Horizontal wells with multiple hydraulic fractures have been used widely in the oil and gas industry. In published literatures, hydraulic fractures are assumed to be fully penetrating the formations. Recent studies have shown that partially penetrating fractures are more likely to occur rather than fully penetrating fractures The purpose of this study is to formulate an analytical model describing the pressure behavior of a horizontal well with partially penetrating hydraulic fractures. This model is used to develop a technique, based on pressure and pressure derivative concept, for interpreting pressure transient tests and forecasting productivity of the well. The fractures in this study were assumed to propagate in an infinite homogenous porous system. Further more, the fractures were assumed to be vertical and inclined. Six main flow regimes can be observed for hydraulic fractures: linear, early radial, second linear, intermediate radial, third linear or elliptical and pseudo-radial flow. Early radial flow represents the radial flow around each fracture may develop for the cases of small penetrating rate. Intermediate radial flow is expected to develop for the case of wide spacing between fractures. Third linear flow may develop for the case of high number of fracture with short spacing between them. Tiab's Direct Synthesis (TDS) technique has been applied using the plots of the pressure and pressure derivative curves. Several unique features of the pressure and pressure derivative plots of partially penetrating fractures models were identified including the points of intersection of straight lines for different flow regimes. These points can be used to verify the results or to calculate unknown parameters. Equations associated with these features were derived and their usefulness was demonstrated. A step-by-step procedure for analyzing pressure tests is included in this paper and illustrated by several numerical examples.

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.

Horizontal wells with multiple zonal isolations have become a common completion technique in the oil and gas industry. Sand problems, damaged zones, and water or gas coning are the main reasons for using isolators to sustain or improve oil and gas recovery. However, they have certain effects on pressure behavior of horizontal wells. This paper introduces new analytical models for studying the effect of this completion technique on pressure behavior of wells with multiple isolated zones. These models have been derived based on the assumption that reservoirs can be divided into multi-subsequent segments of producing and non-producing intervals. Based on the pressure and pressure derivative, the models can be used to estimate the impact of isolators on the pressure behavior. The effects of the number and length of isolators have been investigated for wells having different lengths. A set of type-curves of dimensionless pressure and pressure derivative versus dimensionless time have been generated for two cases. The first case is for wells in an infinite reservoir having one, two or three isolated zones with three different lengths for the horizontal section and six different lengths for the isolators while the second one is for very long wells in an infinite reservoir. These plots can be used for the type curve matching technique to estimate the number, length, and damaged zones location, segments where sand is produced, and intervals of water or gas coning. The main finding is that the pressure of these wells behaves similarly for all cases. The dominant effect of the isolators can only be noticed during the early time flow regimes, i.e. during the early radial or early linear. The behavior of the late time flow regimes, i.e. pseudo radial or late linear due to the boundary effects is not affected by the presence of isolators.

Horizontal wells can greatly increase the contact area of the wellbore and the pay zone; so they are commonly applied in oil reservoirs to enhance the production and ultimate recovery, especially in low permeability formations. The purpose of this study is to develop a technique for the interpretation of transient pressure based on dimensionless pressure and pressure derivative. Type curve matching is one of the techniques that can be used to interpret the pressure data of horizontal wells in finite reservoirs. Starting from very short horizontal wells to extra-long wells, the pressure behavior of the wells has been analyzed for different conditions. The effect of the outer boundaries of the reservoir on the pressure behavior of the horizontal wells has been investigated for different configurations. Rectangular shape reservoirs with different dimensions have been used to study the pressure response in the well. Five flow regimes have been observed for regular length horizontal wells; early radial, early linear flow, pseudo radial flow, channel flow or late linear flow, and pseudo-steady state flow. While only four flow regimes have been observed for the extra-long wells; linear flow, pseudo radial flow, channel flow, and pseudo-steady state or boundary affected flow. Of course, those flow regimes do not always take place under all conditions. Pseudo-steady state flow is expected to occur after long producing time. A pressure drawdown test was solved using the proposed type curve matching technique. The study has shown that the effect of the boundary on the pressure response of the horizontal wells and the type of flow regimes depend on the length of the horizontal wells and the distance to the nearest boundary.

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.