This paper presents a model for predicting the contaminated mixing volume arising in pipeline batch transfers without physical separators. The proposed technique represents an improvement over the existing methods since it takes into account time-dependent flow rates and accurate concentration-varying axial dispersion coefficients. The governing equation of the model forms a nonlinear boundary-value problem that is solved by a finite element method coupled to the Newton’s method. A comparison among the theoretical predictions of this method, a field test, and other classical procedures show that the proposed method exhibits the best estimate over the whole range of admissible concentrations investigated.

No abstract

No abstract

The significant growth in offshore operations increases the risk of a pipeline rupture, even considering the high standards of safety involved. Throughout a submarine leakage, four different amounts of oil may be accounted. The first one is the oil volume released until the leakage detection. The second one is the volume leaked throughout mitigation initiatives (e.g., pump shutdown and valve closure). The third parcel is the amount released by gravitational flow. Finally, the fourth and last amount of oil is released due to the water-oil entrainment, generally known as advective migration. Normally, a considerable amount of oil is released in this step. It begins just after the internal pipeline pressure becomes equal to the external one. The present work continues to introduce a mathematical alternative approach, based on the theories of perturbation and unstable immiscible displacement, to accurately estimate the leakage kinetics and the amount of oil released by the advective migration phenomenon. Situations considering different hole sizes and thicknesses were tested experimentally and through simulations. Additional experiments were accomplished using smooth and rough edge surfaces, besides different slopes (using the horizontal plane as reference). Those experiments permitted a preliminary evaluation of the importance of these factors. The results obtained with the model showed good agreement with the experimental data in many situations considered.

Presented in this paper is a new model for estimating mixing volumes arising in batch transfers in multiproduct pipelines, when variations of the line diameter as well as injection and/or withdrawal of products are present. Besides these novel features, the model incorporates the flow rate variation with time and the use of a more precise effective dispersion coefficient, which is considered to depend on the concentration. The governing equations of the model form a non-linear initial-value problem that is solved by using a predictor-corrector finite difference method. A comparison among several cases studied reveals that the pipeline diameter variation can effectively reduce the amount of mixing volume when compared to a similar transfer carried out in a constant diameter line.