A New Semi-Analytical Model for Thermal Recovery Processes

Pooladi-Darvish, Mehran; Tortike, W.S.; Ali, S.M.

doi:10.2523/29660-ms

Cited by 3 publications

(1 citation statement)

References 9 publications

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“…The oil production rate was calculated with time depending on the heat penetration depth at each time for the elements. Pooladi-Darvish (1995) proposed applying the heat integral method for solving the unsteady-state temperature profile to obtain the differential equation of penetration depth in Butler' model. Heidari et al (2009) modified Pooladi-Darvish's model to consider heat conduction in the normal direction and fluid flow along the interface.…”

Section: Introductionmentioning

confidence: 99%

Analytical Treatment of SAGD - Old and New

Zargar

Ali

2016

Day 1 Tue, June 07, 2016

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Steam-Assisted Gravity Drainage or SAGD is a widely tested method for producing bitumen from oil sands (tar sands). Several analytical treatments of the basic process have been reported. In a typical model, the focus is on bitumen drainage ahead of an advancing steam-bitumen interface. In a few cases, a steady state expression for bitumen drainage rate is obtained. This has been modified by several investigators to include other effects. In all cases, the bitumen rate is obtained with no recourse to the steam injection rate -which is worked out after the fact. The treatment of time dependence, in a few models, is tenuous, building it in partly on the basis of experimental data.In this work, the Steam Assisted Gravity Drainage (SAGD) process is considered to develop during two stages; steam chamber rise (unsteady-state stage) and depletion (steady-state stage). Depletion phase is modelled by two different approaches; Constant Volumetric Displacement (CVD) and Constant Heat Injection (CHI).In the transient steam chamber rise stage of SAGD, initially there is no heat ahead of the rising front but, as the front rises with time, heat accumulates ahead of the front. In the depletion (steady-state) stage, there is a dynamic equilibrium situation. The accumulated heat ahead of the front plays a very important role in this phase of SAGD modelling in order to find the advancing front velocity. There is a reciprocal relation between the advancing front velocity and the amount of stored heat ahead of the front. Higher front velocity leads to lower heat accumulation ahead of the front for mobilizing oil ahead and making it drain. By considering the equilibrium situation for thermal recovery methods with dominant gravity drainage driving force, the advancing front velocity is responsible for heat accumulation ahead of the front and in turn this heated oil drains away and is responsible for advancing the front. Therefore, the key point in the modelling is to determine the advancing front movement that satisfies heat and mass balances over the system under equilibrium.In the CVD (Constant Volumetric Displacement) model, we postulate that the front movement is such that the steam chamber growth is constant, in other words, the oil production rate is constant over time.In this work, it is shown that to obtain a constant oil production rate from a mass balance, the injected heat has to be increased to compensate for the heat loss to the overburden and increasing accumulated heat ahead of the front due to interface extension and decreasing front velocity.In the CHI (Constant Heat Injection) model, heat is injected at a constant rate into the system, which provides heat for the growing steam chamber size, increasing heat loss to the overburden, and heat flow by conduction ahead of the front. In this model, we are computing the front velocity that satisfies heat balance and mass balance for a constant heat injection rate. Decreasing steam chamber velocity with time from this model leads to decreasing oil production rate over the deple...

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Section: Introductionmentioning

confidence: 99%

Analytical Treatment of SAGD - Old and New

Zargar

Ali

2016

Day 1 Tue, June 07, 2016

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Experimental Investigation and Numerical Simulation of Steam Flooding in Heavy Oil Fractured Reservoir

Souraki

Ashrafi

Karimaie

et al. 2011

SPE Western North American Region Meeting

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Nowadays, the most promising methods for recovery of heavy oil and bitumen are thermal recovery processes and among these processes, steam flooding is one of the most important methods. Naturally fractured reservoirs hold over 20 billion barrels of heavy oil which necessitates improvement in understanding of the physical processes that takes place between matrix and fracture during steam injection. This paper addresses experimental and numerical simulation of steam injection in fractured rock. The purpose of the work was to investigate the efficiency and feasibility of steam injection in a core sample which is surrounded by fracture. Athabasca heavy crude oil was used in this study and some PVT properties of the oil was measured experimentally at different temperatures up to 200°C prior to simulation studies. Simulation studies were then conducted on a 20cm long cylindrical sandstone core with a permeability of 640mD. The core was saturated with Athabasca heavy crude oil and is radialy surrounded by a fracture. The results show that steam injection process has great performance and efficiency in fractured systems. However, steam processes are not recommended in very high permeable fractured reservoirs due to high steam oil ratio (SOR). Sensitivity analyses were performed on permeability of the fracture and injection rate. High fracture permeability is effective when the steam injection rate is low but it may have negative effect at earlier times for high injection rates. The effect of different injection rates on recovery performance of the system was investigated using the numerical model. Faster oil recovery and higher SOR was observed with increasing injection rates, eventhough the same ultimate recovery was obtained.

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SAGD Performance with Temperature Dependent Properties - An Analytical Approach

Heidari¹,

Hejazi

Ali

2015

SPE Annual Technical Conference and Exhibition

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Steam-Assisted Gravity Drainage (SAGD) is one of the successful in-situ thermal oil recovery methods in Alberta, Canada. There are several tools for design and evaluation of SAGD projects, for instance thermal reservoir simulators and simple analytical models. Although time consuming, reservoir simulators handle reservoir heterogeneities. On the other hand, existing analytical models are limited to simple configurations with constant rock and fluid properties. Therefore, providing a simple and fast analytical model that can accurately analyze a SAGD project with variable properties is very desirable. In this study, a semi-analytical model is introduced to investigate the effect of temperature dependent properties such as thermal conductivity, heat capacity and rock density on the performance of SAGD process. The semi-analytical model solves transient nonlinear heat transfer equation coupled with the continuity equation in a sequential manner. First, nonlinear, transient partial differential heat transfer equation is transformed to an ordinary differential equation using Kirchhoff's transformation and Heat Integral Method (HIM). The ordinary differential equation is solved by fourth order Runge-Kutta method. Second, the continuity equation is solved using new temperatures and as a result, production rates and shape of steam chamber are determined. The stability of sequential methods is sensitive to the spatial and temporal discretization. A criterion for time step selection is defined based on the Courant number and Peclet number to guarantee the stability of this semi-analytical model. The Courant number depends on the steam temperature and fluid and rock properties of reservoir, i.e. absolute permeability, oil viscosity and porosity. Peclet number depends on the velocity of steam chamber interface, penetration depth of heat and thermal diffusivity at steam temperature. The results of this study illustrate that the temperature dependent physical properties affect the temperature distribution ahead the steam chamber. The impact on the cumulative oil production and production rate is significant. Moreover, several field scale problems were simulated with both the proposed semi-analytical model and a commercial reservoir simulator. It is revealed that, the locations and shapes of steam chamber as well as production rates predicted from semi-analytical model and reservoir simulators are in an excellent agreement. The proposed semi-analytical model runs in a small fraction of runtime of the numerical simulator, yet it provides reasonable results. Thus it has the potential to be used as a tool for quick SAGD evaluations. A runtime comparison between this model and the numerical simulator is also provided.

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A New Semi-Analytical Model for Thermal Recovery Processes

Cited by 3 publications

References 9 publications

Analytical Treatment of SAGD - Old and New

Analytical Treatment of SAGD - Old and New

Experimental Investigation and Numerical Simulation of Steam Flooding in Heavy Oil Fractured Reservoir

SAGD Performance with Temperature Dependent Properties - An Analytical Approach

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