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Abstract For predicting the performance of water injection in naturally fractured reservoirs, scale-up of the recovery data from immersing an oil-saturated core into water is commonly used. Oil recovery from some of the naturally fractured reservoirs of the North Sea has been better than what was predicted using the immersion laboratory experiments. In the field, the matrix blocks do not become surrounded by water at once; they experience an advancing fracture-water level (FWL). In this paper, the results of experiments of water injection in fractured porous media comprising a number of water-wet matrix blocks are reported for the first time. The blocks experienced an advancing fracture-water level (FWL). Immersion-type experiments were performed for comparison; the dominant recovery mechanism changed from co-current to counter-current imbibitions when the boundary conditions changed from advancing FWL to immersion-type. We performed single block experiments of co-current and counter-current imbibitions and found that co-current imbibitions led to more efficient recovery. Kansas chalk and Berea sandstone were investigated. A column of three blocks of Berea sandstone (ฮฆ = 0.22, k = 0.62 ยตm, pore volume (PV) = 8,800 ? 10 m) and a stack of 12 blocks (four rows and three columns) of an outcrop Kansas chalk (ฮฆ = 0.30, k = 0.002 - 0.005 ยตm, PV = 13,900 ? 10 m) were used. Breakthrough recoveries were 0.2 - 0.4 for the Berea and 0.2 - 0.6 of PV for the chalk experiments. Corresponding ultimate recoveries were around 0.5 and 0.65 of PV; oil recovery from low permeability chalk was better than that of high permeability Berea. Fracture apertures in all the above experiments were in the range of 150 - 200 ยตm. An approximate mathematical model was developed for counter-current imbibition. It was found that the late-time matrix-fracture transfer function simplifies to an exponential function. Hence, the physical significance of the empirical transfer function of Aronofsky et al. was demonstrated. The exponential transfer function was incorporated in a model, which was used to match the water injection experiments performed on a stack of very low permeability Austin chalk (ฮฆ = 0.05, k = 0.00001 - 0.00005 ยตm, PV = 287 ? 10 m). These experiments were dominated by counter-current imbibition. Introduction Water injection is known as an important method for oil recovery from some fractured reservoirs. In water-wet fractured reservoirs, the capillary pressure contrast between the fracture and the matrix media provides the main driving force for water imbibition which can be an efficient recovery mechanism. Field application of water injection in fractured reservoirs has been implemented since the early fifties. Many issues, however, remain unresolved in the understanding of this process. Since the early studies, it was understood that recovery behaviour from a block totally covered by water is different than the same block in contact with water from some faces and with oil from other faces. However, the majority of studies have centred on immersion-type boundary conditions. Intuitively, if a block is surrounded by water, oil is forced to flow in the opposite direction of water flow, hence by counter-current imbibition.
- North America > United States > Texas (0.88)
- North America > United States > Kansas (0.55)
- Water & Waste Management > Water Management > Lifecycle > Disposal/Injection (1.00)
- Energy > Oil & Gas > Upstream (1.00)
- North America > United States > Wyoming > Laramie Basin > Niobrara Formation (0.99)
- North America > United States > Nebraska > Laramie Basin > Niobrara Formation (0.99)
- North America > United States > Kansas > Laramie Basin > Niobrara Formation (0.99)
- (47 more...)
Abstract For predicting the performance of water injection in naturally fractured reservoirs, scale-up of the recovery data from immersing an oil-saturated core into water is commonly used. Oil recovery from some of the naturally fractured reservoirs of the North Sea has been better than what is predicted using the immersion laboratory experiments. In the field, the matrix blocks do not become surrounded by water at once; they experience an advancing fracture-water level (FWL). In this paper, the results of experiments of water injection in fractured porous media comprised of a number of water-wet matrix blocks are reported for the first time. The blocks experienced an advancing fracture-water level (FWL). Immersion-type experiments were performed for comparison. The experiments revealed that the dominant recovery mechanism changed from co-current to counter-current imbibition when the boundary conditions changed from advancing FWL to immersion-type. We performed single block experiments of co-current and counter-current imbibition and found that co-current imbibition leads to faster oil recovery. This difference may explain the improved recovery observed in the field, when the blocks are experiencing an advancing FWL. Chalk and Berea sandstone were investigated. A column of three blocks of Berea sandstone (ฮฆ =0.22, k=620 md, pore volume (PV)=8800 cm) and a stack of 12 blocks (4 rows and 3 columns) of an outcrop chalk (ฮฆ =0.30, k=2โ5md, PV=13,900 cm) were used. Breakthrough recoveries were 0.2โ0.4 for the Berea and 0.2โ0.6 of PV for the chalk experiments. Corresponding ultimate recoveries were around 0.5 and 0.65 of PV. Surprisingly, oil recovery from low permeability chalk was better than that of Berea. Fracture apertures in all the above experiments were in the range of 150โ200 ฮผm. Another unique feature of the experiments was utilizing a transparent core-holder, which permitted measurement of FWL and visual identification of the active imbibition mechanisms. An approximate mathematical model was developed for counter-current imbibitions. It was found that the late-time matrix--fracture transfer function simplifies to an exponential function. Hence, the physical significance of the empirical transfer function of Aronofsky et al. (1958) was demonstrated. The transfer function was incorporated in a model, which was used to match the water injection experiments performed on a stack of very low permeability Austin chalk (ฮฆ =0.05, k=0.01-0.05 md, PV=287 cm). These experiments were dominated by counter-current imbibition Introduction Water injection is known as an important method for oil recovery from fractured reservoirs. In water-wet fractured reservoirs, the capillary pressure contrast between the fracture and the matrix media provides the main driving force for water imbibition, which can be an efficient recovery mechanism. Field application of water injection in fractured reservoirs has been implemented since the early fifties. Many issues, however, remain unresolved in the understanding of this process. Since the early studies, it was understood that recovery behavior from a block totally covered by water is different than the same block in contact with water from some faces and with oil from other faces. However, the majority of studies have centered on immersion type boundary conditions.
- North America > United States > Texas (0.48)
- Europe > Denmark > North Sea (0.48)
- North America > United States > West Virginia (0.45)
- (4 more...)
- Water & Waste Management > Water Management > Lifecycle > Disposal/Injection (1.00)
- Energy > Oil & Gas > Upstream (1.00)
Modeling Transverse Imbibition in Double-Porosity Simulators
Beckner, B.L. (Stanford U.) | Firoozabadi, A. (Stanford U.) | Aziz, K. (Stanford U.)
Abstract Published imbibition experiments of an advancing fracture water level surrounding a single matrix block are simulated using various double porosity models. These double porosity formulations are inherently unable to represent transverse imbibition with an advancing water level in the fracture as they are based essentially on one dimensional flow. Gross matches of the experimental and double porosity simulations required shape factors that were unrepresentative of the matrix block size. Increasing the fracture water injection rate required increasing the shape factor in order to achieve gross matches, hence a constant shape factor does not give the best matches with experimental data at different rates. A new double porosity transfer function for transverse imbibition is presented based on a nonlinear diffusion equation model for imbibition and the effective exposure time of elements of the matrix block to fracture water. This formulation uses the physical dimensions of the matrix block directly, i.e. no shape factor, and was effective in matching the experimental data without tuning any parameters. A comparison of a cubical single matrix undergoing fracture waterflooding was made between the various double porosity formulations and a fine grid, single porosity simulation. The conventional double porosity simulations did not this fine grid simulation as well as the proposed double porosity formulation. Introduction Naturally fractured reservoirs present many challenges from a numerical modeling point of view. The bulk of the storage of a naturally fractured reservoir resides in the matrix blocks while the fracture network makes up the dominant reservoir flow paths. The overall performance of any naturally fractured reservoir should then be quite sensitive to rate of fluid exchange between the storage body and the reservoir flow paths. This exchange, the matrix/fracture transfer function, is a critical component of any mathematical model used for the simulation of these reservoirs. In this paper, we will present a model for incorporating the effect of transverse imbibition into the matrix/fracture transfer function. We will test the proposed model with two cases, the published experimental work of Kleppe and Morse and a fine grid simulation of a cubical matrix block undergoing fracture waterflooding. Comparisons of the double porosity imbibition modeling methods presented by Litvak and by Thomas et al. will also be made to these two test cases. Warren and Root presented equations for unsteady-state single phase flow in double porosity reservoirs. Their double porosity domain assumes a continuous. uniform fracture network oriented parallel to the principal axes of permeability. The matrix blocks in this system occupy the same physical space as the fracture network and are assumed to be identical rectangular parallelepipeds with no communication between matrix blocks. Matrix blocks are also assumed to be isotropic and homogeneous. Assuming pseudosteady-state flow between the matrix elements and the fracture network, Warren and Root presented analytical solutions of these double porosity equations for pressure build-up tests. Their matrix/fracture transfer rate is controlled by a geometrical shape factor which is a function of the surface-volume ratio of the matrix blocks. Extension and numerical solution of the Warren and Root double porosity model to multiphase flow in three dimensions was done by Kazemi et al. Attempts to match water imbibition into artificially fractured cores by Kazemi and Merrill showed some success if the matrix block was divided into subdomains. As capillary pressure curves were not measured on the cores, capillary pressure was a parameter that was modified to help fit the recovery curves. cater enhancements of the matrix/fracture transfer function by Gilman and Kazemi included a more realistic gravity potential between the matrix and fracture and the ability to account for fluid transfer to the matrix system due to an imposed pressure gradient in the fracture. The improved gravity transfer was accomplished by gridding the matrix block into subdomains. P. 155^
- North America > United States > Texas (0.46)
- North America > United States > California (0.46)
- Energy > Oil & Gas > Upstream (1.00)
- Water & Waste Management > Water Management > Lifecycle > Disposal/Injection (0.56)
SPE Members Abstract Published imbibition experiments of an advancing fracture water level surrounding a single matrix block are simulated using a fine grid single porosity model and various double porosity models. The fine grid simulations show that a stationary water saturation profile quickly develops and advances in the matrix at the same rate as the fracture water level. A new double porosity transfer function for imbibition dominated matrix/fracture fluid exchange is presented based on stationary profile solutions of the fractional flow equation. This transfer function models the imbibition recovery for these advancing water level experiments better than the conventional double porosity imbibition formulations. It is shown that the stationary profile transfer function is best suited to systems where the time to develop the stationary profile is short relative to the length of the waterflood. The experimental data was also simulated using a diffusion equation with a nonlinear diffusion coefficient in combination with a moving boundary condition as the imbibition model. A constant diffusion coefficient based upon water relative permeability and capillary pressure gradient values at 1 - Sor matched the experimental results as well as the nonlinear diffusion coefficient, but required much less computer time. From analyzing two different diffusion type equations as imbibition models, we show that countercurrent imbibition is not a likely recovery mechanism for this type of advancing water level imbibition experiment. Introduction Naturally fractured reservoirs present one of the most difficult problems in reservoir simulation. The fracture network may be spatially difficult to define while the transfer of fluids from the matrix blocks to the fracture network may be qualitatively described by many different physical mechanisms. This paper will discuss the exchange of fluids via capillary imbibition in a matrix domain of regular, dispersed parallelepipeds within a continuous fracture domain. We will present fine grid simulation of the experimental work of Kleppe and Morsel and present a transfer function that models their single block waterflood better than existing double porosity formulations. The double porosity approach formulated by Barenblatt et al. for single phase flow considered the naturally fractured reservoir to be composed of two superimposed continua, a continuous fracture system and a discontinuous system of matrix blocks. The fracture system has a low storativity and high conductivity while the majority of the oil resides in a matrix block system of low conductivity. The transfer of fluids between these two systems, as described by Barenblatt, assumes pseudosteady-state flow between the matrix blocks and the fracture system. The matrix/fracture transfer function can then be expressed as Darcy's Law with an appropriate geometrical factor that describes the characteristic length and flow area between the matrix blocks and the fracture system. Warren and Root" presented an analytical solution for single-phase, unsteady-state, radial flow in a naturally fractured reservoir and introduced the dual porosity concept to petroleum engineering. They also derived a formula for the shape factor for parallelepiped matrix blocks within an orthonormal fracture system of one, two or three dimensions. The formulation of Warren and Root was extended to a multiphase system by Kazemi et al., who numerically solved for flow in three dimensions. As with the Barenblatt formulation, Kazemi's transfer function assumes pseudosteady-state flow based on potential differences between the matrix node center and the fracture node center within a gridblock. In a later paper Kazemi and Merrill used their simulator to model water imbibition into artificially fractured cores. Most of their simulations involved gridding the matrix block into more than one computational unit, thereby improving the model's performance through enhanced matrix block definition. With a single matrix block per grid block, they presented simulations at two different water injection rates for cores initially saturated with 100 percent diesel oil and for cores with n-decane replacing diesel oil. P. 509^
- Energy > Oil & Gas > Upstream (1.00)
- Water & Waste Management > Water Management > Lifecycle > Disposal/Injection (0.57)
SPE Members Abstract In water-drive gas reservoirs (even with an active aquifer), there is some pressure drop in the reservoir during the course of depletion. Until very recently, the literature assumes that the residual gas left in the water invaded region is constant which remains the same during the depletion process. In order to test the validity of the assumption of a constant value for residual gas saturation in the course of pressure drop in a water-drive gas reservoir, the following experiments were conducted. Three different tests were performed in the vertical direction on each of the core samples. In the first test water was injected into a vertical core (saturated with methane and in some cases with irreducible water) from the lower end at a constant low rate. Water injection was conducted at a pressure of about 217.5 psia [1.500 MPa]. The injection of water was continued for several days. No additional gas was, however, produced once the water breakthrough occurred. The second test comprised the depletion of the core from the upper end at the termination of the water injection period. The depletion was realized by lowering the pressure and producing the fluids. In the third test, water was again injected at the lower end with the same rate as in the first test. A simulation model of an implicit-type was used to analyze the laboratory data. The history matching of the depletion test revealed extreme sensitivity to the mobilized gas saturation value. The laboratory measurements and the simulation results show clearly two distinct values of residual gas saturation. The lower value corresponds to the initial gas entrapment saturation and the higher value relates to the gas saturation being mobilized under expansion. For the cores examined in this research project, these saturation values are about 30 and 40 percent of pore volume, respectively. Introduction Perhaps the most important parameter in predicting the production performance and the recovery factor of water-drive gas reservoirs is residual gas saturation. Laboratory experiments, logging data and reservoir material balance calculations have demonstrated that the trapped gas saturation in the water-invaded region of a gas reservoir could be as high as 50 percent of the pore volume. The experimental study of Geffen, et al., in 1952 on core plugs revealed that the trapped gas saturation varied from 15 to 50 percent of the pore space for various porous media. They also measured the trapped gas saturation in a watered-out gas reservoir by the use of a pressure core barrel and by electric log data. These measurements indicated that high trapped gas saturation is not aboratory phenomenon. In the experiments conducted by Geffen, et al., uncon-solidated sand showed a trapped gas saturation of about 16 percent consolidated sandstones of various formations showed a value of 25 to 38 percent and the trapped gas saturation for the limestone rock of Canyon Reef was about 50 percent. They also examined the effect of the initial water saturation on the trapped gas saturation. Measurements on two dry sandstone cores indicated trapped gas saturation of 33.0 and 32.3 percent of pore volume, and 34.7 and 34.5 percent for the same cores with initial irreducible water saturations. Geffen, et al., concluded that the variation of trapped gas saturation for these rock samples with and without irreducible water was within the accuracy of measurements. In 1963, Chierici, Ciucci and Long reported trapped gas saturation measurements on both consolidated and unconsolidated porous materials. The trapped gas saturation measurements for their measurements varied from some 10 to 30 percent. They also measured the average residual gas saturation during the pressure depletion test under simulated reservoir conditions. The average residual gas saturation was based on material balance calculations at several pressures. For the unconsolidated samples of Ref. 2, there is oticeable increase of residual gas saturation at the flooding pressure as compared with the residual gas saturation at the end of depletion test. However, consolidated sandstone samples did not show a substantial difference between the trapped gas saturation and average residual gas saturations in the depletion experiments. Table 1 shows these measurements. Later in this paper, we will discuss the fact that during the course of depletion, the gas saturation will not be uniform and, therefore, we use the term average residual gas saturation for the depletion experiments in Ref. 2. Keelan and Paugh published measurements of the trapped gas saturation for various carbonate rocks in 1975. They observed that for the carbonate rocks that they examined, trapped gas saturation varies with initial gas in-place and with rock type. With gas in-place in 80 percent of pore space (the remaining 20 percent was filled with water), trapped gas saturation was from 23 percent in one rock type to a high value of 69 percent of pore space in another rock sample. Keelan, et al. attempted to correlate trapped gas saturation as a function of porosity, permeability, initial water saturation and rock type. P. 319^
- North America > United States (0.68)
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- Research Report > New Finding (0.68)
- Research Report > Experimental Study (0.68)
- Geology > Rock Type > Sedimentary Rock > Carbonate Rock (0.74)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (0.65)
- Energy > Oil & Gas > Upstream (1.00)
- Water & Waste Management > Water Management > Lifecycle > Disposal/Injection (0.55)