by normal distributions and that there is no correlation between parameters. The results of uncertainty analysis are presented in the form of cumulative distribution functions (Figure 2) and the P10 and P90 for each variable of interest are reported:
Cumulative Oil Production: P10= 9.2 x 107 m3, P50 = 1.05 x 108 m3, P90 = 1.2 x 108 m3
CSOR: P10 = 2.76, P50 = 3.32, and P90 = 3.88
In addition, the range of variations versus time for each model response is plotted and shown in Figure 3.
The sensitivity/uncertainty analysis was applied to a SAGD well pair case using an appropriate physical-based proxy model. The framework takes the reservoir geological properties and fluid physical properties along with their uncertainties and it then determines the parameters that have a large contribution to the output variables of interest and quantitatively analyzes the potential effects that these uncertainties have on the reservoir performance including cumulative oil production, cumulative steam consumption, and cumulative steam to oil ratio (CSOR) as a function of time. The framework is aimed to assist operators in determining optimal scheduling and planning for field development over the life of a SAGD project, and to mitigate risk during the oil production and reduce uncertainties in critical parts of the process.
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