It is common for field models of tight gas reservoirs to include several wells with hydraulic fractures. These hydraulic fractures can be very long, extending for more than a thousand feet. A hydraulic fracture width is usually no more than about 0.02 ft. The combination of the above factors leads to the conclusion that there is a need to model hydraulic fractures in coarse grid blocks for these field models since it may be impractical to simulate these models using fine grids. In this paper, a method was developed to simulate a reservoir model with a single hydraulic fracture that passes through several coarse gridblocks. This method was tested and a numerical error was quantified that occurs at early time due to the use of coarse grid blocks. Introduction A single hydraulic fracture is conventionally modelled for research purposes using fine grids. In actual field models of tight gas reservoirs, there are several wells with hydraulic fractures (see Figure 1). These hydraulic fractures are usually very long. They can extend in length to more than a thousand feet. These long hydraulic fractures extend for several gridblocks in a simulation model (Figure 1). Therefore, it is very difficult to use fine grids to simulate these actual field models. Some authors(1, 2) suggested the replacement of the hydraulic fracture by an effective wellbore radius, but this technique is only valid when the hydraulic fracture does not extend beyond the boundaries of one gridblock. There were also attempts by another group of authors(3–5) to modify transmissibility multipliers of the gridblocks, which contain hydraulic fractures. However, these attempts were done for hydraulically fractured horizontal wells. In addition, these attempts were based on empirical rules that had no basic theory behind them. In this paper, the means to model hydraulic fractures in coarse gridblocks are demonstrated. Pseudo-permeability values were used to account for the hydraulic fracture passing through the coarse gridblock. Several simulated cases were shown in this paper and compared to rigorous analytical solutions to prove the validity of the method proposed. An alternative way to model hydraulic fractures in coarse gridblocks (also based on theory), developed by Elahmady(6) but not discussed in this paper, was to modify the transmissibility multipliers of the gridblocks that contain the hydraulic fracture. Elahmady(6) cautioned that there are different ways to use transmissibility multipliers depending on the kind of simulator that is used. The authors would like to note that during the course of their study they were aware of the work by Peaceman(7, 8) where the calculated pressures in gridblocks containing wells, pwb must be corrected to formation face pressure, pwf. Peaceman's(7) equation is programmed into any conventional reservoir simulator for the case of radial flow. Elahmady(6) repeated Peaceman's(7) numerical experiments, but for linear flow (which is the focus of this paper) instead of radial flow, and reached a conclusion that pwf = pwb for the case of linear flow.
A straight-line plot of p/z vs. Gp (cumulative gas production) is widely used to estimate the original gas in place. It is known as the p/z plot technique. The linearity of that plot has been historically known to be a unique feature of a volumetric (closed) reservoir. In this paper, we show that a uniqueness problem may exist when using the p/z plot. In other words, if the reservoir is in contact with an aquifer, a straight-line may exist on that plot causing a major overestimation of original gas in place. This uniqueness problem is proved to be due solely to the unsteady state nature of aquifers. A simulation study was performed to determine the conditions for such a misleading straight line. Several examples demonstrate that it is possible to construct a synthetic data set for a water-drive gas reservoir such that a misleading straight-line plot is obtained. This misleading straight-line is shown to be due to certain rate schedules. The conventional material balance equation is coupled with an aquifer mathematical model to obtain this schedule. In this paper, an actual field case is presented as an example of this possible overestimation of original gas in place due to a misleading linear p/z plot. Introduction The material balance equation is an expression of the law of the conservation of mass, which is commonly used in reservoir engineering. For reservoirs with no water influx and no water encroachment and if we neglect formation and water compressibilities, it will have the following form (1) G B g i = G - G p B y which can be written also as Equation (2) Available In Full Paper. If we include all of the forces that we previously neglected, then we will have the following equation (3) G B g i = G - G p B g + W e - W p + G B g i 1 - R M Equation (4) Available In Full Paper. If we neglect the influence of the formation and water compressibility then the Ramagost factor RM will be equal to 1, and therefore Equation (4) will be reduced to the following
Field data and simulated models have revealed that in some cases waterdrive gas reservoirs can be mistakenly misidentified using material balance methods as depletion drive gas reservoirs causing a significant overestimation in gas reserves. The famous straight-line plot of p/z vs. Gp has been traditionally used to estimate original gas in place (and gas reserves) for depletion-drive gas reservoirs. A gas reservoir in contact with an aquifer in transient phase (unsteady-state) and producing under a certain production schedule can plot as a straight-line on a p/z plot masking the existence of an active aquifer and causing a significant overestimation in gas reserves. The authors in this paper simulate synthetic cases of gas reservoir/aquifer models using a forward model and an inverse model that were programmed in visual basic to show that the combination of certain rate schedules and the unsteady state nature of aquifers can cause a straight-line p/z plot in waterdrive gas reservoirs. The authors also demonstrate that the Havlena-Odeh1,2 Plot (also known by some authors in the literature as the Cole3 Plot) for those same cases will also mask the existence of an active transient aquifer giving the same value of overestimated original gas in place (OGIP) as that obtained from the p/z plot. Introduction The material balance equation for a depletion-drive gas reservoir when observed on plots will have what historically is thought to be unique features that help easily to estimate OGIP (and reserves). In this paper, we show that these features are not unique for a depletion-drive reservoir but can happen to exist also in a waterdrive gas reservoir. This causes a clear non-uniqueness problem, which can cause to overestimate OGIP (and Reserves). The material balance equation for a reservoir with no water influx and no water encroachment and if we neglect formation and water compressibilities is shown in Eq. 1 Equation (1) The above equation can be written also as Equation (2) Eq. 2 states that, there is a linear relationship between p/z and the cumulative volume of produced gas Gp as shown in Fig. 1. If the trend of this straight-line is extrapolated to p/z = 0, then we can obtain an estimate of the original gas in place (OGIP), which we will call from here on as G.
fax 01-972-952-9435. AbstractField data and simulated models have revealed that in some cases waterdrive gas reservoirs can be mistakenly misidentified using material balance methods as depletion drive gas reservoirs causing a significant overestimation in gas reserves.The famous straight-line plot of p/z vs. G p has been traditionally used to estimate original gas in place (and gas reserves) for depletion-drive gas reservoirs. A gas reservoir in contact with an aquifer in transient phase (unsteady-state) and producing under a certain production schedule can plot as a straight-line on a p/z plot masking the existence of an active aquifer and causing a significant overestimation in gas reserves.The authors in this paper simulate synthetic cases of gas reservoir/aquifer models using a forward model and an inverse model that were programmed in visual basic to show that the combination of certain rate schedules and the unsteady state nature of aquifers can cause a straight-line p/z plot in waterdrive gas reservoirs.The authors also demonstrate that the Havlena-Odeh 1,2 Plot (also known by some authors in the liteariture as the Cole 3 Plot) for those same cases will also mask the existence of an active transient aquifer giving the same value of overestimated origianal gas in place (OGIP) as that obtained from the p/z plot.
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