Summary This study examines water injection in water-wet fractured porous media and its modeling using the Buckley-Leverett theory. New experimental data on water injection in Berea and Austin chalk matrix block(s) are presented. Water injection in Austin chalk with a permeability of 0.01-0.04 md and porosity of 5% results in about 20% recovery from the rock matrix. In the second part of the paper, we use the Buckley-Leverett displacement in a dual-porosity model to simulate the literature data as well as experimental data from this work. A new model is devised for the simulation of water injection in fractured porous media. A major element of the new model is the multiplication of the transfer flux by the fracture saturation with a power of 1/2. This simple model can account for both cocurrent and countercurrent imbibition and computationally it is very efficient. The results of the proposed model and the fine-grid simulation are in good agreement with the experimental data. Introduction Water injection has been an efficient recovery process in some naturally fractured hydrocarbon reservoirs. Despite the success, the understanding of the true mechanisms and the numerical simulation have to be advanced further. In fact, accurate simulation of water injection in fractured porous media is a real challenge. Fine-grid simulation can provide proper results when fracture capillary pressure and relative permeability are appropriately described; computationally, however, it is very expensive. Dual-porosity models have the advantage of computational efficiency but may be less accurate. A third alternative which can be extremely efficient is the use of the Buckley-Leverett displacement theory1 in a dual-porosity model. Here, matrix blocks feed into the fracture network through a transfer term; flow in the fractured media is represented by the Buckley-Leverett displacement. In an early paper, de Swaan2 modeled water displacement in fractured porous media on the basis of the Buckley-Leverett displacement theory. De Swaan's work is based on certain assumptions; these include: (1) the fracture fractional flow function is equal to the fracture saturation (i.e., $f {w}^{f}=S {w}^{f},$ see the Nomenclature), and (2) the effect of gravity is negligible. The assumption of $f {w}^{f}=S {w}^{f}$ is valid only when oil and water phases have equal viscosities and the fracture relative permeability is equal to saturation. Later, Chen and Liu3 relaxed the assumption of $f {w}^{f}=S {w}^{f}.$ Kazemi, Gillman, and Elsharkawy4 gave examples for the Buckley-Leverett flow in 1D fractured porous media using a model similar to de Swaan's. These authors reported good agreement with experimental data using an empirical transfer term between the fracture and the matrix. Kazemi et al., however, changed the oil viscosity from 4.6 to 0.25 cp to match the laboratory data. The ? parameter of the empirical transfer term was based on the general imbibition recovery data (see Fig. 1 of Ref. 4). The basic idea behind the transfer term in the literature is the use of countercurrent imbibition data for a single matrix block. Pooladi-Darvish and Firoozabadi5,6 have shown that countercurrent imbibition may not describe recovery from a matrix block when the water level advances in the fracture. The source term in the flow equations in the Buckley-Leverett expression for a dual-porosity model is in fact based on a moving fracture water level with saturation change (we will discuss the equations shortly). The moving water level may imply that cocurrent imbibition should also be considered. The major goal of this study is to model water injection in water-wet fractured porous media considering both cocurrent and countercurrent imbibition in the Buckley-Leverett flow. The model will be used to analyze the laboratory data. (A large portion of some fractured reservoirs in the North Sea are strongly water-wet and, therefore, water injection in water-wet fractured media is of practical interest.) In this work, we first report experimental data on water injection in matrix blocks. Two types of rock were used in the experiments:Berea sandstone, andAustin chalk. In the second part, we present mathematical formulation for flow in fractured porous media; water imbibition in a single matrix block for various injection rates is also examined. Using the transfer term from a single block, water imbibition in an aggregate of several matrix blocks is then predicted. Experimental Results An extensive set of data on water injection in Berea sandstone and Kansas outcrop chalk for an aggregate of matrix blocks is presented in Ref. 5. The rock assemblies used in those experiments are shown in Figs. 1a, 1b, and 1c. In addition to the stacked block experiments, Ref. 5 also provides experimental data on imbibition performance of a single matrix block of the Kansas outcrop chalk shown in the right side of Fig. 1a. In this work, we have performed water injection experiments on (1) a single Berea slab (see Fig. 1b, the right side), (2) a single Berea block (see Fig. 1c, the right side), and (3) a stack of Austin chalk blocks (see Fig. 1d). The experimental setup is similar to the one used by Pooladi-Darvish and Firoozabadi.5 The purpose of water injection tests in a single slab or a block is to further improve the understanding of cocurrent and countercurrent imbibition. For the tight Austin chalk of about 0.01 md permeability, the goal is to find out if any oil can be recovered from a very tight rock.

This study examines water injection in water-wet fractured porous media and its modeIing using the BuckIey-Leverett theory. New experimental data on water injection in Berea and Austin chalk matrix block(s) are presented.Water injection in Austin chalk with a permeability of 0.01-0.04 md and porosity of 5°h resuIts in about 20°h recovery from the rock matrix.In the second part of the paper, we use the Buckley-Leverett displacement in a dual-porosity modeI to simulate the the literature data as well as the experiments presented in the fist part. A new model is devised for the simulation of water injection in fractured porous media, A major element of the new model is the multiplication of the !mnsfer flux by the fracture saturation with a power of 1/2. This simple model can account for both co-current and counter-current imbibition and it is computationally very et%cient. The results of the proposed model and the free-grid simulation are in good agreement with the experimental data.

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This study examines water injection in water-wet fractured porous media and its modeling using the Buckley-Leverett theory. New experimental data on water injection in Berea and Austin chalk matrix block(s) are presented. Water injection in Austin chalk with a permeability of 0.01-0.04 md and porosity of 5% results in about 20% recovery from the rock matrix. In the second part of the paper, we use the Buckley-Leverett displacement in a dual-porosity model to simulate the the literature data as well as the experiments presented in the first part. A new model is devised for the simulation of water injection in fractured porous media. A major element of the new model is the multiplication of the transfer flux by the fracture saturation with a power of 1/2. This simple model can account for both co-current and counter-current imbibition and it is computationally very efficient. The results of the proposed model and the fine-grid simulation are in good agreement with the experimental data. P. 21

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