Summary Thermally induced fracturing (TIF) during water injection is a well-established phenomenon. TIF modeling implies solving equations simultaneously that conventional petroleum engineering applications deal with separately. Combining these equations leads to very complex computer programs. This has led to the need for a simple model, which we present in this paper. Coupling analytical expressions representing each of these phenomena, rather than the basic physical equations, has led to a computer program that can be run on a modern desk-top computer. This program has successfully matched the daily wellhead pressure and injection rate during a period of 3 to 5 years for injection wells in complex sandstone/dolomite reservoirs. The model can be used for injection-well monitoring as well as in a predictive mode when planning new water-injection projects. The algorithm is sufficiently simple to be implemented in a conventional reservoir simulator. Introduction The concept of a constant productivity index, extrapolated below bubble point by use of Vogel's curve, is one of the fundamental tools of petroleum engineering. One of its most interesting features is that it depends on reservoir and reservoir properties alone. It is independent of downstream wellbore equipment and surface facilities. One would like to be able to use a similar concept for water injection wells, but, unfortunately, calculating an injectivity index, turns out to be much more complex. Water available for injection is often much colder than the reservoir, and numerous temperature-induced phenomena often having opposite effects occur within the first few days or weeks of injection. From the beginning of injection, the bottomhole flowing temperature decreases and finally reaches a stabilized value depending on surface and reservoir temperature, injection rate, depth, and well completion. During that time, matrix flows will have a reducing effect on injectivity. This is because, in such conditions, the bottom-hole viscosity can often increase two- to four-fold. Also, when water displaces oil, there is a relative-permeability effect tied to the growth of the zone from which oil has been displaced. At the same time, mechanical effects will tend to decrease injectivity inversely. The reservoir stress near the well is reduced when the reservoir is cooled, and fracturing will occur if the reservoir stress falls below bottomhole flowing pressure. This phenomena is called TIF.1–6 It leads to a continuous increase in injectivity when fracture develops. In fact, the final reduced stress is the result of a thermal reducing effect (thermoelasticity) and a fluid-pressure increasing effect (poroelasticity) at the injector. In general, however, the latter is much smaller. As we have shown, the injectivity index cannot be calculated without taking into account the wellbore pressure and temperature performance. Injectivity therefore depends on the situation both upstream (wellbore equipment and surface facilities) and downstream (reservoir properties). Modeling water injectivity therefore leads to very large computer programs in which the complexities of both reservoir models and fracturing simulators are intermingled. The pioneering work of Hagoort7 and Perkins and Gonzalez8 on thermo-poroelasticity were followed by more refined models, such as that published by Dikken and Niko.9 More recently, Settari10,11 and Clifford12 presented three-dimensional (3D) fracturing calculations. This paper presents a model that uses simple analytical formulas representing all these intermingled physical processes that influence the injectivity index. The model has been programmed on a PC and used to match the performance of wells injecting into a complex sandstone/dolomite reservoir in the Gulf of Guinea. Well behavior is modeled as a sequence of timesteps. The basic assumption is that steady-state equilibrium is reached at the end of each timestep. This is a good approximation for long-term well behavior. We do not aim to simulate short-term phenomena such as those encountered during well tests; in our model, reservoir pressure transients are ignored, as are the mechanics of fracture propagation. Our model starts at the wellhead, with a given injection rate and wellhead temperature. The model calculates a wellhead pressure, which can be compared to measurements. The least known parameters are adjusted within their plausible range of values until a satisfactory match is obtained. The algorithm also has been programmed so that when wellhead pressure and temperature are given as data, the model calculates the injection rate. This calculation mode is of particular interest when planning waterfloods. Part 1: The Model Wellbore Temperature Profile. The first task is to calculate bottomhole flowing temperature, ?wf, from surface temperature, injection rate, and wellbore equipment. A linear geothermal gradient is assumed. Bottomhole flowing temperature is calculated from wellhead temperature by dividing the tubing into 25 segments. We use the transient heat-exchange solution13 between each segment and the surrounding earth to calculate the quantity of heat that reaches the water in the tubing. This solution assumes that the well rate is constant. To cope with rate-varying behavior, an effective injection time has been defined with the cumulative injection Wi and the current injection rate i : As long as injection rate does not decrease too abruptly, this simple algorithm gives satisfactory results. The reason that such a simple algorithm works is that most of the heat exchange between an injection well and the surrounding earth takes place at depth, where the well geometry is simplest: a tubing and one casing. On the contrary, such a simple calculation is impossible on a production well because, in this case, the biggest temperature contrast and therefore most of the heat exchange are close to the surface where well geometry and its surroundings are most variable. This algorithm does not give realistic results when the injection rate is reduced abruptly (for instance, when the well is shut in). A smoothing function has therefore been introduced to limit the change in ?wf during any one timestep. Calculation Assuming Radial Injection. We use the term radial injection when flow is radially outwards from the well; the alternative, when the reservoir is fractured by the water injection process, is called fractured injection.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe objective of the analytical simulator presented here is to predict the opposite and complex effects induced by the injected produced water temperature and formation damage on thermally fractured wells. The deposition of solid particles and oil droplets in a fracture and its effect on the Injectivity Index evolution of an injector is then simulated. The principle is to inject cooled waters like sea water for example during a certain period of time to enable the well to develop a thermal fracture. When the fracture is well established, the re-injection of hot produced waters starts. The model takes into account the effect of this new water temperature on the viscous flow and on the fracture shrinkage and closure. In the same time oil droplets and solid particles contained in produced water cause the damage of the reservoir. This tends to open and propagate the fracture under bottom pressure increase. In the simulator, the internal formation damage and the external filter cake deposition in the fracture occur simultaneously. Two internal formation damage deposition models are taken into account. In a first model the internal damage is supposed to be linear and occurring from the fracture faces to the reservoir. In a second model, despite the growth of the fracture, the internal damage is supposed to be radial and occurring from the wall of the well to the reservoir. Also, two exeternal filter cake deposition models are considered: the filter cake deposits only at the fracture tip or on fracture faces. Theoretical field cases were considered in the simulations. The different internal formation damage and filter cake models were combined together to reproduce the injectivity index evolution observed on real fileds. The example presented are chosen to show that, contrarily to common thinkings, the II evolution can be dominated, in certain circumstances, by the internal damage rather then by the external filter cake deposition. With the present choice of data, the II evolution which matches better the commonly observed field reponses is obtained when the internal damage occurs in radial flow whatever the model deposition of the external filter cake is.

This paper was prepared for presentation at the 1999 SPE European Formation Damage Conference held in The Hague, The Netherlands, 31 May–1 June 1999.

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Produced water re-injection (PWRI) for use in pressure maintenance is an alternative to discharge to the environment and is increasingly practised industrially in view of the combination of ever more stringent discharge standards and high water treatment costs. Due to the damaging effects on formations of produced waters it is often necessary to inject in fracturing regime to maintain the desired injection rate. Then the main issues of the process are the impact on well injectivities, fracture growth and sweep efficiency. All these issues are addressed by presenting an onshore field case of PWRI on a low permeability carbonaceous reservoir. Aquifer water has been injected for ten years and progressively substituted by produced waters for the next ten years. This case is well monitored and documented (fall-off and step rate tests, temperature logs, water quality). The main parameters affecting the process are illustrated in diagnostic analysis and the injectivities are satisfactorily reproduced using different simulation techniques. Special care is taken to describe filter cakes properties and distributions behind the fracture faces and inside the de fracture in order to well define the effects on the loss of fracture injectivity. The resulting fracture dimensions are very consistent with the last fall-off measurements and analysis. Finally simulating incrementally this fracture growth in the Eclipse reservoir model it was possible to demonstrate that water breakthrough occurs when the fracture tip reaches laterally higher permeability zones in the producer area and to correlate decreases of water production with injection shut in periods associated with fracture tip closure. Introduction The case presented is an onshore field at 3000 m depth and situated in the south west of France. The reservoir is a very hard carbonate with a Young modulus of 500000 bars. Very significant lateral heterogeneities are existing. The permeabilities in the injection area are less than 1 mD compare to 1–10 mD in the producing area with effective permeabilities of 50–2100 mD due to a natural fissure and fracture network. The basic data at the beginning of injection on 1979 for one typical well are given in table 1. Fresh aquifer waters from another field has been injected peripherial (figure1a) for pressure support at high pressures during 10 years followed by commingle produced water reinjection during another 10 years. Due to the strange behavior of the well different monitoring techniques has been used over the life of the field leading to interpretation difficulties. With the help of the recent improved knowledge on fractured injection regimes and reinjection effects (Ref. 1 to 7) all the field data has been reprocessed and the results of these analysis are discussed in the following chapters. Historical diagnostic analysis The entire historical is presented in figure 1.The different injection periods and tests are mentioned. The first surprise is that at first look there is apparently no effect of produced water re-injection on injectivity. Transforming surface in bottom-hole pressure does not change this observation. Reservoir pressure effects. In fact the reservoir pressure is decreasing significantly during the produced water injection period as shown on figure 2. Then plotting the evolution of the differential pressure (bottom-hole pressure - reservoir pressure) with time on figure 3 shows a significant decrease in injectivity during this last period (increase in pressure for the same rate of 400 m3/d). Pressure rate plot. When the reservoir pressure is varying this plot must also be done using differential pressures otherwise this can lead to big mistakes in the diagnostic of injection regimes. Figure 4 shows that the injection regime is fracturing excepted at the early beginning of injection where the points close to the Y axe correspond to radial flow. Reservoir pressure effects. In fact the reservoir pressure is decreasing significantly during the produced water injection period as shown on figure 2. Then plotting the evolution of the differential pressure (bottom-hole pressure - reservoir pressure) with time on figure 3 shows a significant decrease in injectivity during this last period (increase in pressure for the same rate of 400 m3/d). Pressure rate plot. When the reservoir pressure is varying this plot must also be done using differential pressures otherwise this can lead to big mistakes in the diagnostic of injection regimes. Figure 4 shows that the injection regime is fracturing excepted at the early beginning of injection where the points close to the Y axe correspond to radial flow.