Thermal Modeling of Shut-In Well After Multiphase Hydrocarbon Production

Abstract

When a well that has been producing a mixture of oil, water and gas is shut-in for an extended period of time, the fluid columns expand or contract in response to the temperature changes in the well. These changes in fluid levels in turn, affect the heat transfer in and around the wellbore. This coupled problem of determining the fluid levels as well as the wellbore temperature distribution is addressed. An algorithm is proposed, implemented and discussed for a hydrocarbon that can be modeled as a black-oil. Special cases of the algorithm when one of the phases is absent are also included. This model helps accurate and rigorous prediction of the wellbore temperature distribution and the wellhead pressure during a shut-in. Accurate temperature and pressure estimates in turn lead to better stress calculations to ensure the design of the wellbore with improved integrity of the tubulars. Introduction The problem of determining the wellhead pressure in a well that has been shut-in following the production of hydrocarbons and associated water is of interest to several aspects of the upstream oil industry such as production optimization, well design, well safety monitoring, etc. The wellhead pressure in such a well is a function the shut-in time period and is dependent on of the reservoir fluid characteristics, the proportions of the different fluid phases, the temperature profile in the wellbore at the start of the shut-in period, the far-field undisturbed temperature profile for the well trajectory. In general, immediately after the shut-in the fluids in the well re-arrange themselves in response to the buoyancy forces, with the water settling to the bottom, gas moving to the top and an oil layer forming between the two. This process of rearrangement of fluids is transient and generally lasts a short time. In this paper, this transient process is not addressed; instead, the focus is on the subsequent wellbore processes. Specifically, an analysis is presented on the question of how the fluid interface levels in the wellbore change with time in response to changes in the wellbore temperatures and in the reservoir pressure over the shut-in period, and how they affect the wellhead pressure. The changes in the fluid composition and properties with the changes in pressure and temperature at any location in the wellbore are vital to this analysis. Also not included in the analysis is the transient build up of the reservoir pressure at the perforations. The pressure build up occurs over a short period of time, and this period largely coincides with the transient fluid rearrangement period. The analysis presented here starts with the state of the reservoir subsequent to the transient pressure build up. It is assumed that the proportions of the hydrocarbon fluid and the water in the reservoir, represented by the standard conditions gas-oil-ratio (GOR) and water-oil-ratio (WOR), stay fixed over the shut-in period. The analysis presented here can be readily adapted to the case where these ratios change over time in a prescribed manner. These ratios are assumed to be unaffected by the movements of the fluids in or out of the wellbore during the shut-in. It is assumed that the proportion of the fluids in the wellbore stays consistent with these reservoir fluid ratios over the period of the shut-in; this assumption should hold due to the fluid equilibration owing to the diffusion process over the time periods considered in the present analysis. The nature of the hydrocarbon fluid in the wellbore is also important to the problem under consideration. It is customary in the industry to model the hydrocarbon fluid as either as a black-oil or as a gas condensate fluid (Whitson and Brule1). In this work, a full treatment of the case with black-oil fluids is provided. A discussion is presented to outline the difference in the processes in the shut-in well with these two fluid types; this explains why this solution is not applicable to the gas condensate fluid case and points to the need for additional development in this area.