Rate decline curve analysis is an essential tool in predicting reservoir performance and in estimating reservoir properties. In its most basic form, decline curve analysis is to a large extent based on Arps' empirical models that have little theoretical basis. The use of historical production data to predict future performance is the focus of the empirical approach of decline analysis while the theoretical approach focuses on the derivation of relationships between the empirical model parameters and reservoir rock/fluid properties; thereby establishing a theoretical basis for the empirical models. Such relationships are useful in formulating techniques for reservoir properties estimation using production data. Many previous attempts at establishing relationships between the empirical parameters and the rock/fluid properties have been concerned primarily with the exponential decline of single phase oil reservoirs. A previous attempt to establish the theories of hyperbolic decline of saturated reservoirs (multiphase) have yielded an expression relating the Arps' decline exponent, b, to rock/fluid properties. However, the values of exponent computed from the expression are not constant through time, whereas, the empirically-determined exponent b is a constant value.
Hydraulic fracturing process is an important stimulation technique that has been widely used in conventional and unconventional oil and gas reservoirs. The technique involves creation of fracture or fracture system in porous medium to overcome wellbore damage, to improve oil and gas productivity in low permeability reservoirs or to increase production in secondary recovery operations.
This paper introduces a new technique for interpreting pressures behavior of a horizontal well with multiple hydraulic fractures. The well extends in multi-boundary reservoirs having different configurations. The hydraulic fractures in this model can be longitudinal or transverse, vertical or inclined, symmetrical or asymmetrical. The fractures are propagated in isotropic or anisotropic formations and considered having different dimensions and different spacing. The study has shown that pressure responses and flow regimes are significantly influenced by both reservoir's boundaries and fractures' dimensions. Different flow regimes have been observed for different conditions.
New flow regimes have been introduced in this study. The first one is the early radial flow regime which represents the radial flow around each fracture in the vertical plane resulted due to the partial vertical penetration of hydraulic fractures. The second one is the second linear flow regime which represents the linear flow toward each fractures in the vertical plane normal to the wellbore resulted due to the long spacing between fractures. Third one is the third linear flow regime which represents the linear flow in the vertical plane parallel to the wellbore after the pressure pulse reaches the upper and lower impermeable boundaries.
Horizontal wells with multiple hydraulic fractures have become a common occurrence in the oil and gas industry, especially in tight formations. Published models assume that hydraulic fractures are fully penetrating the formations. However, studies have shown that fractures are not always fully penetrating the formations.
This paper introduces a new technique for analyzing the pressure behavior of a horizontal well with multiple vertical and inclined partially penetrating hydraulic fractures. The hydraulic fractures in this model could be longitudinal or transverse, vertical or inclined, symmetrical or asymmetrical. The fractures are propagated in isotropic or anisotropic formations and considered having different dimensions and different spacing. This technique, based on pressure and pressure derivative concept, can be used to calculate various reservoir parameters, including directional permeability, fracture length and percentage of penetration. The study has shown that the pressure behavior of small penetration rate is similar to the horizontal wells without hydraulic fractures.
A type curve matching technique has been applied using the plots of the pressure and pressure derivative curves. A set of type curves, which will be included in the paper, have been generated for the partially penetrating hydraulic fractures associated to the horizontal wells with different penetration rates. A step-by-step procedure for analyzing pressure tests using these type curves is also included in the paper for several numerical examples.
Copyright 2013, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Production and Operations Symposium held in Oklahoma City, Oklahoma, USA, 2 3 26 March 2013. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract s ubmitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not neces sarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the wr itten consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract A technique using interwell connectivity is proposed to characterize complex reservoir systems and provide highly detailed information about permeability trends, channels, and barriers in a reservoir.
Interwell connectivity, an important element in reservoir characterization, especially for secondary recovery such as waterflooding, is essential when making decisions on well patterns, infill wells, and injection rates for oil recovery optimization. An existing technique uses multivariate linear regression analysis of flow rates in a waterflood to infer interwell connectivity. Advantages of this technique include a simplified one-step calculation and the availability of production data. A capacitance model was introduced as an extension of the technique to account for shut-in periods and changes in bottomhole pressures in the producers; however, this approach is based on trial and error and requires subjective judgment.
This paper presents an alternative analytical approach based on analytic concepts, providing an in-depth understanding of the technique and relationships between interwell connectivity coefficients and other reservoir parameters. The analytical approach uses a mathematical model for bottomhole pressure responses of injectors and producers in a waterflood system. The model is based on a solution for fully penetrating vertical wells in a closed rectangular reservoir with an assumption of steady-state flow. This model is then used to calculate relative interwell permeabilities, which represent the connectivity levels of signal response well pairs.
Different synthetic reservoir models were analyzed, including homogeneous, anisotropic reservoirs, and reservoirs with high-permeability channels and transmissibility barriers. Comparisons with results obtained from previous studies of production data and bottomhole pressure data are presented.
The main findings of this study are: (a) the mathematical model performs well with interwell connectivity coefficients calculated from flow rate data to quantify reservoir parameters; (b) the proposed approach provides a better understanding of interwell connectivity determination from flow rate data;and (c) the results for relative interwell permeability from flow rate data are similar to those obtained from previous studies of bottomhole pressure data.
The reliability of the estimated parameters in well test analysis depends on the accuracy of measured data. Early time data are usually controlled by the wellbore storage effect. However, this effect may last for the pseudo-radial flow or the boundary dominated flow. Eliminating this effect is an option for restoring the real data. Using the data with this effect is another option that can be used successfully for reservoir characterization.
This paper introduces a new technique for interpreting the pressure behavior of horizontal wells and fractured formations with wellbore storage. A new analytical model describes the early time data has been derived for both horizontal wells and horizontal wells intersecting multiple hydraulic fractures. Several models for the relationships of the peak points with the pressure, pressure derivative and time have been proposed in this study for different wellbore storage coefficients. A complete set of type curves has been included for different wellbore lengths, skin factors and wellbore storage coefficients. The study has shown that early radial flow for short to moderate horizontal wells is the most affected flow regime by the wellbore storage. For long horizontal wells, the early linear flow is the most affected flow regime by the wellbore storage effect.
The most important finding in this study is the ability to run a short test and use the early time data only for characterizing the formation. This means there is no need to run a long time test to reach the pseudo-steady state. Therefore, from the wellbore storage dominated flow, the early radial and pseudo-radial flow can be established for horizontal wells and hydraulic fractured formations. A step-by-step procedure for analyzing pressure tests using the analytical models (TDS) and the type curves is also included in this paper for several numerical examples.
Asphaltic and sand production problems are common production challenges in the petroleum industry. Asphaltic problem results from the depositions of heavy material (asphaltene) in the vicinity of the well which may cause severe formation damage. Asphaltic materials are expected to deposit in all type of reservoirs. Sand production refers to the phenomenon of solid particles being produced together with the petroleum fluids. These two problems represent a major concern in oil and gas production systems either in the wellbore section or in the surface treatment facilities. Production data, well logging, laboratory testing, acoustic, intrusive sand monitoring devices, and analogy are different techniques used to predict sand production. This paper introduces a new technique to predict and quantify the skin factor resulting from asphaltene deposition and/or sand production using pressure transient analysis.
Pressure behavior and flow regimes in the vicinity of horizontal wellbore are extremely influenced by this skin factor. Analytical models for predicting this problem and determining how many zones of the horizontal well that are affected by sand production or asphaltic deposition have been introduced in this study. These models have been derived based on the assumption that wellbore can be divided into multi-subsequent segments of producing and non-producing intervals. Producing intervals represent free flowing zones while non producing intervals represent zones where perforations are closed because of sand or asphaltic deposits.
The effective length of the segments of a horizontal well where sand and/or asphaltene are significantly closing the perforations can be calculated either from the early radial or linear flow. Similarly, the effective length of the undamaged segments can be determined from these two flow regimes. The numbers of the damaged and undamaged zones can be calculated either from the intermediate radial (secondary radial) or linear flow if they are observed. If both flow regimes are not observed, the zones can be calculated using type curve matching technique. The paper will include the main type-curves, step-by-step procedure for interpreting the pressure test without using type curve matching technique when all necessary flow regimes are observed. A step-by-step procedure for analyzing pressure tests using the type-curve matching technique will also be presented. The procedure will be illustrated by several numerical examples.
Productivity index and inflow performance of horizontal wells intersecting multiple hydraulic fractures are of great importance. This importance comes from the fact that the fracturing process has become a common stimulation technique in the petroleum industry. However, few models for the productivity index and inflow performance have been presented in the literatures due to the complexity governing this topic.
This paper introduces a new technique for estimating the pseudo-steady state productivity index of horizontal wells intersecting multiple hydraulic fractures. Based on the instantaneous source solutions for the diffusivity equation, seven analytical models have been derived for different source solutions. Four of them represent the effect of the formation height and fracture height (the vertical direction), while the other three represent the solution for the horizontal plane. For vertical hydraulic fractures, the four solutions of the vertical direction, representing the pseudo-skin factor, are almost neglected. The three horizontal plane solutions are the main parameters that control the productivity index and inflow performance of the fractured formations. In this technique, the horizontal wells are acting in finite reservoirs where the pseudo-steady state flow is expected to develop. Reservoir geometry, reservoir properties, and fracture dimensions were considered in this technique. The number of fractures and the spacing between them were also investigated in this study. A new analytical model for estimating the required number of hydraulic fractures has been introduced in this study based on the reservoir drainage area and the surface area of fractures.
The models have been used to establish several plots to estimate the shape factor group based on the number of fractures and the half fracture length. This group is one of the main terms in the productivity index model. Several plots for the shape factor of fractured formations have been introduced in this study. The results obtained from the new technique have been compared with the results from previous models. Several numerical examples will be included in the paper.
Closed perforations and damaged sections are two great challenges in the petroleum industry. Several reasons may cause these problems. Few of them depend on the type of formation and wellbore while others come from drilling, completion and stimulation activates before production process. Production rate and pressure drop may lead significantly to these two problems; therefore, production management sometimes plays great role in controlling them. Millions of dollars are spent annually for the remedial process of these two problems. Therefore the prediction of them is considered of great importance as an attempt to control them or reduce their negative impact on wellbore deliverability.
This paper introduces a new technique to predict closed perforations and damaged sections problems using pressure transient analysis. Pressure behaviors and flow regimes in the vicinity of horizontal wellbores are affected by the existence of the closed perforated zones and the formation sections where the resistance to reservoir fluid flow toward the wellbore is maximized. This resistance occurs because of the damaged permeability and high skin factor. Analytical models for predicting these problems and determining how many zones of the horizontal well that are considerably affected by them have been introduced in this study. These models have been derived based on the assumption that wellbore can be divided into multi-subsequent segments of producing and non-producing intervals. Producing intervals represent free flowing zones where there is no problem and both formation and wellbore are assumed to be clean. Non-producing intervals represent zones where both formation and wellbore's perforations are closed or damaged.
The effective length of horizontal well where the perforated zones and the formation sections can not be considered problematic and the damaged length where both of them are significantly closed and damaged can be calculated. The numbers of the damaged zones can be calculated also. In addition, the locations of the damaged sections or closed perforated zones can be determined. Type-curve matching technique and the analytical models can be used for this purpose.
One of the important petrophysical parameter in reservoir description is the permeability distribution in a given reservoir. It is well known that most reservoir are heterogeneous in nature and homogeneous ones being the few exceptions. Therefore, most reservoirs exist with different degree of permeability anisotropy and reservoir heterogeneity.
This work investigates the relationship between vertical and horizontal permeability in sandstone reservoirs. Various petrophysical properties were estimated from core and log data obtained from a Niger-Delta sandstone reservoir. New and improved correlations between vertical permeability, horizontal permeability, effective porosity and shale fraction were developed for the zones that were analyzed.
These correlations show that there is a strong relationship between vertical permeability, horizontal permeability, effective porosity, and shale fraction for the different zones that were analyzed and that these correlations are affected by the number of flow units in each zone.