A Decline Curve Analysis Model Based on Fluid Flow Mechanisms

Decline curve analysis models are frequently used but still have many limitations. Approaches of decline curve analysis used for naturally-fractured reservoirs developed by water flooding have been few. To this end, a decline analysis model derived based on fluid flow mechanisms was proposed and used to analyze the oil production data from naturallyfractured reservoirs developed by water flooding. Relative permeability and capillary pressure were included in this model. The model reveals a linear relationship between the oil production rate and the reciprocal of the oil recovery or the accumulated oil production. We applied the model to the oil production data from different types of reservoirs and found a linear relationship between the production rate and the reciprocal of the oil recovery as foreseen by the model, especially at the late period of production. The values of the maximum oil recovery for the example reservoirs were evaluated using the parameters determined from the linear relationship. The results demonstrated that the analytical decline analysis model is not only suitable for naturallyfractured reservoirs developed by water flooding but also for other types of water drive reservoirs. An analytical oil recovery model was also proposed. The results showed that the analytical model could match the oil production data satisfactorily. We also demonstrated that the frequently-used nonlinear type curves could be transformed to linear relationships in a log-log plot. This may facilitate the production decline analysis. Introduction Estimating reserves and predicting production in reservoirs has been a challenge for a long time. Many methods have been developed in the last several decades. One frequently-used technique is decline curve analysis approach. There have been a great number of papers on this subject. Most of the existing decline curve analysis techniques are based on the empirical Arps equations: exponential, hyperbolic, and harmonic equations. It is difficult to foresee which equation the reservoir will follow. On the other hand, each approach has some disadvantages. For example, the exponential decline curve tends to underestimate reserves and production rates; the harmonic decline curve has a trendency to overpredict the reservoir performance. In some cases, production decline data do not follow any model but cross over the entire set of curves. Fetkovich combined the transient rate and the pseudosteady-state decline curves in a single graph. He also related the empirical equations of Arps to the single-phase flow solutions and attempted to provide a theoretical basis for the Arps equations. This was realized by developing the connection between the material balance and the flow rate equations based on his previous papers . Many derivations 13 were based on the assumption of single-phase oil flow in closed boundary systems. These solutions were only suitable for undersaturated (single-phase) oil flow. However many oilfields are developed by water flooding. Therefore two-phase fluid flow instead of singlephase flow occurs. In this case, Lefkovits et al. derived the exponential decline form for gravity drainage reservoirs with a free surface by neglecting capillary pressure. Fetkovich et al. included gas-oil relative permeability effects on oil production for solution gas drive through pressure ratio term, This assumes that the oil relative permeability is a function of pressure. It is known that gas-oil relative permeability is a function of fluid saturation which dependents on fluid/rock properties. In water flooding, oil relative permeability can not be approximated as a function of pressure. The pressure during water flooding may increase, decrease, or remain unchanged. The oil production decline because of oil relative permeability reduction is associated with decrease in oil saturation instead of pressure in this case. Masoner correlated oil relative permeability to the Arps decline exponent by assuming a constant pressure potential and a pseudosingle-phase oil flow. Many attempts have been made to interpret the empirical Arps equations or provide some theoretical basis in specific cases. New models with consolidated theoretical background have been few. As Raghavan pointed out in 1993: "Until the 1970s, decline curve analysis was considered to be a convenient empirical procedure for analyzing performance; no particular significance was to be attributed to the values of Di SPE 83470 A Decline Curve Analysis Model Based on Fluid Flow Mechanisms Kewen Li, SPE, and Roland N. Horne, SPE, Stanford University 2 Kewen Li and Roland N. Horne SPE 83470 and b. To an extent this is still true even today". This may be the case still, even though ten years have past. Less attention has been paid to the production decline analysis in naturally-fractured reservoirs developed by water flooding. Aronofsky et al. suggested an empirical model to match oil production by water injection in this type of reservoir. Baker et al. used a similar model to infer the fracture spacing by matching production data from the Spraberry Trend naturally-fractured reservoir. In this article, an analytical model developed by Li and Horne in previous papers was used to conduct production decline analysis for naturally-fractured reservoirs developed by water flooding. The model was developed originally to characterize spontaneous water imbibition in reservoir rock and was confirmed both theoretically and experimentally. Because spontaneous water imbibition is the main fluid flow mechanism that governs the oil production in naturallyfractured reservoirs developed by water injection, it may be reasonable for the model to be applicable in such reservoirs. However it was also found that the model is applicable in other types of reservoirs developed by water injection. Production decline data from different types of waterdrive reservoirs were analyzed as examples of using the new decline analysis model. We would like to clarify that our study and the discussions in this article are limited to two-phase fluid flow. Mathematics The Arps decline curve analysis approach was proposed nearly sixty years ago. However a great number of studies on production decline analysis are still based on this empirical method. Many published papers have tried to interpret the Arps decline equation theoretically. The empirical Arps decline equation represents the relationship between production rate and time for oil wells during pseudosteadystate period and is shown as follows: