Pressure Redistribution and Aquifer Influx Modelling Using Statistical Models, Direct Declining, Sum of Time Step, and Log-Determinant Approach
Authors: Biu Victor T. , Biu Emmanuel , Buduka Stanley , Prince Wachuku 
Published: July 2011

Ultimate recovery from oil and gas reservoirs is usually affected by the aquifer influx either from the perimeter of the reservoir or below and from both. Several methods such as the simple pot aquifer model, Schilthuis Steady state, Hurst-Van Everdingen modified etc to the more complex numerical method have been utilized to history match reservoir performance considering existing boundary conditions and possible reservoir description and from this match infer the reservoir and aquifer properties. Future reservoir aquifer behaviour has also been forecast assuming several operating conditions. However how definite are these boundary conditions (initial, inner and outer) and representative of the reservoir aquifer behaviour infer from these models
This paper focus on pressure redistribution and aquifer influx modelling using simple direct declining, log-determinant, sum of time step and three statistical models. Four theoretical cases were reviewed using simplified reservoir model and result compared with existing aquifer influx correlation.
Results compared with existing aquifer models such as Schilthuis Steady state, Hurst steady state, Hurst-Van -Everdingen modified, Allard & Chen and Cater & Tracy indicates three possible categories of aquifer response such as fast, slow and moderate suitable for matching water influx depending on the reservoir architecture. In all cases review, the sum of time step indicates a faster aquifer response and high cumulative aquifer influx compared to other models, thus applicable if the historical aquifer response is fast. Also the result shows the existing aquifer model lies between the new aquifer models in all cases.
Introduction
The origin of petroleum by geologist describes water as the original fluid existing in the reservoir before being displaced by oil. Due to compaction and continuous diagenesis activities, the molecular chain of the heavy fluid present in the entrapment are broken as lighter fluid like gas escape to form gas cap (pocket of cap) while other co-exist in solution with oil and partly water.
In the industry today, several aquifer models have been developed to estimate and also history water influx based on assumptions that describe the characteristics of the aquifer. Although the simple material balance equation can be used to determine historical water influx provided the original oil-in-place is known from pore volume estimates. This permits evaluation of the constants influx equations so that future water influx rate can be forecasted.
Schilthuis (1936) proposed that for an aquifer that is flowing under the steady-state flow regime, the flow behaviour could be described by Darcy's equation i.e the rate of water influx can be determined by applying Darcy's equation with a water influx constant C which may be calculated from the reservoir historical production data over a number of selected time intervals, provided that the rate of water influx has been determined independently. Although the influx constant can only be obtained when the reservoir pressure stabilizes, however it may be applied to both stabilized and changing reservoir pressures.