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In this paper we develop a stochastic model incorporating a double-Markov modulated mean-reversion model. Unlike a price process the basis process X can take positive or negative values. This model is based on an explicit discretisation of the corresponding continuous time dynamics. The new feature in our model is that we suppose the mean reverting level in our dynamics as well as the noise coefficient can change according to the states of some finite-state Markov processes which could be the economy and some other unseen random phenomenon.

An exploratory appraisal campaign of the greater Musallim Oil Field area was executed in 2003. The main objective was to test the Shuaiba pancake reservoir and to confirm the presence of reservoir on the flanks, prove calibration of the porosity trends derived from acoustic impedance data, provide structural control and determine oil saturations below crestal oil-down-to (ODT) of 1443 mtvdss. The appraisal campaign was designed to test the ODT pancake model concept in Musallim. The pancake concept is a model where 2–12m thick good reservoir zone overlies poor quality reservoir. Based mainly on oil saturations logged from vertical wells, this boundary was previously interpreted as an oil water contact. However saturation changes represent an ODT as a function of reservoir quality, and permeability in particular. Prior to this campaign, two existing flank wells, (Musallim Deep-1H1 and Tibr-1H1) targeted deeper reservoirs as their primary objective but found oil saturations up to 50% below the ODT of 1443 mtvdss, then defined as the OWC in the 2002 Musallim field FDP. The 2003 appraisal campaign by PDO's Near Field Exploration team has proved the viability of the pancake model and significantly increased the reserves of the Musallim Field. It has extended the life of the field and opened up many new development possibilities. Another outcome of the exploratory appraisal campaign was that the eastern flank of the structure came in shallower and was confirmed by Tibr-2 which targeted deeper objectives that resulted in a re-assessment of the velocity model used in depth conversion. Success of the Musallim Rim campaign together with Tibr-2 well shows that these oil rims associated with the Shuaiba pancakes and flank plays are attractive targets. Introduction: The Musallim Field is situated in Central Oman some 40km NNW of Saih Rawl Field and 60 km SE of the Al Huwaisah Field (Fig. 1). The field was discovered in 1971 by Musallim-1 and was appraised by Musallim-2.The field is a low relief anticlinal structure and the hydrocarbons are trapped in the Shuaiba Formation limestone andsealed by overlying Albian Nahr Umr shales. The reservoir fluid consists of 280 API and 4.8 cp oil. It has a GOR of 21 m3/m3 and is undersaturated by some 10167 Kpa compared to the initial reservoir pressure of 17082 kPa. Fig. 1 Regional map of the Arabian Peninsula Regional Setting The area of interest is located in Central Oman sector of PDO's Block-6 concession. The Musallim Field lies between two major oil fields, (Saih Rawl and Al Huwaisah), which are producing from the platform carbonates of the Shuaiba Formation. The Shuaiba in this part of the concession shows a thickness (75 - 82 m). The Musallim field is developed as an elongated NW-SE trending low relief anticline. Stratigraphy The Shuaiba Formation occurs throughout Oman, except where eroded by the base Nahr Umr unconformity in South Oman (Fig. 2). The persistence of the slightly deeper argillaceous facies through the upper part of the Shuaiba in the Lekhwair area reflects a northwards transition into the Bab Member of the Upper Shuaiba described in Abu Dhabi.

In an earlier paper we developed a stochastic model incorporating a double-Markov modulated mean-reversion model. The model is based on an explicit discretisation  of the corresponding continuous time dynamics. Here we discuss parameter estimation via the technique of M-ary detection.