M.H. Sayyouh

Inflow Performance Relationship Correlation for Solution Gas-Drive Reservoirs Using Non-Parametric Regression Technique

Received: March 28, 2017 Revised: May 08, 2017 Accepted: June 13, 2017 Abstract: Background: The Inflow Performance Relationship (IPR) describes the behavior of flow rate with flowing pressure, which is an important tool in understanding the well productivity. Different correlations to model this behavior can be classified into empirically-derived and analytically-derived correlations. The empirically-derived are those derived from field or simulation data. The analytically-derived are those derived from basic principle of mass balance that describes multiphase flow within the reservoir. The empirical correlations suffer from the limited ranges of data used in its generation and they are not function of reservoir rock and fluid data that vary per each reservoir. The analytical correlations suffer from the difficulty of obtaining their input data for its application.

Analytical Decline Curve Analysis Model for Water Drive Gas Reservoirs

Production data analysis is a viable tool for reservoir characterization and estimation of initial gas in place (IGIP) and reserves. Several methods are available to analyse production data starting with Arps classical decline curve analysis (DCA) in 1945 all the way to more sophisticated analytical and advanced DCA techniques. Most of these methods are applicable only for single phase flow in porous media. In this paper, we present a simple analytical decline curve analysis (ADCA) model that takes into account the effect of water influx on gas reservoir performance. We introduced the water influx effect into the pseudo-steady state flow equation which enables us to estimate the reservoir pressure and the IGIP for water drive gas reservoirs. The model is based on coupling the material balance equation for gas reservoirs, aquifer models, and the gas flow equation to calculate the well’s production rate versus time. The model can also estimate reservoir pressure, gas saturation, water production rate, and gas production rate with time. When the model is run in history-match mode to match gas and water production, we can estimate the IGIP, well’s productivity index, and aquifer parameters. The model can also be run in prediction mode to predict gas and water production at any conditions of bottom-hole flowing pressure (BHFP) (or surface tubing pressure) and reserves can be calculated. The model was validated with several simulated cases at variable conditions of rate and pressure. The model was then used to perform decline curve analysis in several field cases. This technique is fast and requires minimum input data. The paper will also present the application of this technique to analyse production data and predict reserves for gas wells producing both gas and water.

Fast and Efficient Sensitivity Calculation Using Adjoint Method for 3 Phase Field-Scale History Matching

Adjoint method-based sensitivity for field-scale history matching with large number of parameters suffers from several limitations. First, the CPU time depends on the data points which are large for any brown fields of long history; second, it requires large memory to save the gridblock pressure and saturation per each time step used in the forward model. Third, it is computationally expensive as it requires solving the Adjoint system of equations backward in time per each forward time step which is usually of high magnitude in case of field scale applications of long history. Lastly, the solver used for solving the Adjoint system of equations needs to be efficient for large-scale applications. We propose an efficient and fast approach for sensitivity calculation based on the Adjoint method to overcome much of the current limitations. First, we use a commercial finite difference simulator, ECLIPSE, as a forward model, which is general and can account for complex physical behavior that dominates most field applications. Second, the production data misfit is represented by a single generalized travel time misfit per well, thus effectively reducing the number of data points into one per well. Third, we solve the Adjoint system of equations backward in time in larger time step that is equivalent to the time of severe changes in pressure and saturation due to the changing of well conditions or introducing new infill wells rather than using the forward model time steps. This approach reduces the computational effort and memory allocated for the sensitivity calculation. Fourth, we use an iterative sparse matrix solver, LSQR, for solving the Adjoint system of equations which shows high stability for field-scale applications. We demonstrate the power and utility of our approach using synthetic and pseudo field examples. The synthetic examples show the robustness and efficiency of our sensitivity calculation approach compared to the perturbation. The pseudo-field example has 10 years of production history with original gas cap and oil-water contact with strong aquifer support. Using well log data, core data, water-cut and gas-oil ratio history from producing wells; we characterize the permeability at each cell, thus demonstrating the feasibility of our approach for field applications. Introduction Conditioning geological models to production data is an important step in reservoir modeling to build a reliable model to be used in predicting the reservoir performance and in proposing the optimum field development plan. Conditioning the geological or the static model to production data is typically known as “History Matching” which is considered the most time consuming phase in building a reliable model for the field. Thus, any reduction in the time taken for this phase is very important to speed up the modeling process as the majority of the development plans should be based on examining it on the model before accepting it for practical application. Accordingly, building reservoir model for each field becomes a commonly used practice in the industry and any improvement in speeding up the reservoir modeling process is highly demanded. Different techniques are proposed to speed up the history matching process where all are grouped under what is called computer assisted or automatic history matching. The automatic history matching procedure involves the following steps; First, the forward model formulation, second, the data misfit calculation, third, the sensitivity coefficient calculation, and finally an optimization algorithm. First, the forward model used is the commonly used finite difference simulation, ECLIPSE, which is general, robust, and can tackle different physical problems.