Simulation of coning in bottom water-driven reservoirs

Bruining, J.; Duijn, C.J. van; Schotting, R. J.

doi:10.1007/bf00136821

Cited by 7 publications

(5 citation statements)

References 20 publications

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“…The analysis presented here has similarities with studies of water coning, [10][11][12][13][14] in which an oil/water interface moves towards a production well ͑a point sink͒. However, gravity, unimportant in the sampling problem, usually plays an important role in coning, for which the interesting case is that of the strongest flow which allows gravitational and viscous forces to balance without the resulting deformed interface being drawn into the well.…”

Section: Discussionmentioning

confidence: 83%

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Optimal probes for withdrawal of uncontaminated fluid samples

Sherwood

2005

Physics of Fluids

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Withdrawal of fluid by a composite probe pushed against the face z = 0 of a porous half-space z Ͼ 0 is modeled assuming incompressible Darcy flow. The probe is circular, of radius a, with an inner sampling section of radius ␣a and a concentric outer guard probe ␣a Ͻ r Ͻ a. The porous rock in 0 ഛ z ഛ ␤a is saturated with fluid 1, and the region z Ͼ ␤a is saturated with fluid 2; the two fluids have the same viscosity. It is assumed that the interface between the two fluids is sharp and remains so as it moves through the rock. The pressure in the probe is lower than that of the pore fluid in the rock, so that the fluid interface is convected with the fluids towards the probe. This idealized axisymmetric problem is solved numerically, and it is shown that an analysis based on far-field spherical flow towards a point sink is a good approximation when the nondimensional depth of fluid 1 is large, i.e., ␤ ӷ 1. The inner sampling probe eventually produces pure fluid 2, and this technique has been proposed for sampling pore fluids in rock surrounding an oil well ͓A. Hrametz, C. Gardner, M. Wais, and M. Proett, U.S. Patent No. 6,301,959 B1 ͑16 October 2001͔͒. Fluid 1 is drilling fluid filtrate, which has displaced the original pore fluid ͑fluid 2͒, a pure sample of which is required. The time required to collect an uncontaminated sample of original pore fluid can be minimized by a suitable choice of the probe geometry ␣ ͓J. Sherwood, J. Fitzgerald and B. Hill, U.S. Patent No. 6,719,049 B2 ͑13 April 2004͔͒. It is shown that the optimal choice of ␣ depends on the depth of filtrate invasion ␤ and the volume of sample required.

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Section: Discussionmentioning

confidence: 83%

“…Sampling would not intentionally be performed at such a point where the filtrate has accumulated. Gravitational effects are important in other axisymmetric Darcy flows, especially the problem of water coning, [10][11][12][13][14] in which an oil/water interface or a saltwater/freshwater interface moves towards a well.…”

Section: Introductionmentioning

confidence: 99%

Optimal probes for withdrawal of uncontaminated fluid samples

Sherwood

2005

Physics of Fluids

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“…Finally, impermeable layers could be introduced to model the finite size of an oil reservoir. In some cases this may lead to no stable cone shape, as in Bruining et al, 19 and in these cases, a time-dependent model would be required to model the evolution of the oil-water interface.…”

Section: Discussionmentioning

confidence: 99%

A boundary integral method applied to the 3D water coning problem

Lucas

Kucera

1996

Physics of Fluids

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Often in oil reservoirs a layer of water lies under the layer of oil. The suction pressure due to a distribution of oil wells will cause the oil-water interface to rise up towards the wells. A three-dimensional boundary integral formulation is presented for calculating the steady interface shape when the oil wells are represented by point sinks. Sophisticated integration techniques are implemented in an effort to obtain accurate results. In particular, the efficiency of various integration methods are compared for this problem, including QUADPACK routines, adaptive methods based on the IMT rule, the Kronrod rule, the method of degenerate quadrilaterals, and the Gauss-Rational rule for infinite integrals. Numerical results for various general multi-sink distributions are discussed, as are some further results for the axisymmetric single well problem.

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“…A variety of analytical solutions for linearized free-surface flows in porous media are presented in the book by Polubarinova-Kochina [ 1962]. Dagan [ 1964Dagan [ , 1966Dagan [ , 1967 Bruining et al [1991], and Lucas et al [1991]. An excellent introduction to BIEM for free-surface flows •in porous media is given in the book by Liggett and Liu [1983] (see also Brebbia et al [1984]).…”

Section: Laplace Equation With Nonlinear Boundary Conditionsmentioning

confidence: 99%

Transient free‐surface groundwater flow due to an array of circular drainage ditches

Gjerde¹,

Tyvand²

1992

Water Resources Research

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The present paper is a numerical study of a transient free‐surface flow into an array of circular drainage ditches in a porous medium. By the boundary integral equation method and a semi‐Lagrangian description of motion, the groundwater table is tracked as a function of time. Primarily, we consider the case of atmospheric pressure along the ditch contour. An analytical small‐time expansion is presented in an appendix. In contrast to the case of constant flux into a sink (Papatzacos, 1989), there is no cusp formation at the free surface. The flux into a ditch is approximately a linearly decreasing function of time. We also include a second version of the boundary condition at the ditch; parts of its contour are impermeable.

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Simulation of coning in bottom water-driven reservoirs

Cited by 7 publications

References 20 publications

Optimal probes for withdrawal of uncontaminated fluid samples

Optimal probes for withdrawal of uncontaminated fluid samples

A boundary integral method applied to the 3D water coning problem

Transient free‐surface groundwater flow due to an array of circular drainage ditches

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