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Abstract This paper discusses the development and field application of a single well, three-phase, numerical, thermal simulation model which represents the coupled wellbore and reservoir mechanics following closure of the annulus steam production, or "casing blow" in producing wells. The goal of the model is to provide an understanding of the physical mechanisms associated with casing blow shut-in which may cause a drop in oil production, and hence, lead to operational procedures which would minimize this lost production. The simulation model accurately represents the exact geometry and dimensions of the wellbore tubing, annulus, and casing. Both counter-current multiphase, annulus flow, and coupled, crossflow effects between the wellbore and reservoir are modeled. Limited entry perfs and wellbore damage effects may also be included. Stable and robust controllers permit true pumped-off conditions to be modeled, as well as multiple casing blow cycles. The model was used to predict the magnitude and duration of oil production loss for a Kern River field pilot following casing blow shut-in. The prediction exactly matched field observations, including changes in the annulus pressure. Prior to casing blow shut-in, oil production is achieved by both gravity drainage and inter-well viscous drag forces. Depending on near well conditions, a variety of responses can be expected following shut-in. Preshut-in wellhead pressure is a key indicator of well response. Wells that were mostly impacted by shut-in generally do not recover without remediation Following shut-in, there is a transient period during which the oil rate transitions form its original decline onto a shallower, gravity drainage curve. As long as the casing blow steam production is shut-in, the drop in oil production seen at shut-in does not return to preshut-in levels, again, without remediation The mechanistic insights gained from the simulation model resulted in successful field strategies to improve or ameliorate the lost oil production following casing blow shut-in. These strategies will be discussed. Introduction A pilot was initiated at Texaco's Kern River field steamflood operations in November, 1994 to ascertain the impact on oil production of shutting in the annulus steam vapor production from producing wells. This pilot was preparatory to full-field casing blow shut-in. A single well simulation model (SWM) was developed with the following main objectives:To provide an interpretation of the pilot observations in terms of physical mechanisms in the wellbore and the reservoir. To design and recommend operational procedures to minimize the oil production loss resulting in the wellbore and the reservoir. To extrapolate the pilot interpretation to a full field scenario, with recommendations for future field and simulation work. Even though the model was developed specifically for Kern River, the methodology is general, and should permit applications to other problems. Consequently, this discussion will be as generic as possible with regard to the model formulations. Model Capabilities To be of practical value in the current context, the SWM must be capable of accurately modeling the following physical wellbore and near wellbore phenomena:–exact geometry and dimensions of the tubing, annulus, and casing, –exact physical properties of the wellbore components, P. 433^
Abstract The simulation of reservoir performance is particularly difficult, compared with the simulation of similar processes, because of the extreme behavior of reservoir pressures and saturations. In particular, the reservoir pressures are very non-linear and exhibit near-singularities at the wells as a result of injection and production. Finite difference methods, which are used almost universally for reservoir simulation, are troublesome with such highly non-linear solutions. Accuracy is reduced and the solutions become more time consuming. This paper describes an attempt to eliminate these nonlinearities from the finite difference solutions by incorporating analytical solutions in the pressure solution. The reservoir pressures are the sum of analytical functions and traditional finite difference solutions. The analytical functions are based on well test equations which describe the pressures around the wells in an infinite, homogeneous system. Although heterogeneities and reservoir geometries make these analytical functions grossly inaccurate for predicting actual reservoir pressures, they do exhibit nonlinearities much like the actual solutions. As a result, the finite difference components become much more linear, improving both the accuracy and the speed of the solution. Several other advantages of this new technology are also demonstrated:–Empirical well equations, which relate cell pressures to well pressures, are unnecessary. –The technique is applicable to Cartesian grids as well as other grid types. –Wells need not be centered in the cells for best results. –Accurate simulations of early-time, pressure transients make well test simulations practical. Introduction Despite the similarity of reservoir simulation with other engineering problems such as laminar fluid flow, conductive heat transfer, and convective/diffusive mass transfer, reservoir simulation is uniquely difficult. These difficulties must be due, at least in part, to the large non-linearities inherent in the solutions. For example, the reservoir pressures develop near-singularities at the wells as illustrated in Figure 1. Unlike the other engineering problems, reservoir simulation results depend on flow through very small areas, the well bores. The wells act much as line sources resulting in the very sharp pressure gradients near them. The accuracy of finite difference solutions deteriorates when the solutions are highly non-linear, as can be easily demonstrated through the Taylor's series derivation of the finite difference approximations to the partial differential terms. The solution speed is also affected. This work investigates the elimination of the near-singularities in the finite difference equations, through the combination of analytical functions. As illustrated in Figure 1, an analytical function which accurately represents the pressure gradients around the well bores is added to the finite difference solution. The analytical solution may not accurately represent the actual reservoir pressure, particularly at large distances from the wells, but it does reduce the non-linear behavior of the finite difference component of the solution. Aftab has tried a similar approach to eliminate both the pressure singularities and the saturation discontinuities. Well Equations This new treatment of reservoir pressures eliminates the need for well equations. In the past, well equations have been used to relate well bore pressures to the well cell pressures. This approach follows Peaceman's classical work of 1978.
Abstract This work presents a new methodology for determining the static formation temperature (Tei) by using transient well-test data. We show how a semianalytic method, involving the rectangular hyperbola technique for obtaining Tei, was used for establishing a region's geothermal gradient. Insights into heat-transfer processes were applied to develop methods of data collection and analysis. Several options were enacted to gather valid transient temperature data. For instance, sensor placement above the test interval ensured that the produced fluid had the opportunity to cool during shut-in periods, thereby creating useful perturbations. Tests accompanied by large pressure drawdowns caused Joule-Thompson heating, leading to subsequent cooling during well shut-in, even when the sensor was at the midpoint of a producing interval. Transient temperature data were gathered during pressure buildup tests in various boreholes ranging from 2,200 to 14,500 ft, encompassing different geologic horizons in Kuwait. Data collected from traditional open- and cased-hole logging were used and compared with the new approach. Statistical analyses clearly showed the superiority of the proposed procedure. Results of the new approach established Kuwait's geothermal gradient (gG) at 0.012 F per ft with a mean surface temperature (MST) of 87.23 F. Introduction Temperatures in the subsurface are related to a region's MST and the depth-dependent temperature or the geothermal gradient. Actually, the temperature of each subsurface geologic formation is dependent upon the composition, thermal properties of formation constituents, and supply of heat from the earth's interior. Therefore, Tei at each of many geologic horizons are needed to be established and combined to determine the geothermal gradient of a region. Accurate knowledge of geothermal gradient is required for many oilfield applications. Some of these applications include evaluating open- and cased-hole logs, designing cementing programs, basin modeling for discerning source rock, modeling steady- and unsteady-state fluid and heat flows in the wellbore designing thermal recovery projects, to name a few. Despite the diversity of needs, very few reliable methods exist for obtaining the true static formation temperature at a given depth, en route to establishing a region's geothermal gradient. Common oilfield practices for obtaining Tei rely on discrete temperature measurements, usually during borehole geophysical logging operations. Such data are frequently obtained in newly drilled wellbores following mud circulation. Complications arise because fluid circulation induces significant cooling to the near-wellbore region, requiring extrapolation of discrete measurements to Tei. In contrast, temperature data acquired while logging cased boreholes, under well shut-in conditions, are improved because measurements are not necessarily preceded by cooling or heating owing to mud circulation. However, no procedures exist for confirmation of thermal equilibrium between borehole fluids and formations. Therefore, understanding heat-transfer mechanisms between the borehole fluids and the formation constitutes the first step in developing reliable modes of data gathering and interpretation methods. Methods are available for estimating the static formation temperature in an openhole situation. These methods include those of Edwardson et al., Tregasser et al. and Dowdle and Cobb. Of these, the method of Dowdle and Cobb, developed in analogy to the pressure analysis or the Horner method, gained wide acceptance because of its simplicity. However, Hasan and Kabir pointed out some of the limitations of the Dowdle-Cobb approach and presented several simplified graphical methods for the Tei evaluation of early-time data. P. 267^
Abstract This paper presents a method to calculate an equivalent production rate and time (tp), that models the transient effect of a multirate production period prior to a buildup test. The proposed solution increases the accuracy of Pressure Transient Analysis (PTA). The traditional Horner method estimates the production time (tp) using the cumulative production and the last production rate; however, this method is an intuitive but not rigorous solution that puts emphasis on the most recent nonzero production rate. There are currently commercial applications that consider the superposition effects of complex production history for PTA analysis, nevertheless, superposition can include a material balance error. The proposed technique is an alternative to superposition that uses the transient effect generated for each production period to estimate the equivalent rate and production time. A reservoir simulation model with known petrophysical parameters, fluid properties, pressure, and temperature, is used as a reference to evaluate the accuracy of the proposed method. The studied reservoir produces through a well that uses a multirate schedule that includes two different scenarios: (1) a progressive increase in each new production rate and (2) a progressive decrease in each new production rate. Then, the well is shut-in, starting a buildup pressure response. Production time and rate are estimated by applying the Horner's approximation and the proposed solution. Finally, the results from both methods are compared with the known parameters of the reference model. The proposed method provides a more accurate solution to buildup analysis compared to the Horner time approximation by using the production rate history. The approach can also be applied to drawdown analysis and pressure derivative analysis, keeping the precision of the calculations.
This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 81101, "Resolving Uncertainties in Historical Data and the Redevelopment of Mature Fields," by I.S. Agbon, SPE, G.J. Aldana, and J.C. Araque, PDVSA-Intevep, and A.A. Mendoza and M.E. Ramirez, PDVSA-EPM, prepared for the 2003 SPE Latin American and Caribbean Petroleum Engineering Conference, Portof- Spain, Trinidad, 27-30 April.